Measured load spectra of the bearing in high-speed train gearbox under different gear meshing conditions

The load spectrum is a crucial factor for assess-ing the fatigue reliability of in-service rolling element bear-ings in transmission systems.For a bearing in a high-speed train gearbox,a measurement technique based on strain detection of bearing outer ring was used to instrument the bearing and determine the time histories of the distributed load in the bearing under different gear meshing conditions.Accordingly,the load spectrum of the total radial load car-ried by the bearing was compiled.The mean value and class interval of the obtained load spectrum were found to vary non-monotonously with the speed and torque of gear mesh-ing,which was considered to be caused by the vibration of the shaft and the bearing cage.As the realistic service load input of bearing life assessment,the measured load spectrum under different gear meshing conditions can be used to pre-dict gearbox bearing life realistically based on the damage-equivalent principle and actual operating conditions.

Simulation study on dynamics of cylindrical gear meshing with the evolution meshing stiffness

Simulation study on the cylindrical gear meshing with the evolution gear meshing stiffness is being done for better understanding the dynamic characteristics of the kinematics.With consideration of damping,bearing clearance and gear backlash nonlinearity,the dynamic model is set up and computed in MATLAB.The analysis about the relationship between the kinematic responses and the meshing stiffness are carried out.And the results showed that as the gear mesh stiffness is changed from small to large,the performance of the system is changed from the harmonic stable periodic motion to with one times,two times,four times,ending chaos of the stability of the bifurcation.The research results would have theoretical guidance value for the fault diagnosis in engineering.

Analysis of the Meshing of Crown Gear Coupling

This paper presents an analysis result of three-dimensional meshing of crown gear coupling （CGC） surfaces of crown gear and internal gear are established. The equation of internal gear surface is given. The equation of conjugate surface of crown gear is solved according to the principle of gearing, and that of non-conjugate crown gear is derived with crown curve of a circular arc. The meshing state of conjugate and non-conjugate surfaces is analyzed through computation of contact lines and points. It is concluded that the meshing of conjugate CGC is line-contact, there are several pairs of teeth engage simultaneously, and non-conjugate CGC has point-contact condition of meshing and only 2 pairs of teeth engage in theory.

Analysis of lubrication performance for internal meshing gear pair considering vibration

The thermal elasto-hydrodynamic lubrication characteristics of the internal meshing gears in a planetary gear train under vibrations were examined considering the influence of the modification coefficient and time-varying meshing stiffness.Based on dynamic theory of the gear system,a dynamic model of the planetary gear train was established.The lubrication performances of modified gear systems under vibrations and static loads were analyzed.Compared with other transmission types,the best lubrication effect could be produced by the positive transmission.A thicker lubricating oil film could be formed,and the friction coefficient and oil film flash temperature are the smallest.Increasing modification coefficient improves the lubrication performance continuously but intensifies the engage-in and tooth-change impact.For the planetary and inner gears,the increase in the modification coefficient also leads a decrease in the oil film stiffness.

Dynamic characteristics of the planetary gear train excited by time-varying meshing stiffness in the wind turbine

Wind power has attracted increasing attention as a renewable and clean energy. Gear fault frequently occurs under extreme environment and complex loads. The time-varying meshing stiffness is one of the main excitations. This study proposes a 5 degree-of-freedom torsional vibration model for the planetary gear system. The influence of some parameters(e.g., contact ratio and phase difference) is discussed under different conditions of a single teeth pair and double pairs of teeth. The impact load caused by the teeth face fault, ramped load induced by the complex wind conditions, and the harmonic excitation are investigated. The analysis of the time-varying meshing stiffness and the dynamic meshing force shows that the dynamic design under different loads can be made to avoid resonance, can provide the basis for the gear fault location of a wind turbine, and distinguish the fault characteristics from the vibration signals.

Study for the Forming Principle of Logix Gear Tooth Profile and Its Mesh Performance

