Finite element analysis of contact fatigue and bending fatigue of a theoretical assembling straight bevel gear pair

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.

Finite Element Analysis of Internal Gear in High-Speed Planetary Gear Units

The stress and the elastic deflection of internal ring gear in high-speed spur planetary gear units are investigated. A rim thickness parameter is defined as the flexibility of internal ring gear. Six evenly spaced linear springs are used to describe the fitting status between internal ring gear and the gearcase. The finite element model of the whole internal ring gear is established by means of Pro/E and ANSYS. The loads on meshing teeth of internal ring gear are applied according to the contact ratio and the load-sharing coefficient. With the finite element analysis (FEA), the influences of flexibility and fitting status on the stress and elastic deflection of internal ring gear are predicted. The simulation reveals that the principal stress and deflection increase with the decrease of rim thickness of internal ring gear. Moreover, larger spring stiffness helps to reduce the stress and deflection of internal ring gear. Therefore, the flexibility of internal ring gear must be considered during the design of high-speed planetary gear transmissions.

Modal analysis of prestressed draft pad of freight wagons using finite element method

The present work intends to investigate dynamic behaviour of draft gear using finite element method. The longitudinal force that the draft gear absorbs usually leads to the failure of its components, especially, the load bearing draft pads. Dynamic behaviour of an individual draft pad and a draft gear is determined and characterized with exciting frequen- cies and corresponding mode shapes. The effect of compressive prestress load on the dynamic behaviour of an individual draft pad is also determined as the draft pads in assembled state are under constant axial compressive force in the draft gear. The vibration characteristics of individual draft pad are compared with draft pads that are part of draft gear. The modal analysis gives us a basis for subjecting a draft pad to higher frequency loading for determining its fatigue behaviour.

FINITE ELEMENT SOLUTION TO COUPLED THERMO－ELASTICCONTACT STRESS AND IMPACTRESPONSE OF MESHING GEARS

A mixed finite element solution of contact stresses in meshing gears is investigated with the consideration of coupled thermo-elastic deformation and impact behavior. A simulation procedure of finite element solution of meshing gears is developed. The versatility of the procedure for both numerical accuracy and computational efficiency is verified by numerical analysis of meshing gear teeth.

Contact Stress Reliability Analysis Model for Cylindrical Gear with Circular Arc Tooth Trace Based on an Improved Metamodel

Although there is currently no unified standard theoretical formula for calculating the contact stress of cylindrical gears with a circular arc tooth trace(referred to as CATT gear),a mathematical model for determining the contact stress of CATT gear is essential for studying how parameters affect its contact stress and building the contact stress limit state equation for contact stress reliability analysis.In this study,a mathematical relationship between design parameters and contact stress is formulated using the KrigingMetamodel.To enhance the model’s accuracy,we propose a new hybrid algorithm that merges the genetic algorithm with the Quantum Particle Swarm optimization algorithm,leveraging the strengths of each.Additionally,the“parental inheritance+self-learning”optimization model is used to fine-tune the KrigingMetamodel’s parameters.Following this,amathematicalmodel for calculating the contact stress of Variable Hyperbolic Circular-Arc-Tooth-Trace(VH-CATT)gears using the optimized Kriging model was developed.We then examined how different gear parameters affect the VH-CATT gears’contact stress.Our simulation results show:(1)Improvements in R2,RMSE,and RMAE.R2 rose from0.9852 to 0.9974(a 1.22%increase),nearing 1,suggesting the optimized Kriging Metamodel’s global error is minimized.Meanwhile,RMSE dropped from3.9210 to 1.6492,a decline of 57.94%.The global error of the GA-IQPSO-Kriging algorithm was also reduced,with RMAE decreasing by 58.69%from 0.1823 to 0.0753,showing the algorithm’s enhanced precision.In a comparison of ten experimental groups selected randomly,the GA-IQPSO-Kriging and FEM-based contact analysis methods were used to measure contact stress.Results revealed a maximum error of 12.11667 MPA,which represents 2.85%of the real value.(2)Several factors,including the pressure angle,tooth width,modulus,and tooth line radius,are inversely related to contact stress.The descending order of their impact on the contact stress is:tooth line radius>modulus>pressure angle>tooth width.(3)Complex interactions are noted among various parameters.Specifically,when the tooth line radius interacts with parameters such as pressure angle,tooth width,and modulus,the resulting stress contour is nonlinear,showcasing amultifaceted contour plane.However,when tooth width,modulus,and pressure angle interact,the stress contour is nearly linear,and the contour plane is simpler,indicating a weaker coupling among these factors.

