1. Gears are used to transmit motion between two shafts where slipping needs to be avoided. Gears have teeth cut along the periphery that mesh to ensure positive drive.
2. Gears can be classified based on the position and orientation of shaft axes, peripheral velocity, type of gearing, and position of teeth on the gear surface. Common types include spur gears, helical gears, bevel gears, and rack and pinion.
3. Involute teeth profiles are commonly used as they satisfy the law of gearing to ensure constant velocity ratio between meshing gears for all positions.
This document provides an introduction to mechanisms and kinematics by Ramesh Kurbet of PESCE Mandya. It defines mechanisms, machines, kinematics, and dynamics. It describes the types of constrained motion and different types of links that make up mechanisms. It also discusses kinematic pairs, degrees of freedom, Grubler's criterion, and common kinematic chains including the four-bar linkage, single slider-crank mechanism, and their inversions in machines.
The document discusses different types of gear trains and belt drives used to transmit power between rotating shafts. It describes four types of gear trains - simple, compound, reverted, and epicyclic gear trains. It also discusses how speed ratios are calculated for different gear train configurations. Additionally, it covers belt drive components like pulleys, different types of belts, materials used for belts, and factors to consider when selecting a belt drive system.
This document contains numerical problems and solutions related to kinematics of spur gears. It includes 5 problems covering topics like calculating addendum, path of contact, arc of contact, contact ratio, angle turned by pinion, and velocity of sliding at different points for different gear configurations. The problems have varying gear parameters like number of teeth, pressure angle, module, pitch circle radius, angular velocity etc. Detailed step-by-step solutions are shown for each problem.
R1. This document discusses cams and followers. It defines a cam as a rotating element that gives reciprocating or oscillating motion to another element called a follower.
R2. Followers are classified based on their contacting surface and motion. Common types include knife edge, roller, flat faced, and spherical faced followers. Reciprocating followers move back and forth, while oscillating followers rotate through a range of motion.
R3. Cams are also classified based on the path of the follower's motion. Radial cams move perpendicular to the cam axis, while offset cams move along an axis offset from the cam center.
Unit-3 - Velocity and acceleration of mechanisms, 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.
Gears are used to transmit power from one machine element to another. Multiple gears can be meshed together to form a gear train that transfers power between shafts. There are four main types of gear trains: simple, compound, reverted, and epicyclic. A simple gear train uses one gear on each shaft, while a compound gear train uses multiple gears on the shafts to bridge larger distances between the driver and driven gears. The speed ratio of a gear train is the ratio of the driver gear's speed to the driven gear's speed.
Unit 6- spur gears, 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.
Gear trains are combinations of wheels that transmit motion from one shaft to another. There are several types of gear trains including simple, compound, epicyclic, and reverted gear trains. A simple gear train contains one gear on each shaft connected by meshing teeth. An epicyclic or planetary gear train contains one or more outer gears that rotate around a central gear. Gear trains can be used to increase or decrease shaft speed and rotate shafts in the same or opposite directions.
This document provides an introduction to mechanisms and kinematics by Ramesh Kurbet of PESCE Mandya. It defines mechanisms, machines, kinematics, and dynamics. It describes the types of constrained motion and different types of links that make up mechanisms. It also discusses kinematic pairs, degrees of freedom, Grubler's criterion, and common kinematic chains including the four-bar linkage, single slider-crank mechanism, and their inversions in machines.
The document discusses different types of gear trains and belt drives used to transmit power between rotating shafts. It describes four types of gear trains - simple, compound, reverted, and epicyclic gear trains. It also discusses how speed ratios are calculated for different gear train configurations. Additionally, it covers belt drive components like pulleys, different types of belts, materials used for belts, and factors to consider when selecting a belt drive system.
This document contains numerical problems and solutions related to kinematics of spur gears. It includes 5 problems covering topics like calculating addendum, path of contact, arc of contact, contact ratio, angle turned by pinion, and velocity of sliding at different points for different gear configurations. The problems have varying gear parameters like number of teeth, pressure angle, module, pitch circle radius, angular velocity etc. Detailed step-by-step solutions are shown for each problem.
R1. This document discusses cams and followers. It defines a cam as a rotating element that gives reciprocating or oscillating motion to another element called a follower.
R2. Followers are classified based on their contacting surface and motion. Common types include knife edge, roller, flat faced, and spherical faced followers. Reciprocating followers move back and forth, while oscillating followers rotate through a range of motion.
R3. Cams are also classified based on the path of the follower's motion. Radial cams move perpendicular to the cam axis, while offset cams move along an axis offset from the cam center.
Unit-3 - Velocity and acceleration of mechanisms, 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.
Gears are used to transmit power from one machine element to another. Multiple gears can be meshed together to form a gear train that transfers power between shafts. There are four main types of gear trains: simple, compound, reverted, and epicyclic. A simple gear train uses one gear on each shaft, while a compound gear train uses multiple gears on the shafts to bridge larger distances between the driver and driven gears. The speed ratio of a gear train is the ratio of the driver gear's speed to the driven gear's speed.
Unit 6- spur gears, 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.
Gear trains are combinations of wheels that transmit motion from one shaft to another. There are several types of gear trains including simple, compound, epicyclic, and reverted gear trains. A simple gear train contains one gear on each shaft connected by meshing teeth. An epicyclic or planetary gear train contains one or more outer gears that rotate around a central gear. Gear trains can be used to increase or decrease shaft speed and rotate shafts in the same or opposite directions.
This document discusses belt drives and friction in bearings. It describes the components and functioning of belt drives, including types of belts, pulleys, velocity ratio calculations considering slippage, power transmission, and centrifugal effects. It also covers flat and conical pivot bearings, describing methods to calculate friction forces and wear for uniform pressure and wear distributions. Key points covered include belt material properties, V-belt wedging action, open and crossed belt drive configurations, and friction force calculations for flat and conical bearings.
This document discusses numerical problems involving spur gear kinematics including:
1. Determining the addendum height, length of contact path, arc of contact, and contact ratio for two mating gears with 20 and 40 teeth.
2. Checking for interference between gears with 13 and 50 teeth, and calculating the necessary pressure angle to eliminate interference.
3. Finding the number of teeth for gears with a 3:1 velocity ratio, their contact measurements, number of teeth in contact, and maximum sliding velocity.
Threaded fasteners such as bolts and nuts are used to join machine parts. They allow parts to be dismantled without damage. Threaded joints provide clamping force through wedge action of threads. They are reliable, have small dimensions, and can be positioned vertically, horizontally, or inclined. However, they require holes which cause stress concentrations and can loosen under vibration. Bolts have heads and threaded shanks, while nuts have internal threads. Washers distribute load and prevent marring. Bolts are subjected to both tension and shear stresses, and standard nuts have a height of 0.8 times the bolt diameter to prevent shear failure. Eccentric loads on bolts cause additional stresses.
The document discusses gears and their classification. It defines various gear types including spur gears, helical gears, bevel gears, worm gears, and rack gears. It covers gear terminology such as pressure angle and describes how parameters like pressure angle and center distance affect gear performance and interference. Methods to avoid interference include increasing center distance, tooth modification, and changing the number of teeth. Backlash is also defined as the clearance between mating gear teeth.
bevel gear screw jack,high speed screw jack,quick lifting screw jack,gear ratio 1:1 screw jack features:
1. Load capacity 25kN to 500kN. When full load, worm torque high speed 92Nm to 4712Nm, low speed 46Nm to 2828Nm.
2. Lift screw diameter 30 mm to 120 mm, screw pitch 6 mm to 16 mm.
3. High gear ratio 1:1, low gear ratio 2:1.
4. Translating screw, rotating screw, keyed screw configurations in upright or inverted mounting orientation.
5. Difference from worm gear screw jack, driven spindle by spiral bevel gear sets.
5. Manual operated bevel gear screw jack by hand wheel or hand crank, or electrically operated bevel gear screw jack by 3-phase or single phase motor or gear motor.
6. Processing lift screw stroke according to clients needs. Under max. compression load, without guides 250mm to 1000mm stroke, with guides 400mm to 2000mm stroke. Under tension load, max. 1500mm to 5500mm stroke.
