Beveloid gears,also known as conical gears,gain more and more importance in industry practice due to their abilities for power transmission between parallel,intersected and crossed axis.However,this type of gearing wi...Beveloid gears,also known as conical gears,gain more and more importance in industry practice due to their abilities for power transmission between parallel,intersected and crossed axis.However,this type of gearing with crossed axes has no common plane of action which results in a point contact and low tooth durability.Therefore,a geometry design approach assuming line contact is developed to analyze the tooth engagement process of crossed beveloid gears with small shaft angle for marine transmission applications.The loaded gear tooth contact behavior is simulated by applying a quasi-static analysis to study the effects of gearing parameters on mesh characteristics.Using the proposed method,a series of sensitivity analyses to examine the effects of critical gearing parameters such as shaft angle,cone angle,helix angle and profile-shift coefficient on the theoretical gear mesh is performed.The parametric analysis of pitch cone design shows that the dominant design parameters represented by the angle between the first principle directions（FPD） and normal angular factor are more sensitive to the shaft and cone angles than they are to the helix angle.The theoretical contact path is highly sensitive to the profile-shift coefficient,which is determined from the theoretical tooth contact analysis.The FPD angle is found to change the distribution of contact pattern,contact pressure and root stress as well as the translational transmission error and the variation of the mesh stiffness significantly.The contact pattern is clearly different between the drive and coast sides due to different designed FPD angles.Finally,a practical experimental setup for marine transmission is performed and tooth bearing test is conducted to demonstrate the proposed design procedure.The experimental result compared well with the simulation.Results of this study yield a better understanding of the geometry design and loaded gear mesh characteristics for crossed beveloid gears used in marine transmission.展开更多
A novel spiral non-circular bevel gear that could be applied to variable-speed driving in intersecting axes was proposed by combining the design principles of non-circular bevel gears and the manufacturing principles ...A novel spiral non-circular bevel gear that could be applied to variable-speed driving in intersecting axes was proposed by combining the design principles of non-circular bevel gears and the manufacturing principles of face-milling spiral bevel gears.Unlike straight non-circular bevel gears,spiral non-circular bevel gears have numerous advantages,such as a high contact ratio,high intensity,good dynamic performance,and an adjustable contact region.In addition,while manufacturing straight non-circular bevel gears is difficult,spiral non-circular bevel gears can be efficiently and precisely fabricated with a 6-axis bevel gear cutting machine.First,the generating principles of spiral non-circular bevel gears were introduced.Next,a mathematical model,including a generating tooth profile,tooth spiral,pressure angle,and generated tooth profile for this gear type was established.Then the precision of the model was verified by a tooth contact analysis using FEA,and the contact patterns and stress distributions of the spiral non-circular bevel gears were investigated.展开更多
The mathematical model of conical involute gears is developed based on the theory of gearing and the generating mechanism. Tooth contact analysis （TCA） is performed to examine the meshing and bearing contact of the ...The mathematical model of conical involute gears is developed based on the theory of gearing and the generating mechanism. Tooth contact analysis （TCA） is performed to examine the meshing and bearing contact of the conical involute gear pairs with intersected and crossed axes. In addition, the principal directions and curvatures of the gear surfaces are investigated and the contact ellipses of the mating tooth surfaces are also studied. Finally, the numerical illustrative examples are provided to demonstrate the computational results, test gears are made for tooth-bearing tests, and the conclusion is verified that the theory has the applicability.展开更多
A complex geometric modeling method of a helical face gear pair with arc-tooth generated by an arc-profile cutting(APC)disc is proposed,and its tooth contact characteristics are analyzed.Firstly,the spatial coordinate...A complex geometric modeling method of a helical face gear pair with arc-tooth generated by an arc-profile cutting(APC)disc is proposed,and its tooth contact characteristics are analyzed.Firstly,the spatial coordinate system of an APC face gear pair is established based on meshing theory.Combining the coordinate transformation matrix and the tooth profile of the cutter,the equations of the curve envelope of the APC face gear pair are obtained.Then the surface equations are solved to extract the point clouds data by programming in MATLAB,which contains the work surface and the fillet surface of the APC face gear pair.And the complex geometric model of the APC face gear pair is built by fitting its point clouds.At last,through the analysis of the tooth surface contact,the sensitivity of the APC face gear to the different types of mounting errors is obtained.The results show that the APC face gear pair is the most sensitive to mounting errors in the tooth thickness direction,and it should be strictly controlled in the actual application.展开更多
