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In a continuous bistable system, when the input signal is continuously increased, the output signal tends to be stable and no longer increases. At this time, the weak signal under strong background noise is difficult to be extracted, which means saturation occurs. Aiming at the saturation characteristics of stochastic resonance (SR), the proposed piecewise nonlinear bistable system (PNBSR) model has achieved certain results. However, the potential barrier in the middle of the PNBSR method still completely uses the potential function of classical bistable stochastic resonance (CBSR). There is no fundamental solution to the fourth-order limitation. This paper explores an improved piecewise mixed stochastic resonance (PMSR) potential model. The fourth-order potential function that restricts particle motion in CBSR is improved to a piecewise second-order potential function. This potential function subverts the shape of the traditional potential function and presents a symmetrical double-hook shape. Based on PMSR model, this paper uses particle swarm optimization (PSO) to select system parameters and elaborates the characteristics of the potential function curve in detail. Under the same conditions, the output signal-to-noise ratio (SNR) curve of the improved system is generally higher than that of the CBSR and PNBSR systems. Experiments on bearings and gears show that the proposed method can accurately extract weak fault features, and the effect is better than the PNBSR method.

In the presence of strong background noise, in view of the difficulty in extracting weak fault features, a new compound tri-stable stochastic resonance (CTSR) model is proposed by combining the Gaussian Potential model and the mixed bi-stable model. Compared with the traditional tri-stable stochastic resonance (TTSR) method, all parameters of CTSR model have no coupling characteristics. Therefore, the output signal-to-noise ratio (SNR) can be easily optimized by adjusting the system parameters. The CTSR model retains the advantages of constraint and continuity of the Gaussian Potential model, and has a higher utilization rate of noise. Finally, through bearing and engineering experiments, the outstanding advantages of the proposed method in feature extraction of weak faults are verified.

Since noise is beneficial to improve weak fault characteristic extraction in nonlinear systems where a stochastic resonance occurs, a new piecewise nonlinear stochastic resonance (PNSR) method is proposed to enhance and extract the incipient fault signatures of machinery and ensure their reliable operation. In this new PNSR method, a piecewise nonlinear potential is employed to overcome the saturated shortcoming of classical bistable potentials, thereby improving and highlighting the performance of stochastic resonance in weak fault characteristic extraction. Moreover, the proposed PNSR method can realize the adjustment of the potential structure by a single parameter, it avoids the shortcoming that the imperfect matching classical bistable stochastic resonance (CBSR) parameters results in low output signal-to-noise ratio (SNR), and further identify fault characteristics are difficult. In addition, the output SNR of the PNSR method is deduced by using adiabatic approximate theory to investigate the effect of system parameter on the PNSR method, and even has higher output SNR compared with the CBSR method and the proposed PNSR method. Finally, the proposed PNSR method is validated by utilizing simulation and bearing experiments. All diagnostic results show that the proposed PNSR method can effectively extract weak fault characteristics, thereby achieving the incipient fault diagnosis of machinery. Compared with the CBSR method, the proposed method has higher spectrum peak values in fault characteristic frequencies. Therefore, it has better recognition degree in whole frequency spectrum.

In this paper, we design a new three-dimensional honeycomb with a negative Poisson’s ratio. A honeycomb cell was first designed by out-of-plane stretching a re-entrant honeycomb and the honeycomb is built by spatially combining the cells. The in-plane response and energy absorption characteristics of the honeycomb are studied through the finite element method (FEM). Some important characteristics are studied and listed as follows: (1) The effects of cell angle and impact velocity on the dynamic response are tested. The results show that the honeycomb exhibits an obvious negative Poisson’s ratio and unique platform stress enhancement effect under the conditions of low and medium velocity. An obvious necking phenomenon appears when the cell angle parameter is 75°. (2) Based on the one-dimensional shock wave theory, the empirical formula of the platform stress is proposed to predict the dynamic bearing capacity of the honeycomb. (3) The energy absorption in different conditions are investigated. Results show that as the impact velocity increases, the energy absorption efficiency gradually decreases. In addition, with the increase of cell angle, the energy absorption efficiency is gradually improved. The above study shows that the honeycomb has good potential in using in vehicle industry as an energy absorption material. It also provides a new strategy for multi-objective optimization of mechanical structure design.

