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
Polymer gears are increasingly replacing metal gears in applications with low to medium torque.Traditionally,polymer gears have been manufactured using injection molding,but additive manufacturing(AM)is becoming incre...Polymer gears are increasingly replacing metal gears in applications with low to medium torque.Traditionally,polymer gears have been manufactured using injection molding,but additive manufacturing(AM)is becoming increasingly common.Among the different types of polymer gears,nylon gears are particularly popular.However,there is currently very limited understanding of the wear resistance of nylon gears and of the impact of the manufacturing method on gear wear performance.The aims of this work are(a)to study the wear process of nylon gears made using the conventional injection molding method and two popularly used AM methods,namely,fused deposition modeling and selective laser sintering,(b)to compare and understand the wear performance by monitoring the evolution of the gear surfaces of the teeth,and(c)to study the effect of wear on the gear dynamics by analyzing gearbox vibration signals.This article presents experimental work,data analysis of the wear processes using molding and image analysis techniques,as well as the vibration data collected during gear wear tests.It also provides key results and further insights into the wear performance of the tested nylon gears.The information gained in this study is useful for better understanding the degradation process of additively manufactured nylon gears.展开更多
Meshing temperature analyses of polymer gears reported in the literature mainly concern the effects of various material combinations and loading conditions,as their impacts could be seen in the first few meshing cycle...Meshing temperature analyses of polymer gears reported in the literature mainly concern the effects of various material combinations and loading conditions,as their impacts could be seen in the first few meshing cycles.However,the effects of tooth geometry parameters could manifest as the meshing cycles increase.This study investigated the effects of tooth geometry parameters on the multi-cycle meshing temperature of polyoxymethylene(POM)worm gears,aiming to control the meshing temperature elevation by tuning the tooth geometry.Firstly,a finite element(FE)model capable of separately calculating the heat generation and simulating the heat propagation was established.Moreover,an adaptive iteration algorithm was proposed within the FE framework to capture the influence of the heat generation variation from cycle to cycle.This algorithm proved to be feasible and highly efficient compared with experimental results from the literature and simulated results via the full-iteration algorithm.Multi-cycle meshing temperature analyses were conducted on a series of POM worm gears with different tooth geometry parameters.The results reveal that,within the range of 14.5°to 25°,a pressure angle of 25°is favorable for reducing the peak surface temperature and overall body temperature of POM worm gears,which influence flank wear and load-carrying capability,respectively.However,addendum modification should be weighed because it helps with load bearing but increases the risk of severe flank wear.This paper proposes an efficient iteration algorithm for multi-cycle meshing temperature analysis of polymer gears and proves the feasibility of controlling the meshing temperature elevation during multiple cycles by tuning tooth geometry.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
The metamaterial based on external meshing gears(MEG)is designed based on the principle of external meshing gear transmission.Based on the meshing transmission principle of external meshing gears and planetary gear tr...The metamaterial based on external meshing gears(MEG)is designed based on the principle of external meshing gear transmission.Based on the meshing transmission principle of external meshing gears and planetary gear trains,the internal and external gear rings are designed.Based on the internal and external gear rings,the metamaterial based on inner and outer planetary gear trains(MIP)is designed to study the shear modulus,Young's modulus,and amplitude-frequency characteristics of the metamaterial based on gears at different angles.The effects of the number of planetary gears on the physical characteristics of the MIP are studied.The results show that the MEG can be continuously adjusted by adjusting the shear modulus and Young's modulus due to its meshing characteristics.With the same number of gears,the adjustment range of the MIP is larger than the adjustment range of the MEG.When the number of planetary gears increases,the adjustment range of the MIP decreases.Moreover,when the metamaterial based on gears rotates,the harmonic response changes with the change of the angle.展开更多
The fixed-setting face-milled curvilinear cylindrical gear features teeth that are arc-shaped along the longitudinal direction.Some researchers hypothesize that this arc-tooth may enhance the lubrication conditions of...The fixed-setting face-milled curvilinear cylindrical gear features teeth that are arc-shaped along the longitudinal direction.Some researchers hypothesize that this arc-tooth may enhance the lubrication conditions of the gear.This study focuses on this type of gear,employing both finite element analysis(FEA)and analytical methods to determine the input parameters required for elastohydrodynamic lubrication(EHL)analysis.The effects of assembly errors,tooth surface modifications,load,and face-milling cutter radius on the lubrication performance of these gears are systematically investigated.The finite element model(FEM)of the gear pair is utilized to calculate the coordinates of contact points on the tooth surface and the corresponding contact pressures at the tooth surface nodes throughout a meshing cycle.Subsequently,the normal load on specific gear teeth is determined using a gradient-based approach.Entrainment speed,slip-to-roll ratio,and effective radius near the contact points on the tooth surface are derived through analytical methods.The data obtained from FEA serve as input parameters for EHL simulations.The lubrication performance of the curvilinear cylindrical gear is evaluated through example studies.The findings indicate that using FEA to provide input parameters for EHL simulations can reveal the occurrence of edge contact phenomena during gear meshing,allowing for a more accurate representation of the gear’s lubrication conditions.The lubrication performance of the curvilinear cylindrical gear is shown to be independent of the face-milling cutter radius but is significantly influenced by the size of the contact pattern on the tooth surface.Curvilinear gears with larger contact patterns demonstrate superior lubrication performance.展开更多
