This paper proposes a new approach to design pinion machine tool-settings for spiral bevel gears by controlling contact path and transmission errors. It is based on the satisfaction of contact condition of three given...This paper proposes a new approach to design pinion machine tool-settings for spiral bevel gears by controlling contact path and transmission errors. It is based on the satisfaction of contact condition of three given control points on the tooth surface. The three meshing points are controlled to be on a predesigned straight contact path that meets the pre-designed parabolic function of transmission errors. Designed separately, the magnitude of transmission errors and the orientation of the contact path are subjected to precise control. In addition, in order to meet the manufacturing requirements, we suggest to modify the values of blank offset, one of the pinion machine tool-settings, and redesign pinion ma- chine tool-settings to ensure that the magnitude and the geometry of transmission errors should not be influenced apart from minor effects on the predesigned straight contact path. The proposed approach together with its ideas has been proven by a numerical example and the manufacturing practice of a pair of spiral bevel gears.展开更多
The aim of this study is to define optimal tooth modifications, introduced by appropriately chosen head-cutter geometry and machine tool setting, to simultaneously minimize tooth contact pressure and angular displacem...The aim of this study is to define optimal tooth modifications, introduced by appropriately chosen head-cutter geometry and machine tool setting, to simultaneously minimize tooth contact pressure and angular displacement error of the driven gear （transmission error） of face-hobbed spiral bevel gears. As a result of these modifications, the gear pair becomes mismatched, and a point contact replaces the theoretical line contact. In the applied loaded tooth contact analysis it is assumed that the point contact under load is spreading over a surface along the whole or part of the ‘‘potential’’ contact line. A computer program was developed to implement the formulation provided above. By using this program the influence of tooth modifications introduced by the variation in machine tool settings and in head cutter data on load and pressure distributions, transmission errors, and fillet stresses is investigated and discussed. The correlation between the ease-off obtained by pinion tooth modifications and the corresponding tooth contact pressure distribution is investigated and the obtained results are presented.展开更多
We focused on the mathematical modeling and characteristics analysis for the nutation drive based on error parameters. The crown gear tooth profile equation was introduced according to the national standard double cir...We focused on the mathematical modeling and characteristics analysis for the nutation drive based on error parameters. The crown gear tooth profile equation was introduced according to the national standard double circular arc tooth profile and based on the equal tooth strength principle. The nutation drive meshing coordinate system was set up by introducing the cone vertex error, tilt error, nutation angle error and spiral angle error. The tooth profile equations of the double circular arc external and internal spiral bevel gears were further obtained based on the crown gear tooth profile equation concerning above mentioned error parameters. The influences of the nutation gear reducer tooth contact conditions were analyzed with the gear tilt error and axial misalignment error. Finally, the correctness of the theoretical analysis was verified by the contact spot test.展开更多
In order to analyze the influence of setting error of tool on both tooth profile and contact characteristic of orthogonal face gear drive,the coordinate systems with and without setting error are established.Moreover,...In order to analyze the influence of setting error of tool on both tooth profile and contact characteristic of orthogonal face gear drive,the coordinate systems with and without setting error are established.Moreover,the equations of tooth profile and contact points of face gear drive are derived by envelope principle.According to the equations,the change of tooth profile and the contact points position on face gear are analyzed.The tooth surface and contact points are obtained by numerical simulation.Results show that the tooth profile and contact characteristic of face gear drive are not sensitive to the setting error of tool.展开更多