A robust controller is developed for the trajectory tracking control of a 6-DOF robotic crusher in task space. Firstly, the dynamic model including the mantle assembly and actuators is derived by Lagrange method according to the virtual work principle. In order to simulate the crushing behavior of cone crusher in the crushing chamber, the trajectory model of the mantle assembly is achieved by ADAMS. Then, a robust controller which contains the dynamic compensation is designed, and the convergence stability of the 6-DOF robotic crusher is strictly proved based on Lyapunov stability theory. Finally, the co-simulation is used to verify that the proposed controller can solve the problem of model uncertainties and external disturbances well. Meanwhile, numerical simulation results of the 6-DOF robotic crusher illustrate the proposed controller is able to effectively reduce the trajectory tracking errors compared with the computed torque controller.

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 this paper, an error model of position and orientation is derived and the errors of actuator lengths are optimized based on genetic algorithm. Firstly, the error model of position and orientation is achieved according to the kinematic analysis, and the influencing factors are quantitatively analyzed. Then, the comprehensive error of position and orientation are given which can be used in the whole crushing cycle. It contains variables of the generalized coordinates. Finally, numerical simulation is used to verify the effectiveness of the proposed approach. The results show that the optimization effect of genetic algorithm is obvious, and all errors are reduced.

For the adjustable parameters stochastic resonance system, the selection of the structural parameters plays a decisive role in the performance of the detection method. The vibration signal of rotating machinery is non-linear and unstable, and its weak fault characteristics are easily concealed by noise. Under strong background noise interference, the detection of fault features is particularly challenging. Therefore, a type of weak fault feature extraction method, named knowledge-based particle swarm optimization algorithm for asymptotic delayed feedback stochastic resonance (abbreviated as KPSO-ADFSR) is proposed. Through deduction under adiabatic approximation, we observe that both the asymmetric parameters, the length of delay and the feedback strength, impact the potential function. After adjusting the asymmetric parameters of the system, the output signal-to-noise ratio (SNR) is used as the fitness function, and the setting of the relationship between the noise intensity and barrier height is used as the prior knowledge of the particle swarm algorithm. Through this algorithm, the delay length and the feedback strength are optimized. This method achieves global optimization of system parameters in a short time; it overcomes the shortcomings of the traditional stochastic resonance method, which has a long convergence time and tends to easily fall into local optimization. It can effectively improve the detection of weak fault features. In the bearing rolling body pitting corrosion failure experiment and steel field engineering experiment, the proposed method could extract the characteristics of a weak fault more effectively than the traditional stochastic resonance method based on the standard particle swarm algorithm.

Planetary gearbox is widely used in rotating machinery and prone to damage and failure due to heavy load and complex operating conditions. Furthermore, due to heavy background noise and complicated transmission path, the fault characteristics imbedded in the acquired signals is very weak and difficult to be extracted. Therefore, it is a challenge task for extracting fault characteristics of planetary gearboxes. To tackle this task, this paper proposes an adaptive stochastic resonance method for weak fault characteristic extraction of planetary gearbox, where a chaos ant colony algorithm characterized global optimization ability is employed to achieve adaptive matching between potential parameters and thereby overcoming the local optimization shortcoming of traditional stochastic resonance. Simulation and planetary gearbox experiments with a missing tooth and broken tooth validate the effectiveness of the proposed method, respectively. The results show that the proposed method is not only able to extract weak fault characteristics but also superior to singular value decomposition method.

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.

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.

This paper proposes a novel 6-DOF robotic crusher that combines the performance characteristics of the cone crusher and parallel robot, such as interparticle breakage and high flexibility. Kinematics and dynamics are derived from the no-load and crushing parts in order to clearly describe the whole crushing process. For the no-load case, the kinematic and dynamic equations are established by using analytical geometry and Lagrange equation. Analytical geometry is mainly used to solve the inverse kinematics and then establish the velocity relationship between generalized coordinates and actuators. Lagrange equation which takes into account the weight of the mantle and actuators is used to solve driving forces of actuators. For the crushing case, crushing pressure is related to the compression ratio and particle size distribution, but the selection and breakage functions should be established first. Because the trajectory model of the mantle is difficult to be established by using analytical method, it can be obtained by an eccentric simulation. The results of input velocities and driving forces of actuators are distinctive due to the eccentric angle and selection of the initial position. Finally, the proposed approach is verified by a numerical example and then the energy consumption is calculated.

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.

Based on the inspection instrument, the paper has offered an equipment inspection instrument regular repairing application system suited to the characteristics of coal enterprises. This system works stably in coal enterprises, effectively completing the measurement and management of equipment inspection, improving the reliability of the equipment, reducing the incidence of failure.