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
Common definition and calculating expressions of end-surface contact ratiofor all type of gears are put forward, and with calculation expressions for involute gears,micro-segments profile gears, and sine-curved profil...Common definition and calculating expressions of end-surface contact ratiofor all type of gears are put forward, and with calculation expressions for involute gears,micro-segments profile gears, and sine-curved profile gears being discussed. The end-surface contactratio of gears is defined as the ratio of the action angle (the rotation angle of gear from gear-into gear-out for one pair of teeth) to the rotation angle per pitch (or central angle per tooth).According to the theory of gearing, equation of the meshing line can be deduced from the toothprofiles of basic rack. Having obtained the equation of the meshing line, and being given theaddendum outline of the gears, the contact ratio can be calculated with the calculation expressions.For the involute gears, this definition has same effect as the well-known definition: ratio of thecontact line to the base pitch. This definition of contact ratio is also suitable to othernon-involute gears, such as micro-segments profile gears, sine-curved profile gears, and can givemore reliable results.展开更多
High-speed trains typically utilize helical gear transmissions,which significantly impact the bearing load capacity and fatigue service performance of the gearbox bearings.This paper focuses on the gearbox bearings,es...High-speed trains typically utilize helical gear transmissions,which significantly impact the bearing load capacity and fatigue service performance of the gearbox bearings.This paper focuses on the gearbox bearings,establishing dynamic models for both helical gear and herringbone gear transmissions in high-speed trains.The modeling particularly emphasizes the precision of the bearings at the gearbox's pinion and gear wheels.Using this model,a comparative analysis is conducted on the bearing loads and contact stresses of the gearbox bearings under uniform-speed operation between the two gear transmissions.The findings reveal that the helical gear transmission generates axial forces leading to severe load imbalance on the bearings at both sides of the large gear,and this imbalance intensifies with the increase in train speed.Consequently,this results in a significant increase in contact stress on the bearings on one side.The adoption of herringbone gear transmission effectively suppresses axial forces,resolving the load imbalance issue and substantially reducing the contact stress on the originally biased side of the bearings.The study demonstrates that employing herringbone gear transmission can significantly enhance the service performance of high-speed train gearbox bearings,thereby extending their service life.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
Tooth modification technique is widely used in gear industry to improve the meshing performance of gearings. However, few of the present studies on tooth modification considers the influence of inevitable random error...Tooth modification technique is widely used in gear industry to improve the meshing performance of gearings. However, few of the present studies on tooth modification considers the influence of inevitable random errors on gear modification effects. In order to investigate the uncertainties of tooth modification amount variations on system＇s dynamic behaviors of a helical planetary gears, an analytical dynamic model including tooth modification parameters is proposed to carry out a deterministic analysis on the dynamics of a helical planetary gear. The dynamic meshing forces as well as the dynamic transmission errors of the sun-planet 1 gear pair with and without tooth modifications are computed and compared to show the effectiveness of tooth modifications on gear dynamics enhancement. By using response surface method, a fitted regression model for the dynamic transmission error（DTE） fluctuations is established to quantify the relationship between modification amounts and DTE fluctuations. By shifting the inevitable random errors arousing from manufacturing and installing process to tooth modification amount variations, a statistical tooth modification model is developed and a methodology combining Monte Carlo simulation and response surface method is presented for uncertainty analysis of tooth modifications. The uncertainly analysis reveals that the system＇s dynamic behaviors do not obey the normal distribution rule even though the design variables are normally distributed. In addition, a deterministic modification amount will not definitely achieve an optimal result for both static and dynamic transmission error fluctuation reduction simultaneously.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
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
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
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