Straight bevel gears are widely applied in automotive, aerospace, chemical and many other fields as one of the most common type of gears. Currently, the researches on straight bevel gears have focused on the fields of...Straight bevel gears are widely applied in automotive, aerospace, chemical and many other fields as one of the most common type of gears. Currently, the researches on straight bevel gears have focused on the fields of fatigue, wear, noise and vibration, while little attention is paid to the effect of multiple alignment errors on the gear tooth wear. To study the influence of alignment errors on the gear tooth wear, a simulated model of a straight bevel gear pair is established. Then, the contact pressure on the tooth surface is analyzed under the various alignment errors according to the Archard wear relationship. The main combinations of alignment errors played vital roles on the tooth wear are investigated. The result shows that under the single alignment error, the contact pressure moves to the tooth heel and increases greatly at here when ？P=0.1 or ？G=0.1; when ？E=–0.03, the contact pressure greatly increases at the tooth heel, but it obviously increases at the tooth toe when ？E=0.03; the alignment error ？γ=1 has little effect on the contact pressure on the tooth surface. Moreover, the combination of ？P, ？G, ？E〈0 and ？γ is the most dangerous type among the multiple alignment errors. This research provides valuable guidelines for predicting the tooth wear under various alignment errors.展开更多
The machining principle and realization method for the continuous generative grinding face gear by a worm wheel are introduced. Based on a five-axis linked CNC grinding machine, a new method is presented to deprive th...The machining principle and realization method for the continuous generative grinding face gear by a worm wheel are introduced. Based on a five-axis linked CNC grinding machine, a new method is presented to deprive the equation of face gear error tooth surface by assuming the tool surface as the error surface, where actual tool installation position error is introduced into the equation of virtual shaper cutter. Surface equations and 3-D models for the face gear and the worm wheel involving four kinds of tool installation errors are established. When compared, the face gear tooth surface machined in VERICUT software for simulation based on this new method and the one obtained based on real process(grinding face gear by using a theoretical worm wheel with actual position errors) are found to be coincident, which proves the validity and feasibility of this new method. By using mesh planning for the rotating projection plane of the face gear work tooth surface, the deviation values of the tooth surface and the difference surface are acquired, and the influence of four kinds of errors on the face gear tooth surface is analyzed. Accordingly, this work provides a theoretical reference for assembly craft of worm wheel, improvement of face gear machining accuracy and modification of error tooth surface.展开更多
Monte Carlo method was adopted to calculate the meshing error considering the manufacture error and assembly error of the meshing point along the time-varying contact line for helical gear pair. The flexural-torsion-a...Monte Carlo method was adopted to calculate the meshing error considering the manufacture error and assembly error of the meshing point along the time-varying contact line for helical gear pair. The flexural-torsion-axis dynamic model coupled was established under the tooth friction force and solved by the perturbation method to compute real dynamic tooth load. The change laws of the friction force and friction torque were obtained in a meshing period. The transmission error formulation was analyzed to introduce meshing excitations. The maximum dynamic transmission error, the maximum meshing force and the maximum dynamic factor were calculated under different speeds, external loads and damping factors. The conclusions can provide theoretical basis for the gear design especially in tooth profile correction.展开更多
The influences of machining and misalignment errors play a very critical role in the performance of the anti-backlash double-roller enveloping hourglass worm gear(ADEHWG).However,a corresponding efficient method for e...The influences of machining and misalignment errors play a very critical role in the performance of the anti-backlash double-roller enveloping hourglass worm gear(ADEHWG).However,a corresponding efficient method for eliminating or reducing these errors on the tooth profile of the ADEHWG is seldom reported.The gear engagement equation and tooth profile equation for considering six different errors that could arise from the machining and gear misalignment are derived from the theories of differential geometry and gear meshing.Also,the tooth contact analysis(TCA) is used to systematically investigate the influence of the machining and misalignment errors on the contact curves and the tooth profile by means of numerical analysis and three-dimensional solid modeling.The research results show that vertical angular misalignment of the worm wheel(Δβ) has the strongest influences while the tooth angle error(Δα) has the weakest influences on the contact curves and the tooth profile.A novel efficient approach is proposed and used to minimize the effect of the errors in manufacturing by changing the radius of the grinding wheel and the approaching point of contact.The results from the TCA and the experiment demonstrate that this tooth profile design modification method can indeed reduce the machining and misalignment errors.This modification design method is helpful in understanding the manufacturing technology of the ADEHWG.展开更多
