Study of Road Surface Roughness Simulation Based on Fractal Interpolation Function
|School||Nanjing Agricultural College|
|Keywords||vehicle engineering road surface roughness fractal theory sacleless range fractal interpolation|
In the field of vehicle engineering,road roughness is the main factor in the environment of vehicle operating and the main sources of incentive and vibration. Resistance and vibration are generated by road roughness while vehicles are running. The resistance depletes vehicles’ power and influences the life-span of vehicle dynamical system and transmission system. And the vibration impacts vehicles’ smooth-going and taking comfortableness, handling stability, traveling speed, bearing system’s reliability and life-span. Study of road roughness is of significance in promoting the development of the field of vehicle engineering.In this paper, the key technological contents, such as characteristic determination of road surface roughness, fractal scaleless range and fractal model, were carried on deep and systematic research, based on the current situation on the road roughness, combined with various of theories and technologies which have been widely used in various fields, such as analytic theory, computing technology, mathematical model.The concrete work is as follows:The measured data of road roughness is analyzed by traditional way. The result shows that more parameters are required when describe the whole characteristic of the road. That is say, the traditional parameter is not the only with the road, it will change with the resolving power of measure equipment. So it is essential to find a new parameter. Since 1975, fractal theory has rapidly developed as a new branch of mathematics theory It has extensive application in describing the signal, the signal dealing and other fields. The research, which confined with surface roughness and fractal theory, has already become an important research branch in crossing science. Numerous researches indicate that fractal dimension can describe essential characteristic of the complicated phenomenon, so in this paper, fractal interpolation function which belongs to fractal theory was used to systematically research into characteristics of measured road roughness.Road roughness is one of kinds of random fractal existed in nature, it is not like fractal in math, which has self-similar or since affine sex in the endless scales. it is only in certain scope. That is to say, fractal characteristics only exist in certain scale.This scale is called scaleless range. Scaleless range is the foundation of study on applying random fractal, the exact solution of scaleless range, not only helps restrain the amount of divergence of fractal, but also is the basis for making Fractal value accurate and reliable. On this basis,sampling interval can be extended, sampling points and sampling intensity can be reduced. Research of scaleless range needs fractal dimension which is an important parameter, thus, this article used Weierstrass-Mandelbrot function,which is a fine model when depict the roughness surface,then the different methods’ applicable range, advantages and disadvantages were confirmed to analyze fractal curves. Ideal fractal curves was generated though Weierstrass-Mandelbrot function to analyze comparatively on different methods by which fractal dimensions was confirmed. Through different computational methods to confirm fractal dimension, we analyzed the scale law linear relation of longitudinal sections of measured road roughness, which is regarded as two-dimensional curve. Then we found there is relevant scale law linear relation in log-log coordinate of the three methods, besides root-mean-square method, remainder- variation method and structure function method. After calculating and analyzing on both non-scale sector and fractal dimension of the three methods, we found that root-mean-square method is quite stable in the non-scale sector instead of remainder- variation method and structure function method. On the other hand, root-mean-square method has both clear physical significance and signal function to the surface profile curve, so root-mean-square method is definitely a efficacious method to calculate the fractal dimension of road roughness.On this basis, this article analyzed different methods of determining the fractal scaleless range. It is found by the comprehensive comparison: Since the correlation coefficient is more objective, simple in calculation and has ideal fit. Therefore, this article is, to use this method to determine scaleless range of road roughness sample.The high-frequency measured discrete data of road surface roughness was made low-frequency data by using scaleless range,Then,the data was simulated by fractal interpolation function,with explicit vertical scale factor adjusting other factors that make error between interpolation functions and the measured data smallest Then the results of fractal model through time-frequency domain and fractal parameters were tested, and the factors which affect the accuracy of fractal interpolation were analyzed. The results indicate that after the low-frequency measured discrete data of road surface roughness is processed by scaleless range, road roughness is simulated by the fractal interpolation function. The simulation result is similar with the original high-frequency road roughness measurement discrete data. That is to prove that it is feasible to use the simulation method.lt has an important reference on objective characterization of road surface roughness, data compression and the manufacture of road surface roughness measuring instruments. Compared with the traditional road roughness model such as white noise model,the fractal interpolation model of road surface roughness can be more used as road input in the simulation of automobile vibration response and this model is closer to the actual road. The application of the road model is verified through Matlab/Simulink test and the actual experiment, with body acceleration, dynamic stroke of suspension and the dynamic load of tyres as validation indexs.