Purpose




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.




Design/methodology/approach




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.




Findings




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.




Originality/value




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.

Analysis of coning and lubrication at flexspline cup and cam interface in conventional harmonic drives

The deformation shape and mechanical property of flex-gear greatly affect the meshing accuracy and service life of harmonic drive, and the stress wave generator plays a decisive role in the deformation shape and mechanical properties of the flexible gear. The investigation on deformation of the flex-gear around the major axis is developed with comparative analysis with three kinds of traditional and commonly used wave generators. Based on the influence of the deformation around the major axis on meshing accuracy and service life, the eccentric arc cam wave generator improved by transition curve for controlling the deformation shape and reducing the deformation stress is developed. Considering the achievable flexibility of spiral with smooth curvature change rate, the contour of the compound curve cam wave generator with arc and spiral is proposed. The deformation of the flex-gear under the influence of this compound curve cam and the standard elliptic cam is further comparative analyzed. The conclusion shows that this compound curve cam can indeed reduce the deformation stress in the meshing area by increasing the meshing width, and correct deformation shape can also be gained by shape control on the whole circumference of the flex-gear’s neutral layer.

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Investigation on Deformation of the Flex-Gear and Optimization Design of Compound Curve Cam Wave Generator with Spiral

The present investigation aims at analysing the effects of surface roughness (three possible types of roughness: isometric, longitudinal and transverse orientation of asperities) on lubrication mechanism at the coning gap which is formed between flexspline cup and cam interface in strain wave gear during assembly of its components. Investigation is further extended to analyse the effects of roughness on lubrication characteristics such as fluid flow speed, fluid flow force and fluid frictional force. In the present investigation at first, generalized Reynolds equation for hydrodynamic lubrication is modified to make it suitable for coning gap and then, micro-polar terms as well as surface roughness terms for all possible roughness (isometric, longitudinal and transverse) are incorporated into it. Conservative form of finite difference method is applied to solve the all three complicated Reynolds equation under suitable boundary conditions. The solution of Reynolds equation is further utilized to derive the lubrication characteristics like fluid flow speed, fluid flow force and fluid frictional force. Methods of finding lubrication pressure profiles and lubrication characteristics under micro-polar fluid with surface roughness are established. Effects of roughness terms on pressure profiles as well as on lubrication characteristics are also established. All analyses are done in dimensionless form. Originality of present investigation is lubrication analysis at the coning gap of strain wave gear under rough surfaces and the finding effects of roughness on it.

Lubrication mechanism and lubrication characteristics analysis at the critical interface of strain wave gear under different types of surface roughness assumptions

Lubrication aspects, at the Wave Generator (WG)-Flexspline (FS) interface of Strain Wave Gearing or Harmonic Drive (HD), are investigated. Geometries of ‘coning’ of FS and its variation with rotation are established to incorporate in hydrodynamic lubrication equation based on generalized Reynolds equation. Non-Newtonian fluid parameters are also incorporated to cover up analysis for odd lubrication conditions that HD faces in many applications. Effort has been given to develop the analytical expression for separation of lubrication film and other various lubrication conditions at WG/FS interface with respect to few general boundary conditions. Results of analytical solutions are also verified in Ansys-APDL environment.

A.K. Ray

Papers

Aspects of lubrication at the wave generator - flexspline interface in strain wave gearing units