Three-Dimensional Conjugate Tooth Surface Design and Contact Analysis of Harmonic Drive with Double-Circular-Arc Tooth Profle

A three-dimensional conjugate tooth surface design method for Harmonic Drive with a double-circular-arc tooth profle is proposed. The radial deformation function of the fexspline (FS), obtained through Finite Element (FE) analysis, is incorporated into the kinematics model. By analyzing the FS tooth enveloping process, the optimization of the overlapping conjugate tooth profle is achieved. By utilizing the hobbing process, the three-dimensional machinable tooth surface of FS can be acquired. Utilizing the coning deformation of the FS, simulations are conducted to analyze the multi-section assembly and meshing motion of the machinable tooth surface. The FE method is utilized to analyze and compare the loaded contact characteristics. Results demonstrate that the proposed design method can achieve an internal gear pair consisting of a circular spline with a spur gear tooth surface and the FS with a machinable tooth surface. With the rated torque, approximately 24% of the FS teeth are engaged in meshing, and more than 4/5 of the tooth surface in the axial direction carries the load. The contact patterns, maximum contact pressure, and transmission error of the machinable tooth surface are 227.2%, 40.67%, and 71.24% of those on the spur gear tooth surface, respectively. It clearly demonstrates exceptional transmission performance.

STUDY ON SENSOR-BASED CONTROL METHOD FOR HARMONIC DRIVE SYSTEM

A new type of robust traje ctory tracking control for harmonic using joint torque sensor and joint acceleration sensor information is concerned with.Joint torque sensor information is used to compensate the uncertainty of link and load parameters. Joint acceleration feedback control will enhace the robustness of the driving system, resist the dynamic uncertainties and disturbing torque acted on the joint axis within definite bandwidth, improve the joint tracking performance, and resist the vibration of the load side of the harmonic drive system. Experimental studies are carried out and comparison of several controllers , such as PD and sensor- based control, the experimental results clearly illustrate the effectiveness of the proposed methods.

Tooth Position and Deformation of Flexspline Assembled with Cam in Harmonic Drive Based on Force Analysis

Deformation of the flexspline is the basis of analyzing tooth trajectory and designing tooth profile.Considering the tooth influence on the position of equivalent neutral layer,a piecewise method for calculating the deformation of flexspline assembled with a cam wave generator is presented in this paper.Firstly,a mechanic model of a ring of uniform thickness in contact with a rigid cam is established.The displacements of the ring inside and outside an unknown wrapping angle are determined by the geometric constraints of the cam profile and the equilibrium rela-tionship,respectively.Meanwhile,the wrapping angle is solved according to the boundary conditions.The assembly forces are derived to investigate the circumferential elongation and strain.Then,considering the tooth effects on the neutral layer of flexspline,the tooth is positioned on the equivalent neutral layer,which is the non-elongation layer within one gear pitch but offset from the geometric mid-layer.The equivalent neutral layer is positioned by the empirical formula of the offset ratio,which is summarized by the orthogonal simulation on finite element models of racks.Finally,finite element models of a ring-shaped and a cup-shaped flexspline assembled with elliptical cam are established to verify the effectiveness and accuracy of the piecewise method.The results show that,compared with the geometric method,the tooth positioning deviation calculated by the piecewise method can be reduced by about 70%with a more accurate deformation description from the geometric condition and mechanic condition inside and outside the wrapping angle.

Torque estimation for robotic joint with harmonic drive transmission based on system dynamic characteristics

In the applications of joint control and robot movement,the joint torque estimation has been treated as an effective technique and widely used.Researches are made to analyze the kinematic and compliance model of the robot joint with harmonic drive to acquire high precision torque output.Through analyzing the structures of the harmonic drive and experiment apparatus,a scheme of the proposed joint torque estimation method based on both the dynamic characteristics and unscented Kalman filter(UKF)is designed and built.Based on research and scheme,torque estimation methods in view of only harmonic drive compliance model and compliance model with the Kalman filter are simulated as guidance and reference to promote the research on the torque estimation technique.Finally,a promoted torque estimation method depending on both harmonic drive compliance model and UKF is designed,and simulation results compared with the measurements of a commercial torque sensor,have verified the effectiveness of the proposed method.

Impulse Controller Design of a Harmonic Drive System with Friction

A friction model was established for impulse control design in a precision control system. First, the physical characteristics of the impulse in momentum, such as motion and energy, were analyzed and formulated. Then, experimental response to a new pulse with two harmonic expansions was studied. The first harmonic is the main pulse to drive the arm, and the second harmonic has two functions： its first half helps the main pulse eliminate the dead zone, and its second half, a negative pulse, stops the arm motion quickly. Finally, an impulse feedback controller was developed. Comparison between simulation and experiments shows the effectiveness of the proposed controller.

