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

Bikash Routh (School of Mechanical Engineering, Vellore Institute of Technology, Vellore, India)
Rathindranath Maiti (Department of Mechanical Engineering, Indian Institute of Technology, Kharagpur, India)
Asok Kumar Ray (Department of Mechanical Engineering, Birla Institute of Technology, Ranchi, India)

Industrial Lubrication and Tribology

ISSN: 0036-8792

Article publication date: 13 November 2017




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.



This research work is an outcome of the general PhD program. There is no specific financial grant for this investigation. However, the second author deeply acknowledges the R&D project Grant No. SR/S3/RM-04/2002, dated 11-07-2002, by the Department of Science and Technology, Government of India, for the initiation of the investigation on HDs.


Routh, B., Maiti, R. and Ray, A.K. (2017), "Analysis of coning and lubrication at flexspline cup and cam interface in conventional harmonic drives", Industrial Lubrication and Tribology, Vol. 69 No. 6, pp. 817-827.



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