This document presents a new mathematical model for evaluating the dynamic load factor of an involute gear tooth with asymmetric profiles. It develops equations for nonlinear time-varying mesh stiffness and dynamic load factor for symmetric and asymmetric spur gear teeth in single and double tooth contact. The model considers various components of tooth deflection. Results show that the asymmetric tooth profiles increase mesh stiffness, reduce transmission error, and increase dynamic load factor compared to symmetric profiles. This indicates asymmetric gears can enhance dynamic behavior and reduce vibration and noise in gear systems.
Analysis of Crack Severity on Power Density Increment of GearsIDES Editor
Helical gears are commonly used in industry as
they have advantages of higher power density, quieter
operation etc., compared to spur gears. Conventional gear
design is based on various design criteria, including durability
and bending strength load rating. In recent times, fracture
failure modes are gaining importance in addition to
conventional failure modes. Stresses due to operating fatigue
loads and internal residual stresses can cause fatigue fracture
failure on the surface, sub-surface of gear flanks or at tooth
root of gears. During gear design, various parameters are
optimized, and one such parameter is the helix angle that is
optimized for power density and gear noise. However, effect of
possible defects (voids and inclusions) in the gear tooth is not
usually considered in these calculations. This paper is a study
on severity of defects in a gear blank relative to power density
increment. Three different gear geometries (spur and helical
gears with two different helix angles) each with similar defects
are considered. Finite Element Analysis (FEA) is used to
analyze Tooth Interior Fracture (TIF), and study variation of
Stress Intensity Factor (SIF) with crack size and helix angle.
It is seen that power density increment of a common gear
blank through helix angle increment poses a higher risk of
crack severity, as the same gear blank is exposed to higher
operating loads.
11.effect of gear design variables on the dynamic stress of multistage gearsAlexander Decker
This document presents a numerical model to simulate and optimize the dynamic stress of multistage spur gears. The model considers time-varying mesh stiffness and frictional torque. It was used to study the effects of three gear design variables - module, pressure angle, and contact ratio - on dynamic stress. Increasing the module increased stress levels, while a pressure angle of 25 degrees and contact ratio of 2.0 reduced stresses the most for the gear train studied. The model can be used as a tool to obtain optimal design parameters for a given multistage gear train.
Effect of gear design variables on the dynamic stress of multistage gearsAlexander Decker
The document describes a numerical model developed to simulate and optimize the dynamic stress of multistage spur gears. The model considers three design variables: module, pressure angle, and contact ratio. Simulation results showed that increasing module and decreasing pressure angle and contact ratio can increase dynamic stress levels. A module of 2.5 and contact ratio of 2.0 were found to yield the lowest dynamic stresses for the given multistage gear train design. The model can be used as a tool to determine optimal gear design parameters for minimizing dynamic stresses.
Finit element in prosthodontics /certified fixed orthodontic courses by India...Indian dental academy
The Indian Dental Academy is the Leader in continuing dental education , training dentists in all aspects of dentistry and offering a wide range of dental certified courses in different formats.
Performance Optimization of Tie rod using FEAIJERD Editor
Structural performance of any mechanical component is measured basically in terms of its natural frequency, deformation, stiffness, maximum stress level, fatigue life etc. In case of vehicle suspension system; however tie rod is mainly under compressive and fluctuating forces encounter from steering and bumping of vehicle. When steering acts to turn the vehicle, tie rod comes under compressive load. And when vehicle running on rough road condition, fluctuating forces.
Comparison of Bending Stresses in Involute and Cycloidal Profile Spur Gear ToothIRJET Journal
The document compares the bending stresses in involute and cycloidal profile spur gears using finite element analysis. Gear models with different modules are created in Creo Parametric software and analyzed in ANSYS. The results show that bending stress decreases with increasing module and is lower for involute gears compared to cycloidal gears of the same module. Involute gear teeth experience less bending stress and are stronger than cycloidal gear teeth. The finite element analysis results are slightly different but comparable to values obtained from Lewis equation.
THE EFFECTS OF BOLT PRELOAD ON VIBRATION AMPLITUDE OF GANTRY CNC ROUTERIAEME Publication
The joint properties significant affect on the dynamic performance and spindle
vibration of gantry CNC router structure. This paper presents the relationship
between the vibration amplitude of the spindle nose of a gantry CNC router and a bolt
pre-tightening force. The dynamic model from machine structures with bolt joints was
developed to consider the impact of a bolt pre-tightening force to spindle vibration of
CNC router structures and dynamic behavior. Based on the dynamic model, harmonic
analysis is conducted to specify the spindle nose’s displacement corresponding to the
different bolt pre-tightening force. The FE analysis results indicate that bolt pretightening
forces have great influence on the spindle nose vibration amplitude and
when the pre-tightening force of bolt joints was increased, the dynamic stiffness of the
spindle also increases while the vibration amplitude decreases. The accuracy and
effectiveness of the model have also been confirmed by experimental results. The
achieved result will enhance the rigidity, improve the vibration resistance of the
machine structure to improve the reliability as well as machining precision, and attain
the best surface quality
This document summarizes a study that analyzed the transient elasto-plastic response of bridge piers subjected to vehicle collision through finite element analysis. Six bridge pier designs with varying geometry and three different concrete grades were simulated when impacted by two types of vehicles. The results revealed how the pier's response depends on its geometry, concrete grade, vehicle speed and mass. The study aimed to investigate the effects of these parameters on the pier considering the material nonlinearity of concrete.
Analysis of Crack Severity on Power Density Increment of GearsIDES Editor
Helical gears are commonly used in industry as
they have advantages of higher power density, quieter
operation etc., compared to spur gears. Conventional gear
design is based on various design criteria, including durability
and bending strength load rating. In recent times, fracture
failure modes are gaining importance in addition to
conventional failure modes. Stresses due to operating fatigue
loads and internal residual stresses can cause fatigue fracture
failure on the surface, sub-surface of gear flanks or at tooth
root of gears. During gear design, various parameters are
optimized, and one such parameter is the helix angle that is
optimized for power density and gear noise. However, effect of
possible defects (voids and inclusions) in the gear tooth is not
usually considered in these calculations. This paper is a study
on severity of defects in a gear blank relative to power density
increment. Three different gear geometries (spur and helical
gears with two different helix angles) each with similar defects
are considered. Finite Element Analysis (FEA) is used to
analyze Tooth Interior Fracture (TIF), and study variation of
Stress Intensity Factor (SIF) with crack size and helix angle.
It is seen that power density increment of a common gear
blank through helix angle increment poses a higher risk of
crack severity, as the same gear blank is exposed to higher
operating loads.
11.effect of gear design variables on the dynamic stress of multistage gearsAlexander Decker
This document presents a numerical model to simulate and optimize the dynamic stress of multistage spur gears. The model considers time-varying mesh stiffness and frictional torque. It was used to study the effects of three gear design variables - module, pressure angle, and contact ratio - on dynamic stress. Increasing the module increased stress levels, while a pressure angle of 25 degrees and contact ratio of 2.0 reduced stresses the most for the gear train studied. The model can be used as a tool to obtain optimal design parameters for a given multistage gear train.
Effect of gear design variables on the dynamic stress of multistage gearsAlexander Decker
The document describes a numerical model developed to simulate and optimize the dynamic stress of multistage spur gears. The model considers three design variables: module, pressure angle, and contact ratio. Simulation results showed that increasing module and decreasing pressure angle and contact ratio can increase dynamic stress levels. A module of 2.5 and contact ratio of 2.0 were found to yield the lowest dynamic stresses for the given multistage gear train design. The model can be used as a tool to determine optimal gear design parameters for minimizing dynamic stresses.
Finit element in prosthodontics /certified fixed orthodontic courses by India...Indian dental academy
The Indian Dental Academy is the Leader in continuing dental education , training dentists in all aspects of dentistry and offering a wide range of dental certified courses in different formats.
