Robots are main elements in Industry 4.0. Research on the design optimization of robots has a great significance in manufacturing industries. There inevitably exist various uncertainties in robot design that have an important influence on the reliability of robots. At present, the design optimization of robots considering the uncertainties is mainly focused on joints design and trajectory optimization. However, for the structural design of robots, deterministic design optimization still plays a leading role. In this paper, a simulation-based reliability design optimization method is proposed to improve the reliability of robots’ structural design. In the proposed method, the Latin hypercube sampling (LHS), computer simulation, response surface method (RSM) and SORA (Sequential Optimization and Reliability Assessment) algorithm are integrated to complete the structural design of the robot. Firstly, samples of the uncertainty design variables were obtained by LHS, and then, the reliability performance constraint functions were firstly constructed through the RSM in which the joint simulation of MTLAB and ANSYS was adopted. Afterwards, the reliability design optimization model was established on the basis of the probabilistic reliability theory. At last, the SORA algorithm was employed to realize the optimization. The design optimization problems of the big arm and the small arm of a 6 Kg industrial robot were considered to verify the proposed method. The results showed that the weights of the big arm and the small arm were, respectively, reduced by 7.73% and 25.70% compared with those of the original design, and the design was more effective in ensuring the reliability requirements compared with the deterministic optimization. Moreover, the results also demonstrated that the proposed method has a better computational efficiency compared with the reliability design optimization of the double-loop method.

A response surface method based on the all sample point interpolation approach (ASPIA) is proposed to improve the efficiency of reliability computation. ASPIA obtains new sample points through linear interpolation. These new sample points are occasionally extremely dense, thus easily generating an ill-conditioned problem for approximation functions. A mobile most probable failure point strategy is used to solve this problem. The advantage of the proposed method is proven by two numerical examples. With the ASPIA, the approximated process can rapidly approach the actual limit equation with accuracy. Additionally, there are no difficulties in applying the proposed ASPIA to the response surface model with or without cross terms. Solution results for the numerical examples indicate that the use of the response surface function with cross terms increases time cost, but result accuracy cannot be improved significantly. Finally, the proposed method is successfully used to analyze the reliability of the hydraulic cylinder of a forging hydraulic press by combining MATLAB and ANSYS software. The engineering example confirms the practicality of this method.

Due to the opaqueness of rock and the limitation of detection technology, it is impossible to accurately describe the crack growth process and determine the law of rock breakage. Based on smoothed particle hydrodynamics and the finite element method (SPH-FEM), a numerical model for high-speed water jet breaking was established in this work to simulate the fragmentation process of rock impacted by a high-speed water jet, and to study the effects of different jet angles on the propagation of microscopic cracks inside the rock. Additionally, we further analyzed the jet impact angle on the microscopic crack propagation trend of the rock by applying confining pressure to the rock. Theoretical and experimental analyses showed that the inclination angle of the jet determined the direction of axial crack propagation in the tension-type center. When the inclination angle of the jet exceeded 20°, the ability of water jet erosion was insufficient, and the efficiency of rock fragmentation was low. However, in the range of 15° to 20°, the capacity of erosion was strong, lamellar crack propagation was obvious, and rock chip block spalling was easily produced. The impact of the water jet on the rock at varying angles under rock confining pressure will make the crack propagation direction deviate from the direction without confining pressure and gradually become parallel to the rock plane, thereby promoting unilateral crack propagation in the direction of water jet impact, making the rock more likely to produce unilateral rock chip spalling.

Reliability-based multidisciplinary design optimization (RBMDO) has been considered as an efficient technology for addressing complex engineering design optimization problems under uncertainties. Current RBMDO methods, however, perform design optimization either in a sequential manner or in an all-at-once manner, which does not support design autonomy in various disciplines and has low computational efficiency. In this article, a reliability-based multidisciplinary concurrent design optimization (RBMCDO) method is proposed to solve the problems of lack of design autonomy and low computational efficiency in current RBMDO methods. In RBMCDO, the multidisciplinary reliability constraints are first transformed into deterministic constraints using the multidisciplinary probabilistic constraint transformation method, developed in this work based on the performance measure approach and Karush–Kuhn–Tucker conditions. The RBMDO problem is then decomposed into several optimization problems of a single discipline, which are solved in parallel based on the collaborative optimization strategy. Two examples are used to verify the proposed method.