During high-speed rotation,the surface of aeronautic spiral bevel gears will generate significant pressure and viscous forces,which will cause a certain amount of windage power loss and reduce the efficiency of the tr...During high-speed rotation,the surface of aeronautic spiral bevel gears will generate significant pressure and viscous forces,which will cause a certain amount of windage power loss and reduce the efficiency of the transmission system.Based on the computational fluid dynamics,this paper analyzes the windage power loss of a single spiral bevel gear and a spiral bevel gear pair under oil injection lubrication.In addition,the shroud is used to suppress gear windage loss,and the clearance size and opening angle of the designed shroud are optimized.Finally,by comparing and analyzing the experimental results,the following conclusions were obtained:(1)For a single gear,the speed is the most important factor affecting windage loss,followed by the hand of spiral,and rotation direction;(2)For gear pairs,under oil injection lubrication,the input speed has the greatest impact on windage power loss,followed by the influence of oil injection port speed,temperature and oil injection port pressure;(3)Installing a shroud is an effective method to reduce windage power loss;(4)In the pure air phase,the smaller the clearance between the shroud and the gear surface,and the smaller the radial direction between the shroud and the shaft,the better the effect of reducing windage;(5)In the two-phase flow of oil and gas,it is necessary to design oil drainage holes on the shroud to ensure the smooth discharge of lubricating oil and improve the drag reduction effect.展开更多
Spiral bevel gears are critical transmission components,and are widely used in the aerospace field.This paper proposes a new multi-DOF envelope forming process for fabricating spiral bevel gears.Firstly,the multi-DOF ...Spiral bevel gears are critical transmission components,and are widely used in the aerospace field.This paper proposes a new multi-DOF envelope forming process for fabricating spiral bevel gears.Firstly,the multi-DOF envelope forming principle of spiral bevel gears is proposed.Secondly,the design methods for the envelope tool geometry and movement are proposed based on the envelope geometry and movement relationships.Thirdly,the metal flow and tooth filling laws are revealed through 3D FE simulation of the multi-DOF envelope forming process of a typical spiral bevel gear.Fourthly,a new method for separating the envelope tool and the formed spiral bevel gear with back taper tooth is proposed to avoid their interference.Finally,experiments on multi-DOF envelope forming of this typical spiral bevel gear are conducted using new heavy load multi-DOF envelope forming equipment.The simulation and experimental results show the feasibility of the proposed multi-DOF envelope forming process for fabricating spiral bevel gears with back taper tooth and the corresponding process design methods.展开更多
Tooth cracks may occur in spiral bevel gear transmission system of the aerospace equipment.In this study,an accurate and efficient loaded tooth contact analysis(LTCA)model is developed to predict the contact behavior ...Tooth cracks may occur in spiral bevel gear transmission system of the aerospace equipment.In this study,an accurate and efficient loaded tooth contact analysis(LTCA)model is developed to predict the contact behavior and time-varying meshing stiffness(TVMS)of spiral bevel gear pair with cracked tooth.The tooth is sliced,and the contact points on slices are computed using roll angle surfaces.Considering the geometric complexity of crack surface,a set of procedures is formulated to generate spatial crack and determine crack parameters for contact points.According to the positional relationship between contact point and crack path,each sliced tooth is modeled as a non-uniform cantilever beam with varying reduced effective load-bearing tooth thickness.Then the compliance model of the cracked tooth is established to perform contact analysis,along with TVMS calculations utilizing three different models.By employing spiral bevel gear pairs with distinct types of cracks as examples,the accuracy and efficiency of the developed approach are validated via comparative analyses with finite element analysis(FEA)outcomes.Furthermore,the investigation on effects of cracks shows that tooth cracks can induce alterations in meshing performance of both entire gear pair and individual tooth pairs,including not only cracked tooth pair but also adjacent non-cracked tooth pairs.Hence,the proposed model can serve as a useful tool for analyzing the variations in contact behavior and meshing stiffness of spiral bevel gears due to different cracks.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