Performance Optimization of Tie rod using FEAIJERD Editor
Structural performance of any mechanical component is measured basically in terms of its natural frequency, deformation, stiffness, maximum stress level, fatigue life etc. In case of vehicle suspension system; however tie rod is mainly under compressive and fluctuating forces encounter from steering and bumping of vehicle. When steering acts to turn the vehicle, tie rod comes under compressive load. And when vehicle running on rough road condition, fluctuating forces.
Comparison of Bending Stresses in Involute and Cycloidal Profile Spur Gear ToothIRJET Journal
The document compares the bending stresses in involute and cycloidal profile spur gears using finite element analysis. Gear models with different modules are created in Creo Parametric software and analyzed in ANSYS. The results show that bending stress decreases with increasing module and is lower for involute gears compared to cycloidal gears of the same module. Involute gear teeth experience less bending stress and are stronger than cycloidal gear teeth. The finite element analysis results are slightly different but comparable to values obtained from Lewis equation.
THE EFFECTS OF BOLT PRELOAD ON VIBRATION AMPLITUDE OF GANTRY CNC ROUTERIAEME Publication
The joint properties significant affect on the dynamic performance and spindle
vibration of gantry CNC router structure. This paper presents the relationship
between the vibration amplitude of the spindle nose of a gantry CNC router and a bolt
pre-tightening force. The dynamic model from machine structures with bolt joints was
developed to consider the impact of a bolt pre-tightening force to spindle vibration of
CNC router structures and dynamic behavior. Based on the dynamic model, harmonic
analysis is conducted to specify the spindle nose’s displacement corresponding to the
different bolt pre-tightening force. The FE analysis results indicate that bolt pretightening
forces have great influence on the spindle nose vibration amplitude and
when the pre-tightening force of bolt joints was increased, the dynamic stiffness of the
spindle also increases while the vibration amplitude decreases. The accuracy and
effectiveness of the model have also been confirmed by experimental results. The
achieved result will enhance the rigidity, improve the vibration resistance of the
machine structure to improve the reliability as well as machining precision, and attain
the best surface quality
This document summarizes a study that analyzed the transient elasto-plastic response of bridge piers subjected to vehicle collision through finite element analysis. Six bridge pier designs with varying geometry and three different concrete grades were simulated when impacted by two types of vehicles. The results revealed how the pier's response depends on its geometry, concrete grade, vehicle speed and mass. The study aimed to investigate the effects of these parameters on the pier considering the material nonlinearity of concrete.
This document analyzes the performance of a deep groove ball bearing with elliptical raceway curvatures using finite element modeling. It studies three cases - a normal ellipse for both races, an inverted ellipse for the outer race with a circular inner race, and varies the radial clearance between 20-60 micrometers. Contact angle, axial play, and contact stresses are calculated analytically and through simulation for different elliptical geometries and clearances. The results provide insights into how elliptical raceway curvatures affect key bearing performance characteristics compared to conventional circular raceways.
IRJET- Investigation of Stresses in Rear Half Axle of an AutomobileIRJET Journal
The document investigates stresses in the rear half axle of an automobile using finite element analysis. It considers various cases like increasing angular velocity, inclination of the axle, and additional loads. Von-Mises and maximum principal stresses increase with higher angular velocity and additional loads. At a constant speed, stresses increase up to a certain inclination angle and then remain similar. Comparing FEA results to analytical calculations shows good agreement at higher angular velocities. The maximum stresses occur at the junction of the axle and gear.
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology.
A Review Paper on Design and Analysis of Helical Gear Using ANSYS, FEM & AGMA...IRJET Journal
This document reviews research on analyzing the strength of helical gear teeth. It summarizes 6 research papers that used theoretical, analytical and finite element methods to calculate bending and contact stresses on helical gear teeth. The studies found that finite element analysis results aligned closely with theoretical values. Key factors analyzed included varying helix angle, face width, pressure angle and material. Increased helix angle and decreased face width were found to increase contact stress. Finite element analysis was found to provide a more accurate model than theoretical equations by considering a continuous load rather than a single point load.
IRJET- Modification of Root Fillet Profile for Optimum Gear LifeIRJET Journal
1. The document discusses the modification of root fillet profiles in spur gears to optimize gear life and reduce failure from pitting.
2. Finite element analysis is conducted in ANSYS on spur gear models with varying root fillet radii. Maximum contact stresses and deformations are compared for different fillet profiles.
3. Experimental analysis is also carried out using the photoelastic method to validate the finite element results. Optimizing the root fillet profile can help improve the strength of gears and increase gear life.
EXPERIMENTAL STUDY ON CONCRETE BOX GIRDER BRIDGE UNDER TRAFFIC INDUCED VIBRATIONIAEME Publication
Many research studies have been carried out based on the ambient vibration test on different types of bridge. In present study, an ambient excitation is used to find the fundamental frequency of vibration of a concrete box girder bridge. Dynamics characteristics of the bridge are identified through traffic induced vibration. The bridge vibration can be recorded for 24 hours using an accelerometer installed on the bridge. The acceleration time histories are recorded using data acquisition system (National Instruments) and recorded signal data were processed using modal analysis performed by using Stochastic Subspace Identification (Time Domain method). The vibration parameters such as modal frequencies, mode shapes and damping ratio were identified for tested bridge.
IRJET- Finite Element Modelling and Simulation of Rubber Component in Predict...IRJET Journal
This document summarizes a study that used finite element modeling and simulation to predict the behavior of rubber components using different hyperelastic material models. Three hyperelastic models - Neo-Hookean, Mooney-Rivlin, and Yeoh - were used to model a rubber bushing component. The Yeoh model provided the best fit to experimental load-displacement test data compared to the other two models, particularly for its ability to capture material behavior at large strains over 200-300%. Finite element analysis was conducted to identify material parameters for each model and compare model predictions to the test data, finding that the Yeoh model most accurately simulated the hyperelastic behavior of the rubber material.
IRJET- The Effect of Tooth Thickness on Root Stress of Internal Spur Gear Mec...IRJET Journal
This document summarizes a study that analyzed the effect of tooth thickness on root stress in an internal spur gear mechanism using finite element analysis. The study found that by increasing the tooth thickness of the pinion gear and decreasing the thickness of the internal gear from the standard value of half the pitch, the maximum bending stresses in the two gears could be balanced. Specifically, a tooth thickness of 0.572 times the pitch for the pinion and 0.428 times the pitch for the internal gear resulted in approximately equal stresses of 47.3 MPa in both gears. This tooth thickness optimization also reduced the total weight of the gear mechanism.
This document summarizes a study that used finite element analysis to analyze stress concentrations at bolt hole locations in lap joints. A 3D finite element model of a lap joint was developed using Abaqus software. Non-linear analysis considered the stress-strain behavior of materials and interactions between bolt and plate surfaces. Parametric studies varied the end distance and compared results to failure criteria in design codes. Stress patterns were compared to bearing capacity equations to determine the optimum end distance that prevents premature failure.
Effect of hyper elastic property on dynamic behaviour of IC EngineIJSRD
In this paper, concept of vibration absorber is discussed with its hyperelastic properties. Rubber pads are inserted between IC Engine and foundation. IC Engine with and without rubber pads are dynamically analysed using FEA software. Both modal and harmonic analysis are performed. The FRFs of two systems are compared for their vibration reduction. Natural frequencies and mode shapes are obtained by modal analysis whereas FRF is obtained by harmonic analysis in FEA software.
This document summarizes a research paper that developed a finite element model to analyze stresses in helical gears during meshing. It describes how helical gears were modeled in SolidWorks and imported into ANSYS for nonlinear contact analysis. Two cases were analyzed: one with the gear fixed and pinion frictionless, and vice versa. Stresses on teeth flanks, fillets, and other parts were obtained. The maximum stress was higher when the pinion was fixed. The model provides a way to analyze gear stresses without assumptions of analytical methods.
