Effect of static transmission error on dynamic responses of spiral bevel gears

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.

Dynamic Fatigue Reliability Analysis of Transmission Gear Considering Failure Dependence

Multiple failuremodes and strength degradation are usually inherent in the gear transmission system,which brings new challenges for conducting fatigue reliability analysis and design.This paper proposes a novel dynamic fatigue reliability analysis method for failure dependence and strength degradation based on the combination of theCopula function and Gamma process.Firstly,the dynamic simulation model of the gear transmission system is established to obtain the dynamic stress-time history.The Gamma process is then used to describe the strength degradation to establish the dynamic stress-strength interference model.The marginal distribution functions of tooth contact fatigue and dedendumbending fatigue are calculated respectively based on the dynamic interferencemodel.Finally,the joint distribution of the two failure modes can be obtained by the t-Copula function to characterize the failure dependence,and so the dynamic fatigue reliability considering failure dependence can be estimated.The effectiveness of the proposed method is illustrated with examples.The results reveal the temporal law of reliability and the effects of failure dependence on dynamic fatigue reliability.

Excitation Prediction by Dynamic Transmission Error under Sliding Friction in Helical Gear System

Monte Carlo method was adopted to calculate the meshing error considering the manufacture error and assembly error of the meshing point along the time-varying contact line for helical gear pair. The flexural-torsion-axis dynamic model coupled was established under the tooth friction force and solved by the perturbation method to compute real dynamic tooth load. The change laws of the friction force and friction torque were obtained in a meshing period. The transmission error formulation was analyzed to introduce meshing excitations. The maximum dynamic transmission error, the maximum meshing force and the maximum dynamic factor were calculated under different speeds, external loads and damping factors. The conclusions can provide theoretical basis for the gear design especially in tooth profile correction.

Analysis on the gear-shifting schedule of hydraulic automatic transmission

With an advanced foreign hydraulic automatic transmission as the objective,an analytical method for the gear-shifting schedule is proposed.First the demanded maximum gradient of test is estimated.Then a test scheme and analytical procedure is formulated by initial test and hypothetical shift parameters.Finally through gear-shifting tests under different road conditions,load,accelerator pedal position limitation,throttle opening and output shaft speed are found to be the gear-shifting parameters.Under a common road condition,the gear-shifting schedule is a double-parameter schedule.Based on the driver＇s demands on braking and dynamic performance,different shift schedules are made under downhill,uphill and quick releasing acceleration pedal conditions.The operation criteria of down-shift schedule on abrupt grade are proposed.

Dynamic Test of Hydro Mechanical Composite Transmission for Cotton Picker

With a transmission system suitable for a medium or large self-propelled cotton picker as the object of the study,the following work focuses on the influence law of an independently designed hydro-mechanical continuously variable transmission(HMCVT)in the process of changing sections.An HMCVT simulation model was established using the multibody dynamics Simulation X software.The accuracy of the simulation model was verified by comparing the numerical values of the output speed of the HMCVT with model predictions.The HMCVT test bench was built independently using a John Deere 4045HYC11 diesel engine as power input.The engine speed,load torque,oil pressure,and flow of speed regulating valve were considered the influencing factors.The sliding friction power was the response index for the segment change process test.We analysed the reasons for the decrease in output speed during the shifting process,and proposed to effectively reduce the stable speed difference before and after the output shaft shifting by shifting the stage ahead(with displacement ratio of-0.96).This study provides a reference value for the smoothness of the HMCVT of the self-propelled cotton picker,and is relevant in promoting the use of the cotton picker.

RESEARCH OF DYNAMIC CHARACTERIATIC FOR TRANSMISSION SYSTEM

The kinetic precision of transmission chain is a key problem in the research of gear cutting machine transmission system.The traditional point of view is to consider the transmission chain as a geometrical meshing system,thus it is deemed that the kinetic precision of the transmission chain only depends on the manufacturing and assembly errors of its transmission parts.But further research reveals that the kinetic precision of transmission system is closely related with the system dynamic effects.Therefore,from the dynamic point of view,it is discerned that not only deems the transmission chain as a geometrical meshing system but also considers it as a dynamic system performing with torsional vibration.On the basis of analyses and processes of measuring data of samples from tests of cutting machine's kinetic precision of transmission chain,the results represent that the influences of dynamic characteristics of the transmission system on its kinetic precision is non negligible.Experimental methods for discerning the transfer function of torsional vibration of gear transmission system and experimental results have been given.

