A novel specific type of worm drive, so-called end face engagement worm gear(EFEWD), is originally presented to minimize or overcome the gear backlash. Different factors, including the three different types, contact...A novel specific type of worm drive, so-called end face engagement worm gear(EFEWD), is originally presented to minimize or overcome the gear backlash. Different factors, including the three different types, contact curves, tooth profile, lubrication angle and the induced normal curvature are taken into account to investigate the meshing characteristics and create the profile of a novel specific type of worm drive through mathematical models and theoretical analysis. The tooth of the worm wheel is very specific with the sine-shaped tooth which is located at the alveolus of the worm and the tooth profile of a worm is generated by the meshing movement of the worm wheel with the sine-shaped tooth, but just the end face of the worm(with three different typical meshing types) is adapted to meshing, and therefore an extraordinary manufacturing methods is used to generate the profile of the end face engagement worm. The research results indicates that the bearing contacts of the generated conjugate hourglass worm gear set are in line contacts, with certain advantages of no-backlash, high precision and high operating efficiency over other gears and gear systems besides the end face engagement worm gear drive may improve bearing contact, reduce the level of transmission errors and lessen the sensitivity to errors of alignment. Also, the end face engagement worm can be easily made with superior meshing and lubrication performance compared with the conventional techniques. In particular, the meshing and lubrication performance of the end face engagement worm gear by using the end face to meshing can be increased over 10% and 7%, respectively. This investigate is expect to provide a new insight on the design of the future no-backlash worm drive for industry.展开更多
To solve the problem for lacking a special mechanical transmission that could provide multiple outputs with high transmission efficiency and good lubrication in the modem industrial, a novel worm gear, named end face ...To solve the problem for lacking a special mechanical transmission that could provide multiple outputs with high transmission efficiency and good lubrication in the modem industrial, a novel worm gear, named end face engagement worm gear, with multiple worm-wheel meshing is proposed for the first time. The essential parameters for the worm gear are optimized to enhance lubrication and meshing properties. Moreover, analysis of variance(ANOVA) is applied to determine the optimum levels and to determine the influence of parameters. The ANOVA results show that the novel end face engagement worm gear with multiple worm wheels provides high lubrication(the lubrication angle is more than 89~) and meshing performance(the induce normal curvature is less than 0.0002 mm '). The interaction between center distance and roller slant distance most strongly influences the lubrication angle(contributed 51.6%), followed by the parameters of center distance(contributed 25.0%), roller slant distance(contributed 16.4%), tooth angle of gear, gear ratio, and roller radius. In addition, roller radius most strongly influences the induced normal curvature(contributed 39.4%), followed by roller slant distance(contributed 15.2%), tooth angle of the gear(contributed 9.0%), center distance, and gear ratio. The proposed worm gear helps to enrich the no-backlash high precision worm drive and the optimal design method can provide a useful reference on performance improvement of other worm gear.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
To improve the cutting performance of an hourglass worm gear hob and the accuracy of the resulting worm gear,the rake angles of the teeth on the pitch circle should be reduced.A method of forming the spiral flutes by ...To improve the cutting performance of an hourglass worm gear hob and the accuracy of the resulting worm gear,the rake angles of the teeth on the pitch circle should be reduced.A method of forming the spiral flutes by using a variable transmission ratio was developed.This method ensures that the rake angles on the indexing torus of each tooth are approximately 0°.Based on the gear meshing theory and the hourglass worm forming method,the discretization mathematical model of the rake face of a planar double enveloping worm gear hob was established by using cylindrical generating surface,and the feed parameters for machining the rake face for a variable transmission ratio were obtained.The spiral flute was simulated and the hob was machined on a four axis CNC milling machine.A contourgraph was used to measure the rake angle.The measurement results showed that the proposed method can reduce the absolute value of the rake angle on both sides of the cutting teeth,which can be used for machining the spiral flute rake face of an hourglass worm gear hob.展开更多