In order to implement the dynamic characteristic of a dual power-split transmission, a dynamic me- chanics model is built. Firstly, according to the method of theoretical analysis of the tooth contact analysis （TCA）...In order to implement the dynamic characteristic of a dual power-split transmission, a dynamic me- chanics model is built. Firstly, according to the method of theoretical analysis of the tooth contact analysis （TCA） and loaded tooth contact analysis （LTCA）, the actual meshing process of each gear pairs is simulated, and the time-varying mesh stiffness excitations are obtained, which can improve the numerical precision. Second- ly, by using the lumped mass method, the bending-torsional coupling three dimensional dynamic model of the dual power-split transmission is established, and the identical dimensionless equations are deduced by elimina- ting the effect of rigid displacement and the method of dimensional normalization. Finally, by the method of the fourth order Runge-Kutta algorithm with variable step lengths, the responses of this system in a frequency domain and time domain are obtained, and the dynamic load change characteristics of each gear pairs are analyzed. The results show that the establishment, solution and analysis of the system dynamics model could provide a basis for the dynamic design, and have an important significance for the dynamic efficiency analysis and dynamic perform- ance optimization design of the dual power-split transmission.展开更多
An approach for the contact analysis and load distribution of double-envelop hourglass worm gearing is presented, which is based on a 3-D elastic contact finite element method (FEM) model that accommodates the influen...An approach for the contact analysis and load distribution of double-envelop hourglass worm gearing is presented, which is based on a 3-D elastic contact finite element method (FEM) model that accommodates the influence of errors and load. As compared with existing tooth contact analysis model that assumes rigidity for the contacting surfaces, the proposed model provides a more realistic analysis on the contact patterns, the distribution of contact load and transmission errors. It is also capable of exploring the influence of different errors on meshing performances, the contact deformation, the shift of the contact zone and load share among the meshing tooth-pairs under different load.展开更多
The transmission characteristics of gear drive can be improved with the use of novel tooth profiles.A theoretical study on tooth profile of the hypocycloid pinwheel transmission and contact analysis of gear pair based...The transmission characteristics of gear drive can be improved with the use of novel tooth profiles.A theoretical study on tooth profile of the hypocycloid pinwheel transmission and contact analysis of gear pair based on finite element method(FEM) are carried out,respectively.The line contact between mated tooth surfaces becomes point contact according to a plus movement.Through loaded tooth contact analysis(LTCA),the contact stress and load distributions for the proposed hypocycloid pinwheel transmission and the traditional one are discussed.The analysis results show that the developed tooth surfaces have anticipatory point contact characteristics under loads and contact fatigue dangerous area locates around the ultimate contact position.展开更多
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
Aviation spiral bevel gears are often generated by spiral generated modified（SGM） roll method.In this style,pinion tooth surface modified generation strategy has an important influence on the meshing and contact per...Aviation spiral bevel gears are often generated by spiral generated modified（SGM） roll method.In this style,pinion tooth surface modified generation strategy has an important influence on the meshing and contact performances.For the optimal contact pattern and transmission error function,local synthesis is applied to obtain the machine-tool settings of pinion.For digitized machine,four tooth surface generation styles of pinion are proposed.For every style,tooth contact analysis（TCA） is applied to obtain contact pattern and transmission error function.For the difference between TCA transmission error function and design objective curve,the degree of symmetry and agreement are defined and the corresponding sub-objective functions are established.Linear weighted combination method is applied to get an equivalent objective function to evaluate the shape of transmission error function.The computer programs for the process above are developed to analyze the meshing performances of the four pinion tooth surface generation styles for a pair of aviation spiral bevel gears with 38/43 teeth numbers.The four analytical results are compared with each other and show that the incomplete modified roll is optimal for this gear pair.This study is an expansion to generation strategy of spiral bevel gears,and offers new alternatives to computer numerical control（CNC） manufacture of spiral bevel gears.展开更多
