This document discusses belt drives and their components. It describes different types of belt drives including open belt drives, crossed belt drives, and quarter turn belt drives. It also discusses different belt drive configurations that use idler pulleys, compound pulleys, stepped pulleys, and fast and loose pulleys to transmit power between shafts over varying distances and speed ratios. The key types of belts are described as flat belts, V-belts, and ropes along with their typical applications and materials. Factors for selecting a belt drive like power, speed, and distance between shafts are also outlined.
The document is a set of lecture notes on gears that discusses various topics including:
- Types of gears like spur gears, helical gears, bevel gears, and worm gears.
- Gear terminology like pitch circle, addendum, dedendum, and module.
- Applications of different gears in devices like electric screwdrivers, steering systems, and material handling equipment.
- Factors that affect gear performance like backlash, which is the play between meshing gear teeth that can cause imprecision.
P=250 kW
N1=300 rpm
D1=1.2 m
θ=π rad
β=22.5°
d=50 mm
m=1.3 kg/m
Pmax=2.2 kN
μ=0.3
Overhang=0.5 m
Shear stress=40 MPa
The document discusses various types of belt and rope drives used to transmit power between rotating shafts. It describes different belt materials, types of belts, components of belt drives, factors affecting power transmission, and applications. It also covers rope drives, materials used for ropes, advantages and disadvantages of rope drives, and considerations in selecting wire ropes
Gears are components that transmit rotational motion between two shafts. There are several types of gears classified by the position of their shafts, including spur gears where the teeth are parallel to the axis of rotation, helical gears which are cut at an angle, and bevel gears where the shafts meet at an angle. Gears are used in many machines and mechanisms to increase torque or change the speed and direction of rotation between two shafts.
Dynamometers are devices used to measure torque and power. There are two main types: absorption dynamometers which measure power by absorbing it, and transmission dynamometers which measure torque transmitted through a shaft. Examples of absorption dynamometers include Prony brake, rope brake, and hydraulic dynamometers. Transmission dynamometers include belt transmission, epicyclic gear train, and torsion dynamometers. Torsion dynamometers work by measuring the angle of twist in a shaft which is directly proportional to the transmitted torque.
The document discusses various concepts related to belt drives, including:
1. Definitions of key terms used in belt drive calculations such as velocity ratio, slip, creep, tension, power transmission.
2. Types of belt drives including open, crossed, and quarter turn drives. Belt drives can also include idler pulleys.
3. Properties of common belt materials like leather, cotton, rubber, and their densities. Recommended belt speeds are between 20-22.5 m/s.
Cams are rotating or reciprocating elements that impart motion to followers. There are various types of cams including wedge, flat, radial, offset, cylindrical, spiral, conjugate, and globoidal cams. Followers can be classified based on their surface contact with the cam, type of motion, and line of motion. Key aspects of cam design include the base circle, prime circle, pitch point, pitch circle, trace point, pitch curve, cam angle, lift, cam profile, and pressure angle. Proper cam design considers factors like wear reduction, side thrust minimization, and optimal follower motion.
This document provides an overview of the design of transmission systems using flexible elements such as belts, ropes, and chains. It discusses the selection and design of v-belts and pulleys, wire ropes, transmission chains and sprockets. Assessment methods for the course include common assessment tests, written assignments, gamification, active learning, and group presentations. Flexible elements are used to transmit mechanical power over comparatively long distances and for conveying purposes. Proper selection and replacement of these elements is important to prevent deterioration.
The document is a set of lecture notes on gears that discusses various topics including:
- Types of gears like spur gears, helical gears, bevel gears, and worm gears.
- Gear terminology like pitch circle, addendum, dedendum, and module.
- Applications of different gears in devices like electric screwdrivers, steering systems, and material handling equipment.
- Factors that affect gear performance like backlash, which is the play between meshing gear teeth that can cause imprecision.
P=250 kW
N1=300 rpm
D1=1.2 m
θ=π rad
β=22.5°
d=50 mm
m=1.3 kg/m
Pmax=2.2 kN
μ=0.3
Overhang=0.5 m
Shear stress=40 MPa
The document discusses various types of belt and rope drives used to transmit power between rotating shafts. It describes different belt materials, types of belts, components of belt drives, factors affecting power transmission, and applications. It also covers rope drives, materials used for ropes, advantages and disadvantages of rope drives, and considerations in selecting wire ropes
Gears are components that transmit rotational motion between two shafts. There are several types of gears classified by the position of their shafts, including spur gears where the teeth are parallel to the axis of rotation, helical gears which are cut at an angle, and bevel gears where the shafts meet at an angle. Gears are used in many machines and mechanisms to increase torque or change the speed and direction of rotation between two shafts.
Dynamometers are devices used to measure torque and power. There are two main types: absorption dynamometers which measure power by absorbing it, and transmission dynamometers which measure torque transmitted through a shaft. Examples of absorption dynamometers include Prony brake, rope brake, and hydraulic dynamometers. Transmission dynamometers include belt transmission, epicyclic gear train, and torsion dynamometers. Torsion dynamometers work by measuring the angle of twist in a shaft which is directly proportional to the transmitted torque.
The document discusses various concepts related to belt drives, including:
1. Definitions of key terms used in belt drive calculations such as velocity ratio, slip, creep, tension, power transmission.
2. Types of belt drives including open, crossed, and quarter turn drives. Belt drives can also include idler pulleys.
3. Properties of common belt materials like leather, cotton, rubber, and their densities. Recommended belt speeds are between 20-22.5 m/s.
Cams are rotating or reciprocating elements that impart motion to followers. There are various types of cams including wedge, flat, radial, offset, cylindrical, spiral, conjugate, and globoidal cams. Followers can be classified based on their surface contact with the cam, type of motion, and line of motion. Key aspects of cam design include the base circle, prime circle, pitch point, pitch circle, trace point, pitch curve, cam angle, lift, cam profile, and pressure angle. Proper cam design considers factors like wear reduction, side thrust minimization, and optimal follower motion.
This document provides an overview of the design of transmission systems using flexible elements such as belts, ropes, and chains. It discusses the selection and design of v-belts and pulleys, wire ropes, transmission chains and sprockets. Assessment methods for the course include common assessment tests, written assignments, gamification, active learning, and group presentations. Flexible elements are used to transmit mechanical power over comparatively long distances and for conveying purposes. Proper selection and replacement of these elements is important to prevent deterioration.
The document discusses different types of brakes used in vehicles and machinery. It defines key terms related to brakes such as tangential braking force, normal force, coefficient of friction, heat generated during braking. It then describes different types of brakes in detail including single block/shoe brake, pivoted block/shoe brake, band brake, band and block brake, internal expanding brake. Equations are provided for calculating forces, torque, energy absorbed during braking. Materials used for brake linings and their properties are also summarized.
This document provides information on cams and cam mechanisms. It defines a cam as a mechanical member that produces motion in a follower through direct contact. Cams are classified based on their shape, the movement of the follower, and the manner of constraint of the follower. Common cam shapes include wedge, plate, cylindrical, and spiral cams. Follower motion types include rise-return-rise, dwell-rise-return-dwell, and dwell-rise-dwell-return-dwell. Constraints include pre-loaded springs, positive-drive, and gravity. Followers are classified based on their shape, motion, and path. The document also provides details on cam nomenclature, problems, and kinematics.
Spring Design, Helical Springs, compression & Extension springs, spring design procedure leaf spring, multi-leaf springs design process and analysis, Role of Spring index in spring design. Springs for Fluctuating loads.
This document provides an overview of transmission of motion and power. It discusses various power transmission elements such as shafts, spindles, axles and bearings. It describes different types of power transmission systems including belt drives, gear drives, and chain drives. Belt drives can be flat belts, V-belts, timing belts, or other configurations. Gear drives include spur gears, helical gears, bevel gears, and worm gears. The document compares characteristics of individual drives versus group drives and advantages of different types of belts and gears.
This presentation provide complete study of governor for GTU as well as PU and other university students. It covers basic terminologies, characteristics of governor, diagram, derivations etc. for proper understanding.
1. The document discusses different types of clutches including positive clutches and friction clutches. It describes the key components and operation of a single plate clutch commonly used in automotive applications.
2. Formulas are presented for calculating the torque capacity of clutches under uniform pressure and uniform wear conditions based on geometric parameters, pressure, and coefficient of friction.
3. The document provides an example problem demonstrating the use of the formulas to design a multi-plate clutch meeting specific torque and speed requirements.
The document discusses different types of power transmission devices including belt drives, chain drives, and gear drives. It focuses on different types of gears, providing details on spur gears, helical gears, bevel gears, worm gears, and their advantages and applications. Key points covered include how helical and bevel gears allow power transmission between non-parallel shafts, how worm gears enable high gear reductions, and the law of gearing which specifies gears must maintain contact through the pitch point.
Design of Roller Chain Drive theory by Prof. Sagar A. DhotareSagar Dhotare
This covers following Points
1. Introduction.
2. Advantages and Disadvantages of Chain Drive over Belt or Rope Drive.
3. Terms Used in Chain Drive.
4. Relation Between Pitch and Pitch Circle Diameter.
5. Velocity Ratio of Chain Drives.
6. Length of Chain and Centre Distance.
7. Classification of Chains.
8. Hoisting and Hauling Chains.
9. Conveyor Chains.
10. Power Transmitting Chains.
11. Characteristics of Roller Chains.
12. Factor of Safety for Chain Drives.
13. Permissible Speed of Smaller Sprocket.
14. Power Transmitted by Chains.
15. Number of Teeth on the Smaller or Driving Sprocket
or Pinion.
16. Maximum Speed for Chains.
17. Principal Dimensions of Tooth Profile.
18. Design Procedure for Chain Drive.
A cam is a rotating machine element which gives reciprocating or oscillating motion to another element known as the follower.Though the cams may be classified in many ways, among them we can classify:
1. Radial or disc cam.
2. Cylindrical cam.
Design of Flat belt, V belt and chain drivesDr. L K Bhagi
Geometrical relationships, Analysis of belt tensions, Condition for maximum power transmission, Characteristics of belt drives, Selection of flat belt, V- belt, Selection of V belt, Roller chains, Geometrical relationship, Polygonal effect, Power rating of roller chains, Design of chain drive, Introduction to belt drives and belt construction, Introduction to chain drives
Working, Construction And Types of Band BrakesKhushal Hudke
Band brakes consist of a flexible band wrapped around a rotating drum that is used to slow or stop the drum's rotation. The band is made of materials like leather or steel lined with friction material. One end of the band is attached to a lever's fulcrum while the other end attaches to the lever at a distance, allowing an external force applied to the lever to tighten the band against the drum. When the band tightens, friction between the band and drum is created, applying a tangential force to the drum to slow or stop its movement. Band brakes can be classified as simple or differential, with differential brakes being self-energizing and potentially self-locking.
The document discusses different types of gears including spur gears, helical gears, herringbone gears, rack and pinion gears, bevel gears, worm gears, and planetary gears. It describes the design and function of each gear type, their advantages and disadvantages, and common applications. Spur gears transmit power between parallel shafts and are used in machines, power plants, and automobiles. Helical gears operate more quietly than spur gears and are used in automobile transmissions. Planetary gears can produce different gear ratios and are commonly used in automatic transmissions.
Module 4 numerical problems on cams - cycloidal motiontaruian
This document provides instructions for constructing the displacement diagram and cam profile for a numerical problem involving cycloidal motion of a cam and roller follower. It describes a 10-step process for drawing the displacement diagram, including constructing the rolling circle, dividing it into parts, and transferring displacement values between the outstroke and return stroke. It also outlines how to account for the offset of the roller follower axis from the cam shaft axis when constructing the cam profile, using base, prime and offset circles.
This document is about power transmission system. It's aimed those interested in learning about mechanical engineering and students who are studying various programmes in engineering. This document only deals with power transmission through flat and v-belts.
KOM - Unit 3 -kinematics of cam mechanismskarthi keyan
This document discusses different types of cam mechanisms. It defines a cam as a mechanical device used to convert rotary motion into reciprocating motion. Cams are classified based on their input and output motions as well as the type of follower used. Different types of cams include wedge cams, spiral cams, radial cams, and cylindrical cams. The document also discusses cam nomenclature and the different types of follower motions including uniform, simple harmonic, uniform acceleration/retardation, and cycloidal motion. Displacement and velocity diagrams are presented for different motion types.
Power transmission involves transferring rotational force from one component to another using gears. Gears come in different types depending on the position of their shafts, including spur gears, helical gears, bevel gears, and worm gears. Gears are used to change rotational speed and torque in machines and vehicles through gear trains and different gear ratios.
The document discusses equivalent dynamical systems used to model the motion of rigid bodies acted on by external forces. It defines an equivalent dynamical system as one where: 1) the sum of the masses equals the total body mass, 2) the center of gravity of the masses matches the body's, and 3) the sum of the mass moments of inertia about the center of gravity equals the body's. It then gives an example of calculating the equivalent dynamical system for a connecting rod suspended and oscillating, determining the radius of gyration and placing one mass at the small end center and solving to find the location of the other mass.
Unit 8-cams, Kinematics of machines of VTU Syllabus prepared by Hareesha N Gowda, Asst. Prof, Dayananda Sagar College of Engg, Blore. Please write to hareeshang@gmail.com for suggestions and criticisms.
BELT DRIVE.pptx, machine element two chapter 3haymanot16
Belt drives transmit power between rotating shafts using belts and pulleys. Belts are loops of flexible material that link shafts mechanically. Power is transmitted from the driver pulley to the belt and then to the driven pulley through friction.