In recent years, a new type of gear named Logix gea r was developed. Actually, the tooth profile of this new type of gear is composed of lots of micro-segment involute curves, and on the profile, there exist lots of points, which their relative curvatures are equal to zero. This can result in the sliding coefficient smaller between two meshed Logix gears, and the mesh ch aracteristic becomes almost rolling transmission from sliding transmission accor dingly. So, this new type of gear has lots of advantages such as higher contact intensity, longer useful life and can easily realize power transfer of bigger tr ansmission ratio than standard involute gear. Study results showed that the cont act fatigue strength is 3 times larger, the bend fatigue strength is 2.5 times l arger, and the minimum tooth number can be decreased to 3, much smaller than tha t of standard involute gear. In this paper, following studies had been done: 1) The formation principle of Logix gear tooth profile was studied. The theoreti cal models describing the geometrical formations of this type of gear and its re lative Logix rack had been deduced. 2) While cutting a Logix gear, its tooth profile is decided by its normal tooth profile of Logix rack. Besides the basic parameters of standard involute gear, L ogix rack has its own specific parameters such as preliminary pressure angle, re lative pressure angle, and preliminary referential circle radius etc. So, the in fluence of connatural parameters of Logix rack on the tooth profile of Logix gea r had been farther studied. Reasonable selection for these parameters had been d iscussed. 3) Several kinds of transition curves for gear’s tooth profile had been introdu ced, its selection used by Logix gear had been described, and also its mathemati cal description model had been deduced. 4) The mesh theories of Logix gears had been developed. It had been proved that the transmission performance between Logix gears coincides with E-W theorem as that of ordinary standard involute gears. The formula calculating superposition coefficient was deduced according to its definition. Different from standard inv olute gears, the parameter of gear number has no effect on the superposition coe fficient of the Logix gears. Accordingly, bigger ratio transmission can be acqui red by means of decreasing the gear number, and its minimum gear number can be r eached to 3, much smaller than the minimum gear number of ordinary standard invo lute gear: 14～17. This is very important to realize the miniaturization of prod uction design. 5) The CAD special software was developed to design all kinds of Logix gears, an d a solid design example was offered. To sum up, by means of above study, the system info about Logix gear had been de veloped and enriched. This has most significant impact on its widely promotion a nd practical application, on the improvement of carrying capacity, miniaturizati on, and life of kinetic transmission products.

Influence Predictions of Contact Effects on Mesh Stiffness of Face Gear Drives with Spur Gear

Mesh stiffness is one of important base parameters of face gear dynamic studies.However,a calculation solution of mesh stiffness of face gear drives is not to be constructed due to complex geometric flakes of face gear teeth.Thus,a calculation solution of mesh stiffness of face gear drives with a spur gear,which is based on the proposed equivalent face gear teeth and Ishikawa model,is constructed,and the influence of contact effects on mesh stiffness of face gear drives is investigated.The results indicate the mesh stiffness of face gear drives is sensitive to contact effects under heavy loaded operating conditions,specially.These contributions will benefit to improve dynamic studies of face gear drives.

Quasi Ellipsoid Gear Surface Reconstruction Based on Meshless Local Petrov-Galerkin Method and Transmission Characteristic

Special transmission 3D model simulation must be based on surface discretization and reconstruction, but special transmission usually has complicated tooth shape and movement, so present software can＇t provide technical support for special transmission 3D model simulation. Currently, theoretical calculation and experimental method are difficult to exactly solve special transmission contact analysis problem. How to reduce calculation and computer memories consume and meet calculation precision is key to resolve special transmission contact analysis problem. According to 3D model simulation and surface reconstruction of quasi ellipsoid gear is difficulty, this paper employes meshless local Petrov-Galerkin （MLPG） method. In order to reduce calculation and computer memories consume, we disperse tooth mesh into finite points--sparseness points cloud or grid mesh, and then we do interpolation reconstruction in some necessary place of the 3D surface model during analysis. Moving least square method （MLSM） is employed for tooth mesh interpolation reconstruction, there are some advantages to do interpolation by means of MLSM, such as high precision, good flexibility and no require of tooth mesh discretization into units. We input the quasi ellipsoid gear reconstruction model into simulation software, we complete tooth meshing simulation. Simulation transmission ratio during meshing period was obtained, compared with theoretical transmission ratio, the result inosculate preferably. The method using curve reconstruction realizes surface reconstruction, reduce simulation calculation enormously, so special gears simulation can be realized by minitype computer. The method provides a novel solution for special transmission 3D model simulation analysis and contact analysis.

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.