Effect of Tooth Profile Modification on Vibration of Power Split Gear Transmission System

Based on Newton ' s second law,the bend-torsion-shaft coupling nonlinear dynamic model and equations of power split gear transmission system are established.According to the principle of tooth profile modification,the tooth profile modification is considered as time-varying gear backlash function acting along the line of action.Then the dynamic functions are solved by using Runge-Kutta numerical method.After analyzing the effect of tooth profile modification quantity( TPMQ) and relative tooth profile modification length( TPML) to the nonlinear dynamic characteristics of power split gear transmission,the following conclusions are drawn:1 The TPMQ of a certain stage transmission affects the vibration of its own stage more significantly than the other stage,and the coupling effect between two stages can be ignored usually in the modification design;2 If the first stage TPMLs are less than 0.3,the influence of the first stage TPMLs to the first stage transmission vibration is much more greatly than the influence of the second stage TPMLs to the first stage transmission vibration,or else both the first and second stage TPMLs affect the first stage transmission vibration largely.The same is true for the second stage TPMLs,and the cutoff value is 0.2;3 The TPMQ affects the vibration of power split gear transmission system more principally than the TPML,and should be top-priority in the modification design.

Effect analysis of friction and damping on anti-backlash gear based on dynamics model with time-varying mesh stiffness

A nonlinear model of anti-backlash gear with time-varying friction and mesh stiffness was proposed for the further study on dynamic characteristics of anti-backlash gear. In order to improve the model precision, applied force analysis was completed in detail, and single or double tooth meshing states of two gear pairs at any timing were determined according to the meshing characteristic of anti-backlash gear. The influences of friction and variations of damping ratio on dynamic transmission error were analyzed finally by numerical calculation and the results show that anti-backlash gear can increase the composite mesh stiffness comparing with the mesh stiffness of the normal gear pair. At the pitch points where the frictions change their signs, additional impulsive effects are observed. The width of impulsive in the same value of center frequency is wider than that without friction, and the amplitude is lower. When gear pairs mesh in and out, damping can reduce the vibration and impact.

Fault diagnosis of AMT gear shifting process based on semi-quantitative SDG model

In order to diagnose gear shifting process in automated manual transmission（AMT）,a semi-quantitative signed directed graph（SDG）model is applied.Mathematical models are built by analysis of the power train dynamic and the gear shifting control process.The SDG model is built based on related priori knowledge.By calculating the fuzzy membership degree of each compatible passway and its possible fault source,we get the possibilities of failure for each possible fault source.We begin with the nodes with the maximum possibility of failure in order to find the failed part.The diagnosis example shows that it is feasible to use the semi-quantitative SDG model for fault diagnosis of the gear shifting process in AMT.

Manual Transmission Gear Rattle Vibration Research Based on Mathematical and Multi-Body Dynamics Co-simulation and Experiment

A method, which compares the angular acceleration and vibration spectrums of shafts and gears with physical characteristics of gearbox as tooth numbers and speed ratios, is proposed to find the source of gear rattle vibration. A mathematical and multi-body dynamics co-simulation model is built to reproduce the gear rattle phenomenon of one typical type of manual transmission. In the model, multi-body dynamics part is used for rotational motion and engagement simulation of gearbox shafts and gears, while mathematical part for control and data processing. The simulation results show that the sound source of the gear rattle from the first gear to the third gear is similar to the experimental results;different parameters like rotating damping, contact stiffness,contact damping, inertia moment and torque fluctuation making effects on gear rattle vibration strength are researched and simulated. The comparison of the simulation and experimental results shows that this method can provide recommendations for solving practical gear rattle problems.

Coordinated shift control of nonsynchronizer transmission for electric vehicles based on dynamic tooth alignment

Multispeed transmissions can enhance the dynamics and economic performance of electric vehicles(EVs),but the coordinated control of the drive motor and gear shift mechanism during gear shifting is still a difficult challenge because gear shifting may cause discomfort to the occupants.To improve the swiftness of gear shifting,this paper proposes a coordinated shift control method based on the dynamic tooth alignment(DTA)algorithm for nonsynchronizer automated mechanical transmissions(NSAMTs)of EVs.After the speed difference between the sleeve(SL)and target dog gear is reduced to a certain value by speed synchronization,angle synchronization is adopted to synchronize the SL quickly to the target tooth slofs angular position predicted by the DTA.A two-speed planetary NS AMT is taken as an example to carry out comparative simulations and bench experiments.Results show that gear shifting duration and maximum jerk are reduced under the shift control with the proposed method,which proves the effectiveness of the proposed coordinated shift control method with DTA.