7. Lift screw end fittings include top plate, clevis end, plain end and threaded end.
8. Full synchronization bevel gear screw jack system, doesn't require right angle bevel gearbox to transmit torque and power, bevel gear screw jacks are directly connected by line shaftings and couplings.
9. Application in steel, pipe, tube, plate, roll forming roller adjustment, feeder straightener rolls adjustment, adjusting synchronous coil feed lines rolls, precision roller leveler, coil sheet slitter line, paint coating line, cut to length line, tension levelling line, continuous galvanizing line, beverage production line, foam concrete cutting machine, sanding machine, heavy vehicles mobile lifting platform, bottle monitoring system height adjustment, conveyor adjustment, plate saw angle adjustment, spray infeed conveyor lift system, theatre stage lifting platform, solar tracker, satellite dish antenna azimuth, raising sluice gate, screw scissor lift table, synchronized lifting system, food processing lifting system, extrusion machine, cnc steel leveling machine, blow molding machine, curing oven lifts, bolted tank, steel shuttering concrete beams adjustment, vintage industrial crank desk, solar panel tracking system, railway maintenance lifting jack, damper adjustment, continuous casting, cnc cut to length machine, robotics arm raising, palletizer, extrusion machine, motorized self-raising tower system, angle tilt adjustments with double clevis, aircraft docking system, open and close flood gates, metallurgy industry, mining industry, chemical industry, construction industry and irrigation industry.
This presentation contains basic idea regarding spur gear and provides the best equations for designing of spur gear. One can Easily understand all the parameters required to design a Spur Gear
The following presentation includes information on gears, application of gears, gear trains, velocity ratio, and few simple solved examples based on the above stated topics
This document discusses key concepts related to helical gears, including:
- Face width is determined by the minimum overlap of 1 tooth over the next, which is recommended to be 15% of the circular pitch. Wider face widths up to 2.5 times the pinion diameter are allowed.
- The formative or equivalent number of teeth for a helical gear accounts for the helix angle, and is calculated as the actual number of teeth divided by the cosine of the helix angle cubed.
- Recommended proportions for helical gears include a pressure angle of 15-25 degrees, helix angle of 20-45 degrees, and specifications for addendum, dedendum, depth, and clearance
This document discusses different types of governors used to regulate the speed of machines like engines. It describes centrifugal governors which are further classified as gravity or spring controlled. Specific governors are explained like the Watt, Porter, Proell, and Hartnell governors. Terminology used in governors like height, equilibrium speed, and sensitiveness are defined. The effort and power calculations for governors are shown. Inertia governors are also introduced which use inertia forces rather than centrifugal forces to respond rapidly to load changes.
D'Alembert's Principle states that the resultant of all external forces and inertia forces acting on a body is zero for the body to be in dynamic equilibrium. Inertia forces are represented as minus mass times acceleration. The principle allows equations of static equilibrium to be applied to bodies undergoing translational motion by considering an imaginary inertia force equal and opposite to actual inertia. Several example problems are provided applying the principle to analyze motion of connected bodies over pulleys, motion on inclined planes, and motion within elevators.
This document discusses gyroscopes and gyroscopic effects. It begins by defining a gyroscope and explaining that gyroscopes resist changes to the direction of their rotational axis, known as the gyroscopic effect. It then provides examples of applications that utilize gyroscopes, such as gyrocompasses, inertial guidance systems, and precession in bearings. The document goes on to define angular momentum and discuss how gyroscopic couples arise due to a change in the direction of angular momentum. It provides figures to illustrate gyroscopic couples and their effects on aircraft when turning. Finally, it analyzes gyroscopic effects on rotating objects like disks, rods, and propellers mounted on bearings.
Cam Mechanism And Flexible Drives
Machine Elements
Basic Explanation
History
Mechanism Explained
Disclaimer: All research materials are internet based. I do not own anything. Video links are included (from youtube).
Correction: Cam mechanism can do vice versa.
Leader: Andrei Matias
Theory of machines_static and dynamic force analysisKiran Wakchaure
This document contains information about static and dynamic force analysis in machines. It discusses various topics including:
1) Types of forces such as static loads, dynamic loads, tension, compression, shear force, and torsion.
2) Laws of motion including Newton's three laws of motion.
3) Moment of inertia which is a mass property that determines the torque needed for angular acceleration. It depends on the shape and mass distribution of an object.
4) Analysis of simple and compound pendulums including calculations of their periodic times and frequencies of oscillation based on length, mass, and radius of gyration.
The document discusses riveted joints. It describes the different types of rivets and rivet heads. The key types of riveted joints are lap joints and butt joints. Important terms used in riveted joints are also defined, such as pitch and margin. Guidelines for the proportions of dimensions for riveted joints are provided. Examples of different double and single riveted lap and butt joints are shown.
This document discusses different types of gear trains:
1. Simple gear train which uses one gear on each shaft to transmit motion.
2. Compound gear train which uses more than one gear on a shaft.
3. Reverted gear train where the first and last gears are co-axial and rotate in the same direction.
4. Epicyclic gear train where the gear axes can move relative to a fixed axis, allowing one gear to drive another in circular motion.
Formulas for speed ratio and train value are provided for each gear train type. Examples of applications like differentials are also mentioned.
Unit 4 Design of Power Screw and Screw JackMahesh Shinde
The document discusses power screws, including their terminology, types of threads, torque analysis, and efficiency. It defines key terms like nominal diameter, pitch, lead, and lead angle. It describes common types of threads like square, ACME, and buttress threads. It discusses torque required to raise and lower loads, including expressions for self-locking and overhauling screws. The document also covers screw efficiency and collar friction torque, providing expressions to calculate overall efficiency. An example calculation is given to find maximum load lifted, efficiency, and overall efficiency of a screw jack.
This document provides a classification of different types of bearings:
1. Based on the direction of load, bearings are classified as radial or thrust bearings. Radial bearings have loads perpendicular to the direction of motion, while thrust bearings have loads along the axis of rotation.
2. Based on the nature of contact, there are sliding contact bearings and rolling contact bearings. Rolling contact bearings use balls or rollers between elements and are also known as anti-friction bearings.
3. Journal bearings are further classified as hydrodynamic or hydrostatic based on their lubrication. Hydrodynamic bearings generate pressure from fluid wedging, while hydrostatic bearings use externally pressur
1. A shaft transmits power and rotational motion and has machine elements like gears and pulleys mounted on it.
2. Press fits, keys, dowel pins, and splines are used to attach machine elements to the shaft.
3. The shaft rotates on rolling contact or bush bearings and uses features like retaining rings to take up axial loads.
4. Couplings are used to transmit power between drive and driven shafts like between a motor and gearbox.
Gears are toothed machine parts that transmit motion between parallel shafts. There are several types of gears including spur gears, helical gears, bevel gears, herringbone gears, and worm gears. The speed ratio of two gears is equal to the number of teeth on the driven gear divided by the number of teeth on the driving gear. Additional key terms described include the pitch circle, addendum circle, dedendum circle, tooth thickness, space width, backlash, pressure angle, and the law governing tooth shape.
This document discusses spur gear machine design and is submitted by a group of students. It covers topics such as the definition of spur gears, classifications of gears according to axis position and peripheral velocity, advantages and disadvantages of gears, terms used in gears including pitch circle and pressure angle, and the law of gearing which states that the common normal at the point of contact between gear teeth must pass through the pitch point. References for further information are also provided.
This document discusses belt drives and friction in bearings. It describes the components and functioning of belt drives, including types of belts, pulleys, velocity ratio calculations considering slippage, power transmission, and centrifugal effects. It also covers flat and conical pivot bearings, describing methods to calculate friction forces and wear for uniform pressure and wear distributions. Key points covered include belt material properties, V-belt wedging action, open and crossed belt drive configurations, and friction force calculations for flat and conical bearings.
This document discusses numerical problems involving spur gear kinematics including:
1. Determining the addendum height, length of contact path, arc of contact, and contact ratio for two mating gears with 20 and 40 teeth.
2. Checking for interference between gears with 13 and 50 teeth, and calculating the necessary pressure angle to eliminate interference.
