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.
The dynamic stability of machining processes is influenced by the dynamic stability of the workpiece and fixture assembly. This effect has not yet been sufficiently considered. Achieving dynamic stability by simply applying a large amount of clamping force is a basic method and involves damages such as elastic deformation of relatively thin workpieces, damage to the clamping surfaces, and high wear of fixture components resulting in malfunction. In spite of this, to the best knowledge of the present authors, the contact stiffness between workpiece and fixture as an influencing parameter has not been sufficiently paid attention by researchers and these parameters have not been taken into account in the equations of dynamic stability. The contact stiffness itself is influenced by the machining parameters. In the present study, the changes in contact stiffness in different machining conditions are investigated as a partial undertaking to fill the gap existing in the modeling of the machining dynamics. In this paper, by defining the mathematical model of the workpiece-fixture system and calculating the matrices of contact stiffness and fixture stiffness, the results of changes in various machining parameters in the stiffness of the workpiece-fixture system have been investigated. The results showed that high contact stiffness cannot be provided simply by applying the maximum force of the clamps. Rather, by increasing the spindle speed, the contact stiffness will increase significantly. Furthermore, by increasing the spindle speed, further increase in the contact stiffness will be achieved with lower feed rates, which will not be economically viable.
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