A geometric modeling method for generating-manufactured spiral bevel gears（SBGs） is proposed. It consists of two steps： （1） creating a reference model by simulating the process of cutting spiral bevel gear,（2） ...A geometric modeling method for generating-manufactured spiral bevel gears（SBGs） is proposed. It consists of two steps： （1） creating a reference model by simulating the process of cutting spiral bevel gear,（2） reconstructing the final solid model by collecting data points from the reference model and fitting these points into NURBS surfaces. In this method,cutting simulation avoids abstruse mathematical theories and complex methods,thus making it convenient to obtain data points on the complex tooth surface before the gear is manufactured and efficient to increase the accuracy of the solid model. Also,the representations of tooth surfaces of the final model is unified as a NURBS surface function. The NURBS surface is continuous and smooth,thus it is available for wide applications in CAD/CAE. The experiment proves that the method can be used to establish an accurate pair of SBG models,thus providing a feasible and effective way for CAD/CAE modeling.展开更多
The generating motion of the generating gear and the work gear on spiral bevel gear NC machining is analyzed. The mathematical model of the tooth surface of spiral bevel gear is presented. A direct interpolation algor...The generating motion of the generating gear and the work gear on spiral bevel gear NC machining is analyzed. The mathematical model of the tooth surface of spiral bevel gear is presented. A direct interpolation algorithm of spiral bevel gear NC machining is proposed, thus establishing the relationship between the motion of the cutter-head center and the rotation of the work gear. The interpolation algorithm is implemented to control the gear cutting on self-developed spiral bevel gear NC cutting machine. An example is given to verify the mathematical model and the interpolation algorithm.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
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
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
Austempered ductile iron （ADI） has several advantages of replacing cast steel and forged steel in many engineering fields. A new Mn-Cu alloyed ADI with excellent mechanical properties has been developed in order to ...Austempered ductile iron （ADI） has several advantages of replacing cast steel and forged steel in many engineering fields. A new Mn-Cu alloyed ADI with excellent mechanical properties has been developed in order to cut the cost and enlarge the application of ADI. The helical bevel gears were made of the new-developed Mn-Cu alloyed ADI. The microstructure and mechanical properties of the standard sample were investigated by optical microscope （OM）, scanning electron microscope （SEM） and performance measurement. The results showed that after a series of treatments, the mechanical properties （Rm 1007. 4 to 1200 MPa, A 5.2% to 8. 8%, HRC 32 to HRC 35, O^K 70 to 120 J/cmz ） of the Mn-Cu alloyed ADI standard sample could reach European standard EN1564-97/ EN-CJS-1000-5. The surface hardness after helical bevel gears meshing was significantly increased due to the formation of martensite. The bench test and traffic running testing results suggested that the new Mn-Cu alloyed ADI with ultimate life and median life respectively exceeding 30×104 and 50 × 10^4 times could replace 20CrMnTi forged steel for manufacturing the EQ140 helical bevel gears.展开更多
This paper presents a method for measurement of deviation of the real gear tooth surface from the theoretical one with a coordinate measurement machine and compensation of repeatable parts. By investigation of charact...This paper presents a method for measurement of deviation of the real gear tooth surface from the theoretical one with a coordinate measurement machine and compensation of repeatable parts. By investigation of characteristics of distortion of the gear tooth surface along the circle direction, the deviation is derived from distortion, and the definition of deviation with the geometrical invariability is proposed. Then the approach for determination of the location and orientation of the gear with respect to the coordinate measurement machine and the measurement way are developed. The deviation is represented with a difference surface, and an algorithm for derivation of parameters of global form deviations from the discrete points has been provided. Finally, the compensation approach is discussed.展开更多
The aim of this work is to propose a 3D FE model of a theoretical assembling straight bevel gear pair to analyze the contact fatigue on the tooth surface and the bending fatigue in the tooth root. Based on the cumulat...The aim of this work is to propose a 3D FE model of a theoretical assembling straight bevel gear pair to analyze the contact fatigue on the tooth surface and the bending fatigue in the tooth root. Based on the cumulative fatigue criterion and the stress-life equation, the key meshing states of the gear pair were investigated for the contact fatigue and the bending fatigue. Then, the reliability of the proposed model was proved by comparing the calculation result with the simulation result. Further study was performed to analyze the variation of the contact fatigue stress and the bending fatigue stress under different loads. Furthermore, the roles of the driving pinion and the driven gear pair were evaluated in the fatigue life of the straight bevel gear pair and the main fatigue failure mode was determined for the significant gear. The results show that the fatigue failure of the driving pinion is the main fatigue failure for the straight bevel gear pair and the bending fatigue failure is the main fatigue failure for the driving pinion.展开更多