3. Finding the number of teeth for gears with a 3:1 velocity ratio, their contact measurements, number of teeth in contact, and maximum sliding velocity.
Threaded fasteners such as bolts and nuts are used to join machine parts. They allow parts to be dismantled without damage. Threaded joints provide clamping force through wedge action of threads. They are reliable, have small dimensions, and can be positioned vertically, horizontally, or inclined. However, they require holes which cause stress concentrations and can loosen under vibration. Bolts have heads and threaded shanks, while nuts have internal threads. Washers distribute load and prevent marring. Bolts are subjected to both tension and shear stresses, and standard nuts have a height of 0.8 times the bolt diameter to prevent shear failure. Eccentric loads on bolts cause additional stresses.
The document discusses gears and their classification. It defines various gear types including spur gears, helical gears, bevel gears, worm gears, and rack gears. It covers gear terminology such as pressure angle and describes how parameters like pressure angle and center distance affect gear performance and interference. Methods to avoid interference include increasing center distance, tooth modification, and changing the number of teeth. Backlash is also defined as the clearance between mating gear teeth.
bevel gear screw jack,high speed screw jack,quick lifting screw jack,gear ratio 1:1 screw jack features:
1. Load capacity 25kN to 500kN. When full load, worm torque high speed 92Nm to 4712Nm, low speed 46Nm to 2828Nm.
2. Lift screw diameter 30 mm to 120 mm, screw pitch 6 mm to 16 mm.
3. High gear ratio 1:1, low gear ratio 2:1.
4. Translating screw, rotating screw, keyed screw configurations in upright or inverted mounting orientation.
5. Difference from worm gear screw jack, driven spindle by spiral bevel gear sets.
5. Manual operated bevel gear screw jack by hand wheel or hand crank, or electrically operated bevel gear screw jack by 3-phase or single phase motor or gear motor.
6. Processing lift screw stroke according to clients needs. Under max. compression load, without guides 250mm to 1000mm stroke, with guides 400mm to 2000mm stroke. Under tension load, max. 1500mm to 5500mm stroke.
7. Lift screw end fittings include top plate, clevis end, plain end and threaded end.
8. Full synchronization bevel gear screw jack system, doesn't require right angle bevel gearbox to transmit torque and power, bevel gear screw jacks are directly connected by line shaftings and couplings.
9. Application in steel, pipe, tube, plate, roll forming roller adjustment, feeder straightener rolls adjustment, adjusting synchronous coil feed lines rolls, precision roller leveler, coil sheet slitter line, paint coating line, cut to length line, tension levelling line, continuous galvanizing line, beverage production line, foam concrete cutting machine, sanding machine, heavy vehicles mobile lifting platform, bottle monitoring system height adjustment, conveyor adjustment, plate saw angle adjustment, spray infeed conveyor lift system, theatre stage lifting platform, solar tracker, satellite dish antenna azimuth, raising sluice gate, screw scissor lift table, synchronized lifting system, food processing lifting system, extrusion machine, cnc steel leveling machine, blow molding machine, curing oven lifts, bolted tank, steel shuttering concrete beams adjustment, vintage industrial crank desk, solar panel tracking system, railway maintenance lifting jack, damper adjustment, continuous casting, cnc cut to length machine, robotics arm raising, palletizer, extrusion machine, motorized self-raising tower system, angle tilt adjustments with double clevis, aircraft docking system, open and close flood gates, metallurgy industry, mining industry, chemical industry, construction industry and irrigation industry.
This presentation contains basic idea regarding spur gear and provides the best equations for designing of spur gear. One can Easily understand all the parameters required to design a Spur Gear
The following presentation includes information on gears, application of gears, gear trains, velocity ratio, and few simple solved examples based on the above stated topics
This document discusses key concepts related to helical gears, including:
- Face width is determined by the minimum overlap of 1 tooth over the next, which is recommended to be 15% of the circular pitch. Wider face widths up to 2.5 times the pinion diameter are allowed.
- The formative or equivalent number of teeth for a helical gear accounts for the helix angle, and is calculated as the actual number of teeth divided by the cosine of the helix angle cubed.
- Recommended proportions for helical gears include a pressure angle of 15-25 degrees, helix angle of 20-45 degrees, and specifications for addendum, dedendum, depth, and clearance
This document discusses different types of governors used to regulate the speed of machines like engines. It describes centrifugal governors which are further classified as gravity or spring controlled. Specific governors are explained like the Watt, Porter, Proell, and Hartnell governors. Terminology used in governors like height, equilibrium speed, and sensitiveness are defined. The effort and power calculations for governors are shown. Inertia governors are also introduced which use inertia forces rather than centrifugal forces to respond rapidly to load changes.
D'Alembert's Principle states that the resultant of all external forces and inertia forces acting on a body is zero for the body to be in dynamic equilibrium. Inertia forces are represented as minus mass times acceleration. The principle allows equations of static equilibrium to be applied to bodies undergoing translational motion by considering an imaginary inertia force equal and opposite to actual inertia. Several example problems are provided applying the principle to analyze motion of connected bodies over pulleys, motion on inclined planes, and motion within elevators.
This document discusses gyroscopes and gyroscopic effects. It begins by defining a gyroscope and explaining that gyroscopes resist changes to the direction of their rotational axis, known as the gyroscopic effect. It then provides examples of applications that utilize gyroscopes, such as gyrocompasses, inertial guidance systems, and precession in bearings. The document goes on to define angular momentum and discuss how gyroscopic couples arise due to a change in the direction of angular momentum. It provides figures to illustrate gyroscopic couples and their effects on aircraft when turning. Finally, it analyzes gyroscopic effects on rotating objects like disks, rods, and propellers mounted on bearings.
Cam Mechanism And Flexible Drives
Machine Elements
Basic Explanation
History
Mechanism Explained
Disclaimer: All research materials are internet based. I do not own anything. Video links are included (from youtube).
Correction: Cam mechanism can do vice versa.
Leader: Andrei Matias
Theory of machines_static and dynamic force analysisKiran Wakchaure
This document contains information about static and dynamic force analysis in machines. It discusses various topics including:
1) Types of forces such as static loads, dynamic loads, tension, compression, shear force, and torsion.
2) Laws of motion including Newton's three laws of motion.
3) Moment of inertia which is a mass property that determines the torque needed for angular acceleration. It depends on the shape and mass distribution of an object.
4) Analysis of simple and compound pendulums including calculations of their periodic times and frequencies of oscillation based on length, mass, and radius of gyration.
The document discusses riveted joints. It describes the different types of rivets and rivet heads. The key types of riveted joints are lap joints and butt joints. Important terms used in riveted joints are also defined, such as pitch and margin. Guidelines for the proportions of dimensions for riveted joints are provided. Examples of different double and single riveted lap and butt joints are shown.
This document discusses different types of gear trains:
1. Simple gear train which uses one gear on each shaft to transmit motion.
2. Compound gear train which uses more than one gear on a shaft.
3. Reverted gear train where the first and last gears are co-axial and rotate in the same direction.
4. Epicyclic gear train where the gear axes can move relative to a fixed axis, allowing one gear to drive another in circular motion.
Formulas for speed ratio and train value are provided for each gear train type. Examples of applications like differentials are also mentioned.
Unit 4 Design of Power Screw and Screw JackMahesh Shinde
The document discusses power screws, including their terminology, types of threads, torque analysis, and efficiency. It defines key terms like nominal diameter, pitch, lead, and lead angle. It describes common types of threads like square, ACME, and buttress threads. It discusses torque required to raise and lower loads, including expressions for self-locking and overhauling screws. The document also covers screw efficiency and collar friction torque, providing expressions to calculate overall efficiency. An example calculation is given to find maximum load lifted, efficiency, and overall efficiency of a screw jack.
This document provides a classification of different types of bearings:
1. Based on the direction of load, bearings are classified as radial or thrust bearings. Radial bearings have loads perpendicular to the direction of motion, while thrust bearings have loads along the axis of rotation.
2. Based on the nature of contact, there are sliding contact bearings and rolling contact bearings. Rolling contact bearings use balls or rollers between elements and are also known as anti-friction bearings.
