Friction Forces in a Linear-Guideway Type Recirculating Ball Bearing Under Grease Lubrication

This paper deals with friction forces in a linear-guideway type recirculating ball bearing (linear bearing) under grease lubrication. During the experiments, the friction force, temperature, and electric contact voltage of a grease lubricated linear bearing (test bearing) without seals were measured. Experimental results showed that the measured friction forces of the test bearing were fluctuated with the ball passage period. The measured time-average friction force FAVG (measured FAVG) was nearly constant when the grease filling rate x (=grease filling volume/internal space of the bearing) ≥0.13, while the measured FAVG decreased as x decreased when x < 0.13. In addition, the measured temperatures were almost constant, and the measured contact voltages indicated that the contacts of the balls and raceways were electrically insulated by the grease film. Next, the expressions of friction forces due to differential slip (FD), elastic hysteresis loss (FE), and rolling traction (FRT) were shown. The calculated FD + FE + FRT for the test bearing was almost equal to the measured FAVG around the grease filling rate of x = 0, while in cases where x > 0, the measured FAVG was greater than the calculated FD + FE + FRT. This means that when x > 0, an agitating resistance (FA) from the grease might cause the measured FAVG to be greater than the calculated FD + FE + FRT. Finally, an expression for the friction force of a linear bearing, FAVG = FD + FE + FRT + FA (which can estimate the measured ones) is proposed.

Analysis of Measured Friction of Rolling Balls in Raceway Grooves

Friction in linear guideways has an influence on the motion accuracy of machine tool drives. As feedback control has a lag to the friction change in reverse motion, a feedforward compensation is generally used in friction models. However, it is difficult to estimate the friction of rolling balls in raceway grooves because it involves both stick and differential slip characteristics. In this paper, a measurement method is presented using an analytical procedure to clarify micro stick and slip factors in rolling friction. In the measurement test, four balls and two raceway grooves are used to measure the friction force under dry and lubricated conditions. The locomotive bristle model is then applied to identify the stick and slip parameters, which are then compared between the various conditions of lubrication.

Inverting measurements of surface slip on the Superstition Hills fault

We derive and test a set of inversions of surface-slip measurements based on the empirical relation u(t) = uf/(1 + T/t)c proposed by Sharp and Saxton (1989) to estimate the final slip uf, the power-law exponent c, and the power-law duration T. At short times, Sharp's relation behaves like the simple power law, u(t) ∼ u1tc, where u1 is the initial slip, that is, the slip at 1 day after the earthquake. At long times, the slip approaches the final slip asymptotically. The inversions are designed in part to exploit the accuracy of measurements of differential slip; that is, measurements of surface slip which are made relative to a set of nails or stakes emplaced after the earthquake. We apply the inversions to slip measurements made at 53 sites along the Superstition Hills fault for the 11 months following the M = 6.2 and 6.6 earthquakes of 24 November 1987. In general, estimates of the initial slip and the power law exponent are well resolved, while estimates of the power-law durations and the final slip are less well resolved because the durations of the surface slip measurements are often less than the derived power-law durations. The slip on the three fault strands is a relatively smooth function of position; the initial slip and final slip are well correlated. The time dependence of surface slip at the 53 sites is roughly similar along the entire fault, where the power-law exponents are distributed as c = 0.14 ± 0.04 and the power-law durations range from 100 < T < 1000 days.

The mechanism of rolling friction II. The elastic range

This paper discusses the mechanism of rolling friction under conditions where the deformations involved are predominantly elastic. Experiments on the rolling of a metal cylinder over a rubber surface show that interfacial slip of the type described by Reynolds is minute and totally insufficient to account for the observed resistance to rolling. It is shown quantitatively that the rolling resistance under these conditions is due to elastic hysteresis losses in the rubber. This accounts for the ineffectiveness of lubricants in reducing the rolling friction. Similar results are obtained for hard spheres rolling on rubber surfaces. If, however, a sphere is rolled in a preformed rubber groove, interfacial slip between the ball and groove may occur since the central band on the ball measures out a larger circle than the bands at the edge of the groove. A simple quantitative theory of this effect is given. This type of slip, first described by Heathcote, is very marked when the groove is deep and of curvature very close to that of the ball; under these conditions a suitable lubricant can effect a considerable reduction in the rolling resistance. For shallower grooves the differential slip is reduced and the Heathcote contribution to the observed rolling resistance becomes trivial. These conclusions are applied to the rolling friction of a hard steel sphere in the equilibrium groove formed in the surface of a softer metal (part I). If the rolling friction is attributed to the Heathcote mechanism a coefficient of friction within the ellipse of contact of the order of u = 1 to 2 must be invoked even in the presence of the best boundary lubricants. This is impossibly high. If, on the other hand, the rolling friction is attributed to hysteresis losses, large loss factors, greater than 20 %, must be invoked for example for copper surfaces. In order to resolve this difficulty a new experimental approach has been adopted in which a copper ball is rolled over an identical copper ball. Because of symmetry conditions at the region of contact both the Reynolds and the Heathcote type of slip are eliminated. The equilibrium rolling friction is found to be as high as that observed when a hard steel sphere rolls in a copper groove. It is concluded that interfacial slip contributes little to the rolling friction although it may play an important part in surface wear. Consequently, lubricants may reduce the amount of wear but have little effect on the rolling resistance. The greater part of this arises from elastic hysteresis losses within the metals themselves.