An accelerated life test model for harmonic drives under a segmental stress history and its parameter optimization

Harmonic drives have various distinctive advantages and are widely used in space drive mechanisms. Accelerated life test （ALT） is commonly conducted to shorten test time and reduce associated costs. An appropriate ALT modet is needed to predict the lifetime of harmonic drives with ALT data. However, harmonic drives which are used in space usually work under a segmental stress history, and traditional ALT models can hardly be used in this situation. This paper proposes a dedicated ALT model for harmonic drives applied in space systems. A comprehensive ALT model is established and genetic algorithm （GA） is adopted to obtain optimal parameters in the model using the Manson fatigue damage rule to describe the fatigue failure process and a cumulative dam- age method to calculate and accumulate the damage caused by each segment in the stress history. An ALT of harmonic drives was carried out and experimental results show that this model is acceptable and effective.

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.

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.

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.

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.

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.

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.

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.

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.

Joint torque-based Cartesian impedance control with friction compensations

In order to investigate the joint torque-based Cartesian impedance control strategies and the influence of compensations for friction, an experimental study on the identification of friction parameters, friction compensation and the Cartesian impedance control are developed for the harmonic drive robot, by using the sensors available in the joint itself. Different from the conventional Cartesian impedance control schemes which are mostly based on the robot end force/torque information, five joint torque-based Cartesian impedance control schemes are considered, including the force-based schemes in Cartesian/joint space, the position-based schemes in Cartesian/joint space and the stiffness control. Four of them are verified by corresponding experiments with/without friction compensations. By comparison, it is found that the force-based impedance control strategy is more suitable than the position-based one for the robot based on joint torque feedback and the friction has even a positive effect on Cartesian impedance control stability.

Deformation analysis of the flexspline of harmonic drive gears considering the driving speed effect using laser sensors

Accurate description of the elastic deformation of the flexspline is the foundation for optimization design of the structure and conjugate profiles of the harmonic drive gear. This paper proposed an experimental method to investigate the effect of the driving speed on the deformation characteristics of the flexspline. First, an experimental apparatus that integrates a special-fabricated micro-displacement platform and a pair of laser displacement sensors is developed, and the radial displacement of the flexspline is measured in vertical and horizontal directions. Next, the deformation analyses of the flexspline at different driving speeds are performed with our method and the conventional method, and the comparison results reveal that the radial displacement of the flexspline is actually composed of both harmonic and random components, and the amplitude decreases and tends to zero with the increase of the driving speed, especially near the closed end of the flexspline. Last, the mechanisms of the inherent multi-frequency and amplitude attenuation characteristics of the radial displacement of the flexspline are discussed. It is indicated that the impact and friction existing in the flexible bearing of the wave generator is likely responsible for the existence of the random component, and the assumption of linear distribution of the ftexspline deformation along the rotating axis is invalid under high speed condition. Our research promotes the further study on the contact-impact problem of the flexible bearing of the wave generator and the transfer characteristic of the elastic deformation of the flexspline.

A method for detection and quantification of meshing characteristics of harmonic drive gears using computer vision

A lack of accurate description of the meshing characteristics and the corresponding frictional mechanism of the harmonic drive gear has limited progress toward modeling the hysteresis stiffness. This paper presents a method for detection and quantification of the meshing characteristics of the harmonic drive gear based on computer vision. First, an experimental set-up that integrates a high speed camera system with a lighting system is developed, and the image processing is adopted to extract and polish the tooth profiles of the meshed teeth pairs in each acquired video sequence. Next, a physical-mathematical model is established to determine the relative positions of the selected tooth pair in the process of the gear engagement, and the combined standard uncertainty is utilized to evaluate the accuracy of the calculated kinematics parameters. Last, the kinematics analysis of the gear engagement under the ultra-low speed condition is performed with our method and previous method, and the influence of the input rotational speed on the results is examined. The results validate the effectiveness of our method, and indicate that the conventional method is not available in the future friction analysis. It is also shown that the engaging-in phase is approximately a uniform motion process, the engaging-out phase is a variable motion process, and these characteristics remain unchanged with the variation of the input rotational speed. Our method affords the ability to understand the frictional mechanism on the meshed contact surfaces of the harmonic drive gear, and also allows for the dynamic monitoring of the meshing properties.

Thermodynamic analysis of a space station remote manipulator with a harmonic drive that considers an integrated thermal protection layer.

To eliminate anomalies and improve the performance of a space station remote manipulator(SSRM) used in a dynamically changeable thermal environment, we analyze the thermodynamic behavior of an SSRM that considers an integrated thermal protection system(ITPS). Solar radiative heat gain and loss become equally significant as conductive heat transfers through the interior of the SSRM on orbit. A thermodynamic model of the SSRM with a sandwich ITPS structure is established on the coupling between harmonic drive and changeable thermal environment. A motion precision is proposed to evaluate thermodynamic behavior under continuously changeable thermal circumstances. Simulation results indicate that the ITPS with a corrugated sandwich structure reduces the maximum amplitude of angular position errors to 41.6%, which helps improve the motion precision of the SSRM. The feasible regions for the SSRM in the Low Earth Orbit(LEO) and Geostationary Earth Orbit(GEO) are analyzed, which shows that the proportion of feasible region in LEO is significantly larger than that in GEO.

Meshing stiffness property and meshing status simulation of harmonic drive under transmission loading

The multitooth meshing state of harmonic drive (HD) is an important basic characteristic of its high transformation precision and high bearing capacity. Meshing force distribution affects the load sharing of the tooth during meshing, and theoretical research remains insufficient at present. To calculate the spatial distributed meshing forces and loading backlashes along the axial direction, an iterative algorithm and finite element model (FEM) is proposed to investigate the meshing state under varied transmission loading. The displacement formulae of meshing point under tangential force are derived according to the torsion of the flexspline cylinder and the bending of the tooth. Based on the relationship of meshing forces and circumferential displacements, meshing forces and loading backlashes in three cross-sections are calculated with the algorithm under gradually increased rotation angles of circular spline, and the results are compared with FEM. Owing to the taper deformation of the cup-shaped flexspline, the smallest initial backlash and the earliest meshing point appear in the front cross-section far from the cup bottom, and then the teeth in the middle cross-section of the tooth rim enter the meshing and carry most of the loading. Theoretical and numerical research show that the flexibility is quite different for varied meshing points and tangential force amplitude because of the change of contact status between the flexspline and the wave generator. The meshing forces and torsional stiffness of the HD are nonlinear with the torsional angle.

Intense ke V IAP generation by orthogonally polarized multicycle midinfrared two-color laser fields

We theoretically investigate the attosecond pulse generation in an orthogonal multicycle midinfrared two-color laser field. It is demonstrated that multiple continuum-like humps, which consist of about twenty orders of harmonics and an intensity of about one order higher than the adjacent normal harmonics, are generated when longer wavelength driving fields are used. By filtering these humps, intense isolated attosecond pulses（IAPs） are directly generated without any phase compensation. Our proposal provides a simple technique to generate intense IAPs with various central photon energies covering the multi-ke V spectral regime by using multicycle midinfrared driving pulses with high pump energy in the experiment.