Engineering Transactions, 21, 3, pp. 363–376, 1973

### Wpływ Zmiany Kąta Działania na Sztywność Łożyska Wieńcowego przy Obciążeniu Złożonym

T. Gibczyńska
Politechnika Krakowska, Kraków
Poland

The paper presents approximate formulae for the stiffness of a double-row collar bearing (3.12) with toroidal raceways and contact angles 0 < α < 90°, loaded by a plate system of forces, in the case of large moments M and small forces Q, H – axial and radial. In the relations derived (3.12), the parameter R/a takes into account the changes of the contact angle resulting from the deformations of both the balls and the raceway. When a = ∞, Eqs. (3.12) reduce to the formulae determining the stiffness of bearings with conical raceways. On the basis of Eqs. (4.2) and the results of [3] – Eqs. (4.1) – the influence of the contact angle changes on the bearing stiffness due to the deformation of balls and the bearing is determined.
The influence is considerable in the case when the bearing is subjected to a combined load with a great axial force component, and the load is transmitted by a single row of balls, Eq. (4.1). Disregarding of the contact angle change makes it impossible to determine the displacements R sin η and xo, which at a → ∞ (conical raceways) also tend to infinity. Thus it follows that in bearings with conical raceways, a single row of balls cannot transmit a combined load since such a system would not be in equilibrium. The only exception is represented by a load consisting of an axial force, a radial force and a moment, when the both forces are related by Eq. (4.3). On the other hand, it follows from the present paper that, for large moments, the influence of contact angle change is rather small; certain rules may be, however, established, namely: (a) With increasing ratio R/a, the generalized displacement sin η decreases independently of the sign of forces Q and H, since the coefficient ψ100 is negative. (b) For R/a → 0, that is for a → ∞, all the generalized displacements tend to finite values corresponding to the generalized displacements of the bearing with conical raceways.

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