Mathematical models for estimating the degree of influence of major factors on performance and accuracy of coordinate measuring machines

¹ Institute of Precision Mechanics and Control of RAS, 24 Working st., Saratov, 410028, Russia
² Perm National Research Polytechnic University, 29 Komsomol pr., Perm, 614990, Russia
³ Yuri Gagarin State Technical University, 77 Politecknicheskaya str., Saratov, 410054, Russia
⁴ Samara National Research University, 34 Moscow Highway, Samara, 443086, Russia

^* Corresponding author: zov17@mail.ru

Abstract

Increased productivity of Coordinate Measuring Machines, while providing given level of accuracy, is complex and actual problem of robotics and metrology. Therefore, this article provides a set of mathematical models that allow for prediction of values for performance and accuracy of advanced Coordinate Measuring Machines based on system dynamics method. The analysis of scientific literature and statistical data of exploitation CMMs Global Performance (DEA, Italy), CMM-750 (Lapik, Russia), FARO Arm 9 (FARO Technologies, USA) has identified 25 major factors of the process control and their mutual impact. Of the 16 basic factors are internal system parameters, 6 input actions and 3 external factors. As a result of the system analysis of the research object identifies the main characteristics of coordinate measuring machines that affect performance and measurement accuracy. We have done a general graph of causal relationships between modeled characteristics, on the basis of which is made up and numerically solved a system of nonlinear differential equations. In developing this system of equations is used in statistical data describing the cause-effect relationship between the internal model parameters and environmental factors. These solutions make it possible to practically interpret developed models and methods of system dynamics used in solving the problem.