Evaluation, calibration, and modal analysis for determination of contact stiffness between workpiece and components of milling fixture

Abstract

The stability of workpiece inside fixture influences the dynamics of machining. Although, the workpiece is uniquely and deterministically positioned and grasped by the fixture, it undergoes small displacements due to the contact compliance resulting from the frictional slip under the external loads and vibrations. The frictional slip of workpiece, along or around the main axes relative to the fixture components is a major cause of instability and the main element influencing the contact stiffness between the workpiece and the fixture. In the present study, a procedure has been developed to evaluate the contact stiffness by employing mathematical and experimental tools. The grasp matrices defined in analytical model were obtained by a combination of calibration and measurement of forces, displacements, and friction coefficient. The contact stiffness was also determined by modal analysis of the assembly of workpiece and fixture and the results were compared. It was evidenced that the dry friction existing in the contact areas between the workpiece and fixture elements could lead to the stick-slip instability, detrimental to the dynamics of machining. The main contribution and novelty of the present study can be outlined, as follows. The contact stiffness between workpiece and fixture was modeled and measured. The frictional slip was modeled and measured in addition to the physical compliances. Dry friction between workpiece and fixture was detected as a source of stick-slip. Procedures were developed to calibrate and measure all forces and displacements. Modal analysis was done as a complementary tool to verify the results.