Identification of wheel–rail contact forces based on strain measurements, an inverse scheme and a finite-element model of the wheel

Abstract

The wheel–rail contact force is an essential parameter in many aspects in railway mechanics, for instance, in rolling contact fatigue analysis. Since the wheel–rail contact force cannot be measured directly, instrumented wheelsets have been developed to collect the radial strains at certain positions on the wheel web. In this paper, an inverse method to estimate the wheel–rail contact force history based on strain measurements is discussed. In the proposed method, the contact force is determined by minimizing the least-squares discrepancy between measured radial strains and corresponding computed strains from a three-dimensional finite-element model of the wheel. The inverse method is compared with the existing method based on direct extraction of the contact force from combinations of measured strains using Wheatstone bridges. Using synthetic data, it is found that the proposed inverse method is insensitive to the eigenmodes of the wheel, as opposed to the existing method. In addition, noise reduction by using Tikhonov regularization and by choosing proper sampling rates are discussed.

A new methodology for the estimation of wheel–rail contact forces at a high-frequency range

“…As a result, the proposed method can be utilized for reconstructing the step and impulse force with proper accuracy. Note that in Figure 15, the step force is applied in the time duration 0:0025 À 0:0035 s, while the estimated force is detected before 0:0025 s. This effect can be clarified using equations (8) and (14); according to equation (8) and lower triangular matrix, the observed strain in a specific time step k is the response of the applied force at step time k and other steps before k. Therefore, there is no strain response as a result of step force at moments before 0:0025 s. However, corresponding to equation (14) due to Tikhonov regularization, the matrix H y is not in the lower triangular part and some nonzero elements appeared in upper triangular part of H y ; consequently, the effect of strain response at time step k can be observed in the estimated force at time step k À 1, k À 2, Á Á Á as illustrated in Figure 15.…”

“…Although instrumented wheelsets have been developed for more than three decades, very few studies have been carried out on the estimation of the highfrequency force (more than 90 Hz) except Ronasi et al [11][12][13][14] Most of the studies have been applied for the frequency range 0-90 Hz, which are able to measure the quasi-static forces. The Ronasi et al method was employed for the vertical force with a frequency range of 100-2000 Hz.…”

Bayesian framework for simultaneous input/state estimation in structural and mechanical systems

“…Substituting Equation 12 for the prior distribution along with Equation 14 for the transition distributions into Equation 11, and combining all constants into a single constant κ, posterior distribution p(x k | Y k−1 ) can be obtained as…”

“…Estimation of the wind load in order to evaluate the health condition of high‐rise structures was conducted in previous studies . Moreover, in the railway transportation, the estimation of the wheel–rail contact forces is crucial to assess rolling contact fatigue and damage detection on the track as well as to certify the vehicle design safety . In addition to the input identification, the state estimation has also received very much attention in the structural dynamics to predict stress and fatigue life, to identify damage, and to determine the response in inaccessible points …”

“…[7][8][9] Moreover, in the railway transportation, the estimation of the wheelrail contact forces is crucial to assess rolling contact fatigue and damage detection on the track as well as to certify the vehicle design safety. [10][11][12] In addition to the input identification, the state estimation has also received very much attention in the structural dynamics to predict stress and fatigue life, to identify damage, and to determine the response in inaccessible points. [13][14][15][16][17][18][19][20][21][22] As a matter of fact, it is not feasible directly to measure the exposed load by transducers when we have not access to the location and sometimes when economic factors are important; however, the transient response at some points are captured utilizing various sensors (strain gauge, accelerometer, and displacement transducer).…”