Cycloid speed reducers are widely used in many industrial areas due to the advantages of compact size, high reduction ratio and high stiffness. However, currently, there are not many analytical models for the mesh sti...Cycloid speed reducers are widely used in many industrial areas due to the advantages of compact size, high reduction ratio and high stiffness. However, currently, there are not many analytical models for the mesh stiffness calculation, which is a crucial parameter for the high-fidelity gear dynamic model. This is partially due to the difficulty of backlash determination and the complexity of multi-tooth contact deformation during the meshing process. In this paper, a new method to calculate the mesh stiffness is proposed including the effects of tooth profile modification and eccentricity error. The time-varying mesh parameters and load distribution of cycloid-pin gear pair are determined based on the unloaded tooth contact analysis （TCA） and the nonlinear Hertzian contact theory, allowing accurate calculations of the contact stiffness of single tooth pair and the torsional stiffness of multi-tooth pairs. A detailed parametric study is presented to demonstrate the influences of tooth profile modification, applied torque and eccentricity error on the torsional mesh stiffness, loaded transmission error, Hertzian contact stiffness and load sharing factor. This model can be applied to further study the lost motion and dynamic characteristics of cycloid speed reducer and assist the optimization of its precision, vibration and noise levels.展开更多
According to the defect of traditional method of determining instantaneous contact regions for conjugate surfaces, a numerical approach to the determination is proposed. A local coordinate system is built by using the...According to the defect of traditional method of determining instantaneous contact regions for conjugate surfaces, a numerical approach to the determination is proposed. A local coordinate system is built by using the surface unit tangent and unit normal at the contact point. Considering that the gap forming the boundary of instantaneous contact region in the direction of the common normal vectors is given, a system of nonlinear equations is built to find the instantaneous contact boundary in local coordinate system, a modified Powell＇s hybrid algorithm of finite-difference approximation to the Jacobian used to solve the system. The new method simplifies the task of determining instantaneous contact regions without calculating curvatm＇e and relative curvature. The validity of the proposed approach is verified by an example of hypoid gears.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
Although a great deal of research has been dedicated to the synthesis of spiral bevel gears, little related to reverse engineering can be found. An approach is proposed to reverse the machine-tool settings of the pini...Although a great deal of research has been dedicated to the synthesis of spiral bevel gears, little related to reverse engineering can be found. An approach is proposed to reverse the machine-tool settings of the pinion of a spiral bevel gear drive on the basis of the blank and tooth surface data obtained by a coordinate measuring machine(CMM). Real tooth contact analysis(RTCA) is performed to preliminary ascertain the contact pattern, the motion curve, as well as the position of the mean contact point. And then the tangent to the contact path and the motion curve are interpolated in the sense of the least square method to extract the initial values of the bias angle and the higher order coefficients(HOC) in modified roll motion. A trial tooth surface is generated by machine-tool settings derived from the local synthesis relating to the initial meshing performances and modified roll motion. An optimization objective is formed which equals the tooth surface deviation between the real tooth surface and the trial tooth surface. The design variables are the parameters describing the meshing performances at the mean contact point in addition to the HOC. When the objective is optimized within an arbitrarily given convergence tolerance, the machine-tool settings together with the HOC are obtained. The proposed approach is verified by a spiral bevel pinion used in the accessory gear box of an aviation engine. The trial tooth surfaces approach to the real tooth surface on the whole in the example. The results show that the convergent tooth surface deviation for the concave side on the average is less than 0.5 μm, and is less than 1.3 μm for the convex side. The biggest tooth surface deviation is 6.7 μm which is located at the corner of the grid on the convex side. Those nodes with relative bigger tooth surface deviations are all located at the boundary of the grid. An approach is proposed to figure out the machine-tool settings of a spiral bevel pinion by way of reverse engineering without having known the theoretical tooth surfaces and the corresponding machine-tool settings.展开更多
A direct digital design method （DDDM） of worm-gear drive is proposed. It is directly based on the simulation of manufacturing process and completely different from the conventional modeling method. The loaded tooth ...A direct digital design method （DDDM） of worm-gear drive is proposed. It is directly based on the simulation of manufacturing process and completely different from the conventional modeling method. The loaded tooth contact analysis （LTCA） method is analyzed, in which the advanced surface to surface searching technique is included. The influence of misalignment errors and contact deformations on contact zone and transmission error （TE） is discussed. Combined modification approach on worm tooth surface is presented. By means of DDDM and LTCA, it is very conven- ient to verify the effect of worm-gear drive＇s modification approach. The analysis results show that, the modification in profile direction reduces the sensitivity of worm-gear drive to misalignment errors and the modification in longitudinal direction decreases the TE. Thus the optimization design of worm-gear drive can be achieved prior to the actual manufacturing process.展开更多