Loaded multi-tooth contact analysis and calculation for contact stress of face-gear drive with spur involute pinion

The analytical method based on "Hertz theory on normal contact of elastic solids" and the numerical method based on finite element method (FEM) calculating the contact stress of face-gear drive with spur involute pinion were introduced, and their relative errors are below 10%, except edge contact, which turns out that these two methods can compute contact stress of face-gear drive correctly and effectively. An agreement of the localized bearing contact stress is gotten for these two methods, making sure that the calculation results of FEM are reliable. The loaded meshing simulations of multi-tooth FEM model were developed, and the determination of the transmission error and the maximal load distribution factor of face-gear drive under torques were given. A formula for the maximal load distribution factor was proposed. By introducing the maximal load distribution factor in multi-tooth contact zone, a method for calculating the maximal contact stress in multi-tooth contact can be given. Compared to FEM, the results of these formulae are proved to be reliable, and the relative errors are below 10%.

METHOD FOR PRECISE CALCULATION OF ROOT STRESS OF SPIRAL BEVEL GEARS

A method for precise calculation of tooth root stress of spiral bevel gears is presentedand developed. On the basis of the machine settings analysis, tooth geometry anaysis and loadedtooth contact analysis, by using the tooth surface distribution load from tooth load analysis, thecalculation model is established and the root stress is calculated by means of finite element meth-od. The method mentioned is verified by a tested gears example.

基于压力角的摆线针轮齿廓曲线优化方法

根据摆线针轮传动理论,提出一种基于压力角的齿廓优化方法。将摆线针轮齿廓分为工作段与非工作段,区分影响工作段压力角的因素为修形参数与设计参数,讨论两类参数对压力角的影响,以此两类参数为设计变量,以工作段平均压力角为目标函数,以运动与润滑要求确定边界条件,对RV⁃550E型减速器摆线轮进行优化设计。结果表明,此方法使算例的工作段平均压力角降低了4.14%,使单齿啮合过程的压力角最大值降低了1.35%,优化前后接触齿对最大Mises应力下降了20.77%,发生位置由摆线轮转移至针轮,模型质量减小了9.38%,在确保无根切现象的同时能获得良好的组合修形效果。

中心距误差对小模数齿轮接触与弯曲强度的影响

为探究小模数齿轮中心距误差对轮齿强度的影响,以及标准GB/T 3480—2021对含中心距误差小模数齿轮强度设计的适用性,推导了含中心距误差的重合度系数、齿廓系数与应力修正系数计算公式,建立了含中心距误差的小模数齿轮有限元接触模型,提出有限元接触模型网格密度的验证方法.对2种计算方法得到的不同中心距误差下接触与弯曲应力进行了对比研究,结果表明,接触区域齿廓有限单元宽度不超过Hertz接触半宽的1/3时,齿轮有限元接触计算精度较高;采用标准GB/T 3480—2021校核含中心距误差的小模数齿轮强度,将产生冗余设计;当中心距误差达到1.33%时,接触应力幅值的最大变化为4.23%,而弯曲应力幅值的最大变化达到了16.25%,中心距误差对小模数齿轮弯曲应力的影响比接触应力更为显著.

裂纹故障下细高齿齿轮齿根动应变研究

为探究裂纹故障对细高齿齿轮齿根动应变的影响规律,采用集中质量法建立齿轮系统动力学模型,将故障下的时变啮合刚度作为输入,对系统动力学方程进行求解得到不同裂纹深度下的齿轮副动态啮合力。利用有限元法建立含裂纹故障齿轮结构动力学分析模型,结合轮齿承载接触分析确定裂纹故障下的齿间载荷分配关系,采用瞬态分析得到齿根应变时域历程,并对不同裂纹深度下的齿根动应变进行分析。仿真结果表明,当从动轮发生裂纹故障后,其齿根动应变故障特征主要表现为啮合区内齿根应变数值的变化,主动轮齿根动应变故障特征主要表现为齿根应变时域历程中出现周期性冲击及幅值衰减,在1.5 mm裂纹深度下主动轮齿根应变峰值因子相对变化量达到12.72%。