3. Journal bearings are further classified as hydrodynamic or hydrostatic based on their lubrication. Hydrodynamic bearings generate pressure from fluid wedging, while hydrostatic bearings use externally pressur
1. A shaft transmits power and rotational motion and has machine elements like gears and pulleys mounted on it.
2. Press fits, keys, dowel pins, and splines are used to attach machine elements to the shaft.
3. The shaft rotates on rolling contact or bush bearings and uses features like retaining rings to take up axial loads.
4. Couplings are used to transmit power between drive and driven shafts like between a motor and gearbox.
Gears are toothed machine parts that transmit motion between parallel shafts. There are several types of gears including spur gears, helical gears, bevel gears, herringbone gears, and worm gears. The speed ratio of two gears is equal to the number of teeth on the driven gear divided by the number of teeth on the driving gear. Additional key terms described include the pitch circle, addendum circle, dedendum circle, tooth thickness, space width, backlash, pressure angle, and the law governing tooth shape.
This document discusses spur gear machine design and is submitted by a group of students. It covers topics such as the definition of spur gears, classifications of gears according to axis position and peripheral velocity, advantages and disadvantages of gears, terms used in gears including pitch circle and pressure angle, and the law of gearing which states that the common normal at the point of contact between gear teeth must pass through the pitch point. References for further information are also provided.
spur gear.pptx, type of gear and design of gearhaymanot16
Gears are used to transmit power between two shafts and can precisely control velocity ratios. Belts and chains are used for larger center distances while gears are used for smaller distances. Gears work by the progressive engagement of teeth and precisely mesh the teeth profiles to maintain a constant velocity ratio between the driving and driven shafts. Gears offer advantages like compact size, positive drives, wide speed ratios and ability to transmit power over varying shaft configurations but require precise alignment and lubrication.
This document discusses gear transmissions. It begins by explaining that slippage commonly occurs in belt or chain drives, reducing the speed ratio between two shafts. Precise machines like clocks require a definitive speed ratio, which can only be achieved with gears. Gears are also needed when the distance between the drive and driven components is very small. The document then discusses various types of gears, classified by position of shafts, surface speed, drive method, and tooth placement. It provides terminology used in gears like pitch circle, pitch point, pressure angle, and explains involute and cycloidal tooth profiles that satisfy the constant velocity ratio condition.
Machine Elements and Design- Lecture 8.pptxJeromeValeska5
Gears transmit power and motion between two shafts. There are different types of gears classified based on the orientation of shafts and teeth. Gear geometry includes parameters like pitch circle, pressure angle, addendum and dedendum. Strength of gear teeth depends on factors like load, tooth dimensions and material properties. Dynamic loads account for inaccuracies and are higher than steady loads. Design considers factors like load calculation, permissible stresses, and load distribution to ensure safe and reliable operation of gear drives.
1. The document provides an introduction to different types of gears including spur gears, helical gears, and bevel gears. It discusses key terms used in gears such as pitch circle, pressure angle, addendum, and defines formulas for calculating values like circular pitch and diametral pitch.
2. Design considerations for gear drives are outlined, including power transmitted, speeds, velocity ratio and center distance. Strength calculations using the Lewis equation and factors for dynamic loading and wear are also covered.
3. The summary provides an overview of the main topics and concepts discussed in the gear document.
The Analysis of The Effect of System Parameters on the RV Reducer Dynamic Cha...IJRESJOURNAL
ABSTRACT: In order to ensure the motion accuracy, transmission efficiency and load carrying capacity of the robot with high precision RV reducer, under the condition of certain parameters, this paper analyzes the contact deformation relationship of the cycloidal gears in theory, the engaging force of the needle teeth, and then obtain the number of teeth when the cycloidal wheel and the needle wheel match wtih each other at the same time. The model of RV-80E reducer was established by using SolidWorks software, and then use the ADAMS to do the dynamics simulation . In this situation, The effect of the meshing force between cycloidal and needle teeth in RV reducer is explored when changing a single parameter such as short range coefficient、the radius of needle tooth’s center circle、the radius of needle tooth、the teeth’s number of cycloidal gear. Then find the best range of parameters to ensure the force between cycloidal and needle teeth .It provides useful conclusions for improving the performance of the overall transmission stability and carrying capacity of the gear unit. It also provides a reference for research methods on dynamics problems which use the virtual prototyping ,and have great significance for the production and design of RV reducer in the future.
Gears: definition, classification with various parameters, detail of each gears, basic and important terms used in gears, Gear trains: definition, classification, detail of each gear train, speed ration and train value of each gear train.
REPORT ON QUALITY CONTROL BY REDUCING REJECTION DUE TO CHIP IMPRESSIONHardik Ramani
This document is a project report submitted by Ramani Hardik V. and Bhesdadiya Parag M. to their professor V.B. Patel at U.V. Patel College of Engineering. The report examines quality control issues related to chip impressions causing rejection of gears during manufacturing at Mahindra Gears & Transmission Pvt. Shaper.Rajkot. The document includes an introduction of the company, definitions of gear terminology, descriptions of gear manufacturing processes like hobbing, and analysis of rejection data through tables and Pareto charts to identify sources of chip impressions.
Three new models for evaluation of standard involute spur gear | Mesh Analysis AliRaza1767
This document proposes three new models for evaluating the mesh stiffness of spur gears. Model 1 considers gear bodies and teeth to be elastic and calculates mesh forces and tooth deflections at different positions. Model 2 considers teeth to be elastic and gear bodies to be rigid. It applies torque to the gear and measures angular displacement. Model 3 uses corner deflection values at arbitrary angles between teeth. Finite element analysis is used to validate the models.
The document discusses stress analysis of spur gear teeth and methods to reduce stress using geometric features. It begins with an introduction to gears and gear terminology. It then discusses fatigue failure in gears and how to design against fatigue. The document presents four studies on spur gear models with varying module and number of teeth. The first study analyzes stress variation along the tooth contact path. The second considers actual contact ratio greater than one. The third compares stress for different gear models. The final study selected the weakest gear profile for further stress relief analysis using geometric features like holes. The goal is to investigate how features can reduce stress concentrations and increase gear life.
This document discusses the measurement of gears. It begins by defining gears and describing the main types: spur, helical, bevel, and worm gears. It then discusses various gear terminology such as pitch circle diameter, pressure angle, and module. The document outlines different potential gear errors such as profile error, pitch error, and runout. It describes methods for measuring gear runout, pitch, and profile, including using an eccentricity tester, point-to-point measurement, and optical projection onto a master profile. The focus is on defining key gear features and concepts, and outlining standard techniques for inspecting gears and detecting manufacturing errors.
The document discusses gear drive systems, specifically focusing on fundamental gear operation and maintenance. It covers why gears are used for power transmission, the basics of how gears transmit motion through conjugate action, common gear tooth profiles like involute and cycloidal curves, and considerations for gear design and lubrication. Involute tooth profiles are most widely used due to advantages like simple manufacturing, ability to transmit motion at varying center distances, and constant pressure angle providing smooth operation. Proper lubrication and avoiding interference or undercutting are important for gear performance and lifespan.
Understand the terminology in gears for mechanical engineers in this PDF. Write to us at info@mindvis.in for your queries or visit www.mindvis.in for more details.
Power transmission involves moving energy from where it is generated to where it is applied. Power is defined as units of energy per unit time. Gears are used to transmit power between rotating or linear shafts by means of teeth that progressively engage. There are different types of gears that transmit motion between parallel shafts, intersecting shafts, and non-parallel shafts. Gear drives are commonly used for power transmission due to their ability to transmit high power and torque over a wide range of speed ratios in a compact package.
This document discusses different types of gears and gear terminology. It begins by listing different types of gears for connecting parallel shafts and intersecting shafts. It then discusses the fundamental law of gear-tooth action, which states that the velocities of two mating gear teeth along their contact normal must be equal. It also introduces important gear terminology like pitch point, pitch circle, addendum, dedendum, pressure angle, and involute curve generation. The document focuses on involute gears and defines key terms used in their analysis.