Mesh stiffness is one of important base parameters of face gear dynamic studies.However,a calculation solution of mesh stiffness of face gear drives is not to be constructed due to complex geometric flakes of face gea...Mesh stiffness is one of important base parameters of face gear dynamic studies.However,a calculation solution of mesh stiffness of face gear drives is not to be constructed due to complex geometric flakes of face gear teeth.Thus,a calculation solution of mesh stiffness of face gear drives with a spur gear,which is based on the proposed equivalent face gear teeth and Ishikawa model,is constructed,and the influence of contact effects on mesh stiffness of face gear drives is investigated.The results indicate the mesh stiffness of face gear drives is sensitive to contact effects under heavy loaded operating conditions,specially.These contributions will benefit to improve dynamic studies of face gear drives.展开更多
In this paper, based on the principle of heat transfer and thermal elastic-plastic theory, the heat treatment process optimization scheme for face gears is proposed according to the structural characteristics of the f...In this paper, based on the principle of heat transfer and thermal elastic-plastic theory, the heat treatment process optimization scheme for face gears is proposed according to the structural characteristics of the face gear and material properties of 12Cr2Ni4 steel. To simulate the effect of carburizing and quenching process on tooth deformation and residual stress distribution, a heat treatment analysis model of face gears is established, and the microstructure, stress and deformation of face gear teeth changing with time are analyzed. The simulation results show that face gear tooth hardness increases, tooth surface residual compressive stress increases and tooth deformation decreases after heat treatment process optimization. It is beneficial to improving the fatigue strength and performance of face gears.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
Aiming at the issue of the grinding integrity of face-gear with worm wheel, the envelope mathematical model of shaper, worm wheel and face-gear is established based on theories of differential geometry and gear mesh. ...Aiming at the issue of the grinding integrity of face-gear with worm wheel, the envelope mathematical model of shaper, worm wheel and face-gear is established based on theories of differential geometry and gear mesh. The judgment of completely grinding the face-gear with the avoidance of singularities is established, and the mathematical expression to show the reason why singularities appear is derived, through the research on the surface contact area and singularity rules of the worm thread surface. The disadvantage of current face-gear grinding method that only part of the working surface of the face-gear can be covered is analyzed and the influence of coefficient of judgment is studied through changing the design parameters.展开更多
The analytical method based on "Hertz theory on normal contact of elastic solids" and the numerical method based on finite element method (FEM) calculating the contact stress of face-gear drive with spur inv...The analytical method based on "Hertz theory on normal contact of elastic solids" and the numerical method based on finite element method (FEM) calculating the contact stress of face-gear drive with spur involute pinion were introduced, and their relative errors are below 10%, except edge contact, which turns out that these two methods can compute contact stress of face-gear drive correctly and effectively. An agreement of the localized bearing contact stress is gotten for these two methods, making sure that the calculation results of FEM are reliable. The loaded meshing simulations of multi-tooth FEM model were developed, and the determination of the transmission error and the maximal load distribution factor of face-gear drive under torques were given. A formula for the maximal load distribution factor was proposed. By introducing the maximal load distribution factor in multi-tooth contact zone, a method for calculating the maximal contact stress in multi-tooth contact can be given. Compared to FEM, the results of these formulae are proved to be reliable, and the relative errors are below 10%.展开更多
Traditional machining methods, such as gear hobbing, gear shaping and gear milling, etc, are commonly used for cutting machining of gear tooth profile, which cannot meet huge machining demand of gears to a certain ext...Traditional machining methods, such as gear hobbing, gear shaping and gear milling, etc, are commonly used for cutting machining of gear tooth profile, which cannot meet huge machining demand of gears to a certain extent. This article proposes to utilize a face-milling machining method in involute gear machining, which can be used to reduce production cost effectively. Cutting vibration generated during cutting machining has a direct effect on the machining accuracy and machined surface quality of workpiece. Therefore, it is desiderated to perform in-depth research regarding this issue. ADAMS software was used to establish a rigid-flexible coupling virtual prototyping model of face-milling gear milling system and a cutting vibration system model. Cutting vibration analysis was performed for face-milling gear by adopting quick sine frequency sweep method, so that the frequency response characteristics of workpiece in three directions X, Y and Z and space were acquired. The research results will provide reference and theoretical foundation for actual application of face-milling gear machining technology.展开更多