弧齿锥齿轮喷丸表面微观形貌仿真与试验验证

喷丸强化工艺能在弧齿锥齿轮表面及次表面引入残余压应力场,提高其疲劳寿命;但工程应用中经常出现不适当的喷丸参数,导致齿轮表面粗糙度显著增加,影响了齿面制造质量。为了准确预测与调控喷丸后齿轮表面微观形貌及表面粗糙度,基于离散元和有限元耦合的方法,提出了一种弧齿锥齿轮齿面喷丸工艺仿真计算方法,表面粗糙度预测与实测误差在20%以内,表明仿真预测方法具有准确性。基于该方法,以某弧齿锥齿轮为研究对象,研究了不同喷丸工艺参数与喷丸后齿面微观形貌的关联规律。研究结果表明,①随着喷丸时间增加,齿面三维粗糙度Sa先显著增加后缓慢下降;②当喷丸时间为50 s时,在本文的工艺参数下能达到满覆盖率;③弹丸速度与弹丸直径对齿面粗糙度均有较大的影响,但弹丸直径的影响更为显著。研究工作为喷丸后弧齿锥齿轮表面的微观形貌准确数值模拟与预测提供了方法基础,为合理制定喷丸工艺参数提供了技术参考。

基于田口-灰色关联法的驱动桥壳多目标优化设计

针对传统方法对驱动桥壳进行结构设计时,产品存在部分性能冗余的问题,本文提出一种结合田口法和灰色关联法的驱动桥壳多目标优化设计方法。以驱动桥壳结构参数为设计变量,桥壳刚度、强度和动态性能为优化目标,采用田口法正交试验设计实验方案,利用有限元法进行驱动桥壳典型工况的仿真分析,在试验数据信噪比分析的基础上结合灰色关联法对驱动桥壳进行多目标优化,得到最优结构参数组合。研究结果表明,优化后驱动桥壳的上述优化目标性能得到提升,验证了联合优化方法的有效性。

齿轨列车轮对-轨道耦合动力学研究

基于显式有限元法建立齿轨列车轮对-轨道有限元分析模型,针对齿轨列车运行具有较大影响的轨道坡度、列车运行速度、轮轨摩擦因数以及牵引系数等关键参数进行研究,重点分析上述参数变化对齿轮齿条、轮轨间垂向接触力与牵引力的影响。结果表明:轨道坡度重力作用对齿轨列车轮对-轨道系统啮合振动具有抑制作用,同时坡度增加,轮轨黏着作用逐渐减弱,因此齿轮齿条承载增加,轮轨承载减小;随牵引系数增加,齿轮承载增加,齿条接触力随牵引转矩增长而增大,而轮轨垂向接触力受其影响并不明显;随着运行速度增长,齿轮与车轮周向速度差增加,使得齿轮齿条间啮合振动加剧,即轮轨与齿条接触力波动范围增加。建议将齿轨列车大坡度路段运行时速度控制在10~15 km/h。

基于黏聚区模型的Z-pin增强复合材料T型接头分层损伤研究

复合材料T型接头Z-pin增强就是将直径非常细的金属或复合材料pin针植入筋条-蒙皮截面,通过Z-pin的桥接牵引提高接头力学性能。采用ABAQUS有限元软件分别建立了T型接头与Zpin增强T型接头的三维数值计算模型。基于黏聚区模型,采用新的简化后Z-pin桥接牵引关系模拟Z-pin增强作用过程。模拟了T型接头的拉伸失效模式,计算了其拉伸强度和总耗散能,对比分析了有无Z-pin增强2种接头的载荷-位移曲线和损伤耗散能-位移曲线。数值计算结果与文献中数据符合较好。结果表明:Z-pin增强T型接头的极限载荷与极限位移相比于无增强T型接头分别提高了66%和304%;2种接头的载荷-位移曲线斜率相同,初始损伤载荷一致;Z-pin增强T型接头在拉伸破坏过程中相比于无增强接头吸收能量多13.74倍。

基于田口法和有限元法的航空薄壁齿轮切削变形研究

为解决航空薄壁齿轮切削加工过程中容易发生变形的问题,以航空薄壁齿轮半精切削加工过程为研究对象,建立航空薄壁齿轮切削过程的有限元仿真模型,基于田口法获取不同切削参数下的3个方向的最大切削力数值,运用有限元法建立基于最大切削力的航空薄壁齿轮受力变形有限元仿真模型,得到不同切削参数对应的变形量,并运用极差分析法分析切削参数与变形的影响程度,优选出最佳切削参数组合。结果显示:背吃刀量对变形影响最大,切削速度对变形影响最小;优选得到的最佳切削参数组合为切削速度376.47 m·min^(-1)或451.79 m·min^(-1)、进给量0.20 mm·r^(-1)、背吃刀量1.0 mm。

