The influences of the fluid capacitance in the oil feed line system on the transient response of hydrostatic guideways

Abstract

A machine tool table supported by externally pressurized guideways can be frequently found to exhibit an underdamped response to squeeze loads when the supply pressure for the hydrostatic guideways is changed by means of the restrictor or the pressure regulator in the pressurized oil feed line in order to obtain suitable bearing characteristics. It is known that the resulting overshoot is largely affected by the oil feed line between the restrictor and the recess, because the oil feed line has some fluid capacitance induced by the compressibility of the pressurized oil, the elastic deformation of the pipe and the intermixing of air into the overall system. To clarify the influences of the fluid capacitance in the oil feed line on the dynamic characteristics of the hydrostatic guideway, the overshoots resulting from step loads have been investigated. Experiments were carried out with a simple model hydrostatic guideway system having a pipe line with large fluid capacitance and the changes of oil film thickness have been measured. From the experimental results, it is shown that the overshoot ratio which is defined as the ratio of the overshoot to the steady displacement of table increases with increasing fluid capacitance in the pipe line and shows a maximum value when the oil film stiffness is a maximum. In the case of constant bearing load condition, the maximum oil film stiffness can be found when the value of pressure ratio p r / p s is not equal to 2 3 but 1 3 , where p r is the recess pressure and p s is supply pressure. To confirm these experimental results, the motion of a table supported on an externally pressurized oil film has been studied theoretically. The results are in good agreement with the experimental results and show that the overshoot rate is governed by a dimensionless characteristic T c which is the ratio of static oil film stiffness K s to compressibility stiffness K c defined as K c = A 2 e / C a and dimensionless static oil film stiffness K s is defined as K s = K s/(W/h) , (where, C a is the fluid capacitance in the pipe line between the recess and the restrictor, A e is the effective area of the pad, W is the bearing load and h is the oil film thickness). The term T c determines the overshoot rate and the overshoot appears in the case when T c > 1. Furthermore, in order to indicate that the optimum pressure ratio p r / p s is equal to 1 3 in the case of constant load, the relationship between the oil film stiffness K s and the pressure ratio p r / p s considering the various bearing conditions have been calculated and it is shown that there are four optimum conditions.