Analyze ball screw feeding system dynamics simulation Based on the ADAMSIJRES Journal
This paper studied the Nan Jing ’ table with high precision manufacturing,use the software of Solidworks to draw the table,and then import to the ADAMS to establish model of ball screw feeding system virtual prototype.For this system,we research its kinematics and dynamic simulation,and then obtain the simulation curve of torque displacement speed and acceleration.In order to analysis this curve,the result of simulation indicate that the stiffness of ball screw have an important effect on the feeding system,increasing the stiffness of ball screw and adjusting the parameter of ball screw,are valid way to reduce the error of table and then raise the precision of table.
This document summarizes a research paper that analyzes the static structural behavior of gear teeth using finite element analysis. It begins with introductions to spur gears and failure modes in gear systems. It then describes creating a 3D model of a gear in CATIA and performing static structural analysis in ANSYS to calculate stresses. The analysis is validated by comparing FEM results with theoretical stress calculations. In summary, it investigates gear stresses using 3D FEM and validates the accuracy of the FEM model.
Design and Analysis of Loading Bracket for Landing Gear Strength TestIRJET Journal
This document describes the design and analysis of a loading bracket used for landing gear strength testing. The loading bracket is designed to withstand heavy vertical, drag, and side loads experienced during testing. The design process involves selecting carbon molybdenum steel, theoretically calculating stresses under each load case, and verifying stresses using ANSYS simulation. The theoretical and ANSYS results are found to be within acceptable limits, confirming the design is sufficient to withstand testing loads.
This document summarizes research on measuring and controlling slip in a continuously variable transmission (CVT). A model was developed to simulate slip between the belt and pulleys in a CVT. Dynamic equations were presented to model forces and motion in the x and y directions. The model uses control forces to regulate slip in both directions by maintaining setpoint levels of slip. Testing showed that allowing small amounts (1-2%) of controlled slip can improve efficiency by reducing the clamping and shifting forces required. While simple, the model provides insight and could be expanded to simulate a more realistic belt and account for ratio changes during shifting. Controlling slip holds potential to improve CVT robustness and fuel efficiency.
1. The document summarizes recent research on gears and bearings, covering topics such as gearbox power loss, tooth stress calculation methods for spur and helical gears, mesh stiffness calculation methods, remanufacturing of large-sized skew bevel gears, dynamic analysis of marine gearboxes with crossed beveloid gears, wear behavior of machine cut polymer gears, spatial curve meshing applied to logarithmic spiral bevel gears, torque loss and wear testing of gear oils with ionic liquid additives, and improved models for calculating time-varying mesh stiffness of cracked spur gears.
2. Various analytical methods and experimental studies on gear and bearing performance, dynamics, contact stresses, mesh stiffness calculation, manufacturing techniques, and
This document summarizes research on using a lattice approach in continuum and fracture mechanics. A 2D panel with a circular hole is discretized using a Voronoi tessellation. The lattice approach is able to approximate strain concentration factors under different loadings. A brittle lattice erosion technique is used to compute the energy release rate and stress intensity factor for a crack emanating from the hole, which matches analytical solutions. The lattice approach can determine fracture properties of materials while being simple in formulation and using crack propagation.
SEISMIC RESPONSE OF UNSYMMETRIC BUILDING WITH OPTIMALLY PLACED FRICTION DAMPERSIAEME Publication
Conventional methods of seismic rehabilitation with concrete shear walls or steel bracing
are not considered suitable for some buildings as upgrades with these methods would have
required expensive and time consuming foundation work. Supplemental damping in
conjunction with appropriate stiffness offers an innovative and attractive solution for the
seismic rehabilitation of such structures. This paper deals with the use of friction damper as a
passive dissipative device in order to seismic retrofit of existing structures and discusses the
optimal placement criteria. To fulfill this objective, six storey and ten storey L-shaped
buildings have been modeled with five different damper location formats in SAP2000 subjected
to El Centro and Utterkashi earthquake records. Non-Linear Modal Time History Method has
been used for the analysis and base shear, joint displacement, member forces and hysteresis
energy has been compared to find out most optimal damper location format.
Design of a testing bench, statistical and reliability analysis of some mecha...IAEME Publication
This document describes the design and manufacturing of a testing bench to determine mechanical properties of materials and stiffness of springs or absorption factors of shock absorbers simultaneously. The testing bench uses combinations of test specimens and springs or shock absorbers. Statistical analysis is conducted on the results to determine mean values and standard deviations of the spring stiffness or material properties such as resilience or tensile strength. Specifically, the testing of ebony wood samples and a spring determined the spring stiffness and wood resilience. Testing of glass samples and a spring or shock absorber yielded the spring/absorber properties and glass tensile strength.
This document summarizes a study on the three dimensional contact stress analysis of straight bevel gear teeth using finite element analysis. A geometric model of a bevel gear tooth was created in ANSYS. The stress distribution at the root of the tooth was evaluated under two loading conditions: a uniformly varying load and a concentrated load at the pitch point. The results found that the stress is highest at the toe side under both loading conditions and decreases towards the heel side. The pitch point loading produced higher stresses than the uniform loading.
This document summarizes a study on modeling and analyzing an involute helical gear using CATIA and ANSYS software. It begins with an introduction to gears and motivation for using numerical analysis methods. It then describes how a helical gear model was generated in CATIA and its stresses were analyzed using ANSYS. Bending stresses from ANSYS were compared to theoretical Lewis equation values and AGMA standards, showing maximum 1.4% deviation. Face width was varied and stresses decreased with increasing width. Overall, complex gear designs require advanced software for accurate modeling and stress analysis to optimize design and prevent failures.
SIMULATION AND ANALYSIS OF TRANSMISSION ERROR IN HELICAL NON CIRCULAR GEAR MO...IAEME Publication
This document summarizes a study on the simulation and analysis of transmission error in helical non-circular gear models. The study used ANSYS software to analyze stresses and transmission errors in helical elliptical gear models with different numbers of teeth. Von-Mises stresses were calculated using ANSYS and Lewis equations, showing good agreement between the two methods. Transmission error was analyzed for gear models with 18 and 19 teeth. Total deformation, stresses, and principal stresses were obtained from the ANSYS simulations. The results indicate that finite element analysis can accurately simulate contact and bending stresses in helical elliptical gears.
This document analyzes the performance of a deep groove ball bearing with elliptical raceway curvatures using finite element modeling. It studies three cases - a normal ellipse for both races, an inverted ellipse for the outer race with a circular inner race, and varies the radial clearance between 20-60 micrometers. Contact angle, axial play, and contact stresses are calculated analytically and through simulation for different elliptical geometries and clearances. The results provide insights into how elliptical raceway curvatures affect key bearing performance characteristics compared to conventional circular raceways.
IRJET- Investigation of Stresses in Rear Half Axle of an AutomobileIRJET Journal
The document investigates stresses in the rear half axle of an automobile using finite element analysis. It considers various cases like increasing angular velocity, inclination of the axle, and additional loads. Von-Mises and maximum principal stresses increase with higher angular velocity and additional loads. At a constant speed, stresses increase up to a certain inclination angle and then remain similar. Comparing FEA results to analytical calculations shows good agreement at higher angular velocities. The maximum stresses occur at the junction of the axle and gear.
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology.
A Review Paper on Design and Analysis of Helical Gear Using ANSYS, FEM & AGMA...IRJET Journal
This document reviews research on analyzing the strength of helical gear teeth. It summarizes 6 research papers that used theoretical, analytical and finite element methods to calculate bending and contact stresses on helical gear teeth. The studies found that finite element analysis results aligned closely with theoretical values. Key factors analyzed included varying helix angle, face width, pressure angle and material. Increased helix angle and decreased face width were found to increase contact stress. Finite element analysis was found to provide a more accurate model than theoretical equations by considering a continuous load rather than a single point load.