There are several types of belt drives depending on the shaft configuration and direction of rotation, including open belt drives, crossed belt drives, quarter turn drives, and drives using idler pulleys. Selection of a belt drive depends on factors like shaft speeds, power needs, and space constraints. Common belt materials include leather, rubber, and plastic. Belt drives are inexpensive and efficient but have limits on power and speed transmission.
This document discusses mechanisms and power transmission elements used in textile machines. It begins with basic definitions of mechanisms and describes how they transmit motion through rigid links and joints. The main power transmission elements discussed are belt drives, gear drives, and their applications in textile machines. Belt drives are the most commonly used and their operation, advantages, disadvantages, and types - including flat, V-belt, and timing belts - are explained in detail. Gear drives provide exact speed ratios but are more complex and expensive. The document also covers related topics like velocity and torque ratios, slip, and power transmission calculations for belts.
The document discusses different types of brakes used in vehicles and machinery. It defines key terms related to brakes such as tangential braking force, normal force, coefficient of friction, heat generated during braking. It then describes different types of brakes in detail including single block/shoe brake, pivoted block/shoe brake, band brake, band and block brake, internal expanding brake. Equations are provided for calculating forces, torque, energy absorbed during braking. Materials used for brake linings and their properties are also summarized.
This document provides information on cams and cam mechanisms. It defines a cam as a mechanical member that produces motion in a follower through direct contact. Cams are classified based on their shape, the movement of the follower, and the manner of constraint of the follower. Common cam shapes include wedge, plate, cylindrical, and spiral cams. Follower motion types include rise-return-rise, dwell-rise-return-dwell, and dwell-rise-dwell-return-dwell. Constraints include pre-loaded springs, positive-drive, and gravity. Followers are classified based on their shape, motion, and path. The document also provides details on cam nomenclature, problems, and kinematics.
Spring Design, Helical Springs, compression & Extension springs, spring design procedure leaf spring, multi-leaf springs design process and analysis, Role of Spring index in spring design. Springs for Fluctuating loads.
This document provides an overview of transmission of motion and power. It discusses various power transmission elements such as shafts, spindles, axles and bearings. It describes different types of power transmission systems including belt drives, gear drives, and chain drives. Belt drives can be flat belts, V-belts, timing belts, or other configurations. Gear drives include spur gears, helical gears, bevel gears, and worm gears. The document compares characteristics of individual drives versus group drives and advantages of different types of belts and gears.
This presentation provide complete study of governor for GTU as well as PU and other university students. It covers basic terminologies, characteristics of governor, diagram, derivations etc. for proper understanding.
1. The document discusses different types of clutches including positive clutches and friction clutches. It describes the key components and operation of a single plate clutch commonly used in automotive applications.
2. Formulas are presented for calculating the torque capacity of clutches under uniform pressure and uniform wear conditions based on geometric parameters, pressure, and coefficient of friction.
3. The document provides an example problem demonstrating the use of the formulas to design a multi-plate clutch meeting specific torque and speed requirements.
The document discusses different types of power transmission devices including belt drives, chain drives, and gear drives. It focuses on different types of gears, providing details on spur gears, helical gears, bevel gears, worm gears, and their advantages and applications. Key points covered include how helical and bevel gears allow power transmission between non-parallel shafts, how worm gears enable high gear reductions, and the law of gearing which specifies gears must maintain contact through the pitch point.
Design of Roller Chain Drive theory by Prof. Sagar A. DhotareSagar Dhotare
This covers following Points
1. Introduction.
2. Advantages and Disadvantages of Chain Drive over Belt or Rope Drive.
3. Terms Used in Chain Drive.
4. Relation Between Pitch and Pitch Circle Diameter.
5. Velocity Ratio of Chain Drives.
6. Length of Chain and Centre Distance.
7. Classification of Chains.
8. Hoisting and Hauling Chains.
9. Conveyor Chains.
10. Power Transmitting Chains.
11. Characteristics of Roller Chains.
12. Factor of Safety for Chain Drives.
13. Permissible Speed of Smaller Sprocket.
14. Power Transmitted by Chains.
15. Number of Teeth on the Smaller or Driving Sprocket
or Pinion.
16. Maximum Speed for Chains.
17. Principal Dimensions of Tooth Profile.
18. Design Procedure for Chain Drive.
A cam is a rotating machine element which gives reciprocating or oscillating motion to another element known as the follower.Though the cams may be classified in many ways, among them we can classify:
1. Radial or disc cam.
2. Cylindrical cam.
Design of Flat belt, V belt and chain drivesDr. L K Bhagi
Geometrical relationships, Analysis of belt tensions, Condition for maximum power transmission, Characteristics of belt drives, Selection of flat belt, V- belt, Selection of V belt, Roller chains, Geometrical relationship, Polygonal effect, Power rating of roller chains, Design of chain drive, Introduction to belt drives and belt construction, Introduction to chain drives
Working, Construction And Types of Band BrakesKhushal Hudke
Band brakes consist of a flexible band wrapped around a rotating drum that is used to slow or stop the drum's rotation. The band is made of materials like leather or steel lined with friction material. One end of the band is attached to a lever's fulcrum while the other end attaches to the lever at a distance, allowing an external force applied to the lever to tighten the band against the drum. When the band tightens, friction between the band and drum is created, applying a tangential force to the drum to slow or stop its movement. Band brakes can be classified as simple or differential, with differential brakes being self-energizing and potentially self-locking.
The document discusses different types of gears including spur gears, helical gears, herringbone gears, rack and pinion gears, bevel gears, worm gears, and planetary gears. It describes the design and function of each gear type, their advantages and disadvantages, and common applications. Spur gears transmit power between parallel shafts and are used in machines, power plants, and automobiles. Helical gears operate more quietly than spur gears and are used in automobile transmissions. Planetary gears can produce different gear ratios and are commonly used in automatic transmissions.
Module 4 numerical problems on cams - cycloidal motiontaruian
This document provides instructions for constructing the displacement diagram and cam profile for a numerical problem involving cycloidal motion of a cam and roller follower. It describes a 10-step process for drawing the displacement diagram, including constructing the rolling circle, dividing it into parts, and transferring displacement values between the outstroke and return stroke. It also outlines how to account for the offset of the roller follower axis from the cam shaft axis when constructing the cam profile, using base, prime and offset circles.
This document is about power transmission system. It's aimed those interested in learning about mechanical engineering and students who are studying various programmes in engineering. This document only deals with power transmission through flat and v-belts.
KOM - Unit 3 -kinematics of cam mechanismskarthi keyan
This document discusses different types of cam mechanisms. It defines a cam as a mechanical device used to convert rotary motion into reciprocating motion. Cams are classified based on their input and output motions as well as the type of follower used. Different types of cams include wedge cams, spiral cams, radial cams, and cylindrical cams. The document also discusses cam nomenclature and the different types of follower motions including uniform, simple harmonic, uniform acceleration/retardation, and cycloidal motion. Displacement and velocity diagrams are presented for different motion types.
Power transmission involves transferring rotational force from one component to another using gears. Gears come in different types depending on the position of their shafts, including spur gears, helical gears, bevel gears, and worm gears. Gears are used to change rotational speed and torque in machines and vehicles through gear trains and different gear ratios.
The document discusses equivalent dynamical systems used to model the motion of rigid bodies acted on by external forces. It defines an equivalent dynamical system as one where: 1) the sum of the masses equals the total body mass, 2) the center of gravity of the masses matches the body's, and 3) the sum of the mass moments of inertia about the center of gravity equals the body's. It then gives an example of calculating the equivalent dynamical system for a connecting rod suspended and oscillating, determining the radius of gyration and placing one mass at the small end center and solving to find the location of the other mass.
Unit 8-cams, Kinematics of machines of VTU Syllabus prepared by Hareesha N Gowda, Asst. Prof, Dayananda Sagar College of Engg, Blore. Please write to hareeshang@gmail.com for suggestions and criticisms.
BELT DRIVE.pptx, machine element two chapter 3haymanot16
Belt drives transmit power between rotating shafts using belts and pulleys. Belts are loops of flexible material that link shafts mechanically. Power is transmitted from the driver pulley to the belt and then to the driven pulley through friction.
There are several types of belt drives depending on the shaft configuration and direction of rotation, including open belt drives, crossed belt drives, quarter turn drives, and drives using idler pulleys. Selection of a belt drive depends on factors like shaft speeds, power needs, and space constraints. Common belt materials include leather, rubber, and plastic. Belt drives are inexpensive and efficient but have limits on power and speed transmission.
This document discusses mechanisms and power transmission elements used in textile machines. It begins with basic definitions of mechanisms and describes how they transmit motion through rigid links and joints. The main power transmission elements discussed are belt drives, gear drives, and their applications in textile machines. Belt drives are the most commonly used and their operation, advantages, disadvantages, and types - including flat, V-belt, and timing belts - are explained in detail. Gear drives provide exact speed ratios but are more complex and expensive. The document also covers related topics like velocity and torque ratios, slip, and power transmission calculations for belts.
Flate belt drive and chain drive by jawad aliJAWAD Ali
1. The document discusses two types of machine drives: flat belt drives and chain drives. It provides details on the components, operation, advantages, and disadvantages of each type of drive.
2. Flat belt drives transmit power between shafts using belts or ropes over pulleys. Key factors that determine the amount of power transmitted include belt velocity, tension, pulley contact arc, and operating conditions.
3. Chain drives avoid slipping between components by using rigid linked chains on sprocket wheels. They provide perfect velocity ratio, occupy less space than belts, allow high power transmission, and can connect multiple shafts. However, they have higher production costs and require more careful maintenance than flat belt drives.
The working of belt drives, their different components, the forces involved and how are they transferred, to create a device of our own, innovating the current belt drive system and developing our own system based on concepts of belt drive.
Design of rope, belt and chain by Aliyi UmerAliyi Umer
The document provides information on different types of belt, rope, and chain drives used for power transmission. It discusses flat belt drives, V-belt drives, rope drives, and chain drives. For each type of drive, it describes the components, operation, advantages and disadvantages. It also provides formulas for calculating important parameters like velocity ratio, power transmitted, stresses, and length of drives. Design procedures and considerations for selecting proper dimensions are discussed. Tables with standard dimensions and specifications for various drives are also included.
It is power point presentation on belt and chain drive. you can find working and mechanism of chain and belt drive and their advantage and disadvantages.....enjoy.
This document summarizes key information about belt drives. It discusses how belts are used to mechanically link rotating shafts and can drive shafts in the same or opposite directions. It then lists advantages like simplicity and cost effectiveness. Different types of belts are described, like flat and round belts, as well as belt drive configurations including open, crossed, and compound drives. Materials used for belts and their properties are outlined. Formulas for velocity ratio considering slippage are also provided.
This document is a summer training report submitted by Asha Kumari to her professor, Mr. Laxman Kumar Pandey, about her training at Vipul Motors. It includes acknowledgments, a table of contents, and sections covering manual transmission systems, automatic transmissions, and continuously variable transmissions. The sections describe the components, functions, and advantages/disadvantages of different transmission types.
Design of transmission systems question bank - GGGopinath Guru
This document contains questions related to the design of various transmission systems including belt drives, chain drives, gear drives, and rope drives. It provides a question bank with multiple choice and numerical questions on the design, selection and analysis of different types of flexible elements and rigid transmissions used to transmit power between rotating shafts. The questions cover topics such as the selection of V-belts and pulleys, flat belts and pulleys, wire ropes and pulleys, transmission chains and sprockets, as well as the design of gears, including spur gears, helical gears, and gear drives.
A belt is a looped strip of flexible material used to mechanically link two o...Salman Jailani
Belt drives use a flexible looped strip called a belt to transmit power between two or more rotating shafts over considerable distances efficiently. There are two main types of belt drives: open belt drives which rotate the driven pulley in the same direction as the driving pulley, and crossed belt drives which rotate the driven pulley in the opposite direction. Belt drives have advantages such as being economical, not requiring parallel shafts, providing overload protection, and having little noise and vibration, but they also have disadvantages such as potential slipping, stretching, and heat buildup limiting their speed and power transmission.
Design, Analysis, and Optimization of Continuous Variable TransmissionIRJET Journal
This document discusses the design, analysis, and optimization of a continuous variable transmission (CVT) system. It aims to identify weaknesses in the existing CVT belt design and increase efficiency. The current design has issues like noise, jerking, and low belt life. A SolidWorks model and Ansys analysis are used to evaluate stresses on the V-belt, made of composite material. The study involves reviewing the existing design, analyzing it, optimizing the design, analyzing the revised design, and comparing results. The belt material is changed from rubber to Kevlar to achieve an optimized design with lower stress and deformation as well as increased life cycle.
IRJET- Sensitivity Analysis Study of CVT Parameters using Mathematical ModelIRJET Journal
This document presents a mathematical model to analyze the sensitivity of continuously variable transmission (CVT) parameters. It discusses the components of a CVT system including V-belts and variable diameter pulleys. The methodology describes developing equations for the primary actuator using centrifugal force on rollers, the V-belt geometry, and the secondary actuator incorporating a helical spring. The results section shows the mathematical model was verified against dynamometer test data and found to be comparable, indicating it can be used to study effects of varying CVT parameters on vehicle performance.
