The influence of the lubricant viscosity on the rolling friction torque Mihaela Rodica D. Bălan a , Vasile Ciprian Stamate a , Luc Houpert b , Dumitru N. Olaru a,n a Technical University “Gheorghe Asachi” Iasi, Department of Mechanical Engineering, Mechatronics and Robotics, Boulevard D. Mangeron 61-63, 700050 Iasi, Romania b TIMKEN Europe, 2 rue Timken, B.P. 60089, 68002 Colmar, France article info Article history: Received 4 October 2013 Received in revised form 20 November 2013 Accepted 28 November 2013 Available online 8 December 2013 Keywords: Rolling friction Lubricated contacts Thrust ball bearing Elastohydrodynamics abstract Authors propose a theoretical model and an experimental methodology for defining the friction torque in a modified thrust ball bearing, operating in mixed and full film lubrication conditions. The friction torque was measured at low loads and large Λ parameter range using a spin-down method. A comprehensive analytical bearing torque model is described using elastic rolling resistance, curvature effects, inertia forces, disc-air resistance and ball-races hydrodynamic rolling forces, the latter explaining 98% of the final bearing torque. Several sets of hydrodynamic rolling force relationships respecting the transition from IVR to EHL lubrication regime were tested. Final numerical results are shown to be very close to the experimental ones in both full film and mixed lubrication conditions. & 2013 Elsevier Ltd. All rights reserved. 1. Introduction The rolling resistant torque of a ball on the raceway in a bearing is due to miscellaneous concepts, including elastic hysteresis losses due to micro slip in the contact and curvature effects, hydrodynamic lubricant resistance, roughness and form deviations effects on torque. The resistant moment around the contact center to rolling due to elastic hysteresis losses in the rolling process and contact micro slips can be approximated by the following relationship [1,2]: MER ¼ 7:48 10 7 d 2  0:33 Q 1:33 1 3:519 10 3 ðk 1Þ 0:8063 n o μ s 0:11 ½Nm ð1Þ Where Q is the normal load, d is the ball diameter, k represents the ratio R y /R x , in which R x and R y are the reduced radii of curvature in the rolling direction and the transverse direction, respectively. The sliding friction coefficient μ s has a maximum value of the order of 0.11 in dry contact conditions, while in the presence of a lubricant film this value decreases [1]. At the contact between a ball and the rolling track in a thrust ball bearing, in the absence of additional spin as a result of zero ball-race contact angle and in the absence of the gyroscopic motions, only two symmetrical lines of pure rolling exist in the contact ellipse [2]. Elsewhere, positive and negative sliding speed can be defined because the contact ellipse is curved in space. As a result of this raceway curvature, an additional moment MC around the contact center can be defined using the following relationship [1,3]: MC ¼ 0:08μ s Qa c 2 R d Nm ½  ð2Þ where μ s is the average friction coefficient on the contact ellipse, defined as a function of the lubrication regime, a c is the major semi-axis of the contact ellipse, R d is the radius of the deformed contact surface R d ¼ 2dRc 2Rc þ d   , in which R c is the transversal curva- ture radius of the rolling track. For a contact between a ball and the raceway in a ball bearing operating in dry conditions the total rolling moment around the contact center can be obtained by summing Eqs. (1) and (2). Dry friction, is however not common in bearings and it is essential to also account for lubricant effects on the final bearing torque. In order to estimate the global friction losses in ball bearings and tapered roller bearings, Houpert [1, 2, 4] devel- oped several analytical models in which the lubrication regime affects both the friction coef ficient μ s and a hydro- dynamic rolling force FR. The accurate estimation of the friction coefficient μ s has been the subject of several theoretical and experimental studies using non- linear visco-elastic and thermal models. Roughness effects on friction are also introduced via the parameter Λ (defined as film thickness divided by the composite RMS surface roughness), [1,11,12, 16]. Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/triboint Tribology International 0301-679X/$ - see front matter & 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.triboint.2013.11.017 n Corresponding author. Tel./fax: +40 0232 232337. E-mail addresses: ro_balan@yahoo.com (M.R.D. Bălan), luc.houpert@timken.com (L. Houpert), dolaru@mail.tuiasi.ro (D.N. Olaru). Tribology International 72 (2014) 1–12