Wear and scuffing failures often occur in marine transmission gears due to high friction and flash temperature at the interface between the meshing-teeth.In this paper,a numerical solution procedure was developed for ...Wear and scuffing failures often occur in marine transmission gears due to high friction and flash temperature at the interface between the meshing-teeth.In this paper,a numerical solution procedure was developed for the predictions of transient friction and flash temperature in the marine timing gears during one meshing circle based on the 3D line contact mixed lubrication simulation,which had been verified by comparing the flash temperature with those from Blok’s theory.The effect of machined surface roughness on the mixed lubrication characteristics is studied.The obtained results for several typical gear pairs indicate that gear pair 4-6 exhibits the largest friction and the highest interfacial temperature increase due to severe rough surface asperity contacts,while the polished gear surfaces yield the smallest friction and the lowest interfacial temperature.In addition,the influences of the operating conditions and the gear design parameters on the friction-temperature behaviors are discussed.It is observed that the conditions of heavy load and low rotational velocity usually lead to significantly increased friction and temperature.In the meantime,by optimizing the gear design parameters,such as the modulus and the pressure angle,the performance of interfacial friction and temperature can be significantly improved.展开更多
Traditional gear weight optimization methods consider gear tooth number, module, face width or other dimension parameters of gear as design variables. However, due to the complicated form and geometric features peculi...Traditional gear weight optimization methods consider gear tooth number, module, face width or other dimension parameters of gear as design variables. However, due to the complicated form and geometric features peculiar to the gear, there will be large amounts of design parameters in gear design, and the influences of gear parameters changing on gear trains, transmission system and the whole equipment have to be taken into account, which increases the complexity of optimization problem. This paper puts forward to apply functionally graded materials（FGMs） to gears and then conduct the optimization. According to the force situation of gears, the material distribution form of FGM gears is determined. Then based on the performance parameters analysis of FGMs and the practical working demands for gears, a multi-objective optimization model is formed. Finally by using the goal driven optimization（GDO） method, the optimal material distribution is achieved, which makes gear weight and the maximum deformation be minimum and the maximum bending stress do not exceed the allowable stress. As an example, the applying of FGM to automotive transmission gear is conducted to illustrate the optimization design process and the result shows that under the condition of keeping the normal working performance of gear, the method achieves in greatly reducing the gear weight. This research proposes a FGM gears design method that is able to largely reduce the weight of gears by optimizing the microscopic material parameters instead of changing the macroscopic dimension parameters of gears, which reduces the complexity of gear weight optimization problem.展开更多
Worm grinding has been applied to manufacture gears to pursue high accuracy and fine surface finish.When the worm used to grind face gears is manufactured with multi-axis computer numerical control(CNC)machining,the m...Worm grinding has been applied to manufacture gears to pursue high accuracy and fine surface finish.When the worm used to grind face gears is manufactured with multi-axis computer numerical control(CNC)machining,the machining accuracy is usually improved by increasing the number of tool paths with more time cost.Differently,this work proposes a generated method to improve the efficiency by dressing the worm surface with only one path,and a closed-loop manufacturing process is applied to ensure the machining accuracy.According to an advanced geometric analysis,the worm surface is practically approximated as a swept surface generated by a planar curve.Meanwhile,this curve is applied as the profile of a dressing wheel,which is used to dress the worm surface.The practical machining is carried out in a CNC machine tool,which was originally used to grind helical gears.Finally,a closed-loop manufacturing process including machining,measurement,and modification is proposed to compensate the machining errors.The proposed method is validated with simulations and practical experiments.展开更多
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.
文摘Polymer gears are increasingly replacing metal gears in applications with low to medium torque.Traditionally,polymer gears have been manufactured using injection molding,but additive manufacturing(AM)is becoming increasingly common.Among the different types of polymer gears,nylon gears are particularly popular.However,there is currently very limited understanding of the wear resistance of nylon gears and of the impact of the manufacturing method on gear wear performance.The aims of this work are(a)to study the wear process of nylon gears made using the conventional injection molding method and two popularly used AM methods,namely,fused deposition modeling and selective laser sintering,(b)to compare and understand the wear performance by monitoring the evolution of the gear surfaces of the teeth,and(c)to study the effect of wear on the gear dynamics by analyzing gearbox vibration signals.This article presents experimental work,data analysis of the wear processes using molding and image analysis techniques,as well as the vibration data collected during gear wear tests.It also provides key results and further insights into the wear performance of the tested nylon gears.The information gained in this study is useful for better understanding the degradation process of additively manufactured nylon gears.