In order to improve the machining efficiency of the dish wheel grinding face gear, two changes are proposed:a disk wheel grinding face gear with a long radius and a multi-axis movement optimization method for tooth su...In order to improve the machining efficiency of the dish wheel grinding face gear, two changes are proposed:a disk wheel grinding face gear with a long radius and a multi-axis movement optimization method for tooth surface correction. Based on the grinding principle of face gears, the equation of the long radius disk wheel is deduced. Based on the structure of the machining tool, the tooth surface equations of the face gear shaped by the long radius disk wheel are established. Furthermore, an optimization model of face gear tooth surface correction is established, and the machine tool motion optimization of face gear tooth surface correction is completed;Finally, a long radius disk wheel grinding face gear test is performed. After the face gear tooth surface correction, the maximum value of the tooth surface deviation is reduced from 180 μm to 16 μm which verified the correctness of the machining method.展开更多
The multistage face gears are the core component of the planetary gear train,which is symmetrically meshed by multiple single-stage face gear and multiple cylindrical gears.However,it is difficult to synchronize the c...The multistage face gears are the core component of the planetary gear train,which is symmetrically meshed by multiple single-stage face gear and multiple cylindrical gears.However,it is difficult to synchronize the contact between face gears and cylindrical gear due to the tooth number differences.Thus,the interference problems between two stages and big stress concentration are obvious.The crown surface configuration technology and structure design were introduced to optimize the meshing condition.To improve the double crown design feasibility and meshing stability,it is necessary to establish a reasonable multistage face gears pair simulation model to evaluate various influence factors on the contact condition and quasi-static characteristics of multistage face gears structure.The relevant scatter plots are fitted by comparing the contact results with different crown quantities and friction coefficients to intuitively obtain the variation regularity of maximum deformation,maximum strain,maximum stress and maximum strain energy.The natural frequency and mode coefficient are also determined by modal analysis under these two conditions.All the above mentioned studies verified the contact conjugate properties of double crown surface configuration were suitable.The results can provide a foundation for structure optimization and transmission reliability of multistage face gears.展开更多
To shorten the process of face gears,the grinding-hardening effect experiment of face gears under minimum quantity lubrication(MQL)was carried out.Firstly,the grinding method of face gears was analyzed based on the en...To shorten the process of face gears,the grinding-hardening effect experiment of face gears under minimum quantity lubrication(MQL)was carried out.Firstly,the grinding method of face gears was analyzed based on the envelope principle,and the control equation of grinding movement was constructed.Secondly,the distribution ratio equation of heat flux density was established,and the theoretical calculation formula of triangle heat source was derived.Thirdly,since a MATLAB calculation program was compiled,the temperature change law under MQL grinding was analyzed.In the end,the influence of grinding parameters on the grinding-hardening layer depth was analyzed.The results demonstrate that MQL grinding achieves the grinding-hardening effect.展开更多
基金Supported by National Natural Science Foundation of China(Grant No.51305356)Spring Sunshine Plan of Ministry of Education of China(Grant No.14202505)Talent Introduction of Xihua University,China(Grant No.Z1220217)
文摘A novel specific type of worm drive, so-called end face engagement worm gear(EFEWD), is originally presented to minimize or overcome the gear backlash. Different factors, including the three different types, contact curves, tooth profile, lubrication angle and the induced normal curvature are taken into account to investigate the meshing characteristics and create the profile of a novel specific type of worm drive through mathematical models and theoretical analysis. The tooth of the worm wheel is very specific with the sine-shaped tooth which is located at the alveolus of the worm and the tooth profile of a worm is generated by the meshing movement of the worm wheel with the sine-shaped tooth, but just the end face of the worm(with three different typical meshing types) is adapted to meshing, and therefore an extraordinary manufacturing methods is used to generate the profile of the end face engagement worm. The research results indicates that the bearing contacts of the generated conjugate hourglass worm gear set are in line contacts, with certain advantages of no-backlash, high precision and high operating efficiency over other gears and gear systems besides the end face engagement worm gear drive may improve bearing contact, reduce the level of transmission errors and lessen the sensitivity to errors of alignment. Also, the end face engagement worm can be easily made with superior meshing and lubrication performance compared with the conventional techniques. In particular, the meshing and lubrication performance of the end face engagement worm gear by using the end face to meshing can be increased over 10% and 7%, respectively. This investigate is expect to provide a new insight on the design of the future no-backlash worm drive for industry.
