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In general machining operations, the cutting tools were held by the draw - in mechanism in the spindle. Insufficient draw - in force would cause poor machining efficiency and quality. So, the draw - in force should be measured peridoically by a set of measurement system after the CNC machine operated for a long time. A set of draw - in force measurement device was designed by Yung - Da Chen in 1996. The force produced by the helical spring in the measurement device balanced the draw - in force produced by Belleville springs. Then the draw - in force produced by Belleville springs. Then the draw - in force could be measured by the displacement variation of the helical spring which was compressing and spinning. General dynamic equations for the springs with circular cross section, varying pitch angle and radius were derived by using Hamilton's Principle and variational method. For a specific spring with constant axial loading and rotation speed, the axial and radial deformation were found in this research. Then, the finite element model built b using finite element analysis software were used to find the axial deformation of the helical spring at specific axial loading and rotation speed. The results we found by FEM analysis and theoretical derivation had the same tendency.
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