Running Torque of Slow Speed Two-Point and Four-Point Contact Bearings

Abstract

A decoupled slow speed friction torque model has been developed to predict the running torque of a double-arched angular contact bearing when operating as a four-point, as well as a two-point contact bearing. The load distribution model from Amasorrain et al. (2003) and the kinematics model developed by Leblanc and Nelias (2007) have been combined after ignoring centrifugal and gyroscopic effects, a valid assumption for slow speed operation. Results from the model are compared with previous literature data, as well as with tests done on a specially-developed friction torque rig. The comparison with the literature results was done for two specific cases: (i) when only one out of the two contact lines in the four-point contact bearing is active (effectively creating a two-point contact bearing); and (ii) where both contact lines in the four-point contact bearing are active. Further, the comparison was done with a custom-built friction torque rig with FAG QJ309 bearings, again for two cases: (i) bearings mounted with a specific clearance (two-point contact); and (ii) bearings mounted with larger size balls to obtain interference (four-point contact). All tests were performed at low speeds. The sliding friction, which is an important input to the friction torque model, is carefully measured on ball-on-plate test using the same interface roughness, speed and contact pressure conditions as seen in the QJ309 friction test. The model comparison with experimental results is covered. The comparison is found to be encouraging, with the RMS difference being less than 7% between the model and experimental data for a four point contact.

An engineering approach for the estimation of slewing bearing stiffness in wind turbine generators

“…The mesh was proved to offer reliable results with affordable computational costs. Regarding contacts, frictional contact is defined for the ball‐raceway contact, with a coefficient of friction of 0.1, ; ring‐flange contact is frictional, too, with a coefficient of friction of 0.3, allowing the sliding or the opening of the joint. Finally, a bonded contact is defined between the different bodies of the rings with a pure penalty formulation (see Figure ).…”

Analytical and Low-Order Numerical Modeling of Ball-to-Ball Contact Friction in Linear Ball Bearings and Ball Screws

“…However, due to the small value of μ (around 0.1 according to experimental measurement in Ref. [7]), ball-to-ball contact frictional forces are at least one order of magnitude smaller than the ball-to-groove contact forces. Therefore, it is reasonable to assume that ball-to-groove contact forces are not affected by ball-to-ball contact friction and the calculation of ball-to-ball contact force and friction is decoupled from ball-to-groove contact forces.…”

“…While experiments are very useful in characterizing friction behavior, they often do not have the breadth of scope and depth of insight provided by physics-based models; they can also be expensive to carry out, often requiring specialized jigs. Consequently, building on Jones' work, several physics-based models of friction in ball bearings have been proposed [2,[4][5][6][7]. The typical modeling process is to derive the relative velocity field between each ball-groove contact and obtain frictional force and moment by integrating infinitesimal frictional stress over the contact area; by establishing the quasistatic equilibrium of frictional force and moment, ball motion and friction are solved iteratively.…”

“…Recently, Leblanc and Nelias [6] extended Jones' model from two-point contact to three-and four-point contact ball bearings. Joshi et al [7] simplified the friction model developed by Leblanc and Nelias [6] for high-load low-speed ball bearings with both two-point contact and four-point contact and validated the simplified model against a specially designed friction torque rig. Halpin and Tran [2] used minimum energy criteria to solve the friction dynamics of four-point contact ball bearings.…”

“…It is found that gyroscopic effect is negligible at low-speed application [2,7]. Ignoring gyroscopic effect, the ball needs to be in quasistatic equilibrium under frictional forces and moments as…”