The research of load spectrum between flexible gear and wave generator of harmonic drive

The harmonic drive is a kind of gear transmission that uses wave generator to produce controllable soft round elastic deformation and engages with rigid gear to transmit motion and power. The load distribution on the surface of the flexible gear and wave generator is an important parameter of studying the deformation of flexible gear and flexible bearing outside the wave generator and is also a necessary condition for studying the fatigue damage of flexible gear under alternating load. In this paper, a 3D model of 32-type 80：1 harmonic drive is build. Based on the generalized Hooke law, a hypothesis of load distribution which is proved to be validity by using finite element simulation is proposed on the interface of flexible gear and wave generator. On this base, the mathematic model and the quantitative calculation formula of the load distribution on the surface of the flexible gear and wave generator are proposed which provide a basis for the dynamic analysis and the fatigue damage of harmonic gear drive.

Research on Influence Mechanism of Transmission Accuracy for Harmonic Drive Mechanism Considering Multi-factor Coupling

The influence mechanism of transmission accuracy for harmonic drive mechanism considering multi-factor coupling was studied. According to analysis of influence factors of transmission accuracy for harmonic drive mechanism, it was obtained that the transmission errors of harmonic drive mechanism include processing errors and installation errors. The transmission error is produced by eccentric vector, it directly affects the rotation angle of output shaft and it makes harmonic drive mechanism produce backlash. Then analyze the movement error caused by the rigid wheel machining error, the flexible wheel machining error, the assembly error of the rigid wheel and the flexible wheel, the wave generator component, and the comprehensive expression method of motion error generated by each error source was obtained. The performance test device of space drive mechanism was used to test, and the law of the transmission accuracy of harmonic drive mechanism with temperature, speed and assembly clearance was obtained. The test results show that the transmission accuracy of harmonic drive mechanism decreases with increasing temperature, and the speed has little effect on the transmission accuracy of harmonic drive mechanism;the assembly quality has a significant impact on harmonic drive accuracy.

Harmonic Drive再添伺服马达减速器新产品

日本Harmonic Drive Systems日前在可将齿轮背隙(Backlash)控制在3分以下的伺服马达减速器“HPG系列”中，又增加了两款新产品。新推出的产品包括支持小容量马达(10～100W)的“型号11”和支持中容量马达(2k～15kW)的“型号65”。这样一来，HPG系列已达6种机型，可支持从10W到15kW的各种伺服马达。价格方面，型号11从44，300日元(约合人民币3400元)起，型号65从22万日元(约合人民币1．7万元)起。

Optimization and experimental research on a new-type short cylindrical cup-shaped harmonic reducer

In order to obtain a new-type short cylindrical cup-shaped flexspline that can be applied to space mechanisms,the APDL language of ANSYS software was employed to develop a parameterized equivalent contact model between a flexspline and a wave generator. The validity of the parameterized equivalent contact model was verified by comparing the results of the analytic value of the contact model and the value calculated by the theoretical formula. The curvilinear trend of stress was obtained by changing the structural parameter of the flexspline. Based on the curvilinear trend of stress,multi-objective optimizations of key structural parameters were achieved. Flexspline,wave generator,and circular spline of a new 32-type short cylindrical cup-shaped harmonic reducer were designed and manufactured. A performance test bench to carry out tests on the harmonic reducer was designed. Contrast experiments were implemented to determine the efficiency of the new 32-type short cylindrical cup-shaped harmonic reducer and the conventional 32-type harmonic reducer under different conditions. The experimental results reveal that there is approximately equality in terms of efficiency between the new 32-type short cylindrical cup-shaped harmonic reducer and the conventional 32-type harmonic reducer. The volume of the flexspline of the new 32-type short cylindrical cup-shaped harmonic reducer is reduced by approximately 30% through multi-objective optimization. When the new 32-type short cylindrical cup-shaped harmonic reducer is used on the wheel of a rover prototype,the mass of the wheel hub is decreased by 0.42 kg. Test analysis of wheel motion verifies that the new 32-type short cylindrical cup-shaped harmonic reducer can meet the requirements regarding bearing capacity and efficiency.

