Stiffness Model of a Die Spring
Forrester, Merville Kenneth
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The objective of this research is to determine the three-dimensional stiffness matrix of a rectangular cross-section helical coil compression spring. The stiffnesses of the spring are derived using strain energy methods and Castiglianoâ s second theorem. A theoretical model is developed and presented in order to describe the various steps undertaken to calculate the springâ s stiffnesses. The resulting stiffnesses take into account the bending moments, the twisting moments, and the transverse shear forces. In addition, the springâ s geometric form which includes the effects of pitch, curvature of wire and distortion due to normal and transverse forces are taken into consideration. Similar methods utilizing Castiglianoâ s second theorem and strain energy expressions were also used to derive equations for a circular cross-section spring. Their results are compared to the existing solutions and used to validate the equations derived for the rectangular cross-section helical coil compression spring. A finite element model was generated using IDEAS (Integrated Design Engineering Analysis Software) and the stiffness matrix evaluated by applying a unit load along the springâ s axis, then calculating the corresponding changes in deformation. The linear stiffness matrix is then obtained by solving the linear system of equations in changes of load and deformation. This stiffness matrix is a six by six matrix relating the load (three forces and three moments) to the deformations (three translations and three rotations). The natural frequencies and mode shapes of a mechanical system consisting of an Additional mass and the spring are also determined. Finally, a comparison of the stiffnesses derived using the analytical methods and those obtained from the finite element analysis was made and the results presented.
- Masters Theses