Optimal Spring Balancing Cylinder Design of an Industrial Robot Using Multi-Disciplinary and Multi-Objective Optimization

Abstract

This article presents an automated approach in optimal design of the spring balancing cylinder of an industrial robot using multi-disciplinary and multi-objective design optimization. Spring balancing cylinder is a mechanical device typically used in industrial robots of high load handling capacity. The objective of use of such device is to effectively balance one of main axes (typically axis-2) subject to the most severe gravitational torque. The spring balancing cylinder consists typically of multiple springs (two or three) co-axially installed inside the cylinder. Design of such balancing device involves about 16 design parameters, including both geometric parameters (free length, wire diameter, spring outer diameter, and number of turns) and parameters defining mounting positions of the device on a robot. Optimal design of such device is to achieve desired balancing, measured by maximum unbalanced static torque of the balanced axis, with minimum weight and volume of the cylinder. More desirably, the trade-off relationship between the maximum static torque measured by a balancing degree index and weight of the balancing cylinder is explored. Design of such balancing device is subject to a number of hard constraints defining fatigue lifetime of the springs and geometric interference between adjacent springs both in radial and axial directions. Solving of this design problem requires use of two different design tools. The first design tool is a robot static design tool. The entire robot statics is modeled. The maximum static torque of the balanced axis is calculated by finding the maximum value of static torques of the axis as function rotational angles of the axis within its limits. The maximum static torque is used as one of the design objectives. The second design tool is a detailed spring dimensioning tool. The overall spring constant and pre-loading force are determined subject to constraints of geometric and fatigue lifetime. The integration of the design tools is accomplished using a commercial software tool modeFrontier. This challenging design problem is formulated into an optimization problem of mixed design variables, multi-objective and multi-constraint nature and solved fully automatically using Multi-Objective Genetic Algorithm (MOGA) implemented in the modeFrontier modeling and optimization environment. The trade-off relationship between the balancing degree and the weight of the springs have been quantitatively explored. Even though some limitations of the developed methodology do exist and need further improvement, it is convinced that the developed approach is ready to be applied in industrial design practice.