Multi-Objective Optimization and Tradespace Analysis of a Mechanical Clock Movement Design

Abstract

Pendulum clocks were the prevalent time keeping standard for centuries to regulate commerce and public activities. These mechanical movements were the most accurate timekeepers globally until replaced by electric clocks. Although mainly used for decorative purposes today, the pendulum clock's working principles and mechanical behavior can serve to demonstrate fundamental science and engineering concepts. The tradeoff between a clock's quality factor, pendulum properties, and period can best be explored with multiple objective optimization and tradespace analysis methods. In this project, a Multi-Objective Genetic Algorithm (MOGA-II) and a Multi-Objective Simulated Annealing (MOSA) optimization approaches are applied to evaluate a Graham escapement street clock for pendulum mass and time accuracy with a range of the period. These clock designs vary the pendulum length, pendulum bob radius, and bob thickness. Horological concepts are used to calculate the overall performance and general utility. The numerical results show a 0.7% increase in the quality factor, and a 0.56% reduction in the mass, while maintaining the designed period by modifying the clock parameters. More importantly, these changes can provide material cost savings in a mass production scenario. Overall, the study highlights the tradeoff designer engineers have considered for decades which can now be visualized using computer tools for greater insight.