Belt drives transmit rotational motion between shafts using pulleys connected by belts. There are several types of belts, including flat, V, and circular belts. A belt drive consists of two pulleys over which an endless belt is passed, transmitting power from the driving pulley to the driven pulley via friction. Different types of pulleys are used depending on the application, including open belt drives where shafts rotate in the same direction, crossed belt drives where shafts rotate in opposite directions, and stepped cone pulleys which allow variable speed control. Belt drives provide an efficient means of power transmission over varying distances with low noise and maintenance requirements.
Worm gears allow rotational speed and torque to be controlled. They are commonly used for tuning stringed musical instruments, in elevator machinery, and differentials in vehicles. Worm gears provide mechanical advantage through gear reduction, allowing smaller rotational forces to overcome larger resistive loads.
This document provides an introduction to flexible drives, specifically belt drives, used in transmission systems. It discusses the basic components and history of flexible drives. Belt drives transmit power between components over distance in a simple and cost-effective manner. The document outlines different types of belts and materials used. It explains key concepts in belt drives such as tight and slack sides, velocity ratio, belt creep, whipping, centrifugal tension, and slip. Flexible drives like belts are widely used to transfer power in machines and industrial applications.
This document appears to be a mini project report on continuously variable transmission (CVT) submitted by four students - Harshal Patil, Pooja Patil, Vijay Patil, and Priyanka Salve - at Vishwakarma Institute of Technology in Pune, India under the guidance of Professor S.P. Joshi. The report includes an introduction to CVTs, descriptions of their key components like pulleys and belts, an overview of different CVT types, and details about the students' own work on developing a CVT model. It aims to explain the technology and operation of CVTs through text, diagrams, and documentation of their hands-on project.
Design and Development of Single-Row Manual Seedling PlanterIRJET Journal
This document describes the design and development of a single-row manual seedling planter. The planter was created to address issues with conventional manual seedling plantation methods, such as being time-consuming, labor-intensive, and causing back pain. The low-cost planter is powered manually and replaces the need for suspensions, gear, chain drives and multiple laborers. It works by using a conveyor belt and dropping cone to deposit seedlings, which are then planted manually with a pushing motion that utilizes front wheel suspensions. The planter aims to reduce costs for small-scale farmers through providing a less strenuous alternative to traditional seedling plantation.
A review on design and development of eccentric shaft for cottonLaukik Raut
This document provides a review and discussion of eccentric shafts, which are important components used in cotton ginning machines to provide oscillatory motion. Eccentric shafts are circular or cam-shaped disks attached off-center to a rotating axle. They are widely used in industries like cotton ginning where their small eccentric distance results in low friction loss and high efficiency. The document discusses the design, operation, and factors that affect the life of eccentric shafts, such as load, geometry, materials, and wear. It also reviews various studies on topics like eccentric mechanisms, eccentricity-related faults, vibration control of eccentric rotors, and designs of eccentric shafts in applications like pumps and robots. The goal of the document is
Power Transmission- Southeast University department of Textile EngineeringFaisal Ahmed Bappi
This document discusses various methods of power transmission, including belt drives, gear drives, chain drives, and rope drives. It provides definitions and classifications for each method. Belt drives can be classified by distance between pulleys, material, and power/speed. Gear drives can be classified by position of axes, peripheral velocity, and type of gearing. Chain drives are classified by usage. Rope drives use fiber or wire ropes. Each method has advantages like efficiency and flexibility, as well as disadvantages like noise and required maintenance. The document concludes that power transmission allows motion from one location to drive other mechanisms and alter characteristics like torque and speed.
This document contains chapter summaries and sample questions for a metallurgy textbook. It covers topics such as crystal structures, solid solutions, phase diagrams, heat treating steel and cast iron, non-ferrous alloys, powder metallurgy, metallography, and non-destructive testing methods. For each chapter, it lists key concepts and provides example questions to test understanding, ranging from defining terms to explaining processes and properties. The document is divided into multiple pages with headings identifying the chapter topics covered.
1. The specimen is cut, mounted, and ground using progressively finer abrasive papers to create a flat surface.
2. The specimen is then polished using diamond and alumina powders to remove fine scratches.
3. Etching with chemical reagents is used to reveal microscopic structures by imparting contrast to grain boundaries and other microstructural features. This final prepared specimen surface can then be examined under a microscope.
This document provides an analysis of past questions from the GTU exam for the course "Material Science & Metallurgy (2131904)" taught at the Darshan Institute of Engineering & Technology. It covers 13 chapters, with multiple questions asked per chapter over several exam periods. The questions assess topics such as crystal structures, defects, phase transformations, alloy design, heat treatments, casting, powder metallurgy, and non-destructive testing. Material characterization techniques like metallography are also addressed. The document aims to help students prepare for this recurring exam by reviewing important concepts and analysis skills tested in prior years.
This document provides an analysis of past exam papers for the course "Kinematics of Machines" taught at Darshan Institute of Engineering & Technology. It covers 4 chapters: Introduction of Mechanisms and Machines, Synthesis and Analysis of Mechanisms, Velocity and Acceleration Analysis, and Special Mechanisms. For each chapter, it lists the theory and example questions asked in previous exams from 2014-2017. The questions cover topics such as kinematic links, inversion of mechanisms, Freudenstein's method of synthesis, velocity/acceleration analysis using Klein's construction and relative velocity method, and special mechanisms including steering gears and straight line motion mechanisms.
This document provides an introduction to gears and gear trains. It defines common terms used in gears such as pitch circle, pitch diameter, pressure angle, addendum, and dedendum. It also classifies gears based on the position of shaft axes (parallel shaft gears include spur gears, helical gears, herringbone gears, bevel gears; intersecting shaft gears include straight bevel gears and spiral bevel gears). The document discusses advantages of gear drives such as transmitting exact velocity ratios and disadvantages such as requiring specialized manufacturing. It provides examples of different types of gears and their applications.
This document discusses friction, clutches, and brakes. It begins with an introduction to friction, describing the different types (dry, skin/greasy, film), laws of friction, and coefficient of friction. It then discusses motion up and down inclined planes, defining the angle of friction and efficiency. Specific topics covered include screw threads, pivot and collar friction, friction clutches, brakes, brake classification, and vehicle braking systems. Problems with friction, clutches, and brakes are also mentioned.
3131906 -CAMS- KINETICS AND DYNAMICS OF MACHINETakshil Gajjar
This document discusses cam and follower classification and terminology. It provides:
1) Classification of followers based on contact surface (knife edge, roller, flat/mushroom faced) and motion (reciprocating, oscillating).
2) Classification of cams as radial or cylindrical.
3) Terminology used in cams including base circle, trace point, pressure angle, pitch point, and lift.
4) Motions of the follower including uniform velocity, simple harmonic motion, uniform acceleration/retardation, and cycloidal motion. Displacement, velocity and acceleration diagrams are provided for uniform velocity and simple harmonic motion cases.
3131906 VELOCITY AND ACCELERATION ANALYSISTakshil Gajjar
This document discusses concepts related to velocity and acceleration analysis in mechanisms. It introduces linear velocity and acceleration, and describes two methods for determining velocity of points on links: the instantaneous center method and relative velocity method. It then applies these concepts to analyze the velocity of points in a slider crank mechanism using a velocity diagram. Finally, it discusses properties of instantaneous centers including the number and types of instantaneous centers in a mechanism.
3131906 - GRAPHICAL AND ANALYTICAL LINKAGE SYNTHESISTakshil Gajjar
The document discusses various methods for synthesizing mechanisms through graphical and analytical means. It describes Freudenstein's equation, which allows analytical synthesis of a four-bar linkage to achieve desired output positions based on input positions. The document also discusses two-position synthesis of slider-crank and crank-rocker mechanisms through graphical construction of limiting positions. Finally, it introduces the inversion method of synthesis for a four-bar linkage using three specified positions of the input and output links.
3131906 - INTRODUCTION OF MECHANISMS AND MACHINES Takshil Gajjar
The document discusses various concepts related to kinematics and mechanisms including:
- Kinematic links that make up mechanisms and their types including rigid, flexible, and fluid links.
- Kinematic pairs and their classification based on relative motion and contact between elements. Common pairs include sliding, turning, rolling, screw, and spherical pairs.
- Kinematic chains formed by coupling kinematic pairs to transmit motion from one link to another. The simplest kinematic chain is the four-bar chain.
- Degrees of freedom and mobility of mechanisms, which is the number of independent coordinates needed to define the configuration. Formulas like Kutzbach's criterion are used to calculate this.
Meaning of constitutional law AND constitutionalismTakshil Gajjar
Constitutional law refers to the body of law that governs the relationships between different government institutions and between the government and citizens. Constitutionalism is the ideology and practice of limiting government power through a constitution in order to protect individual rights and promote democracy. The document discusses the meaning and definitions of constitutional law and constitutionalism.
Indian constitution technical publication bookTakshil Gajjar
The document appears to be a scanned collection of pages from a book or manual. It contains images of many pages with text and diagrams but no clear overall topic or narrative. As it is just scanned pages with no context provided, it is difficult to provide a high-level summary in 3 sentences or less.
The document discusses key aspects of the Indian constitution, including:
1) It provides a timeline of the formation of the Indian constitution from 1946 to 1950, outlining important dates and events such as the establishment of the constituent assembly and adoption of the final constitution.
2) It describes some of the influences on the Indian constitution from other models including the UK, US, Ireland and Canada in areas like parliamentary democracy, fundamental rights, federalism and directive principles.
3) It explains some of the salient features of the Indian constitution such as its length, structure with parts and schedules, borrowing from other systems while adapting to Indian conditions, and establishment through a constituent assembly rather than parliament.
The document appears to be a scanned collection of pages from a book or manual. It contains images of many pages with text and diagrams but no clear overall narrative or topic. As it is an unstructured scan of pages, it is difficult to provide a high-level summary in 3 sentences or less.
The document discusses the history of the Indian Constitution. It covers the development of the constitution from independence to the present day. However, no other details were provided in the document to summarize further in just 3 sentences.
The document discusses the benefits of exercise for mental health. Regular physical activity can help reduce anxiety and depression and improve mood and cognitive function. Exercise causes chemical changes in the brain that may help protect against developing mental illness and improve symptoms for those who already have a condition.
Software Engineering and Project Management - Introduction, Modeling Concepts...Prakhyath Rai
Introduction, Modeling Concepts and Class Modeling: What is Object orientation? What is OO development? OO Themes; Evidence for usefulness of OO development; OO modeling history. Modeling
as Design technique: Modeling, abstraction, The Three models. Class Modeling: Object and Class Concept, Link and associations concepts, Generalization and Inheritance, A sample class model, Navigation of class models, and UML diagrams
Building the Analysis Models: Requirement Analysis, Analysis Model Approaches, Data modeling Concepts, Object Oriented Analysis, Scenario-Based Modeling, Flow-Oriented Modeling, class Based Modeling, Creating a Behavioral Model.
Redefining brain tumor segmentation: a cutting-edge convolutional neural netw...IJECEIAES
Medical image analysis has witnessed significant advancements with deep learning techniques. In the domain of brain tumor segmentation, the ability to
precisely delineate tumor boundaries from magnetic resonance imaging (MRI)
scans holds profound implications for diagnosis. This study presents an ensemble convolutional neural network (CNN) with transfer learning, integrating
the state-of-the-art Deeplabv3+ architecture with the ResNet18 backbone. The
model is rigorously trained and evaluated, exhibiting remarkable performance
metrics, including an impressive global accuracy of 99.286%, a high-class accuracy of 82.191%, a mean intersection over union (IoU) of 79.900%, a weighted
IoU of 98.620%, and a Boundary F1 (BF) score of 83.303%. Notably, a detailed comparative analysis with existing methods showcases the superiority of
our proposed model. These findings underscore the model’s competence in precise brain tumor localization, underscoring its potential to revolutionize medical
image analysis and enhance healthcare outcomes. This research paves the way
for future exploration and optimization of advanced CNN models in medical
imaging, emphasizing addressing false positives and resource efficiency.
Null Bangalore | Pentesters Approach to AWS IAMDivyanshu
#Abstract:
- Learn more about the real-world methods for auditing AWS IAM (Identity and Access Management) as a pentester. So let us proceed with a brief discussion of IAM as well as some typical misconfigurations and their potential exploits in order to reinforce the understanding of IAM security best practices.
- Gain actionable insights into AWS IAM policies and roles, using hands on approach.
#Prerequisites:
- Basic understanding of AWS services and architecture
- Familiarity with cloud security concepts
- Experience using the AWS Management Console or AWS CLI.
- For hands on lab create account on [killercoda.com](https://killercoda.com/cloudsecurity-scenario/)
# Scenario Covered:
- Basics of IAM in AWS
- Implementing IAM Policies with Least Privilege to Manage S3 Bucket
- Objective: Create an S3 bucket with least privilege IAM policy and validate access.
- Steps:
- Create S3 bucket.
- Attach least privilege policy to IAM user.
- Validate access.
- Exploiting IAM PassRole Misconfiguration
-Allows a user to pass a specific IAM role to an AWS service (ec2), typically used for service access delegation. Then exploit PassRole Misconfiguration granting unauthorized access to sensitive resources.
- Objective: Demonstrate how a PassRole misconfiguration can grant unauthorized access.
- Steps:
- Allow user to pass IAM role to EC2.
- Exploit misconfiguration for unauthorized access.
- Access sensitive resources.
- Exploiting IAM AssumeRole Misconfiguration with Overly Permissive Role
- An overly permissive IAM role configuration can lead to privilege escalation by creating a role with administrative privileges and allow a user to assume this role.
- Objective: Show how overly permissive IAM roles can lead to privilege escalation.
- Steps:
- Create role with administrative privileges.
