Stiffness Evaluation: Collinear Stiffness Value Based Approach


Quality control of machines with heavy demands on accuracy and productivity, such as machine tools, coordinate measuring machines, and industrial robots includes stiffness testing as a regular stage [1, 2]. The testing methods are fixed in national and international standards, which quantitatively limit the minimal effective stiffness value. For example, the standard stiffness test for a universal lathe includes measuring radial and axial displacements of the main spindle caused by given active radial and axial force, respectively. For a given pair “force vs. linear displacement” or “torque vs. angle-of-rotation”, the stiffness value has a simple definition as the ratio of the absolute values of the force (torque) to the linear displacement (angle-of-rotation). The same approach presenting stiffness mapping [3] is regularly applied for stiffness control of the parallel kinematics machines (PKMs) such as hexapod-based and tripod-based machines [4–7].

4.1Introduction to stiffness assessment problem
4.2CSV-related definitions and formulations
4.3Evaluation of the minimal CSV
4.4Application to the 3-3 Gough-Stewart platform (GSP)
4.5Workspace of the machine satisfying stiffness limits
4.6CSV of the 5-axis machines
4.7CSV of articulated robots
Topics: Stiffness

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