Gears play an important role in mechanical engineering because of their moment and speed transmission possibilities. Design and optimization of a complete gearbox provide many requirements to the designer. The complex...Gears play an important role in mechanical engineering because of their moment and speed transmission possibilities. Design and optimization of a complete gearbox provide many requirements to the designer. The complex gearbox model consists of many machine elements （shafts, gears, bearings, housing, seals, and shaft-hub connections）. The gearbox must be understood as a system with interactive parts. Next to the calculation of kinematics, load capacities and life times of single elements, aspects of load distribution and efficiency and noise excitation of gearboxes become important. The wide range of knowhow needed mostly cannot be covered by a small number of engineers. The development of automated calculation routines with understandable and comprehensive results is the goal for these research projects that lead to sottware-realizing solutions for engineers to efficiently design, calculate, optimize and verify gearboxes with minimal resources in terms of calculation experts and time.展开更多
This paper proposes a new approach to mial function of transmission error （TE） for spiral design and implement a seventh-order polyno- bevel gears with an aim to reduce the running vibration and noise of gear drive ...This paper proposes a new approach to mial function of transmission error （TE） for spiral design and implement a seventh-order polyno- bevel gears with an aim to reduce the running vibration and noise of gear drive and improve the loaded distribution of the tooth. Based on the constraint conditions of predesigned seventh-order polynomial function curve and the theory of linear algebra, the polynomial coefficients of the seventh-order polynomial function of transmission error can be obtained. By applying a method named reverse tooth contact analysis, the modified roll coefficients as well as parts of machine-tool settings for the face-milling of spiral bevel gears can be individually determined. Therefore, a predesigned seventh-order polynomial function of transmission error for spiral bevel gears can be obtained by the modified roll with high-order coef- ficients, and comparisons of the seventh-order polynomial and parabolic functions of transmission error are also performed. The achievement of spiral bevel gears with the seventh-order function of transmission error can be accomplished on a universal Cartesian-type hypoid gear generator or a numerically controlled cradle-style hypoid gear generator due to its simple generating motion of axes of the cradle and the work piece. The results of a numerical example show that the bending stresses of the tooth of seventh-order are less than those of a parabolic one, while the contact stresses remain almost eouivalent.展开更多
基金supported by Fundamental Research Funds for Central Universities of China (Grant No. CDJXS11111138,Key Projects in the National Science & Technology Pillar Program during the 11th Five-Year Plan Period of China(Grant No. 2011BAF09B07)National Natural Science Foundatlon of China(Grant No. 51175523)
文摘Beveloid gears,also known as conical gears,gain more and more importance in industry practice due to their abilities for power transmission between parallel,intersected and crossed axis.However,this type of gearing with crossed axes has no common plane of action which results in a point contact and low tooth durability.Therefore,a geometry design approach assuming line contact is developed to analyze the tooth engagement process of crossed beveloid gears with small shaft angle for marine transmission applications.The loaded gear tooth contact behavior is simulated by applying a quasi-static analysis to study the effects of gearing parameters on mesh characteristics.Using the proposed method,a series of sensitivity analyses to examine the effects of critical gearing parameters such as shaft angle,cone angle,helix angle and profile-shift coefficient on the theoretical gear mesh is performed.The parametric analysis of pitch cone design shows that the dominant design parameters represented by the angle between the first principle directions（FPD） and normal angular factor are more sensitive to the shaft and cone angles than they are to the helix angle.The theoretical contact path is highly sensitive to the profile-shift coefficient,which is determined from the theoretical tooth contact analysis.The FPD angle is found to change the distribution of contact pattern,contact pressure and root stress as well as the translational transmission error and the variation of the mesh stiffness significantly.The contact pattern is clearly different between the drive and coast sides due to different designed FPD angles.Finally,a practical experimental setup for marine transmission is performed and tooth bearing test is conducted to demonstrate the proposed design procedure.The experimental result compared well with the simulation.Results of this study yield a better understanding of the geometry design and loaded gear mesh characteristics for crossed beveloid gears used in marine transmission.
