13th International Conference on Fracture June 16–21, 2013, Beijing, China -5- 0 0.05 0.1 0.15 0.2 -2.5 -1.5 -0.5 0.5 1.5 2.5 Time(s) The Fourth Axle Box Acceleration(m/s2) Measured acceleration Inversed acceleration 0 0.05 0.1 0.15 0.2 -5 -2.5 0 2.5 5 x 104 Time(s) Vertical Contact Force of the Fourth Wheelset(N) Estimated vertical force Figure 2. Measured and inversed accelerations Figure 3. The estimated vertical dynamic contact force for the fourth axle box for the fourth wheel-set From figure 2, the acceleration of the fourth axle box which identified by the inverse model is very similar to the measured value, and its correlation coefficient is 0.9756, which can be thought as height correlation. Figure 3 shows the inversed vertical dynamic contact force for the fourth wheel-set, unfortunately, it is unable to be compared with measurement value due to the limitation of test-bed. It is worth noting that, due to the limitation of accelerometers in low frequencies, figure 3 is just the vertical dynamic contact force for the fourth wheel-set, the real vertical force should add the weight reaction force. 4. The application of the inverse model in high-speed train The commonly used simulation package, SIMPACK, was used to develop a wagon model based on the same parameters as the inverse model. The parameters of the SIMPACK model were the same as the inverse model which was used to generate wheel-rail forces and accelerations at the axle box. These accelerations will be as the input conditions for the inverse mathematical model. In order to make the SIMPACK model replace a practical field test, the vehicle model developed with SIMPACK needs to be a very refined model which includes the nonlinearity of the wheel-rail contact geometry, the nonlinearity of the wheel-rail creep rate and creep forces, the nonlinearity of the vehicle suspension components, and so on. Taking into account the complexity of the car body systems, as well as many non-linear factors, we need to simplify the body. In this paper, for the vertical and lateral stochastic vibration inverse modeling of the car body, about twenty-seven degrees of freedom are considered. The measured track irregularity from Beijing to Tianjin was used as the input to the SIMPACK with a simulated velocity of 70 m/s. The resulting axle box accelerations were then used as inputs for the inverse model. The wheel-rail forces were estimated using the MATLAB package. The outputs of the inverse model were the axle box accelerations and wheel-rail reacting forces. The vertical and lateral contact forces of the third wheel-set of the inverse model and the SIMPACK simulation were compared, see Figures 4-5. At the same times, the derailment index which is got from the inverse model and the SIMPACK simulation are also compared. See figure 6.
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