Gear downshift control of inverse-automatic mechanical transmission of electric vehicle

In order to improve the driving dynamics and riding comfort of pure electric vehicles,taking a two-speed I-AMT(Inverse-Automatic Mechanical Transmission)with rear friction clutch as the research object,a gear shift strategy,which consists of the open-loop control of the clutch position control and the closed-loop control of the drive motor speed control,is proposed.Considering the inherent time-delay and external disturbances within the motor speed adjustment system,a two DOF(degree-of-freedom)Smith predictor with feedforward input is designed to track the target speed of the drive motor.The feedforward input is used to eliminate the influence of clutch sliding friction on the motor speed control,while the feedback speed tracking controller is applied to realize the speed tracking performance with the existence of time-delay and the external disturbance.In order to verify the effectiveness of the gear shift control strategy and the accuracy of the two DOF Smith controller with feedforward control,simulation results comparison is firstly carried out to illustrate the effectiveness of the control scheme.Then,a light pure electric vehicle equipped with I-AMT was used for downshift experiments under large throttle,which is the most difficult working scenario to control the transmission.The experimental results show that the two DOF Smith controller can eliminate the influence of time-delay on the closed-loop control,and the proposed whole gear shift control strategy can limit the clutch slippage time within 1.5 s,resulting in a smaller shift jerk,thus guarantee the driving dynamics and riding comfort simultaneously.

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。

Vibration performance discrete optimization of a gear system featuring confluence transmission used in marine gearbox

A dynamic model of gear transmission system which includes time-varying meshing stiffness,meshing damp and transmission error is established.Next,the analytical solution of the vibration response would be obtained by solving the dynamic model based on the harmonic balance method.And on this basis,a dynamic performance discrete optimization model of transmission sub-system would be constructed,which sets objective function up from vibration acceleration and the total mass of transmission sub-system,treats the module,number of teeth and helix angle as design variables,and takes gear strength and assembly relationship as constraints.Last,the optimal solution of design variables could be obtained through the multivariable mixed discrete optimization program which based on the branch-bound algorithm.The results show that the vibration acceleration and the total mass of transmission sub-system reduce by 34.6%and 6.8%,respectively.

齿面粗糙度对风电齿轮箱行星轮系动力学特性影响

为研究齿面粗糙度对行星轮系动力学特性的影响,提出行星轮系齿轮副动态承载接触分析与系统振动位移耦合方法。以某型兆瓦级风电齿轮箱行星轮系为研究对象,基于分形理论对轮齿粗糙表面进行分形表征,通过齿轮副啮合变形协调条件,构建齿面动态承载接触状态与构件振动位移、粗糙齿面啮合误差以及摩擦力的关联关系,建立风电齿轮箱行星轮系动力学模型,分析粗糙齿面啮合误差与摩擦力对系统动态特性的影响。结果表明:随着粗糙度的增大,齿面载荷峰值与波动幅值增大,动态啮合刚度幅值出现明显波动,均载性能降低;增大粗糙度会降低行星轮系临界转速,在低转速区域内,其具有激励增振作用,而在临界转速区域附近,其具有阻尼减振作用;摩擦力主要影响行星轮系各构件振动位移,可改变动态啮合力在少齿啮合区的幅值。

柔性齿轮运动特性及其振动抑制性能的实验研究

在三缸发动机平衡轴齿轮传动系统的传动过程中,存在着较大的振动和噪声问题,为此,提出了一种附加阻尼环的齿轮传动系统刚柔耦合模型,对柔性齿轮结构的运动特性及其振动抑制性能进行了实验研究。首先,采用集中质量法,建立了考虑齿轮间隙和时变啮合刚度的附加阻尼环6自由度齿轮传动系统的弯曲-扭转模型,利用石川公式计算出了柔性齿轮的时变啮合刚度,对比了有无阻尼环的齿轮系统的振动响应;然后,搭建了专门的齿轮传动系统测试设备,测试了不同转速下钢齿轮和柔性齿轮的加速度和噪声峰值;最后,设计了激光位移试验台,对比分析了不同转速下齿轮的微抖动,对柔性齿轮的减振效果进行了测试,并验证了理论模型的正确性。研究结果表明:当转速为1000 r/min时,钢齿轮和柔性齿轮的最大加速度信号分别为35.58 m/s^(2)和20.37 m/s^(2);当齿轮转速为4000 r/min时,柔性齿轮的阻尼效果最佳,加速度峰值降低了45.23%,噪声峰值降低了39.06%;钢齿轮的微抖动幅值明显高于柔性齿轮,两者的变化趋势相似。柔性齿轮能有效抑制轮齿微抖动振幅曲线的不平滑、毛刺现象,从而增强了三缸发动机平衡轴系的稳定性。