基金Supported by National Natural Science Foundation of China(Grant Nos.51305356,51575456)Spring Sunshine Plan of Ministry of Education of China(Grant No.14202505)Talent Introduction of Xihua University,China(Grant No.Z1220217)
文摘To solve the problem for lacking a special mechanical transmission that could provide multiple outputs with high transmission efficiency and good lubrication in the modem industrial, a novel worm gear, named end face engagement worm gear, with multiple worm-wheel meshing is proposed for the first time. The essential parameters for the worm gear are optimized to enhance lubrication and meshing properties. Moreover, analysis of variance(ANOVA) is applied to determine the optimum levels and to determine the influence of parameters. The ANOVA results show that the novel end face engagement worm gear with multiple worm wheels provides high lubrication(the lubrication angle is more than 89~) and meshing performance(the induce normal curvature is less than 0.0002 mm '). The interaction between center distance and roller slant distance most strongly influences the lubrication angle(contributed 51.6%), followed by the parameters of center distance(contributed 25.0%), roller slant distance(contributed 16.4%), tooth angle of gear, gear ratio, and roller radius. In addition, roller radius most strongly influences the induced normal curvature(contributed 39.4%), followed by roller slant distance(contributed 15.2%), tooth angle of the gear(contributed 9.0%), center distance, and gear ratio. The proposed worm gear helps to enrich the no-backlash high precision worm drive and the optimal design method can provide a useful reference on performance improvement of other worm gear.
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 the National Natural Science Foundation of China (No. 51475460)
文摘To improve the cutting performance of an hourglass worm gear hob and the accuracy of the resulting worm gear,the rake angles of the teeth on the pitch circle should be reduced.A method of forming the spiral flutes by using a variable transmission ratio was developed.This method ensures that the rake angles on the indexing torus of each tooth are approximately 0°.Based on the gear meshing theory and the hourglass worm forming method,the discretization mathematical model of the rake face of a planar double enveloping worm gear hob was established by using cylindrical generating surface,and the feed parameters for machining the rake face for a variable transmission ratio were obtained.The spiral flute was simulated and the hob was machined on a four axis CNC milling machine.A contourgraph was used to measure the rake angle.The measurement results showed that the proposed method can reduce the absolute value of the rake angle on both sides of the cutting teeth,which can be used for machining the spiral flute rake face of an hourglass worm gear hob.
基金supported by the National Natural Science Foundations of China(Nos.51105194,51375226)the Fundamental Research Funds for the Central Universities(No.NS2015049)
文摘Mesh stiffness is one of important base parameters of face gear dynamic studies.However,a calculation solution of mesh stiffness of face gear drives is not to be constructed due to complex geometric flakes of face gear teeth.Thus,a calculation solution of mesh stiffness of face gear drives with a spur gear,which is based on the proposed equivalent face gear teeth and Ishikawa model,is constructed,and the influence of contact effects on mesh stiffness of face gear drives is investigated.The results indicate the mesh stiffness of face gear drives is sensitive to contact effects under heavy loaded operating conditions,specially.These contributions will benefit to improve dynamic studies of face gear drives.
基金Funded by Key Project of Advanced Research Foundation(No.9140A18020113xx)Advanced Research Foundation Project(No.9140A18020212xx)Advanced Research Projects(Nos.5131802xx and 5131812xx)
文摘In this paper, based on the principle of heat transfer and thermal elastic-plastic theory, the heat treatment process optimization scheme for face gears is proposed according to the structural characteristics of the face gear and material properties of 12Cr2Ni4 steel. To simulate the effect of carburizing and quenching process on tooth deformation and residual stress distribution, a heat treatment analysis model of face gears is established, and the microstructure, stress and deformation of face gear teeth changing with time are analyzed. The simulation results show that face gear tooth hardness increases, tooth surface residual compressive stress increases and tooth deformation decreases after heat treatment process optimization. It is beneficial to improving the fatigue strength and performance of face gears.
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Projects(51275530,51535012) supported by the National Natural Science Foundation of ChinaProject(2011CB706800) supported by the National Basic Research Program of China
文摘Aiming at the issue of the grinding integrity of face-gear with worm wheel, the envelope mathematical model of shaper, worm wheel and face-gear is established based on theories of differential geometry and gear mesh. The judgment of completely grinding the face-gear with the avoidance of singularities is established, and the mathematical expression to show the reason why singularities appear is derived, through the research on the surface contact area and singularity rules of the worm thread surface. The disadvantage of current face-gear grinding method that only part of the working surface of the face-gear can be covered is analyzed and the influence of coefficient of judgment is studied through changing the design parameters.
