Article Analysis of generalized force and its influence on ride and stability of railway vehicle Rakesh Chandmal Sharma 1 , Sakshi Sharma 2 , Sunil Kumar Sharma 3 and Neeraj Sharma 1 Abstract Formulation of a rail vehicle model using Lagrange’s method requires the system’s kinetic energy, potential energy, spring potential energy, Rayleigh’s dissipation energy and generalized forces to be determined. This article presents a detailed analysis of generalized forces developed at wheel–rail contact point for 27 degrees of freedom–coupled vertical–lateral model of a rail vehicle formulated using Lagrange’s method and subjected to random track irregularities. The vertical– lateral ride comfort of the vehicle and the ride index of the vehicle are evaluated based on ISO 2631-1 comfort speci- fications and stability is determined using eigenvalue analysis. The parameters that constitute the generalized forces and critically influence ride and stability have been identified and their influences on the same have been analysed in this work. Keywords Vertical ride; lateral ride; stability; critical speed; generalized force; creep force Introduction The performance of a road or rail vehicle is evaluated based on criterion, that is, ride comfort, stability, curve negotiation and handling and so on. A vehicle model may be formulated using Newton’s method or Lagrange’s method. It is quite difficult to apply Newton’s method to complex system’s having many degrees of freedoms, for example, a rail vehicle system. Lagrange’s method mainly involves the calculation of system energy and is a scalar quantity that can be determined with ease as compared with Newton’s method which involves the calculation of system force which is a vector term and is quite difficult to deal with. The Lagrange’s method also involves the calcu- lation of generalized force of the system which is evaluated using the principle of virtual work. 1 A rail vehicle coach generally consists of a carbody supported on two bogie frames and four wheelaxles. The motion of rail vehicle is coupled, for example, its lateral motion is influenced by vertical irregularities. 2,3 The wheel and rail both have specified profile to interact with each other. The amounts of forces generated at wheel–rail con- tact points of rail vehicle are very high and their evaluation is a complex task. 4,5 The creep forces generated at the contact point are generally non-linear function of contact geometry. The static forces are quite high and required to be accurately estimated. Geometric parameters, that is, wheelgauge and wheelbase of the bogie frame also influ- ence the dynamic behaviour of the rail vehicle. Research- ers in the past have directed their efforts to analyse the wheel–rail interaction and influence of associated para- meters on ride behaviour and lateral stability. 6–9 A rail vehicle is generally examined based on its specific perfor- mance indices. When design parameters are required to be selected there is a trade-off between these performance indices, for example, better ride and curving always requires a softer suspension whereas better stability requires a stiff suspension. The influence of suspension parameters on ride comfort has been well studied by researchers in the past. 10–12 The influence of parameters such as locomotive traction on vehicle ride considering 1 Mechanical Engineering Department, Maharishi Markandeshwar (Deemed to be University), Mullana, Ambala, Haryana, India 2 Department of Mechanical Engineering, J.C. Bose University of Science & Technology, YMCA, Faridabad, Haryana, India 3 Department of Mechanical Engineering, Amity School of Engineering and Technology, Amity University, Uttar Pradesh, Noida, India Corresponding author: Sunil Kumar Sharma, Department of Mechanical Engineering, Amity School of Engineering and Technology, Amity University, Uttar Pradesh, Noida 201313, India. Email: sunilsharmaiitr@gmail.com Noise & Vibration Worldwide 2020, Vol. 51(6) 95–109 ª The Author(s) 2020 Article reuse guidelines: sagepub.com/journals-permissions DOI: 10.1177/0957456520923125 journals.sagepub.com/home/nvw