The paper considers the modification or the manufacture error of cycloidal gear, then analyzes the relationship of pin circle meshed with the modified cycloidal gear, discuases the amount of error that leads to destro...The paper considers the modification or the manufacture error of cycloidal gear, then analyzes the relationship of pin circle meshed with the modified cycloidal gear, discuases the amount of error that leads to destroying conjugate action and results in the changes of tbe instantaneous velocity ratio and so as to affect the smooth operation of cycloidal pin gearing. The idea of the relationship between amount of modification aud manufacture error and the smooth operation can be gotten from the curve diagrams of the instantaneous velocity ratio. Therefore, the directions for improving the reature of the cycloidal pin gear transmission are clear.展开更多
An error processing method is presented based on optimization theory and microcomputer technique which can be successfully used in the cycloidal gear measurement on three dimensional coordinates measuring machine (CMM...An error processing method is presented based on optimization theory and microcomputer technique which can be successfully used in the cycloidal gear measurement on three dimensional coordinates measuring machine (CMM). In the procedure, the minimum quadratic sum of the normal deviation is used as the object function and the equidistant curve is dealed with instead of the teeth profile. CMM is a high accurate measuring machine which can provide a way to evaluate the accuracy of the cycloidal gear completely.展开更多
Many small-size precise plastic helical involutes gears are used in electrical appliances to transmit rotary movements con- tinuously and smoothly. Ball-end milling is an effective method for trial manufacture or smal...Many small-size precise plastic helical involutes gears are used in electrical appliances to transmit rotary movements con- tinuously and smoothly. Ball-end milling is an effective method for trial manufacture or small batch production of this type of gear, but the precision of the gear is usually low. In this research, the main sources of the errors of the gear, machining errors of the tooth profile and trace of the gear obtained were analyzed. The correction amounts for these errors are then determined by using a CNC gear tester. They are used to generate a new 3D-CAD model for gear machining with better nrecision.展开更多
In order to generate the digital gear tooth surfaces(DGTS)with high efficiency and high precision,a method for identification and compensation of machining errors is demonstrated in this paper.Machining errors are ana...In order to generate the digital gear tooth surfaces(DGTS)with high efficiency and high precision,a method for identification and compensation of machining errors is demonstrated in this paper.Machining errors are analyzed directly from the real tooth surfaces.The topography data of the part are off-line measured in the post-process.A comparison is made between two models:CAD model of DGTS and virtual model of the physical measured surface.And a matching rule is given to determine these two surfaces in an appropriate fashion.The developed error estimation model creates a point-to-point map of the real surface to the theoretical surface in the normal direction.A“pre-calibration error compensation”strategy is presented.Through processing the results of the first trail cutting,the total compensation error is predicted and an imaginary digital tooth surface is reconstructed. The machining errors in the final manufactured surfaces are minimized by generating this imaginary surface.An example of ma- chining 2-D DGTS verifies the developed method.The research is of important theoretical and practical value to manufacture the DGTS and other digital conjugate surfaces.展开更多
Geared-rotor systems are critical components in mechanical applications,and their performance can be severely affected by faults,such as profile errors,wear,pitting,spalling,flaking,and cracks.Profile errors in gear t...Geared-rotor systems are critical components in mechanical applications,and their performance can be severely affected by faults,such as profile errors,wear,pitting,spalling,flaking,and cracks.Profile errors in gear teeth are inevitable in manufacturing and subsequently accumulate during operations.This work aims to predict the status of gear profile deviations based on gear dynamics response using the digital model of an experimental rig setup.The digital model comprises detailed CAD models and has been validated against the expected physical behavior using commercial finite element analysis software.The different profile deviations are then modeled using gear charts,and the dynamic response is captured through simulations.The various features are then obtained by signal processing,and various ML models are then evaluated to predict the fault/no-fault condition for the gear.The best performance is achieved by an artificial neural network with a prediction accuracy of 97.5%,which concludes a strong influence on the dynamics of the gear rotor system due to profile deviations.展开更多