混合动力汽车无同步器AMT主动同步控制策略

以混合动力商用车电控机械式自动变速器(Automated Mechanical Transmission,AMT)换挡过程为研究对象,以减小换挡冲击和缩短换挡时间为目的,使用Simulink搭建了包含动力源动态协调与基于最优控制原理的电动机主动同步控制的无同步器换挡控制模型,并使用AMESim建立了动力系统及整车动力学仿真模型;以5挡升至6挡为例,采用AMESim与Simulink开展联合仿真分析,并与传统换挡策略的换挡性能进行了对比。仿真结果表明,换挡过程中,同步时间缩短21.42%,最大冲击度减少24.88%,整个换挡时间缩短18%。最后,基于dSPACE半实物仿真平台对所提控制策略进行了实时验证。

考虑点蚀情况的双渐开线齿轮动态特性研究

齿轮是机械传动系统的核心部件,点蚀与磨损是其主要失效的形式。为解决齿轮发生点蚀失效时双渐开线齿轮的时变啮合刚度与动态特性不明这一问题,采用接触线百分比法求解了发生点蚀时双渐开线齿轮的啮合刚度,并利用有限元法验证了算法的正确性。首先,对不同点蚀情况进行了分类,分析了不同点蚀数量对双渐开线齿轮接触线长度的影响;然后,基于接触线百分比法,利用轮齿载荷与轮齿变形的比值关系求解了不同点蚀情况下齿轮的啮合刚度,采用有限元法验证了算法的正确性,并对比分析了点蚀对双渐开线与普通渐开线齿轮啮合刚度的影响;最后,建立了两种齿轮的柔性多体动力学模型,基于冲激函数法分析了两种齿轮在不同点蚀情况下的动力学特性。研究结果表明:相同工况条件下,随着点蚀程度的加深,两种类型齿轮啮合刚度均不断减小,动态啮合力及振动角加速度幅值增加,其中双渐开线齿轮啮合力最大值为1.24×10^(5)N,角加速度最大值为2.66×10^(6)°/s^(2);相比于普通渐开线齿轮,双渐开线齿轮在点蚀影响下的啮合刚度变化更稳定,加速度幅值波动更平缓,具有更好的抵抗冲击能力和动力传递稳定性。

联合驱动斜齿轮传动系统模式切换过程的动态特性分析

齿轮传动系统作为舰船推进装置的重要组成部分,其在舰船运行模式切换过程中能否保持良好的动态特性对舰船结构安全性及机动性有着重要的影响。本文以某舰船中柴燃联合驱动斜齿轮传动系统为研究对象,建立系统纯扭动力学模型,采用MASTA软件验证该模型的正确性,基于该模型对燃气轮机单机驱动向柴燃联合驱动模式切换时的动力学特性进行分析,寻找模式切换的最佳转速和输入扭矩,探究啮合刚度和双联轴扭转刚度对模式切换过程动态特性的影响。计算结果表明,模式切换时齿轮1的最佳转速为2250 r/min,齿轮7的最佳输入扭矩为3100 Nm;啮合刚度的增大范围在基础值的1~1.2倍时,可以减弱不同切换阶段各齿轮副的振动程度;只要保证双联轴的扭转刚度超过0.8倍的基础值,系统中各齿轮副的振动程度将不再发生明显变化。

考虑磨损故障的双渐开线齿轮传动系统动态特性研究

针对目前双渐开线齿轮(DIG)研究过程中齿廓磨损对双渐开线齿轮动态特性的影响问题,对考虑磨损故障的双渐开线齿轮传动系统动态特性进行了研究。首先,进行了双渐开线齿轮接触线长度与齿面载荷计算,考虑相对滑移距离,建立了等效接触模型;然后,进行了双渐开线齿轮齿面累积磨损量、齿轮齿面累积磨损深度的计算,建立了双渐开线齿轮啮合刚度计算模型,进行了磨损故障的双渐开线齿轮刚度的计算;最后,以一对双渐开线齿轮为研究对象,采用集中质量法建立了6自由度动力学模型,研究了齿面磨损对双渐开线齿轮动力学特性的影响。研究结果表明:在运行1×104次载荷循环后,混合弹流润滑状态下,双渐开线齿轮与普通渐开线齿轮(CIG)在节线附近齿根位置的最大累计磨损量差值为0.00207μm,且双渐开线齿轮节线靠近齿顶位置的磨损小于普通渐开线齿轮的磨损;双渐开线齿轮系统在磨损后振动加速度幅值小于普通渐开线斜齿轮的幅值。通过对不同磨损情况下的时域响应进行研究,发现磨损导致双渐开线齿轮传动系统的振动幅值增大。