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In a harmonic drive during assembly of its components like strain wave generating (SWG) cam, flexspline (FS) and circular spline, a gap is formed between the cam’s outer surface and the FS cup inner surface due to mismatching. This gap, which is known as “Coning”, plays a vital role in the flow of lubricant at that interface. This paper aims to analyse the coning phenomenon and the lubrication mechanism.

In the present investigation, the geometry of the coning gap and its variation with the SWG cam rotation are established. Essentially, the deflection of FS cup and deformation of SWG cam (bearing outer race) are derived to find the gap due to coning. Next, the hydrodynamic lubrication equation is solved to get pressure profiles for this gap under suitable boundary conditions assuming non-Newtonian lubrication.

Methods of estimating the coning gap and lubrication pressure profiles are established. Effects of non-Newtonian terms (coupling number and non-dimentionalized characteristic length) and SWG length (finite, long and short) on pressure profiles are also shown. All analyses are done in non-dimensionalized form.

Establishing the geometry of coning and non-Newtonian hydrodynamic lubrication aspects in the coning in the FS cup and SWG cam interface are the originality of the present investigation.

Because of the compact structure, short flexspline (FS) harmonic drive (HD) is increasingly used. The stress calculation of FS is very important in design and optimization of HD system. This paper aims to study the stress calculation methods for short FS, based on mechanics analysis and finite element method (FEM).

A rapid stress calculation method, based on mechanics analysis, is proposed for the short FS of HD. To verify the stress calculation precision of short FS, a complete finite element model of HD is established. The results of stress and deformation of short FS in different lengths are solved by FEM.

Through the rapid calculation method, the analytical relationship between circumferential stress and length of cylinder was obtained. And the circumferential stress has proportional relation with the reciprocal of squared length. The FEM results verified that the rapid stress calculation method could obtain accurate results.

The rapid mechanics analysis method is practiced to evaluate the strength of FS at the design stage of HD. And the complete model of HD could contribute to improving the accuracy of FEM results.

The rapid calculation method is developed based on mechanics analysis method of cylinder and equivalent additional bending moment model, through which the analytical relationship between circumferential stress and length of cylinder was obtained. The complete three-dimensional finite element model of HD takes the stiffness of bearing into consideration, which can be used in the numerical simulation in the future work to improve the accuracy.

This paper aims to improve the meshing effect of the gear teeth. It is recommended to analyze the deformation difference between the inner and outer surfaces of the flexspline. The purpose of this paper is to modify the profile of the flexspline based on the deformation difference to improve the transmission accuracy and operating life of the harmonic drive.

In this paper, ring theory is used to calculate the deformation difference of the inner and outer surfaces of the flexspline, and the actual tooth profile of the flexspline is corrected based on the deformation difference. Then, the flexspline is divided into multiple sections along the axial direction, so that the three-dimensional tooth profile of the flexspline is modified to improve the gear tooth meshing effect.

This paper proves the effect of the deformation difference between the inner and outer surfaces of the flexspline on the tooth backlash, which affects the transmission accuracy and life of the harmonic drive. It is recommended to modify the tooth profile of the flexspline based on the deformation difference, so as to ensure the tooth meshing effect.

This paper provides a new way for the optimization of the three-dimensional tooth profile design of the harmonic drive.

CURRENT HELICOPTER MAIN TRANSMISSION SYSTEMS must reduce the gas‐turbine engine speed by a typical ratio of 80:1 to drive the main rotor. Existing technology dictates that this ratio is achieved in 3 or 4 stages of gearing, where each stage is either an epicyclic gear assembly, a spiral bevel gear pair or a helical gear pair. Gear tooth reaction forces can be as high as 20,000lbf (90kN) both axially and radially, so large gears and as many as 3 heavy duty rolling elements bearings per gear shaft are required. Transmission systems thus typically account for 10 per cent of all‐up‐weight, the main gearbox taking up 75 per cent of this and the bearings accounting for 20 per cent of the gearbox weight. Scheduled overhaul periods are seldom more than 1,000 flying hr due partly to the likelihood of rolling element bearing fatigue failure and many require overhaul before this time is reached. Thus the research effort on transmission systems, and specifically on gearboxes, is directed in general terms towards achieving:—

This paper aims to present simulation results of a harmonic drive (HD) with involute flexspline (FS) profiles based on two-dimensional (2-D) finite element analysis (FEA).

First, the mathematical model of the FS with involute tooth profile was developed using a straight-edge rack cutter based on the theory of gearing. Then the engaging circular spline (CS) with conjugate tooth profile of FS was derived based on the enveloping theory and theory of gearing. Additionally, a mesh generation program was developed to discretize the FS based on the mathematical model. An elliptical wave generator (WG) was inserted into the FS, and a torque was applied to drive the FS meshing with the CS. The WG and the CS were both assumed to be rigid in the finite element model.

Finally, a 2-D FEA was conducted to explore the stress distribution on the FS, the engagement movement of the FS, the torsional stiffness and the engaged area of teeth of the HD under various conditions. Moreover, this research also studied the effect of changing pressure angle of the involute FS on the performance of the HD.

The simulation model and methodology presented in this paper paved the way for further investigation and optimization of the HD with involute tooth profile FS and conjugate CS.

The simulation model of HD is established on conjugate shape based on the theory of gearing and an automatic mesh generation program is developed to generate the finite element model. The characteristics of the HD can thus be simulated according to the developed model.

Outlines the development of mechanical transmission elements used to drive industrial robots. Examines the performance requirements for precision gears and actuators, concentrating on harmonic drive reduction gearing and the key features which make it superior to conventional transmissions. Concludes that the unique features of the new harmonic drives gears will assist in the realization of completely new robot concepts and that to enable this to happen the process of continuous product development must be on‐going.

The purpose of this paper is to analyze the dependent competing failure reliability of harmonic drive (HD) with strength failure and degradation failure.

Based on life tests and stiffness degradation experiments, Wiener process is used to establish the accelerated performance degradation model of HD. Model parameter distribution is estimated by Bayesian inference and Markov Chain Monte Carlo (MCMC) and stiffness degradation failure samples are obtained by a three-step sampling method. Combined with strength failure samples of HD, copula function is used to describe the dependence between strength failure and stiffness degradation failure.

Strength failure occurred earlier than degradation failure under high level accelerated condition; degradation failure occurred earlier than strength failure under medium- or low-level accelerated condition. Gumbel copula is the optimum copula function for dependence modeling of strength failure and stiffness degradation failure. Dependent competing failure reliability of HD is larger than independent competing failure reliability.

The reliability evaluation method of dependent competing failure of HD with strength failure and degradation failure is first proposed. Performance degradation experiments during accelerated life test (ALT), step-down ALT and life test under rated condition are conducted for Wiener process based step-down accelerated performance degradation modeling.