- Allow user to assume the role.
- Perform administrative actions.
- Differentiation between PassRole vs AssumeRole
Try at [killercoda.com](https://killercoda.com/cloudsecurity-scenario/)
artificial intelligence and data science contents.pptxGauravCar
What is artificial intelligence? Artificial intelligence is the ability of a computer or computer-controlled robot to perform tasks that are commonly associated with the intellectual processes characteristic of humans, such as the ability to reason.
› ...
Artificial intelligence (AI) | Definitio
Applications of artificial Intelligence in Mechanical Engineering.pdfAtif Razi
Historically, mechanical engineering has relied heavily on human expertise and empirical methods to solve complex problems. With the introduction of computer-aided design (CAD) and finite element analysis (FEA), the field took its first steps towards digitization. These tools allowed engineers to simulate and analyze mechanical systems with greater accuracy and efficiency. However, the sheer volume of data generated by modern engineering systems and the increasing complexity of these systems have necessitated more advanced analytical tools, paving the way for AI.
AI offers the capability to process vast amounts of data, identify patterns, and make predictions with a level of speed and accuracy unattainable by traditional methods. This has profound implications for mechanical engineering, enabling more efficient design processes, predictive maintenance strategies, and optimized manufacturing operations. AI-driven tools can learn from historical data, adapt to new information, and continuously improve their performance, making them invaluable in tackling the multifaceted challenges of modern mechanical engineering.
1. Contents
5.1 Introduction ....................................................................................................................................... 5.2
5.2 Selection of Belt drive ....................................................................................................................... 5.2
5.3 Types of Belt drives........................................................................................................................... 5.2
5.4 Law of Belting.................................................................................................................................... 5.7
5.5 Slip of Belt.......................................................................................................................................... 5.8
5.6 Creep of Belt...................................................................................................................................... 5.8
5.7 Length of an Open Belt Drive............................................................................................................ 5.9
5.8 Length of Crossed Belt Drive..........................................................................................................5.10
5.9 Ratio of Friction Tensions...............................................................................................................5.12
5.10 Power Transmitted by a belt ..........................................................................................................5.15
5.11 Angle of Contact or Angle of Lap...................................................................................................5.15
5.12 Centrifugal effect on Belt................................................................................................................5.16
5.13 Maximum Power transmitted by a belt .........................................................................................5.18
5.14 Initial Tension in the Belt ................................................................................................................5.19
5.15 Crowning of Pulley ..........................................................................................................................5.20
5.16 Advantages & Disadvantages of V – Belt drive over Flat Belt drive ............................................5.21
5.17 Rope drive ........................................................................................................................................5.21
5.18 Chain Drive.......................................................................................................................................5.23
5.19 Problems..........................................................................................................................................5.27
2. 5.2
Dr. A. J. Makadia, Department of Mechanical Engineering
Kinematics and Theory of Machines (3131906) |
Unit-5 Belt, Ropes and Chains
5.1 Introduction
Power is transmitted from one shaft to another by means of Belt, rope, chain and gears.
Salient Features:
Belt, rope and chain are used where the distance between the shaft is large. For small distance,
gears are preferred.
Belt, rope and chain are the flexible types of connectors, i.e., they are bent easily.
The flexibility of belt and rope is due to the property of their materials whereas chains have a
number of small rigid elements having relative motion between the two elements.
Belt and rope transmit power due to friction between them and the pulley. If the power transmitted
exceeds the force of friction, the belt or rope slips over the pulley.
Belts and ropes are strained during motion as tensions are developed in them.
Owing to slipping and straining action belts and ropes are not positive drive, i.e., velocity ratio are
not constant. Chain and gears have a constant velocity ratio.
5.2 Selection of Belt drive
Following are the factors which affect the selection of belt drive:
Speed of driving and driven shafts.
Power to be transmitted.
Space available.
Service conditions.
Centre distance between the shafts.
Speed reduction ratio.
5.3 Types of Belt drives
a) Light drives
Small power.
V ≤ 10 m/s Agricultural machine, Small machine.
b) Medium drives
Medium power
22 < V > 10 m/s, Machine tool.
c) Heavy drives
Large power
V > 22 m/s Compressor, generator.
3. Dr. A. J. Makadia, Department of Mechanical Engineering
Kinematics and Theory of Machines (3131906) |
Unit-5 Belt, Ropes and Chains
5.3
5.3.1 Belt drives & its materials
Fig.5.1 - Types of Belts
5.3.1.1 Flat Belt
Used in the industry where a moderate amount of power is transmitted.
Dist. x ≤ 8m or 10m apart with 22 m/sec.
Materials are leather, rubber, canvas, cotton & rubber Balata (higher strength than rubber belt).
5.3.1.2 V- Belt
Used in the industry where a moderate amount of power to be transmitted.
Connect the shaft up to 4m.
Speed ratio can be up to 7 to 1 and belt speed 24 m/sec.
Made of rubber impregnated fabric with the angle of V between 30° to 40°.
Note: In multiple V – belt drive all the belt should be stretch at the same rate so that load is equally
divided. When one of the selves of belt break, the entire set should be replaced at the same drive.
If one belt is replaced the new unworn and unstressed will be more tightly stretched and will more
with different velocity.
5.3.1.3 Ropes
Used where a higher amount of power to be transmitted distance up to 30m apart.
Operating speed is less than 3 m/sec.
Materials for rope are cotton, hemp, manila or wire.
5.3.2 Types of Flat Belt Drives
5.3.2.1 Open Belt Drive
Fig.5.2 - Open belt drive
4. 5.4
Dr. A. J. Makadia, Department of Mechanical Engineering
Kinematics and Theory of Machines (3131906) |
Unit-5 Belt, Ropes and Chains
An open belt drive is used when the driven pulley is desired to rotate in the same direction.
Generally, the centre distance for open belt drive is 14 – 16 m. if the distance is too large, the belt
whips i.e. vibrate in a direction perpendicular to the direction of motion.
For very shorter distance, the belt slips increase.
While transmitting power, one side of the belt is more tightened (known as a tight side) as
compared to other (known as a slack side).
In the case of horizontal drives, it is always desired that the tight side is at the lower side of two
pulleys. This is because the sag of the belt will be more on the upper side than the lower side. This
slightly increases the angle of wrap of the belts on the two pulleys than if the belt had been perfectly
straight between the pulleys.
In case the tight side of the belt is on the upper side, the sag will be greater at the lower side,
reducing the angle of wrap and slip could occur earlier. This ultimately affects the power to be
transmitted.
5.3.2.2 Crossed Belt Drive
Fig.5.3 - Crossed belt drive
A crossed belt drive is used when the driven pulley is to be rotated in the opposite direction to that
of the driving pulley.
A crossed belt drive can transmit more power than an open belt drive as the angle of wrap is more.
However, the belt has to bend in two different planes and it wears out more. To avoid this the shaft
should be placed at a max dist. 20 b where b = width of belt and speed should be less than 15 m
/sec.
5.3.2.3 Quarter Turn Belt Drive / Right Angle Belt Drive
Fig.5.4 - Quarter turn belt drive with guide pulley
5. Dr. A. J. Makadia, Department of Mechanical Engineering
Kinematics and Theory of Machines (3131906) |
Unit-5 Belt, Ropes and Chains
5.5
A guide pulley is used to connect two non-parallel shafts in such a way that they may run in either
direction and still making the pulley to deliver the belt properly in accordance with the law of belting.
A guide pulley can also be used to connect even intersecting shaft also.
5.3.2.4 Belt Drive with Idler Pulley
Fig.5.5 - Belt drive with Idler pulley
With constant use, the belt is permanently stretched in a little longer. This reduces the initial tension
in the belt leading to lower power transmission capacity. However, the tension in the belt can be
restored to the original value.
A bell – crank lever, hinged on the axis of the smaller pulley, supports adjustable weights on its one
arm and the axis of a pulley on the other. The pulley is free to rotate on its axis and is known as an
idler pulley. Owing to weights on one arm of the lever, the pulley exerts pressure on the belt
increasing the tension and the angle of contact. Thus, the life of the belt is increased and the power
capacity is restored to the original value.
The motion of one shaft can be transmitted to two or more than two shafts by using a number of
the idler pulley.
5.3.2.5 Compound Belt Drive / Intermediate Pulley
Fig.5.6 - Compound belt drive
When it is required to have large velocity ratios, ordinarily the size of the larger pulley will be quite
big. However, by using an intermediate (counter-shaft) pulley, the size can be reduced.
6. 5.6
Dr. A. J. Makadia, Department of Mechanical Engineering
Kinematics and Theory of Machines (3131906) |
Unit-5 Belt, Ropes and Chains
5.3.2.6 Stepped / Cone Pulley Drive
Fig.5.7 - Stepped / Cone pulley drive
A stepped cone pulley drive is used for changing the speed of the driven shaft while the main or
driving shaft runs at a constant speed.
This is done by shifting the belt from one part of the step to the other.
5.3.2.7 Fast and Loose Pulley drive
Fig.5.8 - Fast and loose pulley drive
Many times, it is required to drive several machines from a single main shaft. In such a case, some
arrangement to link or delink a machine to or from the main shaft has to be incorporated as all the
machines may not be operating simultaneously. The arrangement usually provided is that of using
a loose pulley along with a fast pulley.
A fast pulley is keyed to the shaft and rotates with it at the same speed and thus transmits power.
A loose pulley is not keyed to the shaft and thus is unable to transmit any power.
Whenever a machine is to be driven, the belt is mounted on the fast pulley and when it is not
required to transmit any power, the belt is pushed to the loose pulley placed adjacent to the fast
pulley.
7. Dr. A. J. Makadia, Department of Mechanical Engineering
Kinematics and Theory of Machines (3131906) |
Unit-5 Belt, Ropes and Chains
5.7
5.4 Law of Belting
The law of belting states that centre line of the belt when it approaches a pulley must lie in the
midplane of that pulley. However, a belt leaving a pulley may be drawn out of the plane of the pulley.
By following this law, non – parallel shafts may be connected by a flat belt.
It should be observed that it is not possible to operate the belt in the reverse direction without
violating the law of belting. Thus, in the case of non – parallel shafts, motion is possible only in one
direction. Otherwise, the belt is thrown off the pulley.
However, it is possible to run a belt in either direction on the pulley of two non – parallel or
intersecting shafts with the help of guide pulleys. The law of belting is satisfied.
5.4.1 Velocity Ratio of Belt Drive
Velocity ratio is the ratio of the speed of driven pulley (N2) to that of a driving pulley (N1)
Let,
N1 = Speed of driving pulley
N2 = Speed of driven pulley
D1 = Diameter of the driving pulley
D2 = Diameter of the driven pulley
T = thickness of the belt
Neglecting slip between belt & pulley and consider belt to be inelastic.
Let, the speed of belt on driving pulley = speed of belt on driven pulley
π
D1 N1
60
= π
D2 N2
60
(D1 + 2
t
2
) N1 = (D2 + 2
t
2
) N2
Or Velocity Ratio (VR)
(VR) =
N2
N1
=
D1 + t
D2 + t
5.4.2 Velocity Ratio of Compound Belt Drive
Let,
D1, D2, D3, D4 = Diameter of pulley
N1, N2, N3, N4 = Speed of pulley
For pulley 1 & 2
N2
N1
=
D1
D2
Eq. (5.1)
For pulley 3 & 4
N4
N3
=
D3
D4
Eq. (5.2)
Multiplying Eq. (5.1) & Eq. (5.2)
8. 5.8
Dr. A. J. Makadia, Department of Mechanical Engineering
Kinematics and Theory of Machines (3131906) |
Unit-5 Belt, Ropes and Chains
N2
N1
×
N4
N3
=
D1
D2
×
D3
D4
𝐍𝟒
𝐍𝟏
=
𝐃𝟏
𝐃𝟐
×
𝐃𝟑
𝐃𝟒
5.5 Slip of Belt
Sometimes, due to insufficient frictional grip, there may be a chance of forwarding motion of belt
without carrying the driven pulley with it. This is called slip of belt and is expressed as a percentage.
Result of slipping is reduced the velocity ratio of the system.
Let,
S1% = Slip between driven & belt
S2% = Slip between belt & follower
Let the velocity of the belt passing over driver per second
V =
π d1 N1
60
−
π d1 N1
60
×
S1
100
=
π d1 N1
60
[1 −
S1
100
]
Eq. (5.3)
The velocity of the belt passing over follower per second
π d2 N2
60
= V − V ∙
S2
100
= V [1 −
S2
100
]
Eq. (5.4)
From Eq. (5.3) & Eq. (5.4)
π d2 N2
60
=
π d1 N1
60
[1 −
S1
100
] × [1 −
S2
100
]
N2
N1
=
d1
d2
[1 −
S1
100
−
S2
100
] … … … … . (Neglecting
S1 S2
100 × 100
)
=
d1
d2
[1 −
(S1 + S2)
100
]
N2
N1
=
d1
d2
[1 −
S
100
]
Where S = S1 + S2 – 0.01 S1S2 = Total Percentage of slip
𝐍𝟐
𝐍𝟏
=
𝐝𝟏 + 𝐭
𝐝𝟐 + 𝐭
[𝟏 −
𝐒
𝟏𝟎𝟎
]
5.6 Creep of Belt
When the belt passes from slack side to tight side, a certain portion of the belt extends and it contracts
again when the belt passes from tight side to slack side. Due to these change of length, there is a relative
motion between belt & pulley surface. This relative motion is called “Creep”.