HEAT-SPINNING TECHNOLOGY OF HARMONIC GEAR-CLOSED FLEXSPLINE

Based on the experiments,heatspinning forming technology of the closed flexspline is studied and forming area and the laws of variations under the different technological parameters are gained.The semifinished flexspline products which can meet the quality demands have been successfully applied by matching the optimum technological parameters in the forming area.The research results create the conditions for spreading and applying the harmonic drive.

考虑多源误差影响的谐波减速器传动误差建模与分析

为解决现有谐波减速器传动误差建模方法的不足,提出一种考虑装配误差、齿面误差的综合误差建模方法。该方法首先建立装配误差和齿面误差数学模型,并进行误差影响参数分析。其次,测量实验样机装配偏心量和歪斜角度,基于模型得到对应偏心误差、歪斜误差模型理论值,齿面加工误差幅值按一般加工工况大小代入模型,得到对应加工误差模型理论值;然后,分别进行500 h、1500 h、3000 h时长的磨损实验,磨损后进行齿面形貌扫描和数据分析,得到对应的齿面形貌参数,基于模型得到对应的磨损误差模型理论值。最后,综合考虑多源误差影响,设置3组同型号样机,进行传动误差实验。实验结果表明:考虑装配偏心、歪斜和齿面加工等影响因素,传动误差的实验测量值与模型理论值误差在1.7~3.3%之间;综合考虑装配偏心、歪斜、齿面加工、齿面磨损等影响因素,在磨损500 h、1500 h、3000 h后传动误差的实验测量值与模型理论值误差分别在-3.45~2.07%、-5.88~-2.94%、1.33~5.33%之间。

基于柔轮裂纹扩展的谐波减速器剩余寿命预测方法

针对单一时频域指标未能较好表征谐波减速器全寿命周期退化特性问题,并考虑柔轮裂纹在不同部位的扩展速率差异性对剩余寿命预测精度的影响,提出一种基于长短期记忆网络和几何平均优化的粒子滤波(LSTM-GMOPF)的谐波减速器剩余寿命预测方法。谐波减速器退化特性难以通过单一时频域指标表征,在基于局部均值分解的振动信号处理的基础上,利用LSTM获取多个时频域指标关系,实现信号特征与退化状态之间的映射;考虑裂纹扩展速率的差异性,基于Paris及Foreman模型构建了谐波减速器前中后3个退化模型状态方程;为缓解粒子权值退化问题,引入双适应度指标,提出了基于GMOPF的状态方程参数更新迭代方法。通过谐波减速器加速寿命试验验证了方法的有效性,对比目前流行方法预测准确性最大提高了16.2%,为谐波减速器可靠性设计提供依据。

考虑逆变器谐波耦合的牵引传动系统机电耦合振动特性研究

作为牵引传动系统能量转换的关键部件,牵引电机在电气激励作用下会受到各种冲击载荷和周期激振力的作用,从而产生机电耦合振动,威胁牵引传动系统的可靠运行。对此,基于双惯量模型对牵引传动系统机电耦合振动特性开展研究。首先,建立牵引电机的双惯量模型,依据此模型对其固有频率进行计算,并介绍了机械传动系统的同频受迫振动模态。其次,根据逆变器的开关特性,着重分析了脉宽调制(PWM)导致的边带谐波转矩对机电耦合同频共振的影响,探索逆变器的频率耦合产生的间谐波对机电耦合系统的影响。接着,以传递函数的形式对考虑双惯量负载的牵引传动系统进行建模,从频域角度对系统机电耦合共振特性进行理论分析。最后,利用硬件在环测试对所分析结果进行验证。

多头双向螺旋面的加工方案研究

在介绍活齿端面谐波齿轮的传动原理及多头双向螺旋面含义的基础上,提出了2种加工多头双向螺旋面的方案,并进行了分析、比较。方案一:先采用三维建模软件(如NX等)对具有不同参数的多头双向螺旋面的零件进行建模,再利用数控立式加工中心进行加工;方案二:利用数控电火花线切割机床与数控回转工作台互相配合,按照多头双向螺旋面形成的原理进行加工。

谐波减速器精度退化失效及相关竞争失效可靠度评估研究

为了准确评估谐波减速器可靠度,实现失效预测和主动维护,提出了一种谐波减速器相关竞争失效可靠度评估方法。首先,根据谐波减速器精度性能退化测试数据,将指数模型应用至精度状态转移方程,采用粒子滤波算法进行了谐波减速器精度退化建模、参数更新和退化趋势分析,实现了谐波减速器精度退化失效寿命分布预测和精度动态可靠度评估;然后,结合谐波减速器强度失效和刚度退化失效的样本及失效寿命分布,基于Copula相关函数,建立了谐波减速器精度失效、刚度失效和强度失效的相关竞争失效动态可靠度评估方法;最后,通过谐波减速器精度、刚度和强度的相关竞争失效分析,得到了谐波减速器加速工况和额定工况下精度退化失效、刚度退化失效和强度失效的失效次序,并通过谐波减速器试验失效样本对所提出方法的有效性进行了验证。