IRJET- Modification of Root Fillet Profile for Optimum Gear LifeIRJET Journal
1. The document discusses the modification of root fillet profiles in spur gears to optimize gear life and reduce failure from pitting.
2. Finite element analysis is conducted in ANSYS on spur gear models with varying root fillet radii. Maximum contact stresses and deformations are compared for different fillet profiles.
3. Experimental analysis is also carried out using the photoelastic method to validate the finite element results. Optimizing the root fillet profile can help improve the strength of gears and increase gear life.
EXPERIMENTAL STUDY ON CONCRETE BOX GIRDER BRIDGE UNDER TRAFFIC INDUCED VIBRATIONIAEME Publication
Many research studies have been carried out based on the ambient vibration test on different types of bridge. In present study, an ambient excitation is used to find the fundamental frequency of vibration of a concrete box girder bridge. Dynamics characteristics of the bridge are identified through traffic induced vibration. The bridge vibration can be recorded for 24 hours using an accelerometer installed on the bridge. The acceleration time histories are recorded using data acquisition system (National Instruments) and recorded signal data were processed using modal analysis performed by using Stochastic Subspace Identification (Time Domain method). The vibration parameters such as modal frequencies, mode shapes and damping ratio were identified for tested bridge.
IRJET- Finite Element Modelling and Simulation of Rubber Component in Predict...IRJET Journal
This document summarizes a study that used finite element modeling and simulation to predict the behavior of rubber components using different hyperelastic material models. Three hyperelastic models - Neo-Hookean, Mooney-Rivlin, and Yeoh - were used to model a rubber bushing component. The Yeoh model provided the best fit to experimental load-displacement test data compared to the other two models, particularly for its ability to capture material behavior at large strains over 200-300%. Finite element analysis was conducted to identify material parameters for each model and compare model predictions to the test data, finding that the Yeoh model most accurately simulated the hyperelastic behavior of the rubber material.
IRJET- The Effect of Tooth Thickness on Root Stress of Internal Spur Gear Mec...IRJET Journal
This document summarizes a study that analyzed the effect of tooth thickness on root stress in an internal spur gear mechanism using finite element analysis. The study found that by increasing the tooth thickness of the pinion gear and decreasing the thickness of the internal gear from the standard value of half the pitch, the maximum bending stresses in the two gears could be balanced. Specifically, a tooth thickness of 0.572 times the pitch for the pinion and 0.428 times the pitch for the internal gear resulted in approximately equal stresses of 47.3 MPa in both gears. This tooth thickness optimization also reduced the total weight of the gear mechanism.
This document summarizes a study that used finite element analysis to analyze stress concentrations at bolt hole locations in lap joints. A 3D finite element model of a lap joint was developed using Abaqus software. Non-linear analysis considered the stress-strain behavior of materials and interactions between bolt and plate surfaces. Parametric studies varied the end distance and compared results to failure criteria in design codes. Stress patterns were compared to bearing capacity equations to determine the optimum end distance that prevents premature failure.
Effect of hyper elastic property on dynamic behaviour of IC EngineIJSRD
In this paper, concept of vibration absorber is discussed with its hyperelastic properties. Rubber pads are inserted between IC Engine and foundation. IC Engine with and without rubber pads are dynamically analysed using FEA software. Both modal and harmonic analysis are performed. The FRFs of two systems are compared for their vibration reduction. Natural frequencies and mode shapes are obtained by modal analysis whereas FRF is obtained by harmonic analysis in FEA software.
This document summarizes a research paper that developed a finite element model to analyze stresses in helical gears during meshing. It describes how helical gears were modeled in SolidWorks and imported into ANSYS for nonlinear contact analysis. Two cases were analyzed: one with the gear fixed and pinion frictionless, and vice versa. Stresses on teeth flanks, fillets, and other parts were obtained. The maximum stress was higher when the pinion was fixed. The model provides a way to analyze gear stresses without assumptions of analytical methods.
Analyze ball screw feeding system dynamics simulation Based on the ADAMSIJRES Journal
This paper studied the Nan Jing ’ table with high precision manufacturing,use the software of Solidworks to draw the table,and then import to the ADAMS to establish model of ball screw feeding system virtual prototype.For this system,we research its kinematics and dynamic simulation,and then obtain the simulation curve of torque displacement speed and acceleration.In order to analysis this curve,the result of simulation indicate that the stiffness of ball screw have an important effect on the feeding system,increasing the stiffness of ball screw and adjusting the parameter of ball screw,are valid way to reduce the error of table and then raise the precision of table.
This document summarizes a research paper that analyzes the static structural behavior of gear teeth using finite element analysis. It begins with introductions to spur gears and failure modes in gear systems. It then describes creating a 3D model of a gear in CATIA and performing static structural analysis in ANSYS to calculate stresses. The analysis is validated by comparing FEM results with theoretical stress calculations. In summary, it investigates gear stresses using 3D FEM and validates the accuracy of the FEM model.
Design and Analysis of Loading Bracket for Landing Gear Strength TestIRJET Journal
This document describes the design and analysis of a loading bracket used for landing gear strength testing. The loading bracket is designed to withstand heavy vertical, drag, and side loads experienced during testing. The design process involves selecting carbon molybdenum steel, theoretically calculating stresses under each load case, and verifying stresses using ANSYS simulation. The theoretical and ANSYS results are found to be within acceptable limits, confirming the design is sufficient to withstand testing loads.
This document summarizes research on measuring and controlling slip in a continuously variable transmission (CVT). A model was developed to simulate slip between the belt and pulleys in a CVT. Dynamic equations were presented to model forces and motion in the x and y directions. The model uses control forces to regulate slip in both directions by maintaining setpoint levels of slip. Testing showed that allowing small amounts (1-2%) of controlled slip can improve efficiency by reducing the clamping and shifting forces required. While simple, the model provides insight and could be expanded to simulate a more realistic belt and account for ratio changes during shifting. Controlling slip holds potential to improve CVT robustness and fuel efficiency.
1. The document summarizes recent research on gears and bearings, covering topics such as gearbox power loss, tooth stress calculation methods for spur and helical gears, mesh stiffness calculation methods, remanufacturing of large-sized skew bevel gears, dynamic analysis of marine gearboxes with crossed beveloid gears, wear behavior of machine cut polymer gears, spatial curve meshing applied to logarithmic spiral bevel gears, torque loss and wear testing of gear oils with ionic liquid additives, and improved models for calculating time-varying mesh stiffness of cracked spur gears.
2. Various analytical methods and experimental studies on gear and bearing performance, dynamics, contact stresses, mesh stiffness calculation, manufacturing techniques, and
This document summarizes research on using a lattice approach in continuum and fracture mechanics. A 2D panel with a circular hole is discretized using a Voronoi tessellation. The lattice approach is able to approximate strain concentration factors under different loadings. A brittle lattice erosion technique is used to compute the energy release rate and stress intensity factor for a crack emanating from the hole, which matches analytical solutions. The lattice approach can determine fracture properties of materials while being simple in formulation and using crack propagation.
SEISMIC RESPONSE OF UNSYMMETRIC BUILDING WITH OPTIMALLY PLACED FRICTION DAMPERSIAEME Publication
Conventional methods of seismic rehabilitation with concrete shear walls or steel bracing
are not considered suitable for some buildings as upgrades with these methods would have
required expensive and time consuming foundation work. Supplemental damping in
conjunction with appropriate stiffness offers an innovative and attractive solution for the
seismic rehabilitation of such structures. This paper deals with the use of friction damper as a
passive dissipative device in order to seismic retrofit of existing structures and discusses the
optimal placement criteria. To fulfill this objective, six storey and ten storey L-shaped
buildings have been modeled with five different damper location formats in SAP2000 subjected
to El Centro and Utterkashi earthquake records. Non-Linear Modal Time History Method has
been used for the analysis and base shear, joint displacement, member forces and hysteresis
energy has been compared to find out most optimal damper location format.