The total effect of creep is to reduce slightly the speed of the driven pulley or follower.
Considering the creep,
Velocity ratio
N2
N1
=
d1
d2
[
E + √σ2
E + √σ1
]
9. Dr. A. J. Makadia, Department of Mechanical Engineering
Kinematics and Theory of Machines (3131906) |
Unit-5 Belt, Ropes and Chains
5.9
Where
σ1 = Stress on the tight side of the belt
σ2 = Stress on the slack side of the belt
E = Young modulus for the belt material
5.7 Length of an Open Belt Drive
Fig.5.9 - 9 Length of an open belt drive
Let r1 , r2 = Radius of larger & smaller pulley.
x = Distance between centre of two pulley.
L = Total Length.
Let the length of the belt,
L = Arc GJE + EF + Arc FKH + GH
= 2 (Arc JE + EF + Arc FK) Eq. (5.5)
Let
Arc EJG = 2 Arc JE = 2 (
π
2
+ α) ∙ r1
Arc FKH = 2 Arc FK = 2 (
π
2
− α) ∙ r2
sin α =
r1 − r2
x
EF = MO2 = √(O1O2)2 − (O1M)2
= √(x)2 − (r1 − r2)2
= x √1 − (
r1 − r2
𝑥
)
2
Expanding by Binominal Theorem
= x [1 −
1
2
(
r1 − r2
𝑥
)
2
+ ⋯ ⋯ ⋯ ] = x −
1
2
(
r1 − r2
x
)
2
10. 5.10
Dr. A. J. Makadia, Department of Mechanical Engineering
Kinematics and Theory of Machines (3131906) |
Unit-5 Belt, Ropes and Chains
Putting value in Eq. (5.5)
∴ L = 2 [(
π
2
+ α) r1 + x −
(r1 − r2)2
2x
+ (
π
2
− α) r2]
= 2 [r1 ∙
π
2
+ r1 ∙ α + x −
(r1 − r2)2
2x
+ r2 ∙
π
2
− r2 ∙ α ]
= 2 [
π
2
(r1 + r2) + α (r1 − r2) + x −
(r1 − r2)2
2x
]
= π (r1 + r2) + 2 α (r1 − r2) + 2x −
(r1 − r2)2
x
[
sin α =
r1 − r2
x
α is small
∴ sin α = α
]
= π (r1 + r2) + 2 (
r1 − r2
𝑥
) (r1 − r2) + 2x −
(r1 − r2)2
x
= π (r1 + r2) + 2
(r1 − r2)2
x
+ 2x −
(r1 − r2)2
x
L = π (r1 + r2) + 2x +
(r1 − r2)2
x
In terms of Radius
𝐋 =
𝛑
𝟐
(𝐝𝟏 + 𝐝𝟐) + 𝟐𝐱 +
(𝐝𝟏 − 𝐝𝟐)𝟐
𝟒𝐱
𝐈𝐧 𝐭𝐞𝐫𝐦𝐬 𝐨𝐟 𝐝𝐢𝐚𝐦𝐞𝐭𝐞𝐫
5.8 Length of Crossed Belt Drive
Fig.5.10 - Length of crossed belt drive
Let r1, r2 = Radius of larger & smaller pulley
x = Distance between centre of two pulley
L = Total Length
11. Dr. A. J. Makadia, Department of Mechanical Engineering
Kinematics and Theory of Machines (3131906) |
Unit-5 Belt, Ropes and Chains
5.11
L = Arc GJE + Arc FKH + EF + GH Eq. (5.6)
Arc GJE = 2 Arc JE = 2 (
π
2
+ α) ∙ r1
Eq. (5.7)
Arc FKH = 2 Arc HK = 2 (
π
2
+ α) ∙ r2
Eq. (5.8)
EF = GH = MO2 = √(O1O2)2 − (O2M)2
= √𝑥2 − (r1 + r2)2
= x √1 − (
r1 + r2
𝑥
)
2
Expanding by Binominal Theorem
= x [1 −
1
2
(
r1 + r2
𝑥
)
2
+ ⋯ ⋯ ⋯ ]
= x −
(r1 + r2)2
2x
Eq. (5.9)
Putting value of Eq. (5.7), Eq. (5.8) & Eq. (5.9) in Eq. (5.6)
∴ L = 2 [r1 (
π
2
+ α) + x −
(r1 + r2)2
2x
+ r2 (
π
2
+ α)]
= 2 [r1 ∙
π
2
+ r1 ∙ α + x −
(r1 + r2)2
2x
+ r2 ∙
π
2
+ r2 ∙ α ]
= 2 [
π
2
(r1 + r2) + α (r1 + r2) + x −
(r1 + r2)2
2x
]
= π (r1 + r2) + 2 α (r1 + r2) + 2x −
(r1 + r2)2
x
[
sin α = α
As α is very small
sin α =
r1 + r2
x
]
= π (r1 + r2) + 2 (
r1 + r2
𝑥
) (r1 + r2) + 2x −
(r1 + r2)2
x
= π (r1 + r2) + 2
(r1 + r2)2
x
+ 2x −
(r1 + r2)2
x
L = π (r1 + r2) + 2x +
(r1 + r2)2
x
In terms of Radius
𝐋 =
𝛑
𝟐
(𝐝𝟏 + 𝐝𝟐) + 𝟐𝐱 +
(𝐝𝟏 + 𝐝𝟐)𝟐
𝟒𝐱
𝐈𝐧 𝐭𝐞𝐫𝐦𝐬 𝐨𝐟 𝐝𝐢𝐚𝐦𝐞𝐭𝐞𝐫
12. 5.12
Dr. A. J. Makadia, Department of Mechanical Engineering
Kinematics and Theory of Machines (3131906) |
Unit-5 Belt, Ropes and Chains
5.9 Ratio of Friction Tensions
5.9.1 Flat Belt
Fig.5.11 - Ratio of Friction Tensions for Flat Belt
T1 = Tensions on tight side.
T2 = Tensions on slack side.
θ = Angle of Lap of the belt over the pulley.
μ= Coefficient of friction between belt & pulley.
Consider a short length of belt PQ subtending an angle of δθ at the centre of the pulley.
R = Normal (Radial) reaction between element length of belt & pulley.
T = Tension on the slack side of the element.
δT = increase in tension on the tight side than that of the slack side.
T + δT = Tension on the tight side of the element.
Tensions T and (T + δT) act in directions perpendicular to the radii drawn at the end of elements. The
friction force F = μR will act tangentially to the pulley rim resisting the slipping of the elementary belt on
the pulley.
Resolving the forces in the tangential direction (Horizontally),
μR + T cos
δθ
2
− (T + δT) cos
δθ
2
= 0
μR + T − (T + δT) = 0
[
As δθ is small
cos
δθ
2
≈ 1
]
R =
δT
μ
Eq. (5.10)
Resolving the forces in Radial Direction (Vertically),
R − T sin
δθ
2
− (T + δT) sin
δθ
2
= 0
13. Dr. A. J. Makadia, Department of Mechanical Engineering
Kinematics and Theory of Machines (3131906) |
Unit-5 Belt, Ropes and Chains
5.13
R − T
δθ
2
− T
δθ
2
−
δT ∙ δθ
2
= 0
[
As δθ is small
sin
δθ
2
≈
δθ
2
δT ∙ δθ
2
→ Neglect
]
R = 2
Tδθ
2
= T δθ
Eq. (5.11)
Comparing Eq. (5.10) and Eq. (5.11)
δT
μ
= T δθ
∴
δT
T
= μ δθ
Integrating between proper limits,
∫
δT
T
T1
T2
= ∫ μ δθ
θ
0
∴ loge
T1
T2
= μθ
Or taking a log to the base 10
𝐓𝟏
𝐓𝟐
= 𝐞𝛍𝛉
2.3 log
T1
T2
= μθ
Note: The above relation is valid only when the belt is on the point of slipping on the pulleys.
5.9.2 V – Belt or Rope
Fig.5.12 - Ratio of Friction Tensions for V-Belt or Rope
14. 5.14
Dr. A. J. Makadia, Department of Mechanical Engineering
Kinematics and Theory of Machines (3131906) |
Unit-5 Belt, Ropes and Chains
In the case of v belt or rope, there are two normal reactions, so the radial reaction is equal to
2R sin α
Thus total friction force = 2F = 2μR
Resolving the forces tangentially,
2μR + T cos
δθ
2
− (T + δT) cos
δθ
2
= 0
2μR + T − T − δT = 0
[
As δθ is small
cos
δθ
2
≈ 1
]
δT = 2μR Eq. (5.12)
Resolving the forces radially,
2R sin α − T sin
δθ
2
− (T + δT) sin
δθ
2
= 0
2R sin α − T
δθ
2
− T
δθ
2
−
δT ∙ δθ
2
= 0
[
As δθ is small
sin
δθ
2
≈
δθ
2
δT ∙ δθ
2
→ Neglect]
2R sin α = 2
Tδθ
2
∴ R =
Tδθ
2 sin α
Eq. (5.13)
From Eq. (5.12) and Eq. (5.13)
δT = 2 μ
Tδθ
2 sin α
or
δT
T
=
μ δθ
sin α
Integrating between proper limits,
∫
δT
T
T1
T2
= ∫
μ δθ
sin α
θ
0
∴ loge
T1
T2
=
μθ
sin α
𝐓𝟏
𝐓𝟐
= 𝐞𝛍𝛉 sin α
⁄
= 𝐞𝛍𝛉 𝐜𝐨𝐬𝐞𝐜𝛂
15. Dr. A. J. Makadia, Department of Mechanical Engineering
Kinematics and Theory of Machines (3131906) |
Unit-5 Belt, Ropes and Chains
5.15
Notes:
The expression is similar to that for a flat belt drive except that μ is replaced byμ sin θ
⁄ , i.e., the
coefficient of friction is increased by 1 sin θ
⁄ . Thus, the ratio T1 T2
⁄ is far greater in the case of V –
belts & ropes for the same angle of lap θ and coefficient of friction μ.
Above expression is derived on the assumption that the belt is on the point of slipping.
5.10 Power Transmitted by a belt
Let
T1 = Tensions on tight side.
T2 = Tensions on slack side.
V = Linear velocity of the belt
P = Power transmitted
P = Net Force ×
Distance moved
second
= (T1 − T2) V
Note:-This relation gives the power transmitted irrespective of the fact whether the belt is on the point of
slipping or not.
If it is the relationship between T1 and T2 for a flat belt is given by T1 T2 = eμθ
⁄ . If it is not, no particular
relation is available to calculate T1and T2.
5.11 Angle of Contact or Angle of Lap
5.11.1Open Belt Drive
Fig.5.13 - Open Belt Drive
r1 = Radius of the larger pulley
r2 = Radius of the smaller pulley
x = Centre distance between two pulley
16. 5.16
Dr. A. J. Makadia, Department of Mechanical Engineering
Kinematics and Theory of Machines (3131906) |
Unit-5 Belt, Ropes and Chains
Angle of contact (θ)
θ = (180 − 2α)°
= (180 − 2α)
π
180
Radian
Where sin α = (
r1 − r2
x
)
5.11.2Cross Belt Drive
Fig.5.14 - Cross Belt Drive
Angle of contact (θ)
θ = (180 + 2α)°
= (180 + 2α)
π
180
Radian
Where sin α = (
r1 + r2
x
)
5.12 Centrifugal effect on Belt
Fig.5.15 - Centrifugal effect on Belt
While in motion, as a belt passes over a pulley, the centrifugal effect due to its own weight tends
to lift the belt from the pulley.
17. Dr. A. J. Makadia, Department of Mechanical Engineering
Kinematics and Theory of Machines (3131906) |
Unit-5 Belt, Ropes and Chains
5.17
The centrifugal force produces equal tensions on the two side of the belt, i.e., on the tight and on
the slack side.
Let,
m = mass of belt per meter length (Kg/m)
v = Linear velocity of belt (m/sec)
r = Radius of pulley
TC = Centrifugal tension on tight side & Slack side
FC = Centrifugal force
FC = mass of element × Acceleration
= (Length of element × mass per unit length) × Acc.
= (r δθ × m) ×
v2
r
Eq. (5.14)
From figure resolving forces radially,
FC = 2 TC sin
δθ
2
= 2 TC
δθ
2
[
δθ
2
is small
sin
δθ
2
≈
δθ
2
]
FC = TCδθ Eq. (5.15)
From Eq. (5.14) and Eq. (5.15),
TCδθ = m v2
δθ
∴ 𝐓𝐂 = 𝐦 𝐯𝟐
∴ To depend on the only velocity of belt and mass of the belt.
Also centrifugal stress in belt =
centrifugal Tension
c s
⁄ Area of belt
=
TC
a
Or
TC = σ ∙ A (Max tension in belt)
Total Tension on tight side = Friction tension + Centrifugal tension
T = T1 + TC
Total Tension on slack side = T2 + TC
18. 5.18
Dr. A. J. Makadia, Department of Mechanical Engineering
Kinematics and Theory of Machines (3131906) |
Unit-5 Belt, Ropes and Chains
5.13 Maximum Power transmitted by a belt
If it is desired that belt transmit maximum power, the following two conditions must be satisfied.