The basic principle of equal base circle bevel gear (EBCBG) is illustrated simply Thetooth surface equation of EBCBG manufactured by end milling cutter with involute profile is de-rived. The tooth form error is analy...The basic principle of equal base circle bevel gear (EBCBG) is illustrated simply Thetooth surface equation of EBCBG manufactured by end milling cutter with involute profile is de-rived. The tooth form error is analyzed on the basis of spherical involute展开更多
基金National Natural Science Foundation of China (50475148)Aeronautical Science Foundation of China (04C53015)Areonautical Sci-tech Innovation Foundation of China (07B53004)
文摘This paper proposes a new approach to design pinion machine tool-settings for spiral bevel gears by controlling contact path and transmission errors. It is based on the satisfaction of contact condition of three given control points on the tooth surface. The three meshing points are controlled to be on a predesigned straight contact path that meets the pre-designed parabolic function of transmission errors. Designed separately, the magnitude of transmission errors and the orientation of the contact path are subjected to precise control. In addition, in order to meet the manufacturing requirements, we suggest to modify the values of blank offset, one of the pinion machine tool-settings, and redesign pinion ma- chine tool-settings to ensure that the magnitude and the geometry of transmission errors should not be influenced apart from minor effects on the predesigned straight contact path. The proposed approach together with its ideas has been proven by a numerical example and the manufacturing practice of a pair of spiral bevel gears.
基金the Hungarian Scientific Research Fund (OTKA) for their financial support of the research under Contract No.K77921
文摘The aim of this study is to define optimal tooth modifications, introduced by appropriately chosen head-cutter geometry and machine tool setting, to simultaneously minimize tooth contact pressure and angular displacement error of the driven gear （transmission error） of face-hobbed spiral bevel gears. As a result of these modifications, the gear pair becomes mismatched, and a point contact replaces the theoretical line contact. In the applied loaded tooth contact analysis it is assumed that the point contact under load is spreading over a surface along the whole or part of the ‘‘potential’’ contact line. A computer program was developed to implement the formulation provided above. By using this program the influence of tooth modifications introduced by the variation in machine tool settings and in head cutter data on load and pressure distributions, transmission errors, and fillet stresses is investigated and discussed. The correlation between the ease-off obtained by pinion tooth modifications and the corresponding tooth contact pressure distribution is investigated and the obtained results are presented.
基金Funded by the National Natural Science Foundation of China(Grant No.51275092)the Program of Fujian Provincial Industrial Robot Basic Components Technology Research and Development Center(Grant No.2014H21010011)the Program of Fujian Provincial Collaborative Innovation Center for High-end Equipment Manufacturing
文摘We focused on the mathematical modeling and characteristics analysis for the nutation drive based on error parameters. The crown gear tooth profile equation was introduced according to the national standard double circular arc tooth profile and based on the equal tooth strength principle. The nutation drive meshing coordinate system was set up by introducing the cone vertex error, tilt error, nutation angle error and spiral angle error. The tooth profile equations of the double circular arc external and internal spiral bevel gears were further obtained based on the crown gear tooth profile equation concerning above mentioned error parameters. The influences of the nutation gear reducer tooth contact conditions were analyzed with the gear tilt error and axial misalignment error. Finally, the correctness of the theoretical analysis was verified by the contact spot test.
基金Supported by the National Natural Science Foundation of China(51105194)the Scientific Research Funding of Nanjing University of Aeronautics and Astronautics(NP2011014)
文摘In order to analyze the influence of setting error of tool on both tooth profile and contact characteristic of orthogonal face gear drive,the coordinate systems with and without setting error are established.Moreover,the equations of tooth profile and contact points of face gear drive are derived by envelope principle.According to the equations,the change of tooth profile and the contact points position on face gear are analyzed.The tooth surface and contact points are obtained by numerical simulation.Results show that the tooth profile and contact characteristic of face gear drive are not sensitive to the setting error of tool.