Design of a testing bench, statistical and reliability analysis of some mecha...IAEME Publication
This document describes the design and manufacturing of a testing bench to determine mechanical properties of materials and stiffness of springs or absorption factors of shock absorbers simultaneously. The testing bench uses combinations of test specimens and springs or shock absorbers. Statistical analysis is conducted on the results to determine mean values and standard deviations of the spring stiffness or material properties such as resilience or tensile strength. Specifically, the testing of ebony wood samples and a spring determined the spring stiffness and wood resilience. Testing of glass samples and a spring or shock absorber yielded the spring/absorber properties and glass tensile strength.
This document summarizes a study on the three dimensional contact stress analysis of straight bevel gear teeth using finite element analysis. A geometric model of a bevel gear tooth was created in ANSYS. The stress distribution at the root of the tooth was evaluated under two loading conditions: a uniformly varying load and a concentrated load at the pitch point. The results found that the stress is highest at the toe side under both loading conditions and decreases towards the heel side. The pitch point loading produced higher stresses than the uniform loading.
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International Journal of Computational Engineering Research (IJCER) is dedicated to protecting personal information and will make every reasonable effort to handle collected information appropriately. All information collected, as well as related requests, will be handled as carefully and efficiently as possible in accordance with IJCER standards for integrity and objectivity.
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Finding the Stresses and Deflection of a Snag Crane Sun Spur Gear Using Fea P...ijceronline
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One of the most important measures of transmission performance is the gear tooth root stress TRS . High root stress can directly damage the gear tooth and indirectly affect the life of the gear. This paper considered reducing the stresses in the base of the change in the gear profile. Accurate calculation of the maximum tooth root stress TRS and deflection is fundamental to the prediction and optimization of gears. The Finite Element Method FEM gives accurate results. But, the calculation requires a lot of resources and time. Moreover, the results obtained from the Lewis, the ISO, and the AGMA methods were useful. This paper approved the results of the new method as useful as other methods. Therefore, in the current results, a new analytical method based on mechanic theory is created using exact profile equations to calculate stress and deflection. Firstly, the load sharing ratio is considered using the Taguchi method. Finally, tooth root stress and deflection are calculated from this profile. The result of tooth root stress obtained from the new method is compared with the FEM method. The result of the new method is found the consistent with FEM method. Khin Khin Thant | Than Than Htike "Analysis of Stress and Deflection of Spur Gear by Using New Analytical Method Based on Taguchi Method and Finite Element Analysis" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-7 | Issue-6 , December 2023, URL: https://www.ijtsrd.com/papers/ijtsrd60165.pdf Paper Url: https://www.ijtsrd.com/engineering/mechanical-engineering/60165/analysis-of-stress-and-deflection-of-spur-gear-by-using-new-analytical-method-based-on-taguchi-method-and-finite-element-analysis/khin-khin-thant
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Car. We propose some new designs, which have an advance for suspension system by improving dynamics.
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system can increase advance in development and have effects on the vehicle dynamics in stability vehicle.
Enhancement of bending strength of helical gears by using asymmetric involute...Omar Sabah
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A novel method for evaluating the dynamic load factor of an involute gear tooth with asymmetric profiles
1. Innovative Systems Design and Engineering www.iiste.org
ISSN 2222-1727 (Paper) ISSN 2222-2871 (Online)
Vol.5, No.10, 2014
17
A Novel Method for Evaluating the Dynamic Load Factor of An
Involute Gear Tooth with Asymmetric Profiles
Husam Saad Hasan *
Prof. Dr. Adnan Naji Jamil Prof. Dr. Mohammed Qasim Abdullah
University of Baghdad , college of Engineering , Mechanical Eng. Dept
* E-mail of the corresponding author: hussamsaad82@yahoo.com
Abstract
In this paper a new generation of asymmetric tooth profile gear is considered to enhance the dynamic behavior
and vibroacoustic properties of toothed gear system. This paper presents a non linear dynamic model as a single
degree of freedom equation for teeth meshing gear system which includes static and dynamic transmission
error in order to investigate the influence of time varying mesh stiffness and periodic tooth errors on dynamic
load factor for symmetric and asymmetric spur teeth profile. A new model of nonlinear time varying mesh
stiffness is based on four types of deflections with consideration a small pressure angle for loaded tooth profile
side and high pressure angle for another side. The complicated variation of meshing stiffness as a function of
contact point along the mesh cycle is studied. Typical dynamic load factor equations are developed for
symmetric and asymmetric tooth gear in single and double tooth contact by studied symmetrictooth with
pressure angle ( 200
/200
) and two pairs of asymmetric teeth (14.50
/250
& 200
/250
). The effect of pressure of
asymmetry and static transmitted load on transmission error and dynamic load factorare studied. The results
indicate enhancement percentage in transmission error and dynamic load factor for asymmetric teeth profile
compare with that symmetric tooth profile .
Keywords: Asymmetric spur gear, Transmission Error , Non-linear mesh stiffness
1. Introduction
For the combination of high speeds and heavy loads encountered in modern engineering applications of the
toothed gear, a precise analysis of the gear dynamic behavior is imperative. A New generation of asymmetric
teeth gear play important role to increase load capacity, endurance ,long life and reduction vibration and noise.
Transmission error (Tm) which is mean the difference between theoretical and actual angular position of
driven gear when driver gear operating at constant speed ,therefore transmission error represent major
excitation source for vibration and noise in geared system ,and reduction in transmission error represent major
aim for researchers many decades ago, moreover gear vibration and noise level arise due to other several
reasons [1] such as the error in the gear teeth profile at the contact point , misalignment between shaft axes ,
impact between mating teeth ,backlash, sliding and rolling friction between mating surface of gears ,bearing
and housing ….etc. Most efforts to reduce the vibration and noise generation at the mesh have been directed
towards improving the accuracy of manufacture. But, experience proves that the improving of manufacturing
accuracy does not reduce the vibration and noise level considerably [2]. Several studies in literature have been
conducted on the design and stress analysis of asymmetric tooth gear, little of them transact this approach
dynamically, kaplelevich[3] present analytical method to design a gear with asymmetric tooth side surface, he
consider a high pressure angle for the drive side and low pressure angle for the coast side teeth , Yang [4]
provide geometrical modeling to design the asymmetric helical gear meshing when assembly errors are present,
he constructed Stress analysis for the helical and the cylindrical form ,Mallesh et al. [5,6] generate asymmetric
spur gear tooth geometry for different pressure angles on drive and coast side using computer programme to
create a finite element model of gear tooth and investigate the effect of bending stress at the critical section for
different pressure angles, different number of teeth and module , Ekwaro-Osire et al. [7] employ the inverse
problem technique for asymmetric gear teeth which include photo elastic experimental work , Wang et al.[8]
extend the edge – based smoothed point interpolation method (ES-IPM) in the bending strength analysis of
asymmetric gear with various drive pressure angles side which generated by a special rack cutter , Agrawal et
al. [9] Had been tested an asymmetric gear virtually with ANSYS code under a predefined loading and it
has been investigated how bending stress changes at the fillet region of the asymmetric gear .Karpat et al . [10]
present dynamic analysis of spur gear with symmetric and asymmetric teeth gear ,they consider high pressure
angle for the drive side and low pressure angle profile for the coast side teeth ,they develop a MATLAB-based
virtual tool to analyze dynamic behavior of spur gears with asymmetric teeth. In This work a new mathematical
model for nonlinear mesh stiffness and dynamic load factor formula are developed for symmetric &
asymmetric teeth meshing gear system then investigate the influence of asymmetry on dynamic load factor
and transmission error .