基金Project(52175361)supported by the National Natural Science Foundation of ChinaProject(2019 CFA 041)supported by the Natural Science Foundation of Hubei Province,ChinaProject(WUT:202407002)supported by the Fundamental Research Funds for the Central Universities,China。
文摘A novel spiral non-circular bevel gear that could be applied to variable-speed driving in intersecting axes was proposed by combining the design principles of non-circular bevel gears and the manufacturing principles of face-milling spiral bevel gears.Unlike straight non-circular bevel gears,spiral non-circular bevel gears have numerous advantages,such as a high contact ratio,high intensity,good dynamic performance,and an adjustable contact region.In addition,while manufacturing straight non-circular bevel gears is difficult,spiral non-circular bevel gears can be efficiently and precisely fabricated with a 6-axis bevel gear cutting machine.First,the generating principles of spiral non-circular bevel gears were introduced.Next,a mathematical model,including a generating tooth profile,tooth spiral,pressure angle,and generated tooth profile for this gear type was established.Then the precision of the model was verified by a tooth contact analysis using FEA,and the contact patterns and stress distributions of the spiral non-circular bevel gears were investigated.
文摘The mathematical model of conical involute gears is developed based on the theory of gearing and the generating mechanism. Tooth contact analysis （TCA） is performed to examine the meshing and bearing contact of the conical involute gear pairs with intersected and crossed axes. In addition, the principal directions and curvatures of the gear surfaces are investigated and the contact ellipses of the mating tooth surfaces are also studied. Finally, the numerical illustrative examples are provided to demonstrate the computational results, test gears are made for tooth-bearing tests, and the conclusion is verified that the theory has the applicability.
基金Project(51805368)supported by the National Natural Science Foundation of ChinaProject(2018QNRC001)supported by the Young Elite Scientists Sponsorship Program,China+1 种基金Project(DMETKF2021017)supported by the Fund of State Key Laboratory of Digital Manufacturing Equipment and Technology,Huazhong University of Science and Technology,ChinaProject(HTL-0-21G07)supported by the National key Laboratory of Science and Technology on Heicopter Transmission,China。
文摘A complex geometric modeling method of a helical face gear pair with arc-tooth generated by an arc-profile cutting(APC)disc is proposed,and its tooth contact characteristics are analyzed.Firstly,the spatial coordinate system of an APC face gear pair is established based on meshing theory.Combining the coordinate transformation matrix and the tooth profile of the cutter,the equations of the curve envelope of the APC face gear pair are obtained.Then the surface equations are solved to extract the point clouds data by programming in MATLAB,which contains the work surface and the fillet surface of the APC face gear pair.And the complex geometric model of the APC face gear pair is built by fitting its point clouds.At last,through the analysis of the tooth surface contact,the sensitivity of the APC face gear to the different types of mounting errors is obtained.The results show that the APC face gear pair is the most sensitive to mounting errors in the tooth thickness direction,and it should be strictly controlled in the actual application.
基金supported by the Natural Science Foundation of China under Grant No.51175423
文摘In order to implement the dynamic characteristic of a dual power-split transmission, a dynamic me- chanics model is built. Firstly, according to the method of theoretical analysis of the tooth contact analysis （TCA） and loaded tooth contact analysis （LTCA）, the actual meshing process of each gear pairs is simulated, and the time-varying mesh stiffness excitations are obtained, which can improve the numerical precision. Second- ly, by using the lumped mass method, the bending-torsional coupling three dimensional dynamic model of the dual power-split transmission is established, and the identical dimensionless equations are deduced by elimina- ting the effect of rigid displacement and the method of dimensional normalization. Finally, by the method of the fourth order Runge-Kutta algorithm with variable step lengths, the responses of this system in a frequency domain and time domain are obtained, and the dynamic load change characteristics of each gear pairs are analyzed. The results show that the establishment, solution and analysis of the system dynamics model could provide a basis for the dynamic design, and have an important significance for the dynamic efficiency analysis and dynamic perform- ance optimization design of the dual power-split transmission.
基金the Doctorate Degree Program Foundation of the Ministry of Education (No. 2000061120)
文摘An approach for the contact analysis and load distribution of double-envelop hourglass worm gearing is presented, which is based on a 3-D elastic contact finite element method (FEM) model that accommodates the influence of errors and load. As compared with existing tooth contact analysis model that assumes rigidity for the contacting surfaces, the proposed model provides a more realistic analysis on the contact patterns, the distribution of contact load and transmission errors. It is also capable of exploring the influence of different errors on meshing performances, the contact deformation, the shift of the contact zone and load share among the meshing tooth-pairs under different load.