The effect of uncertainty and its evolution with time on the system reliability design are investigated in this paper. The system design variables are modeled in Geometric Brownian Motions which using the drift rate and diffusion rate to describe the evolution-based uncertainty of variables. Based on Ito Lemma, the system performance composed with these variables can also be expressed with drift function and diffusion function. Using mathematic transformation for the time series data of each variables, the drift function and diffusion function of the system can be calculated to reflect the system performance evolution uncertainty characteristic. The system evolution-based uncertainty reliability is defined as the probability function of system performance output and allowable performance output. Evolution-based uncertainty design method is developed in which the system can be designed with the specified reliability value at the given time period. The example results show the effectiveness of the proposed method on dealing with the system evolution-based uncertainty.

This article puts forward the time-dependent design method considering the load fluctuation factors for the liner based on the time-varying uncertainty theory. In this method, the time-varying uncertainty design model of liner is constructed by introducing the parameters that affect the wear rate, the volatility and the drift rate. Based on the design example, the timevarying design outline of the moving cone liner is obtained. Based on the theory of minimum wear, the gap curve of wear resistant cavity is designed, and the optimized cavity is obtained by the combination of the thickness of the cone and the cavity gap. Taking the PYGB1821 multi cylinder hydraulic cone crusher as an example, it is proved that the service life of the new liner is improved by more than 14.3%.

The microscopic influence of sliding distance and load on the wear of cone crusher liner is studied. The main factors that affect the hardness of the liner and the material are clearly put forward, and the hardness of the liner is verified according to the national standard to ensure the correctness of the lining and the ore material. Simulation experiments were carried out with EDEM. When the material was certain, the positive pressure and sliding distance between the ore and liner were changed, and the micro wear of the liner was quantitatively calculated by the number of bond keys of the lining plate. The results show that when the liner moves at the same distance, the pressure is greater and the lining plate is seriously worn. When the lining plate is subjected to the same pressure, the moving distance increases, and the lining plate is seriously worn. This method has some reference value for cavity design of new crusher and other material wear research.

Autonomous guided vehicles are becoming extremely important in the mining industry. The underground environment is unique and complex in that the lighting conditions are poor, the roads are difficult to traverse, and no GPS can accurately receive signals in these areas. This paper analyzes the characteristics of commonly used positioning methods given that ordinary positioning and navigation methods do not work effectively underground. We outline the composition and principles in underground guidance of autonomous vehicles using the laser-based positioning system. This system is unique in that it draws on the premise of barcode theory, which allows for a feasible relative navigation system even without a GPS. Algorithms were developed to provide real-time control for an autonomous guided scraper. In the vehicle experiment, the scraper was able to autonomously move along the simulated laneway, and the trial average range longitudinal error was only 15 cm in a 40-m distance. Hence, this new type of positioning and navigation system can accurately and reliably guide vehicles.

As an important component in engine cooling system, the cooling fan has a potent effect on the reliability and economy of the engine. To ensure that the performance of the cooling fan is satisfied with the practical working requirements, the following work is done. Firstly, the experiment of the cooling fan is carried out to get its performance data; Secondly, the performance distribution in actual working condition is simulated with the help of FLUENT; finally, the experiment result which has been fitted by MATLAB is compare with the simulation result. The relative error of the result between the experiment and the simulation is within the pale of 5%, which shows clearly that the performance data from experiments could meet the design requirements.

Using Numerical Methods to research disc separator inner flow field is an important method to optimize the design. This article based on VOF model, N-S equations and RNG k-e model, solved with the SIMPLE algorithm, simulated separator oil-water separation process respectively with initial state filled with water, oil and oil-water mixture this three different initialization conditions by using flunet software. The numerical simulation results show that the initial condition has little effect on the oil-water separation, and eventually a stable layer interface can be formed and purification rate can reach at 98%. There is strong turbulence near the inlet and wastewater outlet, while flow is relatively stable between the discs gaps and near the oil outlet, basically in a laminar flow state. The research results laid a foundation of separator design and optimization and also can reduce the time and cost required for experiments.

The blind number theory and the basic ideas of uncertain variables expressed by blind number were introduced. The mechanical structure time-dependent characteristics variation in stochastic process was deduced. The uncertain variables in time-dependent stochastic process of mechanical structure were expressed in blind number, and its time-dependent reliability optimization design model was built with blind number theory. Furthermore, the corresponding programs in LabVIEW language were compiled, and parameters of vehicle leaf spring were also optimized by these programs. The result shows that blind number as a kind of numerical tool is very convenient and effective for solving the complicated reliability optimization design model. And the method based on blind number can reduce calculation error resulted from data fitting and program in computer easily. The mechanical structure designed based on this method can reach the required reliability at a certain moment in future and ensure its performance optimization. Hence, this method provides important reference on mechanical structure time-dependent reliability optimization design.