2. Mathematical Model
The simplest model, a single degree of freedom (SDOF) model of geared rotor systems shown in Figure ( 1 ) is
2. Innovative Systems Design and Engineering www.iiste.org
ISSN 2222-1727 (Paper) ISSN 2222-2871 (Online)
Vol.5, No.10, 2014
18
considered in this paper ,where shafts and bearing are assumed to be rigid i.e. shafts , bearings are
flexibilities ,the motor and load inertias are not considered in this model. As shown in Fig(1) geared system is
modeled using two rotary inertia J1 , J2 , time varying mesh stiffness K m(t) , mesh damping Cm and e(t)
denote periodic profile error. The governing differential equations of motion for the system can be derived
by using Lagrange method for torsional model as :
(1)
(2)
Where represent base radius for pinion and gear respectively , represent angular
displacement for gear and pinion respectively and & are external torque . reduction in two
equation (1-2) was done to equations above which represent two (DOF ) geared system as :
(3)
Where: (4.a)
F= (4.b)
It is a usual practice to introduce the variable x as:
(5)
Equation (5 ) represent dynamic transmission error which is defined as the difference between the actual and
ideal positions of driven gear which usually expressed as a linear displacement along the line of action .
profile error can be defined as a periodic function :
(6)
Where: mean mesh frequency which equal frequency (Hz) of rotation multiply by number of gear
teeth and pressure angle.
2.1. Static & Dynamic transmission error
Table (1) recognize significantly the difference between loaded and unloaded static & dynamic transmission
error cases , dynamic transmission error can be obtained by solving governing differential equation analytically
or approximately , also we can find loaded static transmission error ( ) by deleting derivatives terms in
equation (3) to :
(7)
2.2 Dynamic mesh load
An alternative formulation for the equation of motion can be given by expressing the dynamic mesh load as [11]:
(8)
Dynamic load factor which define as the ratio between the maximum dynamic load to static load and can be
found from equation as :
(9)
The solution of governing differential equation (3) was obtained by numerical analysis. Classical fourth order
Runge kutta method for initial value problem is used after transform equation (3) into state –space equations .
This method is of simplicity and facility for obtaining transient response , and even response can be obtained for
long time calculation by using Matlab code as well as FFT method can be used to obtain amplitude spectrums in
frequency domain .It should be noted [ 12] that the above equations are valid when there is contact between two
gears .when separation occurs between two gears .because the relative vibrations and backlash between the teeth
of gears ,the dynamic gear load will be zero and the equation of motion will be:
(10)
3. Gear Teeth compliance
When geared system loaded and rotate, many components of deflections occur at mating teeth gear such as
bending ,shear , hertizian and foundation deflection as a result of transmitted load. nonlinearity in mesh stiffness
is considered in this paper to investigate a real perception of dynamic behavior of mating gear.
Symmetric as well as asymmetric spur gear teeth compliance based on bending deflection (positive &
negative ) ,shear deflection , Hertizian deflection and foundation deflection is presented in this work. The
overall deflection for mating gear in the direction of applied load
(11)
3. Innovative Systems Design and Engineering www.iiste.org
ISSN 2222-1727 (Paper) ISSN 2222-2871 (Online)
Vol.5, No.10, 2014
19
3.1 Bending & shear deflection
Bending and shear deflections are calculated based on strain energy theory ,we assume that the tooth is an elastic
beam based on a rigid foundation fig (2) ,and From strain energy theory [ 13]:
Total energy due to external work is :
(12)
Where:
M = Bending moment .
Tangential force
Normal force
Moment of inertia
also:
E = modules of elasticity.
G = shear modules of elasticity.
K = shape form factor.
= pressure angle for loaded side
3.2 Strain energy for symmetric teeth profile
We may consider symmetric gear tooth as a very short cantilever beam with the part inside the base circle
modeled as a rectangular beam , and the part outside the base circle as triangular beam as in fig (2 ) .
From gear tooth definition , we have
(13)
(14)
Denote gear teeth pair . You should be noted that amount of thickness at each tooth section above the base
circle proportional with the height of point of contact.
After integrated equation (12) and simplified the result , we find:
(15)
(16)
(17)
3.3 Strain energy for asymmetric teeth profile
As in previous section asymmetric gear tooth is assumed as a very short cantilever beam with the part inside the
base circle modeled as a rectangular beam , and the part outside the base circle as triangular beam as in fig (2 ) .
Bending moment for mating asymmetric teeth gear teeth will be :
Where: (19)
From involutemetry relationships , we can find as in figure (3)
(20)
3.4 Hertizian & foundation deflection
In this work we consider Hertizian deflection which calculated by Yang & Sun [14]
4. Innovative Systems Design and Engineering www.iiste.org
ISSN 2222-1727 (Paper) ISSN 2222-2871 (Online)
Vol.5, No.10, 2014
20
(21)
Nakada and Utagawa according to ref [15 ] investigate foundation deflection which its consider here as:
(22)
4. Tooth Contact Regions
Mesh stiffness for mating tooth gear varies from one region to another depend on type of contact , usually
mating gear has single and double tooth contact ,the definition of each region represent major aim to investigate
the nonlinearity behavior of mesh stiffness in this region ,let AB represent line of action for mating gear as
shown in figure (4) which divided into multi regions , the segment between c & d represent tooth contact
region . point c would be the intersection point between base circle of gear 1 with addendum circle of gear 2 and
point d will be the intersection point between base circle of gear 2 with addendum circle of gear 1 .Distance
between c & f equal to base pitch. distance . During one mesh cycle for spur gears with low-contact ratio , there
is two cases of contact one tooth pair in contact and two tooth pairs in contact, occurring separately . The
overall mesh stiffness modeled as two spring in series during single tooth contact, and modeled as two spring in
parallel during double tooth contact as:
Km = KI single tooth contact (23)
Km = KI +KII double tooth contact (24)
All following relations for the property of gear involute depend on rotation angle φ and pressure angle Ф
which effect on thickness of tooth gear. , Return to deflection equations we note that all parameters are constant
expect (yc) where:
(25)
The radius rj in above varies from an addendum radius raj to adendum radius rdj, also The radius rj depend
directly on rotation angle and base circle as:
(26)
(27)
Angle αij difference from first meshing gear tooth to second meshing gear tooth , i.e. the relation between
rotation angle of the first meshing gear 1 identified by angle α11,at the same time for gear 2 identified by α21, for
backside contact α12and α22[15]
All parameters in deflections equations are ready to substitute, yci value will be obtain for single and double
tooth contact. We can find mesh stiffness in gear for single and double tooth contact which model as
(28)
(29)
Dynamic load factor for symmetric and asymmetric tooth profile can be obtained by sub overall mesh stiffness
in equation (8) to find dynamic load factor equation for both symmetric and asymmetric tooth profile and for
single and double tooth contact.
Single tooth contact (30)
Double tooth contact (31)
4.1 Dynamic load factor for symmetric tooth profile
Dynamic load factor can be recognized for symmetric tooth profile by substitute unit force per summation of
deflections components equations ( 15-16-17 -21-22 ) with consideration value of hcij for each tooth pair of
contact and for each type of contact( single & Double ) i.e. (yc11,yc12,yc22,yc21)
, then kij for symmetric tooth contact :
[
(32)
4.2 Dynamic load factor for asymmetric tooth profile
Dynamic load factor can be recognized for symmetric tooth profile by substitute unit force per summation of
5. Innovative Systems Design and Engineering www.iiste.org
ISSN 2222-1727 (Paper) ISSN 2222-2871 (Online)
Vol.5, No.10, 2014
21
deflections components equations( 16-17 – 18 – 21 -22) with consideration value of for each tooth pair of
contact and for each type of contact( single & Double ) i.e. ( , then for
asymmetric tooth contact:
(33)
5. Results & Discussion
In order to verify the analytical equations derived in this paper , a computer programs by using Matlap Code is
modeled to estimate nonlinear mesh stiffness of spur gear with symmetric and asymmetric teeth , Equations (3)
solved numerically by using the classical fourth order Runge-Kutta method , the numerical solution of equations
above , namely the relative vibration time domain response of gear is obtained to carry out dynamic transmission
error and dynamic load factor of spur gear with symmetric and asymmetric teeth , A computer program was
developing to simulate the dynamic characteristics of spur gear, the adaptive step size control is employed to
assure convergence of the solution. In order to optimize the design with respect to gear design parameters , the
effect of asymmetry and operating design load was investigated.