In order to effectively improve meshing performance of spiral bevel and hypoid gears generated by the duplex helical method, the effects of straight lined and circular cutting edges profile on meshing and contact of s...In order to effectively improve meshing performance of spiral bevel and hypoid gears generated by the duplex helical method, the effects of straight lined and circular cutting edges profile on meshing and contact of spiral bevel and hypoid gears were investigated analytically. Firstly, a mathematical model of spiral bevel and hypoid gears with circular blade profile was established according to the cutting characteristics of the duplex helical method. Based on a hypoid gear drive, the tooth bearings and the functions of transmission errors of four design cases were analyzed respectively by the use of the tooth contact analysis(TCA), and the contact stresses of the four design cases were analyzed and compared using simulation software. Finally, the curvature radius of the circular profile blade was optimized. The results show that the contact stresses are availably reduced, and the areas of edge contact and severe contact stresses can be avoided by selecting appropriate circular blade profile. In addition, the convex and concave sides are separately modified by the use of different curvature radii of inside and outside blades, which can increase the flexibility of the duplex helical method.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 closed-died cold forging technology of the bevel gears used in Jada car was investigated. With the analysis of the strain field and velocity field of the plastic deformation and the endured forces of the dies, the...The closed-died cold forging technology of the bevel gears used in Jada car was investigated. With the analysis of the strain field and velocity field of the plastic deformation and the endured forces of the dies, the filling rules for the metal were analyzed by the elastic-plastic finite element method （FEM）. The results show that there is a great difference among closed-die cold forging, extrusion and forging, as far as the metal flowing is concerned. The outer addendum cannot be filled completely in the closed-die cold forging of the bevel gears, and the round angle will be formed. But it does not influence the application of the bevel gears. At the beginning, the rigid area is formed in the cavity of the lower die. And then it will move upwards to supply the metal for the gear filling. For the closed-die cold forging of the bevel gears, the force acting on the upper die and the lower die is significantly different.展开更多
The effect of static transmission error on nonlinear dynamic response of the spiral bevel gear system combining with time-varying stiffness and backlash was investigated.Firstly,two different control equations of the ...The effect of static transmission error on nonlinear dynamic response of the spiral bevel gear system combining with time-varying stiffness and backlash was investigated.Firstly,two different control equations of the spiral bevel gear model were adopted,where the static transmission error was expressed in two patterns as predesigned parabolic function and sine function of transmission errors.The dynamic response,bifurcation map,time domain response,phase curve and Poincare map were obtained by applying the explicit Runge-Kutta integration routine with variable-step.A comparative study was carried out and some profound phenomena were detected.The results show that there are many different kinds of tooth rattling phenomena at low speed.With the increase of speed,the system enters into stable motion without any rattling in the region(0.72,1.64),which indicates that the system with predesigned parabolic function of transmission error has preferable capability at high speed.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
Six-axis numerical control spiral bevel gear grinder was taken as the object, multi-body system theory and Denavit-Hartenberg homogeneous transformed matrix （HTM） were utilized to establish the grinder synthesis err...Six-axis numerical control spiral bevel gear grinder was taken as the object, multi-body system theory and Denavit-Hartenberg homogeneous transformed matrix （HTM） were utilized to establish the grinder synthesis error model, and the validity of model was confirmed by the experiment. Additionally, in grinding wheel tool point coordinate system, the errors of six degrees of freedom were simulated when the grinding wheel revolving around C-axis, moving along X-axis and Y-axis. The influence of these six errors on teeth space, helix angle, pitch, teeth profile was discussed. The simulation results show that the angle error is in the range from -0.148 4 tad to -0.241 9 rad when grinding wheel moving along X, Y-axis; the translation error is in the range from 0.866 0 μm to 3.605 3μm when grinding wheel moving along X-axis. These angle and translation errors have a great influence on the helix angle, pitch, teeth thickness and tooth socket.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 novel fiber Bragg grating(FBG)displacement sensor is proposed,which can achieve wide measuring range displacement detection with variable measurement precision due to its mechanical transfer structure of helical bev...A novel fiber Bragg grating(FBG)displacement sensor is proposed,which can achieve wide measuring range displacement detection with variable measurement precision due to its mechanical transfer structure of helical bevel gear.A prototype is designed and fabricated.The maximum detection displacement of this prototype is 1.751 m,and the precision grade changes from 0.2%to 6.7%.Through analyzing the experiment data which is obtained in the calibration experiment,the measuring range of this sensor is from 0 m to 1.532 m,and the wavelength shift errors between experiment data and theory calculation are all less than 5%.展开更多
