A model of the relative compression ratio for single-particle crushed products, based on the distinct element method (DEM) and numerical analysis, was established to describe precisely the crushed products of granular particles during laminated crushing. The relative compression ratio model was used to describe the functional relationship between the total compression ratio and the single-particle compression ratio, which can be described by lognormal distribution. The single-particle crushed products model was used to describe the functional relationship between the single-particle compression ratio and the distribution of single-particle crushed products. The distribution of single-particle crushed products was described by a three-parameter beta distribution. On the basis of the above model, the function of laminated crushed products of granular particles was established. According to the simulation results of EDEM under confining pressure, a functional relationship between total compression ratio, particle size, and height of the granular particles for laminated crushed products of granular particles was built. It was proved that the function of the theoretical particle size distribution coefficient of laminated crushed products of granular particles was not too different from the actual value determined by simulation. The function is universal and can be used to provide a theoretical basis and a design reference for the design of cone crushers, high-pressure roller mills, and other crushing equipment.

In order to reduce wear and increase crushing efficiency of the 6-DOF (degree of freedom) robotic crusher, the maximum single-particle compression ratio function of the granular material and the wear model of the mantle liner under eccentric compression are established. The function and model take into account the influence of crusher parameters and granular material parameters on maximum single-particle compression ratio, which is simulated by EDEM and obtained under different conditions. Combined with previous research, the theoretical distribution of crushed products and the crushing chamber size can be obtained at each time of the whole life cycle of the liner. Compared with the experimental data of Ansteel Group in previous research, the difference between the functional model and the actual results is small. This function is universal and can be used to provide reference for the 6-DOF robotic crusher’s crushing strategy and a theoretical basis and a design reference of the traditional structure cone crusher.

In order to optimize the real-time crushing effect of 6-DOF robotic crusher, a model of energy consumption and a multi-objective optimization control method for 6-DOF robotic crusher are proposed. In optimization function, the optimization objective are total energy consumption, mass fraction of crushed products below 12 mm, energy consumption ratio, and throughput, and optimization variables are position of suspension point, rotational speed and precession angle of the moving cone. Among them, the function of total energy consumption and effective energy consumption is established and the function of total energy consumption is verified in this paper. The function of mass fraction of crushed products below 12 mm is based on previous research. Taking the full load working condition and chamber size of PYGB1821 crusher as an example. The solution of optimization is obtained. Compared with the traditional cone crusher under the same feed size distribution and chamber size, each objective can be effectively optimized, which can effectively reduce energy consumption and increase the crushing efficiency. This method is universal and can be used for the design and control of other crushing equipment.

An evolution-based uncertainty analysis model of bending fatigue failure of involute spur gears is presented. The fluctuation of transmit torque and rotational velocity of gears are introduced to the mild wear model of gear flanks. Then a novel simulation model of tooth profile evolution is developed to describe the change of meshing parameters, which include the tooth load, load angle and bending moment arm. The critical tooth-root bending stress is influenced by these time-varying parameters. Based on the evolution-based uncertainty analysis method, the load is approximately obeying logarithmic normal distribution, the load angle and bending moment arm are approximately obey geometric Brownian motion. Then the critical tooth-root bending stress is calculated as a logarithmic normal distribution quantity over time. Finally, the prediction model of time dependent reliability of the bending load capacity of spur gears is proposed.

The evolution of mechanical parameters, a factor affecting the mechanical reliability, has gathered more attention nowadays. However, studies on time varying uncertainty can hardly be found. A new method based on evolution-based uncertainty design (EBUD) is applied to the design of gear in this paper. Considering the wear evolution over the lifetime, a tooth wear's time-varying uncertainty model based on the continuous-time model and Ito lemma is established. Drift and volatility functions dependent on the drift rate and volatility rate of rotational speed and torque are used to express the time-varying uncertainty of tooth thickness. The method can predict the reliability and provide an instruction in reliability improving, maintenance and repair of the gear system.