Manufacturing Technology 2025, 25(4):531-539 | DOI: 10.21062/mft.2025.052

Analytic Solution of the Motion Equations of the Rolling Stock Chassis Incorporating the Effect of Asymmetry and Kinematics Excitation

Blanka Skocilasova ORCID...1, Frantisek Klimenda ORCID...1, Jan Skocilas ORCID...2, Tereza Jarosova ORCID...1
1 Faculty of Mechanical Engineering, J. E. Purkyne University in Usti nad Labem. Pasteurova 3334/7, 400 01 Usti nad Labem. Czech Republic
2 Faculty of Mechanical Engineering, Czech Technical University in Prague, 4 Technicka, Prague 166 07, Czech Republic

The article provides an analytical solution for the dynamics of a vehicle chassis designed for both road and rail operation, featuring either single or multiple primary linear suspensions using coil springs. It derives the equations of motion for a simplified two-axle chassis model that includes both a basic primary suspension and a simplified chassis suspension. The study focuses on the simplest calculation model to analyze suspension behavior, taking into account the asymmetry in spring stiffness and geometric positioning. There is an unequal distribution of weight across the vehicle body. An analysis is conducted on a comprehensive vehicle model with nine degrees of freedom. The analytical solution is obtained using Lagrange equations of the second kind, alongside various calculation techniques such as Laplace transformation. Due to the scope of the article, calculations of all coefficients of the matrices are not presented, but a link to other works of the authors is given, where these procedures are presented. The proposed analytical solution makes it possible to derive an effective algorithm for the application of computer technology. The use of the proposed procedures allows determining the permissible asymmetry of vehicles for safe driving, taking into account structural asymmetry, kinematic excitation asymmetry (always occurs) and suspension asymmetry (almost always occurs).

Keywords: Vibration, Motion Equations, Rolling stock

Received: July 3, 2025; Revised: July 3, 2025; Accepted: October 4, 2025; Prepublished online: October 22, 2025; Published: November 11, 2025  Show citation

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Skocilasova B, Klimenda F, Skocilas J, Jarosova T. Analytic Solution of the Motion Equations of the Rolling Stock Chassis Incorporating the Effect of Asymmetry and Kinematics Excitation. Manufacturing Technology. 2025;25(4):531-539. doi: 10.21062/mft.2025.052.
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