1. Larger tension must reach the maximum permissible value for the belt.
2. The belt should be on the point of slipping i.e., the maximum frictional force is developed in the belt.
Let
P = (T1 − T2) ∙ v
= T1 (1 −
T2
T1
) ∙ v
= T1 (1 −
1
(
T1
T2
)
) ∙ v
[
T1
T2
= eμθ
1 −
1
eμθ
= k constant]
= T1 k ∙ v
= ( T − TC) ∙ k ∙ v
[
T = T1 + TC
∴ T1 = T − TC
]
= kTv − TC ∙ kv
= kTv − (m v2) ∙ kv
P = kTv − kmv3
Here maximum tension T in the belt should not exceed permissible value. Hence treating T as constant
and differentiating the power with respect to v and equating the same equal to zero.
∴
dP
dv
= kT − 3 v2(k m) = 0
∴ kT = 3 v2
k m
T = 3 mv2
T = 3 TC or 𝐓𝐂 =
𝐓
𝟑
For maximum power transmission, the centrifugal tension in the belt is equal to 1/3 of the maximum
allowable belt tension and belt should be on the point of slipping.
Also T = T1 + TC
19. Dr. A. J. Makadia, Department of Mechanical Engineering
Kinematics and Theory of Machines (3131906) |
Unit-5 Belt, Ropes and Chains
5.19
∴ T1 = T − TC
= T −
T
3
=
2T
3
Also T = 3TC
= 3 ∙ m v2
∴ Vmax = √
T
3m
5.14 Initial Tension in the Belt
When a belt is first fitted to a pair of the pulley, an initial tension T0 is given to the belt when the system is
stationary. When transmitting power, the tension on tight increases to T1 and that on slack side decreases
to T2.
If it is assumed that the material of the belt is perfectly elastic i.e., the strain in the belt is proportional to
stress in it and the total length of the belt remains unchanged, the tension on the tight side will increase
by the same amount as the tension on the slack side decreases. If the change in the tension is δT,
Tension on the tight side T1 = T0 + δT
Tension on the slack side T2 = T0 − δT
∴ T0 =
T1 + T2
2
= Mean of tight side & 𝑠𝑙𝑎𝑐𝑘 𝑠𝑖𝑑𝑒 𝑡𝑒𝑛𝑠𝑖𝑜𝑛𝑠
5.14.1Initial tension with centrifugal tensions
Total tension on tight side = T1 + TC
Total tension on slack side = T2 + TC
Let,
T0 =
T1 + T2
2
=
(T1 + TC) + (T2 + TC)
2
=
T1 + T2 + 2TC
2
T0 =
T1 + T2
2
= TC
∴ T1 + T2 = 2(T0 − TC)
[Let
T1
T2
= eμθ
= k]
k T2 + T2 = 2 (T0 − TC)
T2 = 2
(T0 − TC)
k + 1
20. 5.20
Dr. A. J. Makadia, Department of Mechanical Engineering
Kinematics and Theory of Machines (3131906) |
Unit-5 Belt, Ropes and Chains
Let,
T1 = T2 ∙ k
T1 =
2 k (T0 − TC)
(k + 1)
Eq. (5.16)
∴ T1 − T2 =
2 k (T0 − TC)
(k + 1)
− 2
(T0 − TC)
k + 1
T1 − T2 =
2 (k − 1)(T0 − TC)
(k + 1)
Power transmitted (P) = (T1 − T2)v
=
2 (k − 1)(T0 − TC)
(k + 1)
∙ v
=
2 (k − 1)(T0 − m v2)
k + 1
∙ v
P =
2 (k − 1)(T0v − m v3)
k + 1
To find the condition for maximum power transmission,
dP
dv
= T0 − 3mv2
= 0
∴ T0 = 3mv2
∴ v = √
T0
3m
When the belt drive is started, v = 0 and thus TC = 0 (TC = mv2)
T1 =
2 k T0
k + 1
Eq. (5.17)
5.15 Crowning of Pulley
Fig.5.16 - Crowning of Pulley
21. Dr. A. J. Makadia, Department of Mechanical Engineering
Kinematics and Theory of Machines (3131906) |
Unit-5 Belt, Ropes and Chains
5.21
Pulleys are provided with a slight dwell to prevent the belt from running off the pulley. This is known as the
crowning of the pulley.
Crowning may be tapered or rounded. Normally crown height of 10 mm / m face width is provided.
5.16 Advantages & Disadvantages of V – Belt drive over Flat Belt drive
5.16.1Advantages
V - Belt drive gives compactness due to a small distance.
The drive is positive because slip is less.
V – Belts are made endless, no joint so smooth drive.
Longer life 3 – 5 year.
Easily installed & removed.
The high-velocity ratio may be obtained.
Power transmission is more due to wedging action of the belt in the groove.
V – Belt may be operated in either direction.
5.16.2Disadvantages
V – Belt drive can’t use for a large distance.
V – Belts are not so durable as flat belts.
Construction of pulley for V – Belt is more complicated than the pulleys for a flat belt.
Since V – Belts are subjected to a certain amount of creep, so they are not suitable for constant
speed application such as synchronous machines, timing devices etc.
Belt life is effect with temperature changes, improper belt tension and mismatching of belt length.
The centrifugal tension prevents the use of V – Belts at speed below 5 m/s and above 50 m/sec.
5.17 Rope drive
Rope drive is widely used where a large amount of power is to be transmitted from one pulley to
another over a considerable distance.
Frictional grip in case of rope drives is more than V – drives.
The number of separate drives may be taken from one driving pulley.
5.17.1 Types of Rope Drive
5.17.1.1 Fibre Rope Drive
They are made from Fibrous material each as Hemp, Manila and cotton.
Manila ropes are more durable and stronger than cotton rope. (Hempropes have less strength
compared to Manila ropes).
Cotton ropes are costlier than Manila ropes.
22. 5.22
Dr. A. J. Makadia, Department of Mechanical Engineering
Kinematics and Theory of Machines (3131906) |
Unit-5 Belt, Ropes and Chains
Fig.5.17 - Fibre Rope
5.17.1.2 Wire Rope Drive
Fig.5.18 - Wire Rope
When a large amount of power is to be transmitted over a long distance (≅ 150 m apart) then wire
ropes are used.
The wire ropes are used in elevators, mine hoists, crane, conveyors, and suspension bridges.
The wire rope runs on grooved pulleys, but they rest on the bottom of the grooves and are not
wedged between the sides of the grooves.
Wire ropes are made from cold drawn wires, various materials are wrought iron, cast steel, alloy
steel, copper, bronze, aluminium, alloys, S.S. etc.
5.17.1.2.1 Construction & Designation of Wire rope drive
Fig.5.19 - Construction & Designation of Wire rope drive
23. Dr. A. J. Makadia, Department of Mechanical Engineering
Kinematics and Theory of Machines (3131906) |
Unit-5 Belt, Ropes and Chains
5.23
Fig.5.20 - Sheave for Fibre rope
Fig.5.21 - Sheave for Wire rope
Ratio of Driving tensions = 2.3 log
T1
T2
= μ θ cosecβ
5.18 Chain Drive
A chain is regarded in between the gear drive and the belt drive. Like gears, chains are made of
metal, so it requires lesser space and gives a constant velocity ratio. As a belt, it is used for longer
centre distances.
Advantages
1. Constant velocity due to no-slip, so it is a positive drive.
2. No effect on overload on the velocity ratio.
3. Oil or grease on the surface does not affect the velocity ratio.
4. Chains occupy less space as they made of metals.
5. Lesser loads are put on the shaft.
6. High transmission efficiency due to “No-slip”.
7. Through one chain only motion can be transmitted to several shafts.
Disadvantages
1. It is heavier as compared to the belt.
2. There are gradual stretching and an increase in the length of chains. From time to time some
of its links have to be removed.
3. Lubrication of its parts is required.
4. Chains are costlier compared to belts.
24. 5.24
Dr. A. J. Makadia, Department of Mechanical Engineering
Kinematics and Theory of Machines (3131906) |
Unit-5 Belt, Ropes and Chains
5.18.1Relation between Pitch and Pitch circle diameter for Chain
Fig.5.22 - Relation between Pitch and Pitch circle diameter for Chain
The distance between roller centres of two adjacent links is known as pitch (p) of a chain.
A circle through the roller centre of wrapped chain around a sprocket is called pitch circle and its
diameter as pitch circle diameter (d).
Let,
T = No. of teeth on the sprocket
∅ = Angle subtended by the chord of a link at the centre of the sprocket
r= Radius of the pitch circle
Let,
sin
∅
2
=
p 2
⁄
r
∴ sin
∅
2
=
p
2r
∴ p = 2r sin
∅
2
= 2r sin (
360°
2T
) = 2r sin (
180°
T
)
∴ r =
p
2 sin (
180°
T
)
=
p
2
cosec (
180°
T
)
or
𝐝 = 𝐩 𝐜𝐨𝐬𝐞𝐜 (
𝟏𝟖𝟎°
𝐓
)
5.18.2 Chain Length
Length of a chain may be calculated the same way as for open belt drive.
R & r = Radius of the pitch circle of two sprockets having T & t teeth.
C = centre distance between sprocket = k ∙ p
p = Pitch of chain
25. Dr. A. J. Makadia, Department of Mechanical Engineering
Kinematics and Theory of Machines (3131906) |
Unit-5 Belt, Ropes and Chains
5.25
Let,
L = π (R + r) + 2C +
(R − r)2
C
[
Let
R =
p
2
cosec (
180°
T
)
𝑟 =
p
2
cosec (
180°
t
)]
L =
pT + pt
2
+ 2(kp) +
(
p
2
cosec (
180°
T
) −
p
2
cosec (
180°
t
))
2
kp
[
also circular pitch (p)
p =
πD
T
=
π2R
T
∴ πR =
pT
2
∴ π (R + r) =
pT + pt
2
Also C = k ∙ p ]
= p
[
T + t
2
+
(cosec (
180°
T
) − cosec (
180°
t
))
2
4k
+ 2k
]
5.18.3 Classification of Chains
5.18.3.1 Hoisting Chain
Fig.5.23 - Hoisting Chain
Hoisting chain includes an oval link and stud link chains. An oval link is a common form of hoisting
chain. It consists of an oval link and is also known as coil chain. Such chains are used for lower
speed only.
5.18.3.2 Conveyor Chain
Conveyor chain may be detachable or hook type or closed joint type. The sprocket teeth are so
shaped that the chain should run onto and off the sprocket smoothly without interference.
Such chains are used for low-speed agricultural machinery. The material of the link is usually
malleable cast iron. The motion of the chain is not very smooth.
26. 5.26
Dr. A. J. Makadia, Department of Mechanical Engineering
Kinematics and Theory of Machines (3131906) |
Unit-5 Belt, Ropes and Chains
Fig.5.24 - Conveyor Chain
5.18.3.3 Power transmission chain
These chains are made of steel in which the wearing parts are hardened. They are accurately
machined and run on carefully designed sprockets.
a. Block Chain
Fig.5.25 - Block Chain
This type of chain is mainly used for transmission of power at low speeds. Sometimes they are
also used as conveyor chains in place of malleable conveyor chains.
b. Roller Chain
Fig.5.26 - Roller Chain
A bushing is fixed to an inner link whereas the outer link has a pin fixed to it. There is only sliding
motion between pin and bushing. The roller is made of hardened material and is free to turn on the
bushing.
c. Silent Chain (Inverted tooth chain)
Fig.5.27 - Silent Chain
Though roller chain can run quietly at fairly high speed. The silent chains are used where maximum
quietness is desired. Silent chains do not have rollers. The links are so shaped as to engage directly
with the sprocket teeth. The included angle is either 60° or 75°.
27. Dr. A. J. Makadia, Department of Mechanical Engineering
Kinematics and Theory of Machines (3131906) |
Unit-5 Belt, Ropes and Chains
5.27
5.19 Problems
Ex. 5.1 A shaft runs at 80 rpm and drives another shaft at 150 rpm through a belt drive. The
diameter of the driving pulley is 600 mm. determine the diameter of the driven pulley in
the following cases.
a) Neglecting belt thickness.
b) Taking belt thickness as 5mm.
c) Assuming for case (ii) total slip of 4%.
d) Assuming for case (ii) a slip of 2% on each pulley.
Solution: Given Data:
1 1
2 2
N 80rpm,D 600mm
N 150rpm,D ?
Case (i) Neglected belt thickness
2 1 1
1
2
1 2 2
N N D 80 600
D
D 320mm
N D N 150
Case (ii) Belt thickness = 5mm
1 1
2 1
2
1 2 2
N D t
N D t
D t
N D t N
2 2
80 605
D 5 D 317.67mm
150
Case (iii) Total Slip is 4%
2 1
1 2
N D t S
1
N D t 100
2
2
600 5
150 4
1 D 304.76mm
80 D t 100
Case (iv) Slip 2% on each pulley
2 1
1 2
N D t S
1
N D t 100
1 2 1 2
S S S 0.01S S
2 2 0.01 2 2
3.96
2
2
600 5
150 3.96
1 D 304.88mm
80 D t 100
Ex. 5.2 Two parallel shafts connected by a crossed belt, are provided with pulleys 480 mm and
640 mm in diameters. The distance between the centre line of the shaft is 3 m. Find by how
much the length of the belt should be changed if it is desired to alter the direction of
rotation of the driven shaft.
28. 5.28
Dr. A. J. Makadia, Department of Mechanical Engineering
Kinematics and Theory of Machines (3131906) |
Unit-5 Belt, Ropes and Chains
Solution: Given Data:
R = 320 mm
r = 240 mm
X = C = 3 mtr
For cross belt drive,
180 2
180
cross
R r 320 240 0.320 0.240
sin
C 3 3
L 2 R r 2C Cos
10.75 10 45'
0.1878rad
cross
L 2 0.1878 0.32 0.24 2 3cos 10.75
7.865mtr.