非对称齿轮啮合刚度精确求解及齿廓参数分析

非对称齿轮是一种轮齿两侧采用不同压力角的新型渐开线齿轮,其齿廓参数对齿轮齿廓形状、运动特性、承载能力、传动效率和动力学特性等有至关重要的影响。基于齿轮啮合原理,运用李特文矢量法,根据加工刀具齿廓参数方程推导了非对称齿轮全齿廓方程;应用材料力学理论,建立非对称齿轮时变啮合刚度的数值求解模型,并通过有限元方法验证了该模型的有效性。基于所建立数值分析模型进行算例研究,总结了刀具圆角、压力角和变位系数对齿轮啮合刚度和重合度的影响规律。结果表明,随着轮齿工作侧压力角的增大,齿轮齿根厚度增加,单齿对的啮合刚度加大,齿轮的承载能力得到有效提高。加工工作侧轮齿齿廓刀具圆角的增大,也有利于提高齿轮的啮合刚度;同时,工作侧齿廓压力角的增大会使齿轮的齿顶厚度降低、啮合重合度减小,会导致齿轮的齿顶强度和冲击韧性降低。非对称齿轮齿廓设计时,应根据实际工况合理设置压力角参数。

基于动态啮合刚度的直齿圆柱齿轮动态特性研究

齿轮系统转速直接影响齿轮系统的动态特性,然而在啮合刚度的计算中该因素却被许多学者们忽略。为了研究转速对啮合刚度的影响,基于有限元框架使用平均加速度法提出了一种计算与转速相关的动态啮合刚度的算法,同时对不同转速下的动态啮合刚度进行仿真计算与分析,最后进一步探究了受动态啮合刚度影响后的齿轮系统所具有的相关动态特性。分析表明,动态啮合刚度始终围绕着静态啮合刚度上下波动;随着转速的增加,其波动幅度增加,振荡次数减少;随着转速的变化,动态啮合刚度计算的动态传动误差振幅相对于静态啮合刚度而言大小关系不一致,且计算的齿轮系统共振转速区间或超前或滞后于静态啮合刚度模型;动态啮合刚度影响特定转速区间的齿轮系统的振动周期。对与转速相关的动态啮合刚度的研究可为直齿圆柱齿轮传动性能的改善及减振降噪提供参考。

渐开线变齿厚齿轮啮合冲击分析

基于弹性接触动力学理论和齿轮传动物理模型,对渐开线变齿厚齿轮啮合冲击问题进行了分析,建立了变齿厚齿轮全齿啮合接触冲击模型.通过模拟轮齿啮合接触状态,对轮齿啮合区域展开了讨论,利用LS-DYNA软件进行接触碰撞分析,分别研究了冲击合力和冲击应力随转速和冲击位置的变化规律.结果表明:转速和冲击位置对冲击合力和冲击应力影响显著,且冲击最大应力主要集中在齿顶和轮齿的大小端附近;转速越大,轮齿受载面与非受载面之间的冲击应力相差越大.

双曲型法向圆弧齿轮传动的动力学分析

为探究啮合刚度、传动误差及侧隙对双曲型法向圆弧齿轮传动动态响应的影响,建立齿轮副的动力学方程,并在数值计算的基础上进行仿真分析。运用有限元方法,计算接触位置处的载荷及变形,并对时变啮合刚度、静态传动误差和侧隙进行量化分析。仿真结果表明:对振动位移响应影响最大的是侧隙,其次是时变啮合刚度;对动态啮合力影响最大的则是时变啮合刚度和侧隙。

随机扰动和摩擦下的斜齿轮系统动态特性分析

建立考虑随机扰动和摩擦的8自由度单级斜齿轮传动模型,根据齿轮啮合原理,求解系统所受的摩擦力和摩擦力臂,利用龙格库塔法对微分方程进行求解,结合啮合频率的分岔图、时间历程图和庞加莱映射图等。分析在含摩擦和随机扰动啮合频率作用下系统的动态特性。研究得到,随着啮合频率的增加,系统由周期运动进入混沌运动,摩擦因数不会改变系统的分岔特性,但是会影响混沌区域附近的倍周期现象,随机扰动啮合频率会改变系统分岔特性,使系统提前进入混沌。

斜齿轮动态啮合及疲劳寿命分析

为了对高速斜齿轮啮合进行探究,首先通过有限元法构建多自由度的转子-轴承系统动力学方程,并计算齿轮啮合的固有频率,通过Newmark-β法计算位移响应,之后应用KISSsoft建立几何模型并对其齿形在齿廓和齿向两方面进行修形,应用ANSYS Workbench对修形前、后的斜齿轮副进行瞬态分析,并通过在等效应力、疲劳寿命和安全系数方面进行对比分析。结果表明:修形后的斜齿轮等效应力下降,疲劳寿命增加,安全系数提高,证明该修形方式的可行性,为设计高速斜齿轮啮合研究提供了参考。