基金Supported by National Natural Science Foundation of China(Grant Nos.51175422,61973011)Shaanxi Provincial Natural Science Basic Research Plan of China(Grant No.2022JM-195)+1 种基金Fundamental Research Funds for the Central Universities of Chinathe Research Start-up Funds of Hangzhou International Innovation Institute of Beihang University(Grant No.2024KQ036)。
文摘During high-speed rotation,the surface of aeronautic spiral bevel gears will generate significant pressure and viscous forces,which will cause a certain amount of windage power loss and reduce the efficiency of the transmission system.Based on the computational fluid dynamics,this paper analyzes the windage power loss of a single spiral bevel gear and a spiral bevel gear pair under oil injection lubrication.In addition,the shroud is used to suppress gear windage loss,and the clearance size and opening angle of the designed shroud are optimized.Finally,by comparing and analyzing the experimental results,the following conclusions were obtained:(1)For a single gear,the speed is the most important factor affecting windage loss,followed by the hand of spiral,and rotation direction;(2)For gear pairs,under oil injection lubrication,the input speed has the greatest impact on windage power loss,followed by the influence of oil injection port speed,temperature and oil injection port pressure;(3)Installing a shroud is an effective method to reduce windage power loss;(4)In the pure air phase,the smaller the clearance between the shroud and the gear surface,and the smaller the radial direction between the shroud and the shaft,the better the effect of reducing windage;(5)In the two-phase flow of oil and gas,it is necessary to design oil drainage holes on the shroud to ensure the smooth discharge of lubricating oil and improve the drag reduction effect.
基金the National Science and Technology Major Project of China(No.2019-VII0017e0158)the National Natural Science Foundation of China(No.U21A20131)+1 种基金the Industry-University Research Cooperation Project,China(No.HFZL2020CXY025)the National Key Laboratory of Science and Technology on Helicopter Transmission,China(No.HTL-O-21G05).
文摘Spiral bevel gears are critical transmission components,and are widely used in the aerospace field.This paper proposes a new multi-DOF envelope forming process for fabricating spiral bevel gears.Firstly,the multi-DOF envelope forming principle of spiral bevel gears is proposed.Secondly,the design methods for the envelope tool geometry and movement are proposed based on the envelope geometry and movement relationships.Thirdly,the metal flow and tooth filling laws are revealed through 3D FE simulation of the multi-DOF envelope forming process of a typical spiral bevel gear.Fourthly,a new method for separating the envelope tool and the formed spiral bevel gear with back taper tooth is proposed to avoid their interference.Finally,experiments on multi-DOF envelope forming of this typical spiral bevel gear are conducted using new heavy load multi-DOF envelope forming equipment.The simulation and experimental results show the feasibility of the proposed multi-DOF envelope forming process for fabricating spiral bevel gears with back taper tooth and the corresponding process design methods.
基金co-supported by the National Natural Science Foundation of China (No. 52175104)the Postdoctoral Fellowship Program of CPSF (No. GZC20233008)
文摘Tooth cracks may occur in spiral bevel gear transmission system of the aerospace equipment.In this study,an accurate and efficient loaded tooth contact analysis(LTCA)model is developed to predict the contact behavior and time-varying meshing stiffness(TVMS)of spiral bevel gear pair with cracked tooth.The tooth is sliced,and the contact points on slices are computed using roll angle surfaces.Considering the geometric complexity of crack surface,a set of procedures is formulated to generate spatial crack and determine crack parameters for contact points.According to the positional relationship between contact point and crack path,each sliced tooth is modeled as a non-uniform cantilever beam with varying reduced effective load-bearing tooth thickness.Then the compliance model of the cracked tooth is established to perform contact analysis,along with TVMS calculations utilizing three different models.By employing spiral bevel gear pairs with distinct types of cracks as examples,the accuracy and efficiency of the developed approach are validated via comparative analyses with finite element analysis(FEA)outcomes.Furthermore,the investigation on effects of cracks shows that tooth cracks can induce alterations in meshing performance of both entire gear pair and individual tooth pairs,including not only cracked tooth pair but also adjacent non-cracked tooth pairs.Hence,the proposed model can serve as a useful tool for analyzing the variations in contact behavior and meshing stiffness of spiral bevel gears due to different cracks.