The document discusses different types of gears including spur gears, helical gears, bevel gears, worm gears, and rack and pinion gears. It provides details on gear terminology such as pitch circle, diametral pitch, module, pressure angle, addendum, dedendum, and profile. It also describes cycloidal and involute tooth profiles that are commonly used in gear design. The document is intended to teach the fundamentals and characteristics of different types of gears.
This PPT describes toothed wheels technically called as Gears. It consists of classification of gears that are commonly used in industries. Mostly when any mechanical components came to industrial scenario it deals with dynamic and static characteristics. Metallurgical restriction are also been involved in this .This PPT will definitely clears all the doubts and allow you to think more.
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Kom gears
1. Ramesh Kurbet, Asst. Prof., Dept. of Mech. Engg., PESCE Mandya.
By:
Ramesh Kurbet
Assistant Professor
Department of Mechanical Engineering
PESCE Mandya
GEARS
2. Ramesh Kurbet, Asst. Prof., Dept. of Mech. Engg., PESCE Mandya.
Introduction: We know that the slipping of
a belt or rope is a common phenomenon, in
the transmission of motion or power
between two shafts. In precision machines,
.
Fig.1.: Toothed wheels
in which a definite velocity ratio is of importance (as
in watch mechanism), the only positive drive is by
means of gears or toothed wheels. In order to avoid the
slipping, a number of projections (called teeth) as
shown in Fig. 1. are provided on the periphery of the
one wheel, which will fit into the corresponding
recesses on the periphery of the another wheel. A
friction wheel with the teeth cut on it is known as
toothed wheel or gear.
Classification of Toothed Wheels:
The gears or toothed wheels may be classified as follows :
1.According to the position of axes of the shafts: The axes of the two shafts between
which the motion is to be transmitted, may be (a) Parallel, (b) Intersecting, and (c) Non-
intersecting and non-parallel. The two parallel and co-planar shafts connected by the
gears is shown in Fig.1. These gears are called spur gears and the arrangement is known
as spur gearing. These gears have teeth parallel to the axis of the wheel as shown in
Fig.1.
3. Ramesh Kurbet, Asst. Prof., Dept. of Mech. Engg., PESCE Mandya.
Another name given to the spur gearing is helical gearing, in which the teeth
are inclined to the axis. The single and double helical gears connecting
parallel shafts are shown in Fig. 2 (a) and (b) respectively. The double helical
gears are known as herringbone gears. A pair of spur gears are kinematically
equivalent to a pair of cylindrical discs, keyed to parallel shafts and having a line
contact. The two non-parallel or intersecting, but coplanar shafts connected by gears is
shown in Fig.2(c). These gears are called bevel gears and the arrangement is known as
bevel gearing. The bevel gears, like spur gears, may also have their teeth inclined to the
face of the bevel, in which case they are known as helical bevel gears. The two non-
intersecting and non-parallel i.e. non-coplanar shaft connected by gears is shown in
Fig.2 (d). These gears are called skew bevel gears or spiral gears and the arrangement is
known as skew bevel gearing or spiral gearing. This type of gearing also have a line
contact, the rotation of which about the axes generates the two pitch surfaces known as
hyperboloids.
Fig.2.
4. Ramesh Kurbet, Asst. Prof., Dept. of Mech. Engg., PESCE Mandya.
2. According to the peripheral velocity of the gears: The gears, according to
the peripheral velocity of the gears may be classified as : (a) Low velocity, (b)
Medium velocity, and (c) High velocity. The gears having velocity less than 3
m/s are termed as low velocity gears and gears having velocity between 3 and
15 m/s are known as medium velocity gears. If the velocity of gears is more than 15
m/s, then these are called high speed gears.
3. According to the type of gearing: The
gears, according to the type of gearing
may be classified as : (a) External gearing,
(b) Internal gearing, and (c) Rack and
pinion. In external gearing, the gears of the
two shafts mesh externally with each other
as shown in Fig.3 (a). The larger of these
two wheels is called spur wheel and the
smaller wheel is called pinion. In an
external gearing, the motion of the two
wheels is always unlike, as shown in Fig. 3
(a). In internal gearing, the gears of the two shafts mesh internally with each other as
shown in Fig.3 (b). The larger of these two wheels is called annular wheel and the
smaller wheel is called pinion. In an internal gearing, the motion of the two wheels is
always like, as shown in Fig.3 (b).
5. Ramesh Kurbet, Asst. Prof., Dept. of Mech. Engg., PESCE Mandya.
Fig.3. Fig. 4. Rack and pinion
Sometimes, the gear of a shaft meshes externally and internally with the gears in a
*straight line, as shown in Fig.4. Such type of gear is called rack and pinion. The
straight line gear is called rack and the circular wheel is called pinion. A little
consideration will show that with the help of a rack and pinion, we can convert linear
motion into rotary motion and vice-versa as shown in Fig.4.
4. According to position of teeth on the gear surface: The teeth on the gear surface may
be (a) straight, (b) inclined, and (c) curved. We know that the spur gears have straight
teeth where as helical gears have their teeth inclined to the wheel rim. In case of spiral
gears, the teeth are curved over the rim surface.
6. Ramesh Kurbet, Asst. Prof., Dept. of Mech. Engg., PESCE Mandya.
Advantages and Disadvantages of Gear Drive
The following are the advantages and disadvantages of the gear drive as compared to
belt, rope and chain drives :
Advantages
1. It transmits exact velocity ratio.
2. It may be used to transmit large power.
3. It has high efficiency.
4. It has reliable service.
5. It has compact layout.
Disadvantages
1. The manufacture of gears require
special tools and equipment.
2. The error in cutting teeth may cause
vibrations and noise during operation.
7. Ramesh Kurbet, Asst. Prof., Dept. of Mech. Engg., PESCE Mandya.
Terms Used in Gears The following terms, which will be mostly used in this
chapter, should be clearly understood at this stage. These terms are illustrated
in Fig. 5.
Fig. 5. Terms used in gears
1. Pitch circle: It is an imaginary
circle which by pure rolling action,
would give the same
motion as the actual gear.
2. Pitch circle diameter: It is the
diameter of the pitch circle. The
size of the gear is usually specified
by the pitch circle diameter. It is
also known as pitch diameter.
3. Pitch point: It is a common point
of contact between two pitch
circles.
4. Pitch surface: It is the surface of the rolling discs which the meshing gears have
replaced at the pitch circle.
5. Pressure angle or angle of obliquity: It is the angle between the common normal to
two gear teeth at the point of contact and the common tangent at the pitch point. It is
usually denoted by φ. The standard pressure angles are 12.5° and 20°.
8. Ramesh Kurbet, Asst. Prof., Dept. of Mech. Engg., PESCE Mandya.
6. Addendum: It is the radial distance of a tooth from the pitch circle to the
top of the tooth.
7. Dedendum: It is the radial distance of a tooth from the pitch circle to the
bottom of the tooth.
8. Addendum circle: It is the circle drawn through the top of the teeth and is concentric
with the pitch circle.
9. Dedendum circle: It is the circle drawn through the bottom of the teeth. It is also
called root circle.
Note : Root circle diameter = Pitch circle diameter × cos φ, where φ is the pressure
angle.
10. Circular pitch: It is the distance measured on the circumference of the pitch circle
from a point of one tooth to the corresponding point on the next tooth. It is usually
denoted by pc.
Mathematically, Circular pitch, pc = π D/T
where D = Diameter of the pitch circle, and T = Number of teeth on the wheel.
A little consideration will show that the two gears will mesh together correctly, if the
two wheels have the same circular pitch.
Note : If D1 and D2 are the diameters of the two meshing gears having the teeth T1 and
T2 respectively, then for them to mesh correctly,
9. Ramesh Kurbet, Asst. Prof., Dept. of Mech. Engg., PESCE Mandya.
11. Diametral pitch: It is the ratio of number of teeth to the pitch circle
diameter in millimetres.
It is denoted by pd . Mathematically, Diametral pitch,
where T = Number of teeth, and D = Pitch circle diameter.
12. Module: It is the ratio of the pitch circle diameter in millimeters to the number of
teeth. It is usually denoted by m.