A sample gear pair given in table (2) is used to prove the accuracy of theoretical analysis in this paper
for computing nonlinear mesh stiffness and compare result with shing [15 ] model.
Fig (6 ) shows non linear mesh stiffness for single and double tooth contact for properties listed in
table (2) with symmetric tooth profile. This result match with a result obtained by shing[15] with percentage
difference around 6 - 7 % along the line of contact , this difference between results due to the effect of
component of bending deflection which investigated in this paper , fig (6 )shows mesh stiffness varying with
rotation angle φ , and this behavior can be varying with time by substitute this angle by the speed of mating
gear in program script , nonlinearity indicted in fig ( 6) confirm that the time varying mesh stiffness represent
major reason for noise and vibration in geared system.
In this study, three different gear pairs are considered to investigate the effect of asymmetry on mesh
stiffness, static transmission error, dynamic transmission error and dynamic load factor , a new modified of
asymmetric gear with low pressure angle for loaded side and high pressure angle for unloaded side which
developed by Abdullah [16] is consider in this paper .
Fig (7 ) shows mesh stiffness varying with time for three gear pairs ,first is symmetric with 200
pressure angle for both sides of gear tooth , second is asymmetric with 200 pressure angle for loaded side and
250 for unloaded side, third is asymmetric with 14.50 pressure angle for loaded side and 250 for unloaded side,
fig (7 ) shows increasing in mesh stiffness in asymmetric cases compare with that symmetric case due to
increasing in tooth thickness and appear a new value (e) in asymmetric tooth profile as it investigated in
theoretical analysis in this paper . The behavior of non linear mesh stiffness in double tooth contact for three
cases is the same ,but this difference occur in single tooth contact , the length of line of contact for single and
double tooth contact for two pairs (200
/200
& 200
/250
) is the same and difference appear in third pair
(14.50
/250
) due to difference in contact ratio which is (1.46) for first two pairs and (1.64) for third pair .The
length of line of contact for single tooth contact in first two pairs is longer that third pair and versa reverse.
Dynamic transmission error and dynamic load factor computational program should be verified with
existing researches , Singh et el [17] predicate dynamic load factor analytically and compare them work with
experimental results of Kubo. .experimental results and the relevant system parameters are extracted from recent
paper by Ozguven and Houser [ 12] , properties of Ohio's model are listed in table(3) , minimum unloaded static
transmission error is obtained by tooth profile modification ,fig (8) shows predication of dynamic load
factor based on theoretical analysis and Ohio's model , where results indicate accepted error ,there might be
several reasons for difference like the activity of the computer model used to calculate unloaded static
transmission error and little knowledge of some parameters such as tip relief amount and relief position , it is
very important in fig ( 8) to note that the resonant frequency did not appear in fundamental frequency , the
peak of curve occur in the other frequency named transition frequency [17 ] ,this frequency recognize when
mating gear transits from no impact to single sided impact regimes below and above resonance ,respectively .
Fig (9 ) show the effect of symmetry on dynamic load factor, for normal operating speed (below 5000
rpm ) the dynamic load factor for all pairs close to one ,this is mean that the dynamic load coincides with static
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ISSN 2222-1727 (Paper) ISSN 2222-2871 (Online)
Vol.5, No.10, 2014
22
load closely, fig(9 ) shows enhancement in dynamic load factor for gear pair (14.50
/250
) compare with gear
pairs (200
/200
& 200
/250
) at operating speed (5000 – 1000 rpm ) with enhancement up to 36% around resonant
rotational speed ( about 10000 rpm) . after rotational speed ( 11000 rpm ) gear pairs (200
/200
& 200
/250
)
show an advantage in dynamic load factor compare with gear pair (14.50
/250
) with difference around 50% ,
generally , the peak of dynamic load factor for asymmetric teeth increase with increasing pressure angle on the
loaded and unloaded side, its (3.84) for asymmetric tooth (200
/250
) , and (4.51) for asymmetric tooth
( 14.50
/250
) ,while it is about (3.54) for classical symmetric tooth (200
/200
) , shifting between resonant rational
speed ( 9605,10544,11493 rpm) due to algorithm of transition frequency [17] ,i.e. resonant frequency in fig (9 )
did not concedes fundamental frequency .
Fig ( 10) investigate the asymmetry effect on dynamic transmission error which varying with rotational
speed , below( 10000 rpm ) each asymmetric teeth (14.50
/250
& 200
/250
) show enhancement comparing with
symmetric tooth (200
/200
) with difference about 48% . as in dynamic load factor curves symmetric tooth
(200
/200
) indicate low dynamic transmission error in high operating speed ( up to 12000 rpm ) ,but unlike
dynamic load factor , the difference between dynamic transmission error for three gear pairs reduce and
concedes after 14000 rpm closely. Fig (10 ) prove that asymmetric teeth show decreasing in dynamic
transmission error at normal operating speed which is represent major reason for enhancement noise in geared
system as many literature confirm [1].
Smith [1] developing Matlap program to generate static transmission error for spur and helical
gear ,geometrical modification parameters such as tip relief, crowning with misalignment and interference
considered in this program, smith program employed in this work to investigate the effect of asymmetry on
static transmission error within mesh cycle , fig (11 ) shows static transmission error for three gear pairs ,
asymmetric tooth (14.50
/250
) recorded lower transmission error compare with other pairs , the decreasing
between amplitude of static transmission error for asymmetric tooth (14.50
/250
) and amplitude static
transmission error for symmetric tooth (200
/200
) was 12% , while the decreasing of amplitude static
transmission error for asymmetric tooth (200
/250
) and amplitude static transmission error for symmetric tooth
(200
/200
) was 6% . static transmission error shows that the peak of transmission error occur at the center of
single tooth contact ,generally, enhancement of static transmission error by using asymmetric teeth leads to
optimization problem of dynamic load factor and dynamic transmission error equations by reducing the
fundamental harmonics of loaded static transmission error ,and this reduction increase with increasing of
pressure angle for loaded and unloaded side .Table ( 4) shows the influence of asymmetry and static transmitted
load on dynamic load factor ,it's obvious that the dynamic load factor change inversely with static transmitted
load ,also asymmetric tooth (14.50
/250
) indicate less dynamic load factor compare with asymmetric tooth
(200
/250
) and symmetric tooth (200
/200
) , percentage difference of dynamic load factor between three pairs
decrease when static transmitted load increase, its about 16 % at 500 N ,and 6% at 2500 N.
7. Conclusions
1- Increasing in tooth mesh stiffness for asymmetric teeth (200
/250
& 14.50
/250
) compare with
symmetric tooth (200/200 ) ,this increasing generate decreasing in static transmission error .
2- Asymmetric tooth (14.50
/250
) remarked better results for dynamic load factor and dynamic
transmission error comparing with symmetric tooth (200/200 ) and asymmetric tooth (200
/250
) at
operating rotational speed below 12000 rpm with percentage enhancement for dynamic load factor
36% around resonant rotational speed ,and percentage enhancement for dynamic transmission error
36% around resonant rotational speed about 48% around resonant rotational speed .