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A geometric modeling method for generating-manufactured spiral bevel gears（SBGs） is proposed. It consists of two steps： （1） creating a reference model by simulating the process of cutting spiral bevel gear,（2） reconstructing the final solid model by collecting data points from the reference model and fitting these points into NURBS surfaces. In this method,cutting simulation avoids abstruse mathematical theories and complex methods,thus making it convenient to obtain data points on the complex tooth surface before the gear is manufactured and efficient to increase the accuracy of the solid model. Also,the representations of tooth surfaces of the final model is unified as a NURBS surface function. The NURBS surface is continuous and smooth,thus it is available for wide applications in CAD/CAE. The experiment proves that the method can be used to establish an accurate pair of SBG models,thus providing a feasible and effective way for CAD/CAE modeling.
文摘The generating motion of the generating gear and the work gear on spiral bevel gear NC machining is analyzed. The mathematical model of the tooth surface of spiral bevel gear is presented. A direct interpolation algorithm of spiral bevel gear NC machining is proposed, thus establishing the relationship between the motion of the cutter-head center and the rotation of the work gear. The interpolation algorithm is implemented to control the gear cutting on self-developed spiral bevel gear NC cutting machine. An example is given to verify the mathematical model and the interpolation algorithm.
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.
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.
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.
文摘Austempered ductile iron （ADI） has several advantages of replacing cast steel and forged steel in many engineering fields. A new Mn-Cu alloyed ADI with excellent mechanical properties has been developed in order to cut the cost and enlarge the application of ADI. The helical bevel gears were made of the new-developed Mn-Cu alloyed ADI. The microstructure and mechanical properties of the standard sample were investigated by optical microscope （OM）, scanning electron microscope （SEM） and performance measurement. The results showed that after a series of treatments, the mechanical properties （Rm 1007. 4 to 1200 MPa, A 5.2% to 8. 8%, HRC 32 to HRC 35, O^K 70 to 120 J/cmz ） of the Mn-Cu alloyed ADI standard sample could reach European standard EN1564-97/ EN-CJS-1000-5. The surface hardness after helical bevel gears meshing was significantly increased due to the formation of martensite. The bench test and traffic running testing results suggested that the new Mn-Cu alloyed ADI with ultimate life and median life respectively exceeding 30×104 and 50 × 10^4 times could replace 20CrMnTi forged steel for manufacturing the EQ140 helical bevel gears.
文摘This paper presents a method for measurement of deviation of the real gear tooth surface from the theoretical one with a coordinate measurement machine and compensation of repeatable parts. By investigation of characteristics of distortion of the gear tooth surface along the circle direction, the deviation is derived from distortion, and the definition of deviation with the geometrical invariability is proposed. Then the approach for determination of the location and orientation of the gear with respect to the coordinate measurement machine and the measurement way are developed. The deviation is represented with a difference surface, and an algorithm for derivation of parameters of global form deviations from the discrete points has been provided. Finally, the compensation approach is discussed.
基金Project(51105287) supported by the National Natural Science Foundation of ChinaProject(2012BAA08003) supported by the Key Research and Development Project of New Products and New Technologies of Hubei Province, ChinaProject(2011-P05) supported by the State Key Laboratory of Materials Processing and Die & Mould Technology, Huazhong University of Science and Technology,China
文摘The aim of this work is to propose a 3D FE model of a theoretical assembling straight bevel gear pair to analyze the contact fatigue on the tooth surface and the bending fatigue in the tooth root. Based on the cumulative fatigue criterion and the stress-life equation, the key meshing states of the gear pair were investigated for the contact fatigue and the bending fatigue. Then, the reliability of the proposed model was proved by comparing the calculation result with the simulation result. Further study was performed to analyze the variation of the contact fatigue stress and the bending fatigue stress under different loads. Furthermore, the roles of the driving pinion and the driven gear pair were evaluated in the fatigue life of the straight bevel gear pair and the main fatigue failure mode was determined for the significant gear. The results show that the fatigue failure of the driving pinion is the main fatigue failure for the straight bevel gear pair and the bending fatigue failure is the main fatigue failure for the driving pinion.