Mathematically, Module, m = D /T
Note : The recommended series of modules in Indian Standard are 1, 1.25, 1.5, 2, 2.5, 3,
4, 5, 6, 8, 10, 12, 16, and 20. The modules 1.125, 1.375, 1.75, 2.25, 2.75, 3.5, 4.5, 5.5,
7, 9, 11, 14 and 18 are of second choice.
13. Clearance: It is the radial distance from the top of the tooth to the bottom of the
tooth, in a meshing gear. A circle passing through the top of the meshing gear is known
as clearance circle.
14. Total depth: It is the radial distance between the addendum and the dedendum
circles of a gear. It is equal to the sum of the addendum and dedendum.
15. Working depth: It is the radial distance from the addendum circle to the clearance
circle. It is equal to the sum of the addendum of the two meshing gears.
10. Ramesh Kurbet, Asst. Prof., Dept. of Mech. Engg., PESCE Mandya.
16. Tooth thickness: It is the width of the tooth measured along the pitch
circle.
17. Tooth space: It is the width of space between the two adjacent teeth
measured along the pitch circle.
18. Backlash: It is the difference between the tooth space and the tooth thickness, as
measured along the pitch circle. Theoretically, the backlash should be zero, but in actual
practice some backlash must be allowed to prevent jamming of the teeth due to tooth
errors and thermal expansion.
19. Face of tooth: It is the surface of the gear tooth above the pitch surface.
20. Flank of tooth: It is the surface of the gear tooth below the pitch surface.
21. Top land: It is the surface of the top of the tooth.
22. Face width: It is the width of the gear tooth measured parallel to its axis.
23. Profile: It is the curve formed by the face and flank of the tooth.
24. Fillet radius: It is the radius that connects the root circle to the profile of the tooth.
25. Path of contact: It is the path traced by the point of contact of two teeth from the
beginning to the end of engagement.
26. Length of the path of contact: It is the length of the common normal cut-off by the
addendum circles of the wheel and pinion.
27. Arc of contact: It is the path traced by a point on the pitch circle from the
beginning to the end of engagement of a given pair of teeth.
11. Ramesh Kurbet, Asst. Prof., Dept. of Mech. Engg., PESCE Mandya.
The arc of contact consists of two parts, i.e. (a) Arc of approach. It is the
portion of the path of contact from the beginning of the engagement to the
pitch point.
(b) Arc of recess. It is the portion of the path of contact from the pitch point to
the end of the engagement of a pair of teeth.
Note : The ratio of the length of arc of contact to the circular pitch is known as contact
ratio i.e. number of pairs of teeth in contact.
Condition for Constant Velocity Ratio of Toothed Wheels–
Law of Gearing: Consider the portions of the two teeth, one
on the wheel 1 (or pinion) and the other on the wheel 2, as
shown by thick line curves in Fig. 6. Let the two teeth come in
contact at point Q, and the wheels rotate in the directions as
shown in the figure.
Fig. 6. Law of gearing
Let T-T be the common tangent and MN be the common normal
to the curves at the point of contact Q. From the centres O1 and
O2, draw O1M and O2N perpendicular to MN. A little
consideration will show that the point Q moves in the direction
QC, when considered as a point on wheel 1, and in the direction
QD when considered as a point on wheel 2.
12. Ramesh Kurbet, Asst. Prof., Dept. of Mech. Engg., PESCE Mandya.
Let v1 and v2 be the velocities of the point Q on the wheels 1 and 2
respectively. If the teeth are to remain in contact, then the components of
these velocities along the common normal MN must be equal.
∴ v1cos α =v2cos β
13. Ramesh Kurbet, Asst. Prof., Dept. of Mech. Engg., PESCE Mandya.
From above, we see that the angular velocity ratio is inversely proportional to
the ratio of the distances of the point P from the centres O1 and O2, or the
common normal to the two surfaces at the point of contact Q intersects the
line of centres at point P which divides the centre distance inversely as the
ratio of angular velocities. Therefore in order to have a constant angular velocity ratio
for all positions of the wheels, the point P must be the fixed point (called pitch point)
for the two wheels. In other words, the common normal at the point of contact between
a pair of teeth must always pass through the pitch point. This is the fundamental
condition which must be satisfied while designing the profiles for the teeth of gear
wheels. It is also known as law of gearing.
Notes : 1. The above condition is fulfilled by teeth of involute form, provided that the
root circles from which the profiles are generated are tangential to the common normal.
2. If the shape of one tooth profile is arbitrarily chosen and another tooth is designed to
satisfy the above condition, then the second tooth is said to be conjugate to the first. The
conjugate teeth are not in common use because of difficulty in manufacture, and cost of
production.
3. If D1 and D2 are pitch circle diameters of wheels 1 and 2 having teeth T1 and T2
respectively, then velocity ratio,
14. Ramesh Kurbet, Asst. Prof., Dept. of Mech. Engg., PESCE Mandya.
Velocity of Sliding of Teeth:
The sliding between a pair of teeth in contact at Q occurs along the common
tangent T-T to the tooth curves as shown in Fig. .6. The velocity of sliding is
the velocity of one tooth relative to its mating tooth along the common
tangent at the point of contact.
The velocity of point Q, considered as a point on wheel 1, along the common tangent T-
T is represented by EC. From similar triangles QEC and O1MQ,
Similarly, the velocity of point Q, considered as a point on wheel 2, along the common
tangent T -T is represented by ED. From similar triangles QED and O2 NQ,
15. Ramesh Kurbet, Asst. Prof., Dept. of Mech. Engg., PESCE Mandya.
Notes : 1. We see from equation (ii), that the velocity of sliding is proportional
to the distance of the point of contact from the pitch point.
2. Since the angular velocity of wheel 2 relative to wheel 1 is (ω1 + ω2 ) and
P is the instantaneous centre for this relative motion, therefore the value of vs
may directly be written as vs (ω1 + ω2 ) QP, without the above analysis.
Involute Teeth: An involute of a circle is a plane
curve generated by a point on a tangent, which
rolls on the circle without slipping or by a point on
a taut string which in unwrapped from a reel as
shown in Fig.7. In connection with toothed wheels,
the circle is known as base circle. The involute is
traced as follows : Let A be the starting point of the
involute. The base circle is divided into equal
number of parts e.g. AP1, P1P2, P2P3 etc. The
tangents at P1, P2, P3 etc. are drawn and the length
P1A1, P2A2, P3A3 equal to the arcs AP1, AP2 and
AP3 are set off. Joining the points A, A1, A2, A3
etc. we obtain the involute curve AR.
Fig. 7. Construction of involute
16. Ramesh Kurbet, Asst. Prof., Dept. of Mech. Engg., PESCE Mandya.
Length of Path of Contact: Consider a pinion driving the wheel as shown in
Fig. 8. When the pinion rotates in clockwise direction, the contact between a
pair of involute teeth begins at K (on the flank near the base circle of pinion or
the outer end of the tooth face on the wheel) and ends at L (outer end of the
tooth face on the pinion or on the flank near the base circle of wheel). MN is the
common normal at the point of contacts and the common tangent to the base circles.
The point K is the intersection of the addendum circle of wheel and the common
tangent. The point L is the intersection of the addendum circle of pinion and common
tangent.
If the wheel is made to act as a driver and the
directions of motion are reversed, then the contact
between a pair of teeth begins at L and ends at K.
We know that the length of path of contact is the
length of common normal cutoff by the addendum
circles of the wheel and the pinion. Thus the length
of path of contact is KL which is the sum of the
parts of the path of contacts KP and PL. The part
of the path of contact KP is known as path of
approach and the part of the path of contact PL is
known as path of recess. Fig. 8. Length of path of contact
17. Ramesh Kurbet, Asst. Prof., Dept. of Mech. Engg., PESCE Mandya.
rA = O1L = Radius of addendum circle of pinion,
RA = O2K = Radius of addendum circle of wheel,
r = O1P = Radius of pitch circle of pinion, and
R = O2P = Radius of pitch circle of wheel.