基金Supported by National Natural Science Foundation of China(Grant No.51105287)Innovative Research Team Development Program of Ministry of Education of China(Grant No.IRT13087)
文摘Straight bevel gears are widely applied in automotive, aerospace, chemical and many other fields as one of the most common type of gears. Currently, the researches on straight bevel gears have focused on the fields of fatigue, wear, noise and vibration, while little attention is paid to the effect of multiple alignment errors on the gear tooth wear. To study the influence of alignment errors on the gear tooth wear, a simulated model of a straight bevel gear pair is established. Then, the contact pressure on the tooth surface is analyzed under the various alignment errors according to the Archard wear relationship. The main combinations of alignment errors played vital roles on the tooth wear are investigated. The result shows that under the single alignment error, the contact pressure moves to the tooth heel and increases greatly at here when ？P=0.1 or ？G=0.1; when ？E=–0.03, the contact pressure greatly increases at the tooth heel, but it obviously increases at the tooth toe when ？E=0.03; the alignment error ？γ=1 has little effect on the contact pressure on the tooth surface. Moreover, the combination of ？P, ？G, ？E〈0 and ？γ is the most dangerous type among the multiple alignment errors. This research provides valuable guidelines for predicting the tooth wear under various alignment errors.
基金Projects(51535012,U1604255)supported by the National Natural Science Foundation of ChinaProject(2016JC2001)supported by the Key Research and Development Project of Hunan Province,China
文摘The machining principle and realization method for the continuous generative grinding face gear by a worm wheel are introduced. Based on a five-axis linked CNC grinding machine, a new method is presented to deprive the equation of face gear error tooth surface by assuming the tool surface as the error surface, where actual tool installation position error is introduced into the equation of virtual shaper cutter. Surface equations and 3-D models for the face gear and the worm wheel involving four kinds of tool installation errors are established. When compared, the face gear tooth surface machined in VERICUT software for simulation based on this new method and the one obtained based on real process(grinding face gear by using a theoretical worm wheel with actual position errors) are found to be coincident, which proves the validity and feasibility of this new method. By using mesh planning for the rotating projection plane of the face gear work tooth surface, the deviation values of the tooth surface and the difference surface are acquired, and the influence of four kinds of errors on the face gear tooth surface is analyzed. Accordingly, this work provides a theoretical reference for assembly craft of worm wheel, improvement of face gear machining accuracy and modification of error tooth surface.
基金Supported by National Basic Research Program of China("973"Program,No.2013CB632305)
文摘Monte Carlo method was adopted to calculate the meshing error considering the manufacture error and assembly error of the meshing point along the time-varying contact line for helical gear pair. The flexural-torsion-axis dynamic model coupled was established under the tooth friction force and solved by the perturbation method to compute real dynamic tooth load. The change laws of the friction force and friction torque were obtained in a meshing period. The transmission error formulation was analyzed to introduce meshing excitations. The maximum dynamic transmission error, the maximum meshing force and the maximum dynamic factor were calculated under different speeds, external loads and damping factors. The conclusions can provide theoretical basis for the gear design especially in tooth profile correction.
基金supported by National Natural Science Foundation of China(Grant Nos. 50775190No.51275425)+2 种基金Spring Sunshine Plan of Ministry of Education of China(Grant No. 10202258)Talent Introduction of Xihua UniversityChina(Grant No. Z1220217)
文摘The influences of machining and misalignment errors play a very critical role in the performance of the anti-backlash double-roller enveloping hourglass worm gear(ADEHWG).However,a corresponding efficient method for eliminating or reducing these errors on the tooth profile of the ADEHWG is seldom reported.The gear engagement equation and tooth profile equation for considering six different errors that could arise from the machining and gear misalignment are derived from the theories of differential geometry and gear meshing.Also,the tooth contact analysis(TCA) is used to systematically investigate the influence of the machining and misalignment errors on the contact curves and the tooth profile by means of numerical analysis and three-dimensional solid modeling.The research results show that vertical angular misalignment of the worm wheel(Δβ) has the strongest influences while the tooth angle error(Δα) has the weakest influences on the contact curves and the tooth profile.A novel efficient approach is proposed and used to minimize the effect of the errors in manufacturing by changing the radius of the grinding wheel and the approaching point of contact.The results from the TCA and the experiment demonstrate that this tooth profile design modification method can indeed reduce the machining and misalignment errors.This modification design method is helpful in understanding the manufacturing technology of the ADEHWG.