For open belt drive,
open 1 2 1 2
2
open
2
L r r 2 r r 2x cos
R r
L R r 2C
C
0.32 0.24
0.32 0.24 2 3
3
7.761mtr.
1 2
r r
sin
X
0.320 0.240
3
1 31'
Angleis smallapprox.
relationcanbeused.
Let the length of belt reduced by,
cross o
L L 7.865 7.761
0.104mtr.
Ex. 5.3 A belt runs over a pulley of 800 mm diameter at a speed of 180 rpm. The angle of the lap
is 165° and the maximum tension in the belt is 2kN. Determine the power transmitted if the
coefficient of friction is 0.3.
Solution: Given Data:
1
T 2000N
d 0.8mtr.
N 180rpm
165 rad
180
2.88rad
0.3
Let,
29. Dr. A. J. Makadia, Department of Mechanical Engineering
Kinematics and Theory of Machines (3131906) |
Unit-5 Belt, Ropes and Chains
5.29
0.8 180
dN
V 7.54 m/ sec
60 60
1
10
2
T
2.3log
T
1
10
2
T
2.3log 0.3 2.88
T
1
2
T
2.37
T
1
1
2
T 2000N
T 2000
T 843N
2.37 2.37
1 2
Power T T v
2000 843 7.54
8724 W
P 8.724kW
Ex. 5.4 A casting weights 6 kN and is freely suspended from a rope which makes 2.5 turns round
a drum of 200 mm diameter. If the drum rotates at 40 rpm, determine the force required
by a man to pull the rope from the other end of the rope. Also, find the power to raise the
casting. The coefficient of friction is 0.25.
Solution: Given Data:
1
2
W T 6000N
2.5 2 15.70rad
d 0.20mtr.
N 40rpm
0.25
T ?
P ?
Let,
0.2 40
dN
V 0.419 m/ sec
60 60
1
10
2
T
2.3log 0.25 15.70
T
1
2
2
T
50.87 T 117.93N
T
1 2
Power T T v
6000 117.93 0.419
2464 Watt
P 2.46kW
30. 5.30
Dr. A. J. Makadia, Department of Mechanical Engineering
Kinematics and Theory of Machines (3131906) |
Unit-5 Belt, Ropes and Chains
Ex. 5.5 A belt drive transmits 8 kW of power from a shaft rotating at 240 rpm to another shaft
rotating at 160 rpm. The belt is 8 mm thick. The diameter of smaller pulley is 600 mm
and the two shafts are 5 m apart. The coefficient of friction is 0.25. If the maximum
stress in the belt is limited to 3 N/mm2
. Find the width of the belt for (i) open belt drive
and (ii) crossed belt drive.
Solution: Given Data:
3
1 1
2
2
P 8 10 watt
N 240rpm ,d 0.600m(Smaller pulley)
N 160rpm
x 5m
0.25
t 8mm
3N/mm
Let,
1 1 2 2
N d N d
1 1
2
2
N d 240 0.6
d 0.900mtr.(bigger pulley)
N 160
(i) Open Belt drive
Angle of contact 180 2
180
180 2 1.71
180
3.08rad
1 2
r r 0.450 0.300
sin
X 5
1.71
Let,
1
10
2
T
2.3log 0.25 3.08
T
1
2
T
2.16
T
1 2
1 2
1 2
Power T T v
8000 T T 7.54
T T 1061
1 1
d N
Velocity v
60
0.6 240
60
v 7.54m/ sec
Let,
1
Max tensionT b t
1975 b t
1975 3 b 8
b 82.29mm
1
1 2
2
1 2
T
2.16 & T T 1061
T
T 914N,T 1975N
31. Dr. A. J. Makadia, Department of Mechanical Engineering
Kinematics and Theory of Machines (3131906) |
Unit-5 Belt, Ropes and Chains
5.31
(ii) Cross belt drive
Angle of contact 180 2
180
180 2 8.62
180
3.443rad
1 2
r r 0.450 0.300
sin
X 5
8.62rad
1
10
2
T
2.3log 0.25 3.443
T
1
2
T
2.36
T
Let,
1
Max tensionT b t
1
1 2
2
2 1
T
T T 1061& 2.36
T
T 780N,T 1840N
1840 3 b 8
b 76.6mm
Ex. 5.6 A 100 mm wide and 10 mm thick belt transmits 5 kW of power between two parallel shafts.
The distance between the shaft centres is 1.5 m and the diameter of the smaller pulley is
440 mm. The driving and the driven shafts rotate at 60 rpm and 150 rpm respectively. The
coefficient of friction is 0.22. Find the stress in the belt if the two pulleys are connected by
(i) an open belt drive (ii) a cross belt drive.
Solution: Given Data:
3
1
2 2
open
cross
b 100mm , t 10mm
P 5 10 watt
x 1.5m
N 60rpm
N 150rpm ,d 440mm
0.22
?
?
Let,
1 1 2 2
N d N d
2 2
1
1
1
N d 150 440
d
N 60
d 1100mm
(i) Open Belt drive,
32. 5.32
Dr. A. J. Makadia, Department of Mechanical Engineering
Kinematics and Theory of Machines (3131906) |
Unit-5 Belt, Ropes and Chains
Angle of contact 180 2
180
180 2 12.7
180
2.697rad
1 2
r r 550 220
sin
X 1.5
0.55 0.22
1.5
12.70
Let,
1
10
2
T
2.3log 0.22 2.697
T
1
2
T
1.81 ______(1)
T
1 2
3
1 2
1 2
Power T T v
5 10 T T 3.535
T T 1414.5N _____(2)
2
2 N
t
v r r
2 60
considering thickness of
belt
3535mm/ sec
v 3.535m/ sec
From equation (1) & (2)
1
2
T 3160.8 N
T 1746.2 N
Max tensioninthebelt T b t
3160.8 100 10
2
3.16N/mm
(ii) Cross Belt drive,
Angle of contact 180 2
180
1 2
r r 0.55 0.22
sin
X 1.5
30.88
180 2 30.88
180
4.22
Let,
1
10
2
T
2.3log 0.22 4.22
T
1
2
T
2.53
T
33. Dr. A. J. Makadia, Department of Mechanical Engineering
Kinematics and Theory of Machines (3131906) |
Unit-5 Belt, Ropes and Chains
5.33
1 2
Power T T v
1 2
5000 T T 3.535
1
1 2
2
2 1
T
T T 1414.5 & 2.53
T
T 924.5N, T 2339N
1 2
T T 1414.5N
Max tensioninthebelt T b t
2339 100 10
2
2.339 N/mm
Ex. 5.7 An open belt drive is required to transmit 10 kW of power from a motor running at 600 rpm.
The diameter of the driving pulley is 250 mm. Speed of the driven pulley is 220 rpm. The
belt is 12 mm thick and has a mass density of 0.001 g/mm2
. Safe stress in the belt is not
to exceed 2.5 N/mm2
. Two shafts are 1.25 m apart. Take µ = 0.25. Determine the width of
the belt.
Solution: Given Data:
3
1
1
2
3
3
3 3 3
3 3 3
2 6 2
P 10 10 watt
N 600rpm
x 1.5m
Speedof DrivingpulleyN 600rpm
Diameter of drivingpulley d 250mm
Speedof DrivenpulleyN 220rpm
t 12mm
10
1
0.001g /mm kg 10 kg /m
10 10 m
2.5N/mm 2.5 10 N/m
x 1.25m
0.25
b ?
Let,
1 1 2 2
N d N d
1 1
2
2
2
N d 600 250
d
N 220
d 681.81mm
Let,
2 N
t t
v r r
2 2 60
2 600
12
125
2 60
8230mm / sec
v 8.23m / sec
34. 5.34
Dr. A. J. Makadia, Department of Mechanical Engineering
Kinematics and Theory of Machines (3131906) |
Unit-5 Belt, Ropes and Chains
Let,
1 2
P T T v
3
1 2
10 10 T T 8.23
1 2
T T 1215 _____(1)
Let,
1
10
2
1
2
T
2.3log
T
0.25 2.79
T
2.01 ______(2)
T
1 2
openbelt drive
r r
180 2 rad where sin
180 X
340.90 125
180 2 9.94
180 1.25
2.79 9.94rad
From equation (1) & (2)
2
1
T 1203N
T 2418N
Centrifugal Tension (Tc)
2
C
2
C
T mv
(12b)(8.23)
T 812.8bN
3
m Mass of belt /unitlength
volumeperunitlength
x sectionalarea length
width thickness length
b 0.012 1 10
12b
Max tensioninthebelt T b t
6
2.5 10 b 0.012
30,000b
Let,
1 C
T T T
30,000b 2418 812.8b
b 0.0828m
b 82.8mm
35. Dr. A. J. Makadia, Department of Mechanical Engineering
Kinematics and Theory of Machines (3131906) |
Unit-5 Belt, Ropes and Chains
5.35
Ex. 5.8 Two parallel shafts that are 3.5 m apart are connected by two pulleys of 1 m and 400 mm
diameter. The larger pulley being the driver runs at 220 rpm. The belt weight 1.2 kg/meter
length. The maximum tension in the belt is not to exceed 1.8 kN. The coefficient of friction
is 0.28. Owing to slip on one of the pulleys, the velocity of the driven shaft is 520 rpm only.
Determine:
(i) Torque on each shaft
(ii) Power transmitted
(iii)Power lost in friction
(iv) The efficiency of the drive
Solution: Given Data:
1 1
2 2
3
x 3.5m
d 1m, N 220rpm
d 0.400m, N 520rpm
m 1.2kg /m
t 1.8 10 N
0.28
Let,
1 1
d N
v
60
1 220
60
v 11.52m / sec 10
2
C
2
C
T mv
1.2(11.52)
T 159N
For open belt drive,
180 2 rad
180
180 2(4.91)
180
2.97rad
1 2
r r
where sin
X
0.5 0.2
3.5
4.91
Let,
1
10
2
T
2.3log 0.28 2.97
T
1 C
3
1
1
2
Max Tension
T T T
1.8 10 T 159
T 1641N
T 714N
1
2
T
2.299
T
36. 5.36
Dr. A. J. Makadia, Department of Mechanical Engineering
Kinematics and Theory of Machines (3131906) |
Unit-5 Belt, Ropes and Chains
1.
1 2 1
L
Torqueonlargerpulley T T r
(1641 714) 0.5
T 463.5 N m
1 2 2
S
Torque onsmallerpulley T T r
(1641 714) 0.200
T 185.4 N m
2.
1 2
Power transmitted P T T v
(1641 714) 11.52
10679 watt
P 10.679kw
3. Power lost in friction,
1 1
in
2 N T 2 220 463.5
InputPowerP 10678 watt
60 60
2 2
out
2 N T 2 920 185.4
OutputPowerP 10096 watt
60 60
PowerLoss 10678 10096 582watt
4. The efficiency of the drive
( ) ,
OutputPower 10096
0.945 94.5%
InputPower 10678
Ex. 5.9
A V- belt drive with the following data transmits power from an electric motor to
compressor:
Power transmitted = 100 kW
Speed of the electric motor = 750 rpm
Speed of compressor = 300 rpm
Diameter of compressor pulley = 800 mm
Centre distance between pulleys = 1.5 m
Max speed of the belt = 30 m/sec
Mass of density = 900 kg / m3
C/s area of belt = 350 mm2
Allowable stress in the belt = 2.2 N / mm2
Groove angle of pulley = 38°= 2β
Coefficient of friction = 0.28
Determine the number of belts required and length of each belt.
Solution: Let,
1 1 2 2
N d N d
2 2
1
1
N d 300 800
d 320mm
N 750
Let centrifugal tension (TC)
37. Dr. A. J. Makadia, Department of Mechanical Engineering
Kinematics and Theory of Machines (3131906) |
Unit-5 Belt, Ropes and Chains
5.37
2
C
2
T mv
0.315(30) 283.5N
6
m Mass of belt / length
Area length density
350 10 1 900
0.315kg /m
v 30m/ sec
Let Maximum Tension in belt,
T b t
2.2 350
T 770N
Let,
1 C
T T T
1 C
1
T T T
770 283.5
T 486.5N
1 2
openbelt drive
r r
180 2 rad sin
180 X
400 160
180 2 9.20
180 1.5
2.82rad 9.20rad
Let,
1
10
2
T
2.3log cosec
T
0.28 2.82
sin19
1
2
T
11.3
T
2
T 43.1N
1 2
Power T T v
(486.5 43.1)30
13302 Watt
P 13.3kW
Totalpower transmitted 100
No.of belt 7.51 8belts
Power transmitted / belt 13.3
Length of belt drive (using approximate relation),
2
1 2
o 1 2
r r
L r r 2x
x
2
0.4 0.16
0.4 0.16 2(1.5)
3
o
L 4.79m
38. 5.38
Dr. A. J. Makadia, Department of Mechanical Engineering
Kinematics and Theory of Machines (3131906) |
Unit-5 Belt, Ropes and Chains
Ex. 5.10 Determine the maximum power transmitted by a V – belt drive having the included v –
groove angle of 35°. The belt used is 18 mm deep with 18 mm maximum width and weight
300 g per metre length. The angle of the lap is 145° and the maximum permissible stress
is 1.5 N/mm2
. µ = 0.2.
Solution: Given Data:
6 2
max
V BeltDrive
2 35
t 18mm, w 18mm
m 0.3kg /m
145 rad 2.53rad
180
1.5 10 N/m
0.2
P ?