基金Project(2011CB706800-G)supported by the National Basic Research Program of ChinaProject(51375159)supported by the National Natural Science Foundation of China+1 种基金Project(20120162110004)supported by the Postdoctoral Science Foundation of ChinaProject(2015JJ5020)supported by the Science Foundation of Hunan Province,China
文摘In order to effectively improve meshing performance of spiral bevel and hypoid gears generated by the duplex helical method, the effects of straight lined and circular cutting edges profile on meshing and contact of spiral bevel and hypoid gears were investigated analytically. Firstly, a mathematical model of spiral bevel and hypoid gears with circular blade profile was established according to the cutting characteristics of the duplex helical method. Based on a hypoid gear drive, the tooth bearings and the functions of transmission errors of four design cases were analyzed respectively by the use of the tooth contact analysis(TCA), and the contact stresses of the four design cases were analyzed and compared using simulation software. Finally, the curvature radius of the circular profile blade was optimized. The results show that the contact stresses are availably reduced, and the areas of edge contact and severe contact stresses can be avoided by selecting appropriate circular blade profile. In addition, the convex and concave sides are separately modified by the use of different curvature radii of inside and outside blades, which can increase the flexibility of the duplex helical method.
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.
文摘The closed-died cold forging technology of the bevel gears used in Jada car was investigated. With the analysis of the strain field and velocity field of the plastic deformation and the endured forces of the dies, the filling rules for the metal were analyzed by the elastic-plastic finite element method （FEM）. The results show that there is a great difference among closed-die cold forging, extrusion and forging, as far as the metal flowing is concerned. The outer addendum cannot be filled completely in the closed-die cold forging of the bevel gears, and the round angle will be formed. But it does not influence the application of the bevel gears. At the beginning, the rigid area is formed in the cavity of the lower die. And then it will move upwards to supply the metal for the gear filling. For the closed-die cold forging of the bevel gears, the force acting on the upper die and the lower die is significantly different.
基金Project(2011CB706800) supported by the National Basic Research Program of ChinaProject(51275530) supported by the National Natural Science Foundation of China
文摘The effect of static transmission error on nonlinear dynamic response of the spiral bevel gear system combining with time-varying stiffness and backlash was investigated.Firstly,two different control equations of the spiral bevel gear model were adopted,where the static transmission error was expressed in two patterns as predesigned parabolic function and sine function of transmission errors.The dynamic response,bifurcation map,time domain response,phase curve and Poincare map were obtained by applying the explicit Runge-Kutta integration routine with variable-step.A comparative study was carried out and some profound phenomena were detected.The results show that there are many different kinds of tooth rattling phenomena at low speed.With the increase of speed,the system enters into stable motion without any rattling in the region(0.72,1.64),which indicates that the system with predesigned parabolic function of transmission error has preferable capability at high speed.
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.
基金Project(2005CB724104) supported by the Major State Basic Research Development Program of ChinaProject(1343-77202) supported by the Graduate Students Innovate of Central South University
文摘Six-axis numerical control spiral bevel gear grinder was taken as the object, multi-body system theory and Denavit-Hartenberg homogeneous transformed matrix （HTM） were utilized to establish the grinder synthesis error model, and the validity of model was confirmed by the experiment. Additionally, in grinding wheel tool point coordinate system, the errors of six degrees of freedom were simulated when the grinding wheel revolving around C-axis, moving along X-axis and Y-axis. The influence of these six errors on teeth space, helix angle, pitch, teeth profile was discussed. The simulation results show that the angle error is in the range from -0.148 4 tad to -0.241 9 rad when grinding wheel moving along X, Y-axis; the translation error is in the range from 0.866 0 μm to 3.605 3μm when grinding wheel moving along X-axis. These angle and translation errors have a great influence on the helix angle, pitch, teeth thickness and tooth socket.
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supported by the National Natural Science Foundation of China(Nos.61174018,41472260 and 41202206)
文摘A novel fiber Bragg grating(FBG)displacement sensor is proposed,which can achieve wide measuring range displacement detection with variable measurement precision due to its mechanical transfer structure of helical bevel gear.A prototype is designed and fabricated.The maximum detection displacement of this prototype is 1.751 m,and the precision grade changes from 0.2%to 6.7%.Through analyzing the experiment data which is obtained in the calibration experiment,the measuring range of this sensor is from 0 m to 1.532 m,and the wavelength shift errors between experiment data and theory calculation are all less than 5%.