From Fig. 8, we find that radius of the base circle of pinion, O1M = O1P cos φ = r cos φ
and radius of the base circle of wheel, O2N = O2P cos φ = R cos φ
Now from right angled triangle O2KN,
18. Ramesh Kurbet, Asst. Prof., Dept. of Mech. Engg., PESCE Mandya.
Length of Arc of Contact: We know that the arc of contact is the path traced
by a point on the pitch circle from the beginning to the end of engagement of
a given pair of teeth. In Fig. .8., the arc of contact is EPF or GPH.
Considering the arc of contact GPH, it is divided into two parts i.e. arc GP and
arc PH. The arc GP is known as arc of approach and the arc PH is called arc of recess.
The angles subtended by these arcs at O1 are called angle of approach and angle of
recess respectively.
We know that the length of the arc of approach (arc GP)
and the length of the arc of recess (arc PH)
Since the length of the arc of contact GPH is equal to the sum of the length of arc of
approach and arc of recess, therefore,
Length of the arc of contact
Contact Ratio (or Number of Pairs of Teeth in Contact) :
The contact ratio or the number of pairs of teeth in contact is defined as the ratio of the
length of the arc of contact to the circular pitch. Mathematically,
Contact ratio or number of pairs of teeth in contact
where pc=Circular pitch=πm, and m = Module.
19. Ramesh Kurbet, Asst. Prof., Dept. of Mech. Engg., PESCE Mandya.
Notes : 1. The contact ratio, usually, is not a whole number. For example, if
the contact ratio is 1.6, it does not mean that there are 1.6 pairs of teeth in
contact. It means that there are alternately one pair and two pairs of teeth in
contact and on a time basis the average is 1.6.
2. The theoretical minimum value for the contact ratio is one, that is there must always
be at least one pair of teeth in contact for continuous action.
3. Larger the contact ratio, more quietly the gears will operate.
1) The number of teeth on each of the two equal spur gears in mesh are 40. The teeth
have 20° involute profile and the module is 6 mm. If the arc of contact is 1.75 times the
circular pitch, find the addendum.
Solution: Given : T = t = 40 ; φ = 20° ; m = 6 mm
We know that the circular pitch, pc = π m = π × 6 = 18.85 mm
∴ Length of arc of contact = 1.75 pc = 1.75 × 18.85 = 33 mm
and length of path of contact = Length of arc of contact × cos φ = 33 cos 20° = 31 mm
Let RA = rA = Radius of the addendum circle of each wheel.
We know that pitch circle radii of each wheel, R = r = m.T / 2 = 6 × 40/2 = 120 mm
and length of path of contact
20. Ramesh Kurbet, Asst. Prof., Dept. of Mech. Engg., PESCE Mandya.
2) Two involute gears of 20° pressure angle are in mesh. The number of teeth on pinion
is 20 and the gear ratio is 2. If the pitch expressed in module is 5 mm and the pitch line
speed is 1.2 m/s, assuming addendum as standard and equal to one module, find :
1. The angle turned through by pinion when one pair of teeth is in mesh ; and
2. The maximum velocity of sliding.
Solution. Given : φ = 20° ; t = 20; G = T/t = 2; m = 5 mm ; v = 1.2 m/s ; addendum = 1
module = 5 mm
1. Angle turned through by pinion when one pair of teeth is in mesh
We know that pitch circle radius of pinion, r = m.t / 2 = 5 × 20 / 2 = 50 mm and
pitch circle radius of wheel, R = m.T / 2 = m.G.t / 2 = 2 × 20 × 5 / 2 = 100 mm
...(T=G.t)
∴ Radius of addendum circle of pinion, rA = r + Addendum = 50 + 5 = 55 mm
and radius of addendum circle of wheel, RA = R + Addendum = 100 + 5 = 105 mm
21. Ramesh Kurbet, Asst. Prof., Dept. of Mech. Engg., PESCE Mandya.
We know that length of the path of approach (i.e. the path of contact when
engagement occurs),
And the length of path of recess (i.e. the path of contact when disengagement occurs),
Length of the path of contact,
KL=KP+PL=12.65+11.5=24.15 mm
22. Ramesh Kurbet, Asst. Prof., Dept. of Mech. Engg., PESCE Mandya.
3) The following data relate to a pair of 20° involute gears in mesh : Module = 6 mm,
Number of teeth on pinion = 17, Number of teeth on gear = 49 ; Addenda on pinion and
gear wheel = 1 module.
Find : 1. The number of pairs of teeth in contact ; 2. The angle turned through by the
pinion and the gear wheel when one pair of teeth is in contact, and 3. The ratio of
sliding to rolling motion when the tip of a tooth on the larger wheel (i) is just making
contact, (ii) is just leaving contact with its mating tooth, and (iii) is at the pitch point.
Solution. Given : φ = 20° ; m = 6 mm ; t = 17 ; T = 49 ; Addenda on pinion and gear
wheel = 1 module = 6 mm
23. Ramesh Kurbet, Asst. Prof., Dept. of Mech. Engg., PESCE Mandya.
1. Number of pairs of teeth in contact We know that pitch circle radius of
pinion, r = m.t / 2 = 6 × 17 / 2 = 51 mm
and pitch circle radius of gear, r = m.T / 2 = 6 × 49 / 2 = 147 mm
∴ Radius of addendum circle of pinion, rA = r + Addendum = 51 + 6 = 57 mm
and radius of addendum circle of gear, RA = R + Addendum = 147 + 6 = 153 mm
We know that the length of path of approach (i.e. the path of contact when engagement
occurs),
25. Ramesh Kurbet, Asst. Prof., Dept. of Mech. Engg., PESCE Mandya.
Interference in Involute Gears: Fig. 8. shows a pinion with centre O1, in mesh with
wheel or gear with centre O2. MN is the common tangent to the base circles and KL is
the path of contact between the two mating teeth. A little consideration will show, that if
the radius of the addendum circle of pinion is increased to O1N, the point of contact L
will move from L to N.
26. Ramesh Kurbet, Asst. Prof., Dept. of Mech. Engg., PESCE Mandya.
When this radius is further increased, the point of contact L will be on the
inside of base circle of wheel and not on the involute profile of tooth on
wheel. The tip of tooth on the pinion will then undercut the tooth on the wheel
at the root and remove part of the involute profile of tooth on the wheel.
This effect is known as interference,
and occurs when the teeth are being cut.
In brief, the phenomenon when the tip
of tooth undercuts the root on its mating
gear is known as interference.
Similarly, if the radius of the addendum
circle of the wheel increases beyond
O2M, then the tip of tooth on wheel
will cause interference with the tooth on
pinion. The points M and N are called
interference points. Obviously,
interference may be avoided if the path
of contact does not extend beyond
interference points. The limiting value
of the radius of the addendum circle of
the pinion is O1N and of the wheel is
O2M.
Fig. 8. Interference in involute gears
27. Ramesh Kurbet, Asst. Prof., Dept. of Mech. Engg., PESCE Mandya.
From the above discussion, we conclude that the interference may only be
avoided, if the point of contact between the two teeth is always on the
involute profiles of both the teeth. In otherwords, interference may only be
prevented, if the addendum circles of the two mating gears cut the common
tangent to the base circles between the points of tangency.
From Fig. 8, we see that
When interference is just avoided, the maximum length of path of contact is MN when
the maximum addendum circles for pinion and wheel pass through the points of
tangency N and M respectively as shown in Fig. 8. In such a case, Maximum length of
path of approach, MP = r sin φ
and maximum length of path of recess, PN = R sin φ
∴Maximum length of path of contact, MN = MP + PN = r sin φ + R sin φ = (r + R) sinφ
and maximum length of arc of contact
28. Ramesh Kurbet, Asst. Prof., Dept. of Mech. Engg., PESCE Mandya.
Minimum Number of Teeth on the Pinion in Order to Avoid Interference:
We have already discussed in the previous article that in order to avoid interference, the
addendum circles for the two mating gears must cut the common tangent to the base
circles between the points of tangency. The limiting condition reaches, when the
addendum circles of pinion and wheel pass through points N and M (see Fig. 8.)
respectively. Let t = Number of teeth on the pinion,,
T = Number of teeth on the wheel, m = Module of the teeth,
r = Pitch circle radius of pinion = m.t / 2, G = Gear ratio = T / t = R / r
φ = Pressure angle or angle of obliquity. From triangle O1NP,
29. Ramesh Kurbet, Asst. Prof., Dept. of Mech. Engg., PESCE Mandya.
Let Ap. m = Addendum of the pinion, where Ap is a fraction by which the standard
addendum of one module for the pinion should be multiplied in order to avoid
interference.
