Influence of wave generator profile on the pure kinematic error and centrodes of harmonic drive

A novel method based on mechanical analysis for the stretch of the neutral line of the flexspline cup of a harmonic drive

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 flexspline 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.

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

Optimal design of wave generator profile for harmonic gear drive using support function

Purpose




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).




Design/methodology/approach




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.




Findings




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.




Research limitations/implications




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.




Originality/value




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.

Study of a harmonic drive with involute profile flexspline by two-dimensional finite element analysis

The parametric design of double-circular-arc tooth profile and its influence on the functional backlash of harmonic drive

Tooth effects on assembling bending stress of flexible tooth rim in harmonic drive

Harmonic drive has widespread applications in power transmission for its compact size and high speed reduction ratio. Flexspline usually endures large deformation under assembly force from wave generator. In transmission state, driving force leads to multiple teeth engagement between flexspline and circular spline. Large deformation of the flexspline and contact relations between flexspline and wave generator, flexspline and circle spline make the problem more complicated than other transmission device ever. To simplify the geometry relation of flexspline, one of the assumptions in harmonic drive analysis is no elongation of neutral line, which leads to great simplification in deformation and engagement analysis of flexspline. With help of the classic relationship and finite element analysis (FEA), the rationality of the assumption is estimated in both assembly state and working state here. The geometric expressions of neutral lines are introduced first, and the elongation of the neutral lines is derived for commonly used wave generators. Then a FEA model of a flexspline in harmonic drive with eccentric double-disk roller wave generator is built, and the contact relation is defined between wave generator and flexspline. Contact analysis is carried out in assembly state and working state respectively. The elongation of the neutral line is calculated by the radial and tangential displacements. The elongation in assembly state and transmission state is compared with the original circumference length and the elongation strain is given. The research shows that the assumption is approximative in assembly state and transmission state. The elongation should be considered in harmonic drive under transmission loading.

The investigation of elongation of the neutral line in harmonic drive

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 relationship, 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.

Jingzhong Xing

Papers

The parametric design of double-circular-arc tooth profile and its influence on the functional backlash of harmonic drive

A novel method based on mechanical analysis for the stretch of the neutral line of the flexspline cup of a harmonic drive

Tooth effects on assembling bending stress of flexible tooth rim in harmonic drive

The investigation of elongation of the neutral line in harmonic drive

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