基金Supported by National Key R&D Program of China(Grant No.2019YFE0121300)。
文摘Meshing temperature analyses of polymer gears reported in the literature mainly concern the effects of various material combinations and loading conditions,as their impacts could be seen in the first few meshing cycles.However,the effects of tooth geometry parameters could manifest as the meshing cycles increase.This study investigated the effects of tooth geometry parameters on the multi-cycle meshing temperature of polyoxymethylene(POM)worm gears,aiming to control the meshing temperature elevation by tuning the tooth geometry.Firstly,a finite element(FE)model capable of separately calculating the heat generation and simulating the heat propagation was established.Moreover,an adaptive iteration algorithm was proposed within the FE framework to capture the influence of the heat generation variation from cycle to cycle.This algorithm proved to be feasible and highly efficient compared with experimental results from the literature and simulated results via the full-iteration algorithm.Multi-cycle meshing temperature analyses were conducted on a series of POM worm gears with different tooth geometry parameters.The results reveal that,within the range of 14.5°to 25°,a pressure angle of 25°is favorable for reducing the peak surface temperature and overall body temperature of POM worm gears,which influence flank wear and load-carrying capability,respectively.However,addendum modification should be weighed because it helps with load bearing but increases the risk of severe flank wear.This paper proposes an efficient iteration algorithm for multi-cycle meshing temperature analysis of polymer gears and proves the feasibility of controlling the meshing temperature elevation during multiple cycles by tuning tooth geometry.
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supported by the Guangxi Science and Technology Major Program of China(Nos.AA23073019 and AA24263074)the National Natural Science Foundation of China(No.52265004)+7 种基金the Guangxi Natural Science Fund for Distinguished Young Scholars of China(No.2024JJG160014)the Innovation Project of Guangxi Graduate Education of China(No.YCSW2024119)the Open Fund of State Key Laboratory of Intelligent Manufacturing Equipment and Technology of China(No.IMETKF2025021)the Open Research Fund of State Key Laboratory of Precision Manufacturing for Extreme Service Performance-Central South University of China(No.Kfkt2023-06)the Open Fund of High-end Basic Component Innovation Station of China(No.KY01080030124001)the Open Fund for Academician Mao Ming's Workstation of China(No.XSJSFW-QNKXJ-202404-007)the Technology Innovation Platform Project of China Aviation Engine Group Corporation(No.CXPT-2023-044)the Open Fund for Innovation Workstation in the National Defense Science and Technology Innovation Special Zone(Xi'an Jiaotong University).
文摘The metamaterial based on external meshing gears(MEG)is designed based on the principle of external meshing gear transmission.Based on the meshing transmission principle of external meshing gears and planetary gear trains,the internal and external gear rings are designed.Based on the internal and external gear rings,the metamaterial based on inner and outer planetary gear trains(MIP)is designed to study the shear modulus,Young's modulus,and amplitude-frequency characteristics of the metamaterial based on gears at different angles.The effects of the number of planetary gears on the physical characteristics of the MIP are studied.The results show that the MEG can be continuously adjusted by adjusting the shear modulus and Young's modulus due to its meshing characteristics.With the same number of gears,the adjustment range of the MIP is larger than the adjustment range of the MEG.When the number of planetary gears increases,the adjustment range of the MIP decreases.Moreover,when the metamaterial based on gears rotates,the harmonic response changes with the change of the angle.
基金funded by the Sichuan Science and Technology Program(Project Nos.2024NSFSC0140,2023NSFSC0414,2022NSFSC0454)Panzhihua City Provincial Targeted Financial Resources Transfer Payment(Grant No.222Y2F-GG-04)+4 种基金Open Project of the Key Laboratory of Process Equipment and Control in Sichuan Province(ProjectNo.GK202211)Cultivation Research Project of PanzhihuaUniversity(ProjectNo.2023PY11)Open Project of Sichuan Provincial Engineering Technology Research Center for Advanced Manufacturing of Titanium Alloys(Project No.TM-2023-Z-02)Open Project of Panzhihua Key Laboratory of Advanced Manufacturing Technology(Project No.2022XJZD05).
