# Optimized Design of Flexible Quick-Change System Based on Genetic Algorithm and Monte Carlo Method
## 3 Results and Discussion  
### Mechanical Properties of the Different Zero Point Positioning Unit Layouts  
The mechanical analysis of the flexible quick-change system is carried out with the extreme working load (the maximum cutting force in the process) at the highest point of the maximum workpiece. With the difference in number and position of the zero point clamping units, the mechanical distribution of the system is shown in Figure 6.  
We can see that the maximum shear force, torsion force, and overturning moment of the zero point positioning system are solely proportional to the number of distributions. The greater the number of zero point clamping units distributed, the greater the force the system can withstand, allowing it to be more widely applied to working circumstances, thus expanding capacity and improving scale efficiency. The inner circle of the flexible quick-change process system is thought to use a square triangular layout in order to meet the demands of multi-species and multi-process flexible quick-change tooling, subject to the restriction of the minimum workpiece size. When the number of distributions is the same, the distance between the two points reduces, the maximum overturning force increases, and the torsional force increases, while the difference in magnitude is extremely minor. This is true for the layout of the outer ring as well. The main reason is that the maximum overturning force and torsion force on the system are the vector sum of the forces that all the zero point clamping units can withstand. Additionally, when the outer ring layout is square quadrilateral, the force on the system is greater than when it is square triangle, showing that the force on the outer ring layout is stronger when it is square quadrilateral, reflecting that the more balanced and symmetrical the system layout is, the better the stability is, and the wider the working conditions may be adjusted. Comprehensively considering economic factors, mechanical properties, and assembly convenience, the number of outer ring distributions is chosen to be four for further research. Based on the above analysis, the initialized layout is determined to have four positioning pins on the outer ring and three on the inner ring. Then using MATLAB R 2019 b to apply a genetic algorithm, the calculation results are x = 1.57, r = 537.67, and y = 6.5688 \(\times\) 10\({}^{3}\) mm. The optimized layout is shown in Figure 7.  
The flexible quick-change system's structural layout, which consists of three orthogonal and orthotic quadrilaterals, is symmetrical and balanced. The multi-point design of the outer ring's stability analysis shows that it can adapt to a wider variety of operating conditions and that its shear force, torsion force, and overturning moment are greater and more stable. Because the layout spacing is taken into more consideration based on the  
Figure 6: Mechanical analysis of a flexible quick-change process system. experiment and the optimized system's equivalent average strain is lower for the outer four and inner three layouts, the repetitive positioning accuracy is improved. Optimization of Positioning Error of a Flexible Quick-Change Process System Based on the Monte Carlo Method  
The relationship between the flexible quick-change process system and the six components of workpiece posture deviation is analyzed, predicted, and quantitatively described using the Monte Carlo method. Guaranteeing the improvement of the dimensional fit tolerance of each component of the flexible quick-change process system as well as the improvement of the mating type of the positioning elements, enhancing the flexibility of the system's positioning accuracy. \[\mathrm{q}_{\mathrm{w}}= \begin{bmatrix}\Delta\mathrm{x}\\ \Delta\mathrm{y}\\ \Delta\mathrm{z}\\ \Delta\mathrm{x}\\ \Delta\mathrm{\beta}\\ \Delta\mathrm{y}\end{bmatrix} =