Optimal In-Operation Redesign of Mechanical Systems Considering Vibrations—A New Methodology Based on Frequency-Band Constraint Formulation and Efficient Sensitivity Analysis

The vibrational behavior of components in mechanical systems like drives and robots can become critical under changes in the system properties or loading in operation. Such undesired vibration can lead to detrimental conditions including excess wear, fatigue, discomfort, and acoustic emissions. Systems are designed to avoid certain frequencies to avoid such problems, but system parameters can change during operation due damage, wear, or change in loading. An example is the change in system properties or operation state that then activates resonance frequencies in our system. Therefore, this work has the goal of modifying the modal behavior of a system to avoid vibrational problems. Methods of design optimization are applied to find a new optimum design for this altered condition. Here, this is limited to the addition of mass in order to move the resonance frequency out of critical ranges. This though requires a new formulation of the optimization problem. We propose a new constraint formulation to avoid frequency ranges. To increase efficiency, a reduced analytical sensitivity analysis is introduced. This methodology is demonstrated on two test cases: a two-mass oscillator followed by a test case of higher complexity which is a gear housing considering over 15,000 design variables. The results show that the optimization solution gives the position and amount of mass added, which is a discrete solution that is practically implementable.