基金National Natural Science Foundation of China(No.51205425)National Science&Technology Pillar Program during the 12th Five-Year Plan Period of China(No.2013BAF01B04)
文摘The transmission characteristics of gear drive can be improved with the use of novel tooth profiles.A theoretical study on tooth profile of the hypocycloid pinwheel transmission and contact analysis of gear pair based on finite element method(FEM) are carried out,respectively.The line contact between mated tooth surfaces becomes point contact according to a plus movement.Through loaded tooth contact analysis(LTCA),the contact stress and load distributions for the proposed hypocycloid pinwheel transmission and the traditional one are discussed.The analysis results show that the developed tooth surfaces have anticipatory point contact characteristics under loads and contact fatigue dangerous area locates around the ultimate contact position.
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.
文摘Aviation spiral bevel gears are often generated by spiral generated modified（SGM） roll method.In this style,pinion tooth surface modified generation strategy has an important influence on the meshing and contact performances.For the optimal contact pattern and transmission error function,local synthesis is applied to obtain the machine-tool settings of pinion.For digitized machine,four tooth surface generation styles of pinion are proposed.For every style,tooth contact analysis（TCA） is applied to obtain contact pattern and transmission error function.For the difference between TCA transmission error function and design objective curve,the degree of symmetry and agreement are defined and the corresponding sub-objective functions are established.Linear weighted combination method is applied to get an equivalent objective function to evaluate the shape of transmission error function.The computer programs for the process above are developed to analyze the meshing performances of the four pinion tooth surface generation styles for a pair of aviation spiral bevel gears with 38/43 teeth numbers.The four analytical results are compared with each other and show that the incomplete modified roll is optimal for this gear pair.This study is an expansion to generation strategy of spiral bevel gears,and offers new alternatives to computer numerical control（CNC） manufacture of spiral bevel gears.
基金Project(51575062)supported by the National Natural Science Foundation of ChinaProject(51605049)supported by the National Natural Science Foundation for Young Scholar of ChinaProject(BA2015177)supported by the Science and Technology Achievements Transformation Program of Jiangsu Province of China
文摘Cycloid speed reducers are widely used in many industrial areas due to the advantages of compact size, high reduction ratio and high stiffness. However, currently, there are not many analytical models for the mesh stiffness calculation, which is a crucial parameter for the high-fidelity gear dynamic model. This is partially due to the difficulty of backlash determination and the complexity of multi-tooth contact deformation during the meshing process. In this paper, a new method to calculate the mesh stiffness is proposed including the effects of tooth profile modification and eccentricity error. The time-varying mesh parameters and load distribution of cycloid-pin gear pair are determined based on the unloaded tooth contact analysis （TCA） and the nonlinear Hertzian contact theory, allowing accurate calculations of the contact stiffness of single tooth pair and the torsional stiffness of multi-tooth pairs. A detailed parametric study is presented to demonstrate the influences of tooth profile modification, applied torque and eccentricity error on the torsional mesh stiffness, loaded transmission error, Hertzian contact stiffness and load sharing factor. This model can be applied to further study the lost motion and dynamic characteristics of cycloid speed reducer and assist the optimization of its precision, vibration and noise levels.
基金National Education Dep.of China (No. 20060056016)National Hi-tech Research and Development Program of China(863 Program, No. 2007AA042005, No. 2006AA 04Z146).
文摘According to the defect of traditional method of determining instantaneous contact regions for conjugate surfaces, a numerical approach to the determination is proposed. A local coordinate system is built by using the surface unit tangent and unit normal at the contact point. Considering that the gap forming the boundary of instantaneous contact region in the direction of the common normal vectors is given, a system of nonlinear equations is built to find the instantaneous contact boundary in local coordinate system, a modified Powell＇s hybrid algorithm of finite-difference approximation to the Jacobian used to solve the system. The new method simplifies the task of determining instantaneous contact regions without calculating curvatm＇e and relative curvature. The validity of the proposed approach is verified by an example of hypoid gears.
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.
