A theoretical derivation has yielded a general expression for the operating torque of a tapered roller bearing under pure thrust load. Experimental data have been obtained to enable determination of the constant and exponents to make this expression usable. Further theoretical analysis has extended the use of the thrust load equatiorz to pure radial and combined radial and thrust loads. Comparison of calculated and measured operating torques under radial load has ver$ed the theoretical derivation.The bearing geometry variables from the basic torque equation have been combined into a G factor which represents the heat generation potential of a bearing. NOMENCLATURE a, b = exponents Di = mean cone race diameter, in Do = mean cup race diameter, in D, = pitch diameter = $ (Di + Do), in D = mean roller diameter, in ei, e, = offset of centroid of pressure distribution from geometric center of contact (see Fig. 8), in E' = combined modulus of elasticity, Ib/in2 F, = bearing thrust load, Ib F, = bearing radial load, Ib f~ = equivalent thrust load factor G = bearing geometry factor h = cone rib-roller end contact height, inJ , = SjZivall's radial integral k, k', k" = constants K = bearing K factor = ratio of basic dynamic radial load rating to basic dynamic thrust load rating 1 = roller-race contact length, in m = torque per roller Ib-in M = total bearing torque, Ib-in A typical bearing application illustrates use of ihe equations.
In this paper the author has developed a model for calculating the torque of a tapered roller bearing, including both the rolling resistance generated at the roller-cone and roller-cup contacts and the sliding resistance generated at the roller end-rib contact. Expressions for the tangential rolling resistance and roller end sliding friction have been applied to the roller and equations of equilibrium written for the roller. This approach is very sound and should result in a model that will describe the bearing torque as a function of the operating conditions. This assumes that the model includes all of the major sources of resistance to motion. However, the model developed did not agree with the experimental data generated under conditions where the rolling resistance was the primary source of bearing torque. In particular, the author's equation (7) predicts the rolling torque to be nearly independent of load while the experimental data show torque to be related to load to the 0.3 power. A correction is then made to the original equation to obtain agreement with the experimental results. While this is a valid approach to developing a usable equation, it is suggested that by questioning the initial model shown in Fig. 3, one might conclude that all of the pertinent forces are not included.In Fig. A-l the normal roller reaction is shown offset due to the skewed pressure distribution. The author shows the roller moment to be the product of the roller reaction and offset distance, but does not actually apply this moment to the roller in Fig. 3. It is suggested that the proper application of this moment to the roller would allow load to be adequately accounted for in the model. In [Dl], Hamrock and Jacobson derived an expression for the distance to the center of pressure. When this is converted into a dimensional form, it is found that the moment (product of the roller reaction and the offset distance) is related to the load raised to the 0.37 power, which agrees with the author's experimental data.At this conference in 1972, this discussor presented reference [17] in which a rolling torque model for tapered roller bearings was developed. The basis for that model was applying the roller reaction through the center of pressure. This allows a bearing torque equation to be written that is dependent only on the offset distance since all of the other variables can be determined by geometry and kinematic considerations. The experimental data then was used to establish the exponents on load, viscosity and speed. A load exponent of 0.33 was found to describe the torque-load relationship.The author's equations (26) and (27) require detailed knowledge of the bearing's internal geometry. This makes it difficult for a design engineer to utilize the information presented in this paper because the details necessary are not readily available. Does the author plan to pull the bearing geometry data into a number similar to the G factor developed in reference [17]?The term describing the torque contribution of the roller end-rib con...
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