Modelling of joint friction in robotic manipulators with gear transmissions

This paper analyses the problem of modelling joint friction in robotic manipulators with gear transmissions in the sliding regime, i.e. at joint velocities varying from close to zero until their maximum appearing values. It is shown that commonly used friction models that incorporate Coulomb, (linear) viscous and Stribeck components are inadequate to describe the friction behaviour for the full velocity range. A new friction model is proposed that relies on insights from tribological models. The basic friction model of two lubricated discs in rolling-sliding contact is used to analyse viscous friction and friction caused by asperity contacts inside gears and roller bearings of robot joint transmissions. The analysis shows different viscous friction behaviour for gears and pre-stressed bearings. The sub-models describing the viscous friction and the friction due to the asperity contacts are combined into two friction models; one for gears and one for the pre-stressed roller bearings. In this way, a new friction model is developed that accurately describes the friction behaviour in the sliding regime with a minimal and physically sound parametrisation. The model is linear in the parameters that are temperature dependent, which allows to estimate these parameters during the inertia parameter identification experiments. The model, in which the Coulomb friction effect has disappeared, has the same number of parameters as the commonly used Stribeck model. The model parameters are identified experimentally on a Staubli Rx90 industrial robot.