| Running-in attractor is a stable and time-space ordered structure formed in the running-in process. Based on fractal and chaos theories, the evolvement and system dependence of running-in attractors were studied to enrich the running-in theory, realize the dynamic description of friction and wear process, and provide the theoretical basis for the running-in design.Phase trajectory theory in chaos was used to describe the running-in attractors intuitively. In order to quantitatively study the running-in attractors and their evolvement, besides an existing parameter correlation dimension, predictability and entropy were introduced to characterize the running-in attractors, two characteristic parameters, i.e., enclosing radius and average distance between phase points were proposed innovatively. The enclosing radius was used to describe the size of spatial range in which the attractors exists. The average distance between phase points was used to describe converging degree and density of the attractors.Both rotating and reciprocating friction tests were performed throughout wear process. The running-in attractors was reconstructed from friction force, friction coefficient and friction temperature. The phase trajectory and the characteristic parameters were computed, and their dynamic evolvements were studied. The friction force in reciprocating motion changes periodically, which makes the nonlinearity be covered by periodicity, thus the chaos theory is not applicable any more. In this case, the friction coefficient was used instead of friction force for nonlinear analysis. Friction force, friction coefficient and friction temperature follow the same dynamic evolution law in both rotating and reciprocating motion. In the running-in wear stage, the phase trajectory converges and forms running-in attractors. In the steady wear stage, the attractors possess a steady trajectory. In the rapid wear stage, the trajectory diverges and the attractors disappear. The enclosing radius, the average distance between phase points and the predictability decrease in running-in wear stage, remain stable in steady wear stage, and finally increase in rapid wear stage. The evolvements of the correlation dimension and the entropy are contrary to the enclosing radius, the average distance between phase points and the predictability. Friction signals that extracted from the same system evolve consistently. The consistency is specifically manifested in two aspects: the trajectory and the characteristic parameters of friction signals evolve in the same way, the converging-stable-diverging of trajectory and the increase or decrease of characteristic parameters are synchronous for friction signals.It was demonstrated that running-in attractors have the properties of low energy dissipation, boundness, high density, fractional dimension and intrinsic randomness. The boundness is external binding of running-in attractors. It determines the range of trajectory and phase points, which leads to low energy dissipation and high density. The intrinsic randomness is an internal motivation to make the structure of attractors more complicate. It makes the trajectory moves irregularly and enhances the space filling ability of trajectory, which leads to fractional dimension and high density. The variation of these properties indicates the occurrence of dynamic abrupt change. The detecting methods for dynamic abrupt changes were classified into three categories, i.e., the detecting methods based on bound, density and intrinsic randomness. Among these methods, the detecting method based on intrinsic randomness is most widely used. However, it is only applicable for two time series whose trajectories have similar position and size, meanwhile, the significance of dynamic difference depends on scale. The normalization preprocessing and the scale-independent processing were added to solve these problems. Following the two steps, the application scope of improved method was expanded and the scale-independent result was obtained. The dynamic abrupt changes in friction force and friction coefficient were detected by the improved method. The detection results show that dynamic abrupt changing region, dynamic stable region and dynamic abrupt changing region occur in sequence during wear process. The three regions correspond to the forming, maintaining and disappearing stage of running-in attractors, respectively.The running-in tests were performed by sliding a pin(GCr15) against a disc(45 steel) to investigate the dependence of characteristic parameters of running-in attractors on system parameters. The results show that correlation dimension and entropy of running-in attracor decrease with initial surface roughness of pin, increase with load and velocity; enclosing radius and average distance between phase points increase with initial surface roughness of pin, load and velocity; predictability increases with initial surface roughness of pin, and decreases with load and velocity, the initial surface roughness of disc has little influence on these parameters. To describe the system dependence of running-in attractors, predication models for the characteristic parameters were established by surface response method and based on the test result.The running-in attractor was used to assess the running-in quality and instruct running-in design. Since a great correlation dimension is always accompanied by a great entropy and a small predictability, enclosing radius and average distance between phase points evolve in a similar way, correlation dimension and enclosing radius are chosen to assess the running-in quality. Further, the system dependence was used to instruct running-in design. The theoretical analysis and experiment results of friction vibration and noise suggest that a great correlation dimension and small enclosing radius indicate a high quality running in. Therefore, the great correlation dimension, the less enclosing radius and short running-in time were considered as three goals of running-in design. The Pareto optimal solutions and corresponding parameter sets were obtained by using the fast elitist non-dominated sorting genetic algorithm. According to the computing results, the roughness of harder surface should be small, while the roughness of softer surface can be chosen in a large range. The combination of great roughness of softer surface with great load or great velocity should be avoided to ensure running-in quality. The combination of small roughness of softer surface with small load or small velocity should be avoided as well to ensure running-in time. |
