# Development of a New Vertical Dynamic Model of a Rail Vehicle for the Analysis of Ride Comfort
## 1 Introduction
After that, this method was used in several studies, and it has been shown that the approach has a good agreement in the appropriate frequency range [7; 14; 15]. In this method, the car body is presented as a Euler-Bernoulli beam with a constant profile section, including mass, length, moment of inertia (pitch axis) and the bending modulus parameters. However, this method uses partial differential equations and the solution is more time-consuming than ordinary differential equations. Assembling rigid bodies is used for practical reasons, such as analyzing ride quality and comfort in the frequency range of interest. The method has been used in several studies for long and heavy vehicles, to predict the responses of the car body [16; 17]. Apart from that, the method is used for the dynamic behavior analysis of freight vehicle car bodies [18]. The assembling of rigid bodies is not as accurate a method as the finite element and beam methods in calculating the body dynamic displacements, but it enables engineers to analyze the car body dynamic responses in an easy and efficient way within a moderate accuracy range. This method is used in the current study to build a vertical dynamic model of a rail vehicle that incorporates car body flexibility for ride comfort analysis. The approach is novel and has the advantage of replacing a complex three-dimensional model with a simplified yet accurate model that specifically targets vertical dynamics behavior for a fast ride comfort analysis. The main purpose of the study is to develop a high-speed rail vehicle model with flexible car body characteristics for ride comfort analysis, using the assembling of rigid bodies approach in an OOM environment, so that the model can be used for analysis in an efficient and accurate way with a low computational cost. A new methodology and the rail vehicle model can be useful, considering the challenges that modern high-speed rail vehicles need to face. This study consists of two phases (see Figure 1). Firstly, real track irregularity data and rigid car body models are created and simulated. After that, a flexible car body model is built with Dymola and compared to the flexible model of the same vehicle in Vampire [19]. The validation process is realized using Vampire. There are significant advantages to validating the object-oriented model using a model in Vampire, which is validated using experiments. Also, the commercial software is specifically designed for rail vehicle dynamic analysis. Therefore, it can be used to generate a variety of test data to compare the results of Dymola. The simulations were performed in a time domain and different travel speeds were considered. The results suggest that the Dymola model has good agreement, compared to Vampire, in terms of car body-related ride comfort analysis. In this study, it is shown that the assembling of rigid bodies, combined with OOM, can be beneficial in providing moderately accurate and efficient analysis in the design phase of high-speed rail vehicles, when the model is enhanced with a suitable mathematical approach, e.g., a flexible car body approach.