Let,
Max tensioninthebelt T b t
1.5 18 18
486N
T
Velocity forMaxPower v
3m
486
3 0.3
v 23.23m/sec
Now,
1
10
2
T
2.3log cosec
T
0.2 2.53
sin 17.5
1
2
T
5.39
T
Let,
2
C
2
Cen T mv
trifug
0.
al Tensi
3(23.23 6
o
) N
n
1 2
C
OR
Max Tensioncondi.
T 486
T 162N
3 3
Let,
1 C
T T T
39. Dr. A. J. Makadia, Department of Mechanical Engineering
Kinematics and Theory of Machines (3131906) |
Unit-5 Belt, Ropes and Chains
5.39
1 C
T T T 486 162 324N
1
2
T
5.39
T
2
T 60.2N
1 2
Max Power P T T v
324 60.2 23.23
6128.074 Watt
P 6.12kW
Ex. 5.11 The grooves on the pulleys of a multiple rope drive have an angle of 50° and accommodate
rope of 22 mm diameter having a mass of 0.8 kg/metre length for which a safe operating
tension of 1200 N has been laid down. The two pulleys are of equal size. The drive is
designed for max power conditions. Speeds of both pulleys are 180 rpm. Assuming µ =
0.25. Determine the diameter of pulleys and no. of ropes when power is transmitted 150
kW.
Solution: Given Data:
1 2
1 2
3
1 2
RopeDrive
2 50
d dia.of rope 22mm
m 0.8kg /m
T 1200N
d d dia.of pulley 180
Max Power conditions
N N 180rpm
0.25
P 150 10 Watt
d d ?
No.ofRopes ?
1
ForMax Power Conditions....
2 2
T T 1200 800N
3 3
1 C
T T T
C 1
T T T 1200 800 400N
2
C
2
T m v
400 0.8 v
v 22.36m / sec
OR
T 1200
v
3m 3 0.8
22.36m / sec
Let,
1 1
D N
Velocity v
60
1
D 180
23.36
60
1
D 2.37m
40. 5.40
Dr. A. J. Makadia, Department of Mechanical Engineering
Kinematics and Theory of Machines (3131906) |
Unit-5 Belt, Ropes and Chains
Let,
1
10
2
T
2.3log cosec
T
1
0.25 180
180 sin25
1
2
T
6.42
T
2
T 124.61N
1 2
PowerP T T v
800 124.61 22.36
P 15.10kW /Rope
TotalPower 150kW
No.of Ropes 9.93 10Ropes
Power /Rope 15.10kW
Ex. 5.12
The following data relate to a rope drive
Power transmitted = 20kW
Diameter of pulley = 480 mm
Speed = 80 rpm
Angle of lap on smaller pulley = 160°
No. of Ropes = 8
Mass of Rope / m length = 48 G2 kg
Limiting working tension = 132 G2
Coefficient of friction = 0.3
Angle of groove = 44°
If G is the girth of rope in m, determine the initial tension and diameter of each rope.
Solution: Given Data:
3
2
2
0
P 20 10 Watt
d dia.of pulley 0.48m
N 80rpm
160 rad
180
n No.of Ropes 8
m 48 G kg /m
T 132G kN
0.3
2 44
T ?
dia.of Rope ?
Let,
3
20 10
Power transmitted /Rope 2500 Watt
8
dN 0.48 80
Velocity of Rope 2.01m /sec
60 60
41. Dr. A. J. Makadia, Department of Mechanical Engineering
Kinematics and Theory of Machines (3131906) |
Unit-5 Belt, Ropes and Chains
5.41
Let,
1 2
PowerP T T v
1 2
2500 T T 2.01
1 2
T T 1244N
Let,
1
10
2
T
2.3log cosec
T
1
0.3 160
180 sin22
1
2
T
9.38
T
1
2
Solving equation
T 1392.44
T 148.44
1.
1 2
0
T T
Initial TensionT 770.44N
2
2. Diameter of Rope (D)
1 C
3 2 2 2
Total Tension T T T
132 10 G 1392.44 48 G (2.01)
G 0.1028
Now Girth(Circumference)of Rope D
0.1028 D D 0.032m
Ex. 5.13 2.5 kW power is transmitted by an open belt drive. The linear velocity of the belt is 2.5
m/sec. The angle of the lap on the smaller pulley is 165°. The coefficient of friction is 0.3.
Determine the effect on power transmission in the following cases:
(i) Initial tension in the belt is increased by 8%.
(ii) Initial tension in the belt is decreased by 8%.
(iii)The angle of the lap is increased by 8% by the use of an idler pulley, for the same
speed and the tension on the tight side.
(iv) Coefficient of friction is increased by 8% by suitable dressing to the friction surface
of the belt.
Solution: Let,
1 2
PowerP T T v
1 2
2500 T T 2.5
1 2
T T 1000N ______(1)
42. 5.42
Dr. A. J. Makadia, Department of Mechanical Engineering
Kinematics and Theory of Machines (3131906) |
Unit-5 Belt, Ropes and Chains
Also,
1
10
2
T
2.3log 0.3 165
T 180
1
2
T
2.37 _____(2)
T
By Solving,
2
1
T 729.9N
T 1729.92N
1 2
0
T T
Initial Tension T 1229.9N
2
Initial Tension increased by 8%,
0
T 1229.9 1.08 1328.30N
1 2
0
T T
Or T
2
1 2
1 2
T T
1328.30 T T 2656.60N _____(3)
2
As µ and θ remain unchanged,
1
2
T
2.37 _____(4)
T
By solving equation (3) & (4),
1
2
T 1868.3N
T 788.30N
Let,
1 2
PowerP T T v
1868.3 788.30 2.5
P 2.7kW
2.7 2.5
increaseinpower 0.08 8%
2.5
Initial Tension decreased by 8%,
0
T 1229.9 1 0.08 1131.50N
1 2
0
T T
Or T
2
1 2
1 2
T T
1131.50 T T 2263N _____(5)
2
As µ and θ remain unchanged,
43. Dr. A. J. Makadia, Department of Mechanical Engineering
Kinematics and Theory of Machines (3131906) |
Unit-5 Belt, Ropes and Chains
5.43
1
2
T
2.37 _____(6)
T
By solving equation (5) & (6),
1
2
T 1591.5N
T 671.5N
Let,
1 2
PowerP T T v
1591.5 671.5 2.5
P 2.3kW
2.5 2.3
decreaseinpower 0.08 8%
2.5
The angle of Lap (θ) is increased by 8% with the same speed and T1,
Let,
1
10
2
T
2.3log 0.3 165 1.08
T 180
1
2
T
2.54
T
T1 is the same.
1
2
T 1729.92N
T 681.07N
1 2
PowerP T T v
1729.92 681.07 2.5
P 2.62kW
2.62 2.5
increaseinpower 0.048 4.8%
2.5
Coefficient of friction is increased by 8%,
Let,
1
10
2
T
2.3log
T
0.3 1.08 165
180
1
2
T
2.54 _____(7)
T
Let,
1 2
0
T T
T 1229.9
2
44. 5.44
Dr. A. J. Makadia, Department of Mechanical Engineering
Kinematics and Theory of Machines (3131906) |
Unit-5 Belt, Ropes and Chains
1 2
T T 2459.8N _____(8)
By solving equation (7) & (8),
2
1
T 694.9N
T 1764.9N
Let,
1 2
PowerP T T v
1764.9 694.9 2.5
P 2.67kW
2.67 2.5
increaseinpower 0.07 7%
2.5
Ex. 5.14 In a belt-drive, the mass of the belt is 1 kg/m length and its speed is 6 m/sec. The drive
transmits 9.6 kW of power. Determine the initial tension in the belt and strength of the belt.
The coefficient of friction is 0.25 and the angle of the lap is 220°.
Solution: Given Data:
3
0
m 1kg /m
v 6m / sec
P 9.6 10 Watt
T ?
Strength ?
0.25
220 rad
180
Let,
1 2
PowerP T T v
1 2
9600 T T 6
1 2
T T 1600N ______(1)
Let,
1
10
2
T
2.3log
T
0.25 220
180
1
2
T
2.31 _____(2)
T
Solving equation (1) & (2),
1
2
T 2594N
T 994N
Let,
45. Dr. A. J. Makadia, Department of Mechanical Engineering
Kinematics and Theory of Machines (3131906) |
Unit-5 Belt, Ropes and Chains
5.45
2
C
2
Centrifugal Tension T mv
1(6) 36N
1 2
0 C
T T 2594 994
Initial Tension T T 36 1830N
2 2
1 C
Strengthof thebelt Total Tensionontight side
T T
2594 36 2630N
Ex. 5.15 In an open bet drive, the diameters of the larger and smaller pulley are 1.2 m & 0.8 m
respectively. The smaller pulley rotates at 320 rpm. The centre distance between the
shafts is 4 m. When stationary, the initial tension in the belt is 2.8 kN. The mass of the belt
is 1.8 kg/m and µ = 0.25. Determine the power transmitted.
Solution: Given Data:
1 1
2 2
0
d 1.2m, N ?
d 0.8m, N 320rpm
x 4m
T 2800N
m 1.8kg /m
0.25
Power ?
2 2
d N 0.8 320
Velocity of Belt 13.40m /sec
60 60
2
C
2
Centri T mv
1.8(13
fugal Tensi
.4) 3
on
23.4N
1 2
0 C
1 2
T T
Initial TensionT T
2
T T
2800 323.4
2
1 2
T T 4953N _____(1)
For open belt drive,
Angle of contact 180 2
180
1 2
r r 0.6 0.4
sin
X 4
2.86
180 2 2.86
180
3.042rad
Let,
1
10
2
T
2.3log
T
0.25 3.042
46. 5.46
Dr. A. J. Makadia, Department of Mechanical Engineering
Kinematics and Theory of Machines (3131906) |
Unit-5 Belt, Ropes and Chains
1
2
T
2.14 _____(2)
T
By solving equation (1) & (2),
1
2
T 3376N
T 1577N
1 2
PowerP T T v
3376 1577 13.4 24106 Watt 24.10kW
Ex. 5.16 The initial tension in a belt drive is found to be 600 N and the ratio of friction tension is 1.8.
The mass of the belt is 0.8 kg/m length. Determine:
(i) The velocity of the belt for maximum power transmission
(ii) Tension on the tight side of the belt when it is started
(iii)Tension on the tight side of the belt when running at maximum speed
Solution: (i) Velocity of the belt (v)
Let max power condition for initial tension,
0
T 600
v 15.81m/ sec
3m 3 0.8
(ii) Tension on tight side when belt is started v = 0, TC = 0
0
1
2 1.8 600
2k T
T 771.4N
k 1 1.8 1
(iii) Tension on the tight side when the belt is running at max speed
0 C
1
1
2k T T
T
k 1
2 1.8 600 199.7
1.8 1
T 514.6N
2
C
2
T mv
0.8 15.8 199.7N
Or
1 2
0 C
T T
T T
2 …………….. with this equation you can solve the problem.
1 2
0 C
1
1
1
T T
T T
2
T
T
1.8
600 199.7
2
T 514.6N
47. Dr. A. J. Makadia, Department of Mechanical Engineering
Kinematics and Theory of Machines (3131906) |
Unit-5 Belt, Ropes and Chains
5.47
Ex. 5.17 The driving pulley of an open belt drive is 800 mm diameter and rotates at 320 rpm while
transmitting power to a driven pulley of 250 mm diameter. The Young’s modulus of
elasticity of the belt material is 110 N/mm2
. Determine the speed lost by the driven pulley
due to creep if the stresses in the tight and slack sides of the belt are found to be 0.8
N/mm2
and 0.32 N/mm2
respectively.
Solution: Given Data:
1 1
2
2
2
1
2
2
OpenBeltDrive
D 0.8m, N 320rpm
D 0.250m
E 110 N/mm
0.8N / mm
0.32N /mm
Let,
2
2 1
1 2 1
E
N D
( VelocityRatio withcreep)
N D E
2
110 0.32
800
N 320 1021rpm
250 110 0.8
Let velocity ratio without creep,
2 1
1 2
N D
N D
2
800
N 320 1024rpm
250
Speedlost due tocreep 1024 1021 3rpm
Ex. 5.18 The centre to centre distance between two sprockets of a chain drive is 600 mm. The chain
drive is used to reduce the speed from 180 rpm to 90 rpm on the driving sprocket has 18
teeth and a pitch circle diameter of 480 mm. Determine:
(i) No. of teeth on the driven sprocket
(ii) Pitch and the length of chain
Solution: Given Data:
1 1
2 2
C Centre distancebetweensprocket 600mm
N 180rpm ,T 18 teeth
N 90rpm ,T ?
1.
2 1 1
2 1
1 2 2
N T N
T T
N T N
180
18 36 Teeth
90
48. 5.48
Dr. A. J. Makadia, Department of Mechanical Engineering
Kinematics and Theory of Machines (3131906) |
Unit-5 Belt, Ropes and Chains
2. Pitch of the chain (p)
180 180
p 2R sin 2 0.240 sin 0.04183m 41.83mm
T 36
3. Length of chain (L)
2
180 180
cosec cosec
T t T t
L p 2k
2 4k
2
180 180
cosec cosec
36 18 36 18
L 0.04183 2 14.343
2 4 14.343
C centre dist.betweensprocket
k p
C 0.600
k 14.343
p 0.04183
Therefore, L 2.351m
References:
1. Theory of Machines, Rattan S S, Tata McGraw-Hill
2. Theory of Machines, Khurmi R. S., Gupta J. K., S. Chand Publication