Calculation of clamping error when mounting a workpiece on fixture supports

This article examines the conditions for reliable clamping of workpieces in fixtures, which are one of the main elements in a technological system. In order to calculate clamping error of workpieces in fixtures empirical relationships of nonlinear character are currently used. Values of the coefficients included in these relationships are only specified for steel or cast iron workpieces. The paper presents the technique for calculating the clamping error of workpieces mounted on fixture supports with spherical heads, which allow to achieve the greatest locating precision. Practically, this technique allows to perform the calculation of the specified error for different fixturing conditions of workpieces. Mathematical relationships for calculation of the error for machining workpieces of any modern engineering materials are obtained. Comparative analysis of the obtained relationships for the standard conditions of force contact of the support elements with the workpiece showed that the clamping error calculated in accordance with the obtained relationships and taking into account friction forces in the contact area of the supports with the surface of steel workpiece almost coincides with the error determined by formulas given in the reference literuture. It is demonstrated that with the decrease in clamping force the elastic displacements at the interface are negligible and the clamping error can be calculated through a simplified relationship.