基金Project(50875263) supported by the National Natural Science Foundation of ChinaProject(2011CB706800) supported by the National Basic Research Program of ChinaProject(2010ssxt172) supported by the Natural Science Foundation of Hunan Province,China
文摘The analytical method based on "Hertz theory on normal contact of elastic solids" and the numerical method based on finite element method (FEM) calculating the contact stress of face-gear drive with spur involute pinion were introduced, and their relative errors are below 10%, except edge contact, which turns out that these two methods can compute contact stress of face-gear drive correctly and effectively. An agreement of the localized bearing contact stress is gotten for these two methods, making sure that the calculation results of FEM are reliable. The loaded meshing simulations of multi-tooth FEM model were developed, and the determination of the transmission error and the maximal load distribution factor of face-gear drive under torques were given. A formula for the maximal load distribution factor was proposed. By introducing the maximal load distribution factor in multi-tooth contact zone, a method for calculating the maximal contact stress in multi-tooth contact can be given. Compared to FEM, the results of these formulae are proved to be reliable, and the relative errors are below 10%.
基金financially supported by Natural Science Foundation of Liaoning Province(20170540778),People's Republic of China
文摘Traditional machining methods, such as gear hobbing, gear shaping and gear milling, etc, are commonly used for cutting machining of gear tooth profile, which cannot meet huge machining demand of gears to a certain extent. This article proposes to utilize a face-milling machining method in involute gear machining, which can be used to reduce production cost effectively. Cutting vibration generated during cutting machining has a direct effect on the machining accuracy and machined surface quality of workpiece. Therefore, it is desiderated to perform in-depth research regarding this issue. ADAMS software was used to establish a rigid-flexible coupling virtual prototyping model of face-milling gear milling system and a cutting vibration system model. Cutting vibration analysis was performed for face-milling gear by adopting quick sine frequency sweep method, so that the frequency response characteristics of workpiece in three directions X, Y and Z and space were acquired. The research results will provide reference and theoretical foundation for actual application of face-milling gear machining technology.
基金Supported by Key Project of Advanced Research Foundation(9140A18020113)Advanced Research Foundation Project(9140A18020212)+1 种基金Advanced Research Project(51318025131812)
文摘In order to improve the machining efficiency of the dish wheel grinding face gear, two changes are proposed:a disk wheel grinding face gear with a long radius and a multi-axis movement optimization method for tooth surface correction. Based on the grinding principle of face gears, the equation of the long radius disk wheel is deduced. Based on the structure of the machining tool, the tooth surface equations of the face gear shaped by the long radius disk wheel are established. Furthermore, an optimization model of face gear tooth surface correction is established, and the machine tool motion optimization of face gear tooth surface correction is completed;Finally, a long radius disk wheel grinding face gear test is performed. After the face gear tooth surface correction, the maximum value of the tooth surface deviation is reduced from 180 μm to 16 μm which verified the correctness of the machining method.
基金This work was supported by the National Natural Science Foundation of China(grant number 51575191).
文摘The multistage face gears are the core component of the planetary gear train,which is symmetrically meshed by multiple single-stage face gear and multiple cylindrical gears.However,it is difficult to synchronize the contact between face gears and cylindrical gear due to the tooth number differences.Thus,the interference problems between two stages and big stress concentration are obvious.The crown surface configuration technology and structure design were introduced to optimize the meshing condition.To improve the double crown design feasibility and meshing stability,it is necessary to establish a reasonable multistage face gears pair simulation model to evaluate various influence factors on the contact condition and quasi-static characteristics of multistage face gears structure.The relevant scatter plots are fitted by comparing the contact results with different crown quantities and friction coefficients to intuitively obtain the variation regularity of maximum deformation,maximum strain,maximum stress and maximum strain energy.The natural frequency and mode coefficient are also determined by modal analysis under these two conditions.All the above mentioned studies verified the contact conjugate properties of double crown surface configuration were suitable.The results can provide a foundation for structure optimization and transmission reliability of multistage face gears.
基金Supported by the Innovative Research Project of Basic Products of State Administration of Science,Technology and Industry for National Defense(237099000000170006)。
文摘To shorten the process of face gears,the grinding-hardening effect experiment of face gears under minimum quantity lubrication(MQL)was carried out.Firstly,the grinding method of face gears was analyzed based on the envelope principle,and the control equation of grinding movement was constructed.Secondly,the distribution ratio equation of heat flux density was established,and the theoretical calculation formula of triangle heat source was derived.Thirdly,since a MATLAB calculation program was compiled,the temperature change law under MQL grinding was analyzed.In the end,the influence of grinding parameters on the grinding-hardening layer depth was analyzed.The results demonstrate that MQL grinding achieves the grinding-hardening effect.