基金supported by Aero Propulsion Test and Demonstration of Commission of Science and Technology and Industry for Nation Defense,China (Grant No. APTD-1001B)
文摘Although a great deal of research has been dedicated to the synthesis of spiral bevel gears, little related to reverse engineering can be found. An approach is proposed to reverse the machine-tool settings of the pinion of a spiral bevel gear drive on the basis of the blank and tooth surface data obtained by a coordinate measuring machine(CMM). Real tooth contact analysis(RTCA) is performed to preliminary ascertain the contact pattern, the motion curve, as well as the position of the mean contact point. And then the tangent to the contact path and the motion curve are interpolated in the sense of the least square method to extract the initial values of the bias angle and the higher order coefficients(HOC) in modified roll motion. A trial tooth surface is generated by machine-tool settings derived from the local synthesis relating to the initial meshing performances and modified roll motion. An optimization objective is formed which equals the tooth surface deviation between the real tooth surface and the trial tooth surface. The design variables are the parameters describing the meshing performances at the mean contact point in addition to the HOC. When the objective is optimized within an arbitrarily given convergence tolerance, the machine-tool settings together with the HOC are obtained. The proposed approach is verified by a spiral bevel pinion used in the accessory gear box of an aviation engine. The trial tooth surfaces approach to the real tooth surface on the whole in the example. The results show that the convergent tooth surface deviation for the concave side on the average is less than 0.5 μm, and is less than 1.3 μm for the convex side. The biggest tooth surface deviation is 6.7 μm which is located at the corner of the grid on the convex side. Those nodes with relative bigger tooth surface deviations are all located at the boundary of the grid. An approach is proposed to figure out the machine-tool settings of a spiral bevel pinion by way of reverse engineering without having known the theoretical tooth surfaces and the corresponding machine-tool settings.
基金This project is supported by National Natural Science Foundation of China (No.E50575234).
文摘A direct digital design method （DDDM） of worm-gear drive is proposed. It is directly based on the simulation of manufacturing process and completely different from the conventional modeling method. The loaded tooth contact analysis （LTCA） method is analyzed, in which the advanced surface to surface searching technique is included. The influence of misalignment errors and contact deformations on contact zone and transmission error （TE） is discussed. Combined modification approach on worm tooth surface is presented. By means of DDDM and LTCA, it is very conven- ient to verify the effect of worm-gear drive＇s modification approach. The analysis results show that, the modification in profile direction reduces the sensitivity of worm-gear drive to misalignment errors and the modification in longitudinal direction decreases the TE. Thus the optimization design of worm-gear drive can be achieved prior to the actual manufacturing process.
文摘Gears play an important role in mechanical engineering because of their moment and speed transmission possibilities. Design and optimization of a complete gearbox provide many requirements to the designer. The complex gearbox model consists of many machine elements （shafts, gears, bearings, housing, seals, and shaft-hub connections）. The gearbox must be understood as a system with interactive parts. Next to the calculation of kinematics, load capacities and life times of single elements, aspects of load distribution and efficiency and noise excitation of gearboxes become important. The wide range of knowhow needed mostly cannot be covered by a small number of engineers. The development of automated calculation routines with understandable and comprehensive results is the goal for these research projects that lead to sottware-realizing solutions for engineers to efficiently design, calculate, optimize and verify gearboxes with minimal resources in terms of calculation experts and time.
基金the National Science Foundation of China (Nos.51205310 and 51175423)the Fundamental Research Funds for the Central Universities (Nos.2013G3252005 and 2013G2252027)
文摘This paper proposes a new approach to mial function of transmission error （TE） for spiral design and implement a seventh-order polyno- bevel gears with an aim to reduce the running vibration and noise of gear drive and improve the loaded distribution of the tooth. Based on the constraint conditions of predesigned seventh-order polynomial function curve and the theory of linear algebra, the polynomial coefficients of the seventh-order polynomial function of transmission error can be obtained. By applying a method named reverse tooth contact analysis, the modified roll coefficients as well as parts of machine-tool settings for the face-milling of spiral bevel gears can be individually determined. Therefore, a predesigned seventh-order polynomial function of transmission error for spiral bevel gears can be obtained by the modified roll with high-order coef- ficients, and comparisons of the seventh-order polynomial and parabolic functions of transmission error are also performed. The achievement of spiral bevel gears with the seventh-order function of transmission error can be accomplished on a universal Cartesian-type hypoid gear generator or a numerically controlled cradle-style hypoid gear generator due to its simple generating motion of axes of the cradle and the work piece. The results of a numerical example show that the bending stresses of the tooth of seventh-order are less than those of a parabolic one, while the contact stresses remain almost eouivalent.