We know that the addendum of the pinion
30. Ramesh Kurbet, Asst. Prof., Dept. of Mech. Engg., PESCE Mandya.
This equation gives the minimum number of teeth required on the pinion in order to
avoid interference.
Notes : 1. If the pinion and wheel have equal teeth, then G = 1. Therefore the above
equation reduces to
2. The minimum number of teeth on the pinion which will mesh with any gear (also
rack) without interference are given in the following table :
Table 1. Minimum number of teeth on the pinion
Minimum Number of Teeth on the Wheel in Order to Avoid Interference:
Let T = Minimum number of teeth required on the wheel in order to avoid interference,
and AW.m = Addendum of the wheel, where AW is a fraction by which the standard
addendum for the wheel should be multiplied.
31. Ramesh Kurbet, Asst. Prof., Dept. of Mech. Engg., PESCE Mandya.
we have from triangle O2MP
33. Ramesh Kurbet, Asst. Prof., Dept. of Mech. Engg., PESCE Mandya.
Undercutting:
Figure.9. shows a pinion, A portion of its dedendum falls inside the base
circle. The profile of the teeth inside the base circle is radial. If the addendum
of the mating gear is more than the limiting value, it interferes with the dedendum of the
pinion and the gears are locked. However, if a cutting rack having similar teeth is used
to cut the teeth in the pinion, it will remove that portion of the pinion tooth which would
have interfered with the gear as shown in Fig.9.(b). A gear having its material removed
in this manner is said to be undercut and the process, undercutting. In a pinion with
small number of teeth, this can seriously weaken the tooth.
Fig.9
34. Ramesh Kurbet, Asst. Prof., Dept. of Mech. Engg., PESCE Mandya.
Determine the minimum number of teeth required on a pinion, in order to
avoid interference which is to gear with,
1. a wheel to give a gear ratio of 3 to 1 ; and
2. an equal wheel. The pressure angle is 20° and a standard addendum of 1
module for the wheel may be assumed.
Solution. Given : G = T / t = 3 ; φ = 20° ; AW = 1 module
1. Minimum number of teeth for a gear ratio of 3 : 1
We know that minimum number of teeth required on a pinion,
2. Minimum number of teeth for equal wheel We know that minimum number of teeth
for equal wheel,
35. Ramesh Kurbet, Asst. Prof., Dept. of Mech. Engg., PESCE Mandya.
A pair of involute spur gears with 16° pressure angle and pitch of module 6
mm is in mesh. The number of teeth on pinion is 16 and its rotational speed is
240 r.p.m. When the gear ratio is 1.75, find in order that the interference is
just avoided ;
Solution. Given : φ = 16° ; m = 6 mm ; t = 16 ; N1 = 240 r.p.m. or ω1 = 2π × 240/60 =
25.136 rad/s ; G = T / t = 1.75 or T = G.t = 1.75 × 16 = 28
1. Addenda on pinion and gear wheel We know that addendum on pinion
1. The addenda on pinion and gear wheel ;
2. The length of path of contact ; and
3. The maximum velocity of sliding of teeth on either side
of the pitch point.
and addendum on wheel
36. Ramesh Kurbet, Asst. Prof., Dept. of Mech. Engg., PESCE Mandya.
2. Length of path of contact
We know that the pitch circle radius of wheel, R=(m.T)/ 2=(6*28) / 2=84 mm
and pitch circle radius of pinion, r=(m.t)/ 2=(6*16)/ 2=48 mm
∴ Addendum circle radius of wheel, RA=R+Addendum of wheel=84+10.76=94.76 mm
& addendum circle radius of pinion, rA = r + Addendum of pinion =48 + 4.56 = 52.56
mm
We know that the length of path of approach,
37. Ramesh Kurbet, Asst. Prof., Dept. of Mech. Engg., PESCE Mandya.
3. Maximum velocity of sliding of teeth on either side of pitch point
Let ω2 = Angular speed of gear wheel.
Two gear wheels mesh externally and are to give a velocity ratio of 3 to 1. The teeth are
of involute form ; module = 6 mm, addendum = one module, pressure angle = 20°. The
pinion rotates at 90 r.p.m. Determine : 1. The number of teeth on the pinion to avoid
interference on it and the corresponding number of teeth on the wheel, 2. The length of
path and arc of contact, 3.The number of pairs of teeth in contact, and 4. The maximum
velocity of sliding.
Solution. Given : G = T / t = 3 ; m = 6 mm ; AP = AW = 1 module = 6 mm ; φ = 20° ;
N1 = 90 r.p.m. or ω1 = 2π × 90 / 60 = 9.43 rad/s
1. Number of teeth on the pinion to avoid interference on it and the corresponding
number of teeth on the wheel
We know that number of teeth on the pinion to avoid interference,
= 18.2 say 19 Ans.
38. Ramesh Kurbet, Asst. Prof., Dept. of Mech. Engg., PESCE Mandya.
and corresponding number of teeth on the wheel, T = G.t = 3 × 19 = 57 Ans.
2. Length of path and arc of contact, We know that pitch circle radius of
pinion,
r = m.t / 2 = 6 × 19/2 = 57 mm
∴ Radius of addendum circle of pinion, rA = r + Addendum on pinion (AP) = 57 + 6 =
63 mm
and pitch circle radius of wheel, R = m.T / 2 = 6 × 57 / 2 = 171 mm
∴ Radius of addendum circle of wheel,
RA=R+Addendum on wheel (AW)=171+6=177 mm
We know that the path of approach (i.e. path of contact when engagement occurs),
and the path of recess (i.e. path of contact when disengagement occurs),
39. Ramesh Kurbet, Asst. Prof., Dept. of Mech. Engg., PESCE Mandya.
3. Number of pairs of teeth in contact
We know that circular pitch, pc = π . m = π . 6 =18.852 mm
∴ Number of pairs of teeth in contact
A pinion of 20 involute teeth and 125 mm pitch circle diameter drives a rack. The
addendum of both pinion and rack is 6.25 mm. What is the least pressure angle which
can be used to avoid interference ? With this pressure angle, find the length of the arc of
contact and the minimum number of teeth in contact at a time.
Solution. Given : T = 20 ; d = 125 mm or r = OP = 62.5 mm ; LH = 6.25 mm
Least pressure angle to avoid interference
Let φ = Least pressure angle to avoid interference.
We know that for no interference, rack addendum
40. Ramesh Kurbet, Asst. Prof., Dept. of Mech. Engg., PESCE Mandya.
Length of the arc of contact
We know that length of the path of contact,
∴ Length of the arc of contact
Minimum number of teeth
We know that circular pitch,
pc = πd/T = π .125/ 20 =19.64 mm
41. Ramesh Kurbet, Asst. Prof., Dept. of Mech. Engg., PESCE Mandya.
Comparison of Involute and Cycloidal tooth profile
Involute Cycloidal
1.Interference occurs No Interference occurs
2.Pressure angle remains constant
throughout the operation.
Pressure angle varies. It is zero at pitch
point and maximum at the start and end
of engagement.
3.Variation in centre distance does not
affect the velocity ratio.
Centre distance should not vary.
4.Easier to manufacture. It is difficult to manufacture as two
curves hypo and epicycloids are
required.
5. Weaker teeth. Strong teeth and smooth operation.
6. Contact takes place between convex
surfaces and so comparatively more
wear and tear.
Concave flank makes contact with
convex flank. Thus there is less wear and
tear
Application of cycloidal Gears
1.Cycloidal gears are extensily used in watches, clocks and instruments where
interference and strength are prime conditions.
2. Cast bull geras of proper mill machinery.
3. Crusher drives a suger mills