常规和Z-Pin复合材料加筋板面内剪切屈曲破坏过程分析

为对复合材料加筋板屈曲至失效的全过程进行准确的分析,尤其是对后屈曲阶段的脱粘、开裂等局部损伤、损伤扩展至整体失效过程进行分析,本文考虑了层内和层间的失效分析方法,即层内采用三维Hashin准则和失效后的刚度折减模拟损伤和损伤扩展,层间采用VCCT结合Cohesive单元模拟层间脱粘和扩展.以上损伤失效模型通过场变量子程序USDFLD写入ABAQUS软件的计算过程,而后用于对常规和Z-pin复合材料加筋板面内剪切屈曲试验过程的分析.通过与试验采集数据的比较,验证了方法的有效性.

Fatigue fracture analysis of gear teeth using XFEM

Gear teeth in gear transmission systems suffer seriously from fatigue failure during service. In this work, a 2 D double-tooth model was constructed with periodic boundary conditions. The fatigue fracture behavior of gear teeth was analyzed using the extended finite element method(XFEM), with emphases on the impacts of initial crack geometries and cyclic load factors. The results suggested that the shortest fatigue life is expected for 0° orientation cracks initiating at the maximum principal stress. Cracks that initiate closer to the bottom land of gear tooth are relatively safe. Moreover, to evaluate the fatigue load conditions, load ratio, load range, and mean load should be all taken into considerations. Further XFEM simulation for material selection was performed to guide the gear design. Among various material parameters, the material constant C and tensile strength are the most significant ones in determining the fatigue life.

Theoretical calculation and experimental study on the load distribution coefficient (LDC) of three-ring gear reducer

In this paper, primary manufacturing and assembling errors of three-ring gear reducer （TRGR） are analyzed. TRGR is a new transmission type whose eccentric phase difference between middle ring plate and side ring plates is 120°, Its mass of middle ring plate is equal to that of side ring plate or 180°, and its inass of middle ring plate is twice of that of side ring plate, which affects load distribution between ring plates. The primary manufacturing and assembling errors include eccentric error of eccentric sheath E111, internal gear plate E1 and output external gear E11. A new theoretical method is presented in this paper, which converts load on ring plates into the dedendum bending stress of ring plate to calculate load distribution coefficient （ LDC ）, by means of gap element method （GEM）, one of finite element method （FEM）. The theoretical calculation and experimental study, which measures ring plate dedendum bending stress by means of sticking strain gauges on the dedendum of middle ring plate internal gear and side ring plate internal gears, are presented. The theoretical calculation and comparison with experiment result of LDC are implemented an two kinds of three-ring gear reducers whose eccentric phase difference between eccentric sheaths is 120° and 180°respectively. The research indicates that the result of theoretical calculation is consistent with that of experimental study. That is to say, the theoretical calculation method is feasible.

Effects of forging parameters on uniformity in deformation and microstructure of AZ31B straight spur gear

The effects of forging parameters on the deformation and microstructure distributions of as-forged straight spur gears wereinvestigated by finite element(FE)simulation and statistical analysis method.Spur gear forging using the movable cavity die designwas investigated by integrating the FE method with the microstructure evolution models for AZ31B magnesium alloys.The requiredinputs such as flow stress curves and microstructure evolution models,were obtained through the Gleeble thermal mechanical testingand quantitative metallography analysis method.Numerical simulation and experimental examination confirm that both thedeformation and microstructure are non-uniformly distributed in the as-forged gears.Decreasing deformation temperature orincreasing strain rate is beneficial to obtaining fine-grained microstructure but is harmful to the uniformity in deformation ormicrostructure.The level of the non-uniformity results from the complex shape of gear and the friction between the billet and dies,which is closely associated with the characteristics of flow stress curve.

Magnetic Equivalent Circuit Modeling of an Axial-Field Magnetic Gear

This paper presents a two-dimensional(2D)magnetic equivalent circuit(MEC)model to investigate the magnetic field distribution in the air-gap of an axial-field magnetic gear(AFMG).The MEC model is configured as a meshed reluctance network(RN)with permanent magnet magnetomotive-force sources.The MEC model based on RN is considered as a good compromise between accuracy and computational effort.This is a new model that will allow a faster analysis and design for the AFMG.Flux density in the air-gap is calculated with the proposed model and verified by finite element simulations.