Boundary lubrication in screw-nut transmissions

Abstract: This report deals with the function of screw-nut transmissions (powerscrews). Two aspects of this function have been investigated. Owing to different running parameters, primarily sliding speed and average pressure between the sliding surfaces of the thread, the coefficient of friction and the efficiency will vary within wide limits. The running parameters can be summarized in a dimensionless number, the Sommerfeldt number S. The problem, which has reference to boundary lubrication, is solved by a theoretical model. The model is based on two types of interaction between the sliding surfaces, namely solid friction at asperity peaks and liquid friction in the voids between the asperities. An optimal interval of the Sommerfeldt number, where the coefficient of friction is at its minimum, has been established: 0.025 < S opt < 0.042. As a result of friction between the sliding surfaces, heat is developed, which is conducted through the material of the screw and nut. The developed heat can cause high temperatures on the sliding surfaces of the thread. The capability of performance is limited by the development of high temperatures in the thread, where the running temperature of the actual lubricant must not be exceeded. Physically, the phenomenon relates to heat conduction. A theoretical model is put forward. In the model the screw is replaced by a cylindrical rod and a hollow cylinder corresponds to the nut. The equation of heat conduction is stated and solved for the case ofsteady state in the actual regions. It is shown that an infinitely thin wall of the hollow cylinder is the most severe case with a maximum rise in temperature. The result is presented in the form of a diagram with dimensionless temperature, rod speed and length of cylinder. The report ends with recommendatons for how the results can be used for designing screw-nut transmissions. In this context three numerical examples are given.