Stiffness design of machine tool structures by a biologically inspired topology optimization method

• Identify possible contributions the growth concept can make to machine tool design.
• Propose a mathematical explanation for the optimality of plant morphogenesis.
• Extend the existing growth theories for global coordinative design applications.
• Investigate into the existing growth algorithm and suggest possible improvements.
• The re-design of an actual machine column validates the method׳s effectiveness.

This paper introduces a novel approach for designing the stiffener layout inside large machine tools by applying the self-optimal growth principle of plant ramifications in nature. Firstly, numerical studies are carried out in order to confirm the potential of leaf venation as concept generators for creating the optimal load-bearing topology for stiffened machine tool structures. Then, a mathematical model explaining the optimality of plant morphogenesis is presented. Based on this, an evolutionary algorithm is developed, which uses three growth strategies to determine the candidate stiffeners to grow or atrophy with respect to the loads applied. The proposed growth-based method could generate a distinct stiffener layout, which is different to those produced by the conventional topology optimization methods, and thus offers unique possibilities of improving the design efficiency and commonality for machine tool development. The suggested approach is finally applied to the re-design of an actual grinding machine column, on which the numerical analyses and experimental tests conducted exemplify the performance enhancement, and therefore is a good choice for the stiffener layout design of machine tool structures.