文摘The fixed-setting face-milled curvilinear cylindrical gear features teeth that are arc-shaped along the longitudinal direction.Some researchers hypothesize that this arc-tooth may enhance the lubrication conditions of the gear.This study focuses on this type of gear,employing both finite element analysis(FEA)and analytical methods to determine the input parameters required for elastohydrodynamic lubrication(EHL)analysis.The effects of assembly errors,tooth surface modifications,load,and face-milling cutter radius on the lubrication performance of these gears are systematically investigated.The finite element model(FEM)of the gear pair is utilized to calculate the coordinates of contact points on the tooth surface and the corresponding contact pressures at the tooth surface nodes throughout a meshing cycle.Subsequently,the normal load on specific gear teeth is determined using a gradient-based approach.Entrainment speed,slip-to-roll ratio,and effective radius near the contact points on the tooth surface are derived through analytical methods.The data obtained from FEA serve as input parameters for EHL simulations.The lubrication performance of the curvilinear cylindrical gear is evaluated through example studies.The findings indicate that using FEA to provide input parameters for EHL simulations can reveal the occurrence of edge contact phenomena during gear meshing,allowing for a more accurate representation of the gear’s lubrication conditions.The lubrication performance of the curvilinear cylindrical gear is shown to be independent of the face-milling cutter radius but is significantly influenced by the size of the contact pattern on the tooth surface.Curvilinear gears with larger contact patterns demonstrate superior lubrication performance.
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.
文摘Common definition and calculating expressions of end-surface contact ratiofor all type of gears are put forward, and with calculation expressions for involute gears,micro-segments profile gears, and sine-curved profile gears being discussed. The end-surface contactratio of gears is defined as the ratio of the action angle (the rotation angle of gear from gear-into gear-out for one pair of teeth) to the rotation angle per pitch (or central angle per tooth).According to the theory of gearing, equation of the meshing line can be deduced from the toothprofiles of basic rack. Having obtained the equation of the meshing line, and being given theaddendum outline of the gears, the contact ratio can be calculated with the calculation expressions.For the involute gears, this definition has same effect as the well-known definition: ratio of thecontact line to the base pitch. This definition of contact ratio is also suitable to othernon-involute gears, such as micro-segments profile gears, sine-curved profile gears, and can givemore reliable results.
基金financial support provided by the National Key Research and Development Project of China(Grant No.2022YFB3402901)the National Natural Science Foundation of China(Grant No.52305070,52302467)。
文摘High-speed trains typically utilize helical gear transmissions,which significantly impact the bearing load capacity and fatigue service performance of the gearbox bearings.This paper focuses on the gearbox bearings,establishing dynamic models for both helical gear and herringbone gear transmissions in high-speed trains.The modeling particularly emphasizes the precision of the bearings at the gearbox's pinion and gear wheels.Using this model,a comparative analysis is conducted on the bearing loads and contact stresses of the gearbox bearings under uniform-speed operation between the two gear transmissions.The findings reveal that the helical gear transmission generates axial forces leading to severe load imbalance on the bearings at both sides of the large gear,and this imbalance intensifies with the increase in train speed.Consequently,this results in a significant increase in contact stress on the bearings on one side.The adoption of herringbone gear transmission effectively suppresses axial forces,resolving the load imbalance issue and substantially reducing the contact stress on the originally biased side of the bearings.The study demonstrates that employing herringbone gear transmission can significantly enhance the service performance of high-speed train gearbox bearings,thereby extending their service life.
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.
基金Supported by National Natural Science Foundation of China(Grant No.51375013)Anhui Provincial Natural Science Foundation of China(Grant No.1208085ME64)
文摘Tooth modification technique is widely used in gear industry to improve the meshing performance of gearings. However, few of the present studies on tooth modification considers the influence of inevitable random errors on gear modification effects. In order to investigate the uncertainties of tooth modification amount variations on system＇s dynamic behaviors of a helical planetary gears, an analytical dynamic model including tooth modification parameters is proposed to carry out a deterministic analysis on the dynamics of a helical planetary gear. The dynamic meshing forces as well as the dynamic transmission errors of the sun-planet 1 gear pair with and without tooth modifications are computed and compared to show the effectiveness of tooth modifications on gear dynamics enhancement. By using response surface method, a fitted regression model for the dynamic transmission error（DTE） fluctuations is established to quantify the relationship between modification amounts and DTE fluctuations. By shifting the inevitable random errors arousing from manufacturing and installing process to tooth modification amount variations, a statistical tooth modification model is developed and a methodology combining Monte Carlo simulation and response surface method is presented for uncertainty analysis of tooth modifications. The uncertainly analysis reveals that the system＇s dynamic behaviors do not obey the normal distribution rule even though the design variables are normally distributed. In addition, a deterministic modification amount will not definitely achieve an optimal result for both static and dynamic transmission error fluctuation reduction simultaneously.