文摘The paper considers the modification or the manufacture error of cycloidal gear, then analyzes the relationship of pin circle meshed with the modified cycloidal gear, discuases the amount of error that leads to destroying conjugate action and results in the changes of tbe instantaneous velocity ratio and so as to affect the smooth operation of cycloidal pin gearing. The idea of the relationship between amount of modification aud manufacture error and the smooth operation can be gotten from the curve diagrams of the instantaneous velocity ratio. Therefore, the directions for improving the reature of the cycloidal pin gear transmission are clear.
文摘An error processing method is presented based on optimization theory and microcomputer technique which can be successfully used in the cycloidal gear measurement on three dimensional coordinates measuring machine (CMM). In the procedure, the minimum quadratic sum of the normal deviation is used as the object function and the equidistant curve is dealed with instead of the teeth profile. CMM is a high accurate measuring machine which can provide a way to evaluate the accuracy of the cycloidal gear completely.
文摘Many small-size precise plastic helical involutes gears are used in electrical appliances to transmit rotary movements con- tinuously and smoothly. Ball-end milling is an effective method for trial manufacture or small batch production of this type of gear, but the precision of the gear is usually low. In this research, the main sources of the errors of the gear, machining errors of the tooth profile and trace of the gear obtained were analyzed. The correction amounts for these errors are then determined by using a CNC gear tester. They are used to generate a new 3D-CAD model for gear machining with better nrecision.
文摘In order to generate the digital gear tooth surfaces(DGTS)with high efficiency and high precision,a method for identification and compensation of machining errors is demonstrated in this paper.Machining errors are analyzed directly from the real tooth surfaces.The topography data of the part are off-line measured in the post-process.A comparison is made between two models:CAD model of DGTS and virtual model of the physical measured surface.And a matching rule is given to determine these two surfaces in an appropriate fashion.The developed error estimation model creates a point-to-point map of the real surface to the theoretical surface in the normal direction.A“pre-calibration error compensation”strategy is presented.Through processing the results of the first trail cutting,the total compensation error is predicted and an imaginary digital tooth surface is reconstructed. The machining errors in the final manufactured surfaces are minimized by generating this imaginary surface.An example of ma- chining 2-D DGTS verifies the developed method.The research is of important theoretical and practical value to manufacture the DGTS and other digital conjugate surfaces.
文摘Geared-rotor systems are critical components in mechanical applications,and their performance can be severely affected by faults,such as profile errors,wear,pitting,spalling,flaking,and cracks.Profile errors in gear teeth are inevitable in manufacturing and subsequently accumulate during operations.This work aims to predict the status of gear profile deviations based on gear dynamics response using the digital model of an experimental rig setup.The digital model comprises detailed CAD models and has been validated against the expected physical behavior using commercial finite element analysis software.The different profile deviations are then modeled using gear charts,and the dynamic response is captured through simulations.The various features are then obtained by signal processing,and various ML models are then evaluated to predict the fault/no-fault condition for the gear.The best performance is achieved by an artificial neural network with a prediction accuracy of 97.5%,which concludes a strong influence on the dynamics of the gear rotor system due to profile deviations.
文摘The basic principle of equal base circle bevel gear (EBCBG) is illustrated simply Thetooth surface equation of EBCBG manufactured by end milling cutter with involute profile is de-rived. The tooth form error is analyzed on the basis of spherical involute
