Mechanical component’s dimension design with required reliability by the Monte Carlo method

Xiaobin Le

Wentworth Institute of Technology

Abstract:

The mechanical component dimensions due to manufacturing tolerance should be treated as a random variable.  Material mechanical properties such as yield strength, ultimate strength, and fatigue strength are random variables too due to some defects randomly distributed inside materials and some inevitable slightly-variation in chemical composition, heat treatment, and manufacturing forming process during manufacturing of the materials.  loads on a batch of the same mechanical components are certainly random variables because a load on each individual component of the same batch of component is certainly different in the different service environments.  So, reliability is a better design parameter to measure the safety status of a component. 

The mechanical component will be safe and reliable only if it is designed with the required reliability.  Therefore, the mechanical component design should be the dimension design with the required reliability.  It is always a difficult issue conducting a mechanical component’s dimension design with required reliability for a mechanical component under specified load conditions.  Two difficulties for this task are: (1) The governing equations are hard to be built for some cases such as components under cyclic loading.  The governing equation means that an equation links dimension, load, material strength and reliability; and (2) The computational method is complicated because all design parameters are described by the probabilistic distribution function. 

This paper will present a Mechanical component’s dimension design with the required reliability by the Monte Carlo method.  First, the paper will show how to create governing equations for typical simple static loading, static combined loads and cyclic loads. For a component under a simple static load, the governing equations can be created by comparing component strength such as yield strength or ultimate strength with the component’s maximum stress.  For a component under combined static loading, the failure theories such as the maximum shear stress theory, the distortion energy theory or the Mohr-Columbian theory can be used to create the governing equations.   For a component under cyclic load, the P-S-N curve theory could be used to create the governing equation.  But the K-D model proposed by the author can be implemented to create a governing equation for a component under any type of cyclic load.  Then, the paper will present the dimension design computational method and procedure.  Since the governing equations are typically statistically expressed and all design parameters are treated as random variables, there is no analytical solution for lots of design cases.  Since the personal computer is available for almost every design engineer, the author proposes the  dimension computational method by the Monte Carlo Method.  The flowchart will be presented for this method and the MATLAB program will be used to compile a program to conduct the dimension design with the required reliability.   Finally, four examples will be presented to show how to implement this dimension design computational method for dimension design with required reliability.  

Keywords: Mechanical Design, Reliability, Computational method, Failure theory, reliability-based design, The Monte Carlo Method. 


Mechanical Component\u2019s Dimension Design With Required Reliability by the Monte Carlo Method

Division / Sponsors: 
Aerospace, Bioengineering, Applied Mechanics, Design Engineering Division, Advanced Energy Systems, Manufacturing Engineering Division, Noise Control and Acoustics, Nondestructive Evaluation, Diagnosis, and Prognosis (NDPD), Nuclear Engineering Division, Process Industries Division, Fluids Engineering, Heat Transfer, Materials, Microelectromechanical Systems, Safety Engineering and Risk Analysis, Computers & Information in Engineering


Paper Proceedings: https://asmedigitalcollection.asme.org/IMECE/IMECE2020/volume/84478

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