基金the Hungarian Scientific Research Fund (OTKA) for their financial support of the research under Contract No.K77921
文摘The aim of this study is to define optimal tooth modifications, introduced by appropriately chosen head-cutter geometry and machine tool setting, to simultaneously minimize tooth contact pressure and angular displacement error of the driven gear （transmission error） of face-hobbed spiral bevel gears. As a result of these modifications, the gear pair becomes mismatched, and a point contact replaces the theoretical line contact. In the applied loaded tooth contact analysis it is assumed that the point contact under load is spreading over a surface along the whole or part of the ‘‘potential’’ contact line. A computer program was developed to implement the formulation provided above. By using this program the influence of tooth modifications introduced by the variation in machine tool settings and in head cutter data on load and pressure distributions, transmission errors, and fillet stresses is investigated and discussed. The correlation between the ease-off obtained by pinion tooth modifications and the corresponding tooth contact pressure distribution is investigated and the obtained results are presented.
基金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(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.
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(51905118)supported by the National Natural Science Foundation of ChinaProject(3072020CF0306)supported by the Fundamental Research Funds for the Central Universities,China。
文摘Wear and scuffing failures often occur in marine transmission gears due to high friction and flash temperature at the interface between the meshing-teeth.In this paper,a numerical solution procedure was developed for the predictions of transient friction and flash temperature in the marine timing gears during one meshing circle based on the 3D line contact mixed lubrication simulation,which had been verified by comparing the flash temperature with those from Blok’s theory.The effect of machined surface roughness on the mixed lubrication characteristics is studied.The obtained results for several typical gear pairs indicate that gear pair 4-6 exhibits the largest friction and the highest interfacial temperature increase due to severe rough surface asperity contacts,while the polished gear surfaces yield the smallest friction and the lowest interfacial temperature.In addition,the influences of the operating conditions and the gear design parameters on the friction-temperature behaviors are discussed.It is observed that the conditions of heavy load and low rotational velocity usually lead to significantly increased friction and temperature.In the meantime,by optimizing the gear design parameters,such as the modulus and the pressure angle,the performance of interfacial friction and temperature can be significantly improved.
基金Supported by National Hi-tech Research and Development Program of China(863 Program,Grant No.2015AA042505)
文摘Traditional gear weight optimization methods consider gear tooth number, module, face width or other dimension parameters of gear as design variables. However, due to the complicated form and geometric features peculiar to the gear, there will be large amounts of design parameters in gear design, and the influences of gear parameters changing on gear trains, transmission system and the whole equipment have to be taken into account, which increases the complexity of optimization problem. This paper puts forward to apply functionally graded materials（FGMs） to gears and then conduct the optimization. According to the force situation of gears, the material distribution form of FGM gears is determined. Then based on the performance parameters analysis of FGMs and the practical working demands for gears, a multi-objective optimization model is formed. Finally by using the goal driven optimization（GDO） method, the optimal material distribution is achieved, which makes gear weight and the maximum deformation be minimum and the maximum bending stress do not exceed the allowable stress. As an example, the applying of FGM to automotive transmission gear is conducted to illustrate the optimization design process and the result shows that under the condition of keeping the normal working performance of gear, the method achieves in greatly reducing the gear weight. This research proposes a FGM gears design method that is able to largely reduce the weight of gears by optimizing the microscopic material parameters instead of changing the macroscopic dimension parameters of gears, which reduces the complexity of gear weight optimization problem.
基金Project(2019 YFB 2004700)supported by the National Key R&D Project of ChinaProject(HTL-O-19 K 02)supported by National Key Laboratory of Science and Technology on Helicopter Transmission,Nanjing University of Aeronautics and Astronautics,China。
文摘Worm grinding has been applied to manufacture gears to pursue high accuracy and fine surface finish.When the worm used to grind face gears is manufactured with multi-axis computer numerical control(CNC)machining,the machining accuracy is usually improved by increasing the number of tool paths with more time cost.Differently,this work proposes a generated method to improve the efficiency by dressing the worm surface with only one path,and a closed-loop manufacturing process is applied to ensure the machining accuracy.According to an advanced geometric analysis,the worm surface is practically approximated as a swept surface generated by a planar curve.Meanwhile,this curve is applied as the profile of a dressing wheel,which is used to dress the worm surface.The practical machining is carried out in a CNC machine tool,which was originally used to grind helical gears.Finally,a closed-loop manufacturing process including machining,measurement,and modification is proposed to compensate the machining errors.The proposed method is validated with simulations and practical experiments.