微半球陀螺交直流混合电压切换驱动方法研究

微半球谐振陀螺的标度因数受阻尼不均匀程度和幅值控制精度影响,保证陀螺结构高度对称性的同时,驱动模态幅值控制精度也尤为重要。针对常见一倍频、1/2倍频电压驱动方式存在同频驱动噪声干扰和补偿相位延时导致微半球谐振陀螺驱动模态幅值控制精度较低,标度因数稳定性不足等问题,由于起振后陀螺等效驱动形式变化,基于微谐振子电压驱动原理构建了稳幅阶段微谐振子动态振动模型,提出了一种用于稳幅阶段的同相位二倍频电压驱动方式,设计了一种用于陀螺模态控制的交直流混合电压切换驱动方法,避免了相位补偿和同频驱动引起的幅值波动干扰。最后经力平衡模式仿真试验对比验证,混合电压切换驱动方法下驱动模态幅值控制精度提升5.882%,陀螺仪标度因数稳定性提高6.625%。

谐波驱动系统Back-stepping滑模控制研究

针对谐波传动系统动力学模型中存在的柔性变形、摩擦和运动误差等非线性因素。为了提高系统的传动精度,针对系统非线性刚度和静态误差因素进行了建模,并提出了一种Back-stepping滑模控制方法。利用Lyapunov稳定性理论,证明了闭环系统的误差是一致有界的。仿真结果表明,与PID控制相比,采用Back-stepping滑模控制,系统传动误差曲线峰峰值减小66.63%;负载端角速率误差曲线峰峰值减小77.35%。Back-stepping滑模控制能有效地补偿系统传动误差,抑制其负载端的速度波动,提高了系统的传动精度。

直流母线小电容永磁同步电机驱动系统网侧电流谐波抑制策略

直流母线采用小电容永磁同步电机驱动系统具有降低成本和延长运行寿命的优势。但在系统运行时网侧电流中存在大量的谐波,这将会影响网侧电流质量。为了改善小电容永磁同步电机(PMSM)驱动系统的网侧电能质量,该文提出一种基于阻抗重塑的有源阻尼控制方法,以抑制网侧电流谐波。通过对驱动系统进行建模,分析影响网侧电流谐波的因素,建立母线电流与网侧电流的数学关系。采用有源阻尼控制方法,提取母线电压谐波信号,以最优电压补偿的方式构建反馈回路,重塑驱动系统的特定频率处的等效阻抗,以实现网侧电流谐波的改善。同时,为了抑制电压补偿模块对电流内环扰动的影响,设计电流环级联双频陷波器,并通过系统极点图进行了稳定性分析。仿真结果和实验分析验证了所提控制方法的有效性。

基于承载与寿命的谐波传动柔轮结构优化

针对当前谐波传动产品承载力不足与易发生疲劳破坏的问题,对核心部件柔轮进行了应力分析、疲劳寿命计算与结构优化。运用光滑圆柱薄壳理论推导柔轮的理论应力表达式,通过ABAQUS软件进行有限元分析结果验证。采用多轴疲劳理论计算柔轮的理论疲劳寿命,利用Fe-Safe软件进行疲劳分析结果对比。以柔轮主要结构参数为输入变量、以承载能力与疲劳寿命为优化目标进行结构优化设计。结果表明,通过柔轮理论应力及疲劳寿命计算方法所得的结果与有限元结果基本吻合,结构优化方法亦能够平衡谐波传动承载能力与疲劳寿命之间的矛盾。

一种应用于半桥拓扑的斜率补偿电路

针对在峰值电流控制模式下半桥型开关电源存在次谐波振荡的问题,提出一种新型斜率补偿电路。该斜率补偿电路由少量外围常用器件构成,其补偿深度可由外围器件参数进行调节,与开关驱动信号完全保持同步。基于LTspice搭建斜率补偿电路的仿真模型,仿真结果表明,该电路补偿效果良好。样机实测结果也验证了该斜率补偿电路的有效性。所提电路适用于选择峰值电流模式但电源管理芯片内部没有斜率补偿电路的应用场合。