曲面综合法少齿数弧齿锥齿轮加工参数计算仿真与切齿试验

少齿数高减比齿轮传动具有体积小和轻量化的优势。根据综合变位和节锥外啮合原理,设计了一对高减速比弧线等高齿锥齿轮,给出了相关的几何限制条件,推导了大、小轮齿面方程。大轮采用成形法加工,小轮采用单面展成法加工,为弥补大轮齿廓曲率的不足,小轮刀齿采用圆弧刃修形,采用曲面综合法优化求解了小轮加工参数;通过建立ease-off差齿面,对齿面修形梯度、传动误差、接触路径与接触线进行了仿真。切齿和滚检试验,验证了高减比弧齿锥齿轮几何设计、刀盘修形加工方法的可行性。

基于媒介齿轮的修正型渐开线包络环面蜗杆传动啮合性能分析

环面蜗杆传动因其多齿啮合特性而具有承载能力强等优势,但其约束数相应增加,对制造误差及装配误差更为敏感。为降低重载环面蜗杆传动的误差敏感性,提出了一种修正型渐开线齿轮包络环面蜗杆传动。构建渐开线齿轮与媒介齿轮及环面蜗杆三者之间的啮合几何学模型,建立了传动副空间点接触局部共轭接触分析方法;通过数值分析及有限元仿真分析,揭示了修正型渐开线齿轮包络环面蜗杆传动啮合特性的变化规律。结果表明,该新型环面蜗杆传动具有较低的误差敏感性,同时保持了高载荷下的承载能力。针对某人机交互7000 m自动化钻机重载机器人回转关节,研制了修正型渐开线包络环面蜗杆传动减速器样机,并进行了相关性能试验,验证了理论分析的准确性。

基于齿廓曲线的外啮合齿轮泵排量计算

渐开线外啮合齿轮泵以结构简单、造价低廉等优点而在矿山、工程等领域应用广泛,但目前关于精准计算其瞬时流量、排量的文献较少。为此,基于齿轮啮合机制、轮齿齿廓性质以及转角和啮合点的关系,建立齿轮泵瞬时输出流量的数学及仿真模型。针对齿轮泵重合度、齿轮变位、卸荷槽、侧隙等影响因素对模型进行论证,进而提出一种精准计算渐开线外啮合齿轮泵排量的方法,并采用Simulink仿真软件对不同类型外啮合齿轮泵的瞬时流量进行仿真模拟。同时利用3种不同型号齿轮泵验证排量公式,其最大误差在5%以内。验证计算模型有效性后,基于MATLAB设计了齿轮泵计算辅助平台,实现了外啮合齿轮泵瞬时流量、排量性能可视化,以简化计算流程,适应工程化应用。

考虑齿形误差影响的摆线针轮承载特性分析

针对缺乏考虑齿形误差的承载分析软件,导致分析结果不符合实际工程状况的问题,提出了1种包含摆线轮齿形误差的摆线针轮副承载特性分析方法。利用三次非均匀B样条准确描述出包含齿形误差的摆线轮实际齿廓,构建并分析了摆线针轮误差齿廓接触分析模型(error tooth contact analysis,E-TCA),得到了初始啮合位置参数及啮合间隙。在此基础上,建立了齿形误差影响下的摆线针轮副负载接触分析模型,确定了零部件多体接触之间的力矩平衡和变形协调关系,利用能量最低原理获取了真实承载特性。通过有限元模型验证了RV-40E型号减速器的摆线针轮承载特性。结果表明:由于齿形误差的影响,啮合齿数减少了1对,啮合应力和传动误差增大了5.3%和5.7%。

蜗杆-斜齿轮传动齿面啮合干涉分析

蜗杆-斜齿轮传动具有传动比大、传动平稳等优点,广泛应用于各种小型交错轴传动。与蜗杆完全共轭的理论斜齿轮与常规的标准斜齿轮存在齿形差异,因此蜗杆和标准斜齿轮传动存在齿面间的啮合干涉,会影响传动性能。基于螺旋面圆柱蜗杆与斜齿轮的双参数包络成形原理,建立了阿基米德蜗杆和齿槽法向直廓蜗杆与斜齿轮的啮合方程,推导了理论共轭斜齿轮齿面,并与实际标准斜齿轮齿面比较,分析了传动过程中齿面接触干涉区域和干涉量。分析结果表明,蜗杆头数和节圆半径对蜗杆齿轮传动的啮合干涉有影响,增加蜗杆头数、减小蜗杆节圆半径都会使干涉量增加;在相同的蜗杆设计参数条件下,齿槽法向直廓蜗杆的干涉量要大于阿基米德蜗杆,以上结论为蜗杆斜齿轮传动的设计提供了参考依据。