3- the peak of dynamic load factor for asymmetric teeth increase with increasing pressure angle on the
loaded and unloaded side, its (3.84) for asymmetric tooth (& 200
/250
) , and (4.51) for asymmetric tooth
(14.50
/250
) ,while it is about (3.54) for classical symmetric tooth (200
/200
) .
4- Asymmetric tooth (14.50
/250
) remarked lowest static transmission error compare with other teeth ,
the decreasing between amplitude of static transmission error for asymmetric tooth (14.50
/250
) and
amplitude of static transmission error for symmetric tooth (200/200 ) was 12% , while the decreasing
of amplitude static transmission error for asymmetric tooth (200
/250
) and amplitude static
transmission error for symmetric tooth (200
/200
) was 6% .
5- The dynamic load factor change inversely with static transmitted load ,where asymmetric tooth
(14.50
/250
) remarked less dynamic load factor compare with other teeth , percentage difference of
dynamic load factor between three pairs decrease when static transmitted load increase, it's about 16 %
at 500 N ,and 6% at 2500 N.
References
[1] J. Derk Smith, "Gear Noise and Vibration ", by Marcel Dekker, Inc. New York , 2nd edition ,2003.
[2] Kissling, U., “Noise and Vibration Reduction in Cylindrical Gears by an Accurate Optimizing Procedure
7. Innovative Systems Design and Engineering www.iiste.org
ISSN 2222-1727 (Paper) ISSN 2222-2871 (Online)
Vol.5, No.10, 2014
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Implemented in KISSsoft”, Proceedings of International Gearing Conference, France, 1999.
[3] Alex kapelevich ," DIRECT DESIGN OF ASYMMETRIC GEARS: APPROACH AND APPLICATION ",
publish in JSME International Conference on Motion and Power Transmissions May 13-15, 2009, Matsushima
Isles Resort, Japan .
[4] shyue – cheng Yang ," Mathematical model of a helical gear with asymmetric involute teeth and its analysis ",
publish in the international journal of advanced manufacture technology , pp 448 – 456 , September 2005,vol.
26 , issue 5-6.
[5] G.Mallesh, V B Math , Venkatesh , Shankarmurthy H J, Shiva Prasad P and Aravinda k ," Para metric
analysis of Asymmetric Spur Gear Tooth " , publish in 14th National Conference on Machines and
Mechanisms(NaCoMM09),NIT, Durgapur, India, December 17-18, 2009.
[6] G.Mallesh, V B Math , Ashwij , Prabodh Sai Dutt R and Rajendra Shanbhag , " Effect of Tooth Profile
Modification In Asymmetric Spur Gear Tooth Bending Stress By Finite Element Analysis " , publish in 14th
National Conference on Machines and Mechanisms (NaCoMM09),NIT, Durgapur, India, December 17-18, 2009.
[7] S. Ekwaro-Osire , F. Karpat , I. Durukan, F.M. Alemayehu and J.F. Cárdenas-García ," An Inverse Problem
Technique for Spur Gears with Asymmetric Teeth", Proceedings of the SEM Annual Conference June 1-4, 2009
Albuquerque New Mexico USA .
[8] S. Wang , G. R. Liu, G. Y. Zhang and L. Chen ," Accurate Bending Strength Analysis of The Asymmetric
Gear Using The Novel ES-PIM With Triangular Mesh " , publish in International Journal of Automotive and
Mechanical Engineering (IJAME) , Volume 4, pp. 373-397, July-December 2011, University Malaysia Pahang .
[9] Sumit Agrawal and R. L. Himte , " Evaluation of Bending Stress at Fillet Region of an Asymmetric Gear
with a Hole as Stress Relieving Feature using a FEA Software ANSYS ", publish in International Journal of
Computer Applications (0975 – 8887) ,Volume 51– No.8, August 2012 .
[10] Fatih Karpat , S. Ekwaro-Osire , Kadir Cavdar and Fatih C. Babalik ," Dynamic analysis of involute spur
gears with asymmetric teeth " , International Journal of Mechanical Sciences 50 (2008) 1598–1610 .
[11] Virgil ATANASIU and Dumitru LEOHCHI ," The Effect of Cyclic Varying Mesh Sttifness On Dynamic
Motion Characteristics of Spur Gears" , Fascicle of Management and Technological Engineering, Volume VI
(XVI),pp 124-1130, 2007 .
[12] H.nevzat Ozguven and D.Houser ," Dynamic Analysis of High Speed Gears By Using Loaded Static
Transmission error " , journal of sound and vibration , (1988), 125 (1), 71-83.
[13] E.J.Hearn ," Mechanics of Materials 1", Butterworth-Heinemann publish ,oxford , third edition , 1997.
[14] Yang D.C.H. and Sun Z.C. , " A rotary Model for Spur Gear Dynamics ", ASME journal of
Mechanics ,Transmission and Automation of Design , 1985,Vol. 109 , pp. 189 – 196 .
[15] T.K Shing , " Dynamics and control of Geared Servomechanisms with Backlash and Friction consideration
",PHD thesis , Maryland university ,1994.
[16] Mohammad Qasim Abdullah and Muhsin Jabir Jweeg ," Analytical Solution of Bending Stress Equation for
Symmetric and Asymmetric Involute Gear Teeth Shapes with and without Profile Correction", Innovative
Systems Design and Engineering , ISSN 2222-1727 (PAPER) ISSN 2222-2871 Vol 3, No 6, 2012.
[17] R . Singh , Donald Houser and Ahmet Kahraman ,"Non-linear Dynamic Analysis of Geared Systems ",
technical repor , Nasa lewis Research center , 1990, Nasa contractor Report 4338 .
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Figure (1) : a spur gear pair model
Figure(2) : Gear tooth Geometry
Figure (3) : derivations of tooth thickness
Figure (4) : Tooth contact regions
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Figure (5) : Rotation angles relationship
Low Torque High Torque
Low Speed Unloaded static transmission error loaded static transmission error
High Speed Unloaded dynamic transmission error loaded dynamic transmission error
Table (1) : loaded and unloaded Static & Dynamic Transmission Error
Properties Pinion Gear
Module (mm) 2
Pressure angle 200
200
No. of Teeth 20 80
Modules of elasticity (N/m2
) 2.06 ˣ 1011
2.06 ˣ 1011
Damping ratio 0.05
Moment of inertia ( kg. m2
) 1.528 ˣ 10-5
39 ˣ 10-4
Face width (mm) 10 10
Table (2) : Properties of Shing' s Gear pair [15]
Properties Pinion Gear
Module (mm) 3.75
Pressure angle 200
200
No. of Teeth 25 25
Modules of elasticity (N/m2
) 2.06 ˣ 1011
2.06 ˣ 1011
Damping ratio 0.05
Transmitted load ( kg. m2
) 2295
Static transmission error (micron) 1.92
Mesh stiffness (N/m) 3.8E8
Table (3) : properties of Ref[17] gear pair
Load (N)
6000rpm
Symmetric
20/20
Asymmetric 20/25 Asymmetric
14.5/25
500 2.57 2.33 2.15
1000 1.78 1.66 1.57
1500 1.52 1.44 1.38
2000 1.39 1.32 1.28
2500 1.31 1.26 1.23
Table (4) : The Effect of Transmitted load on Dynamic load Factor , mo = 7 mm , face width = 60 mm .
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26
Figure (6) : Mesh Stiffness during Mesh cycle Vs. Rotation angle.
Figure (7) : Effect of Variation of Asymmetry on Mesh stiffness during Mesh cycle.
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Figure (8): Comparison of Evaluated Dynamic load Factor
Figure (9): The Effect of Asymmetry on Dynamic load Factor
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Figure (10): The Effect of Asymmetry on Dynamic Transmission Error
Figure (11): The Effect of Asymmetry on Static Transmission Error
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