DYNAMICS OF DRAFT GEAR FOR FREIGHT STOCK VEHICLE

Abstract

Longitudinal train dynamics affects passenger comfort, vehicle stability, consignment safety in freight vehicles, rolling-stock design and rolling-stock metal fatigue. Hence, the development of mathematical model for studying the dynamics of draft gear, which is the most important component in any longitudinal train simulation, is significant. It is also quite challenging to model and simulate various aspects like nonlinearity of coupler slack/air gaps, nonlinearities of spring material (polymer and steel) and friction present in the wedge system. Along with these complexities, the dynamic behaviour of the common wagon connection system can be examined in presence of vertical track irregularities. Review has revealed that the dynamic behaviour of train-consist is evaluated with the mass of draft gear lumped with the wagon mass. This work attempts to investigate the dynamic behaviour of a train-consist while considering nonlinearity, due to draft pad geometry and material, as an influencing parameter. This has been achieved by considering the mass of two draft gears lumped as single mass with stiffness and damping on either of the lumped mass (of draft gears). Initially, linear stiffness is considered between the masses. Force-displacement curve obtained from uniaxial loading of the draft gear is used for modelling the wagon connection of train-consist to include geometric and material nonlinearity. Curve fitting technique has been used to obtain a curve mathematically equivalent to the loading curve. The fitted curve is cubic or a third order polynomial. A mathematical model with five degrees of freedom for a train-consist to include the draft gear mass is developed. A system of differential equations which forms the equations of motion for the train-consist is established to describe the longitudinal dynamic behaviours of a train-consist. These equations of motion are coupled second order nonhomogeneous nonlinear differential equations. A Simulink based model is developed in MATLAB environment. The dynamic behaviour of draft gear is analysed for various running conditions like accelerating the vehicle to different speeds or braking the vehicle from different speeds, viz., 40, 60 and 75 km/h. The acceleration and braking values considered are those currently used by Indian Railways. The dynamics of draft gear for different loading conditions of train-consist is also a matter of investigation. Accordingly, two load conditions corresponding to empty wagon and fully loaded wagon are considered. In unloaded condition, the self-weight of freight wagon is considered, whereas for the loaded condition, the maximum load on freight wagon corresponds to the contemporary Indian conditions. The mass of locomotive is selected in such a way that it represents the mass of almost all types of commercially used locomotives. Running speed of iv 100 km/h is considered to check the prospect of using current draft gears for increased speed of freight wagons. The mass of draft gear has been fixed at 1 ton by considering the mass of the autocoupler assembly between two wagons. The response characteristics are analysed considering time history of draft gear travel, relative velocity of wagons, wagon force and draft gear capacity. Fast Fourier transform and phase trajectory plots have been used to identify the system behaviour. The present study also investigates the modal behaviour of draft gear which constitutes of draft pads, top follower, shoes and wedge, all assembled in a housing. It is the draft pad which ensures absorption of impact load and thus the proper functioning of draft gear. The modal behaviour of draft pad is also investigated here. As the draft pads (six in number) are assembled within the draft gear housing under a preload, the effect of preload on the dynamics of an individual draft pad is also evaluated. Since, the period of first preventive maintenance of draft gear is fixed at the end of sixth year after its installation; it is quite evitable that the draft gear during this period may function with defective draft pads within. The dynamics of both, the draft gear as well as an individual draft pad is evaluated considering crack as a defect. A survey was carried out at Indian Railways Workshop located at Jagadhri, (Harayana, India) and Lucknow (Uttar Pradesh, India) to determine the shape, size and locations of the crack and has been modelled accordingly in the current work. The dynamic behaviour of draft pad and draft gear is investigated using finite element method (FEM) for healthy and defective conditions. Initially, the vibration characteristics of individual draft pad and draft gear are determined using FEM for healthy conditions. A comparison of mode shapes of draft pad and draft gear is carried out with a view of identifying participating modes of an individual draft pad in draft gear. The effect of defect / crack on the natural frequency of draft pad and draft gear is also investigated. A mathematical model of draft pad is formulated to predict the effect of crack on its modal frequency. The crack is modelled as a semi-elliptical in two directions, viz., lateral and longitudinal direction, of the draft pad. Different damage scenarios have been simulated by varying the width as well as aspect ratio of the crack to identify its effect on fundamental frequency. The effect of the presence of crack on the draft pad with its orientation and location on the modal frequency of the draft gear is also evaluated. The draft gear consists of six draft pads assembled in series (one above another) and they are always under a constant axial compressive prestress even in unloaded condition. As prestress influences the values of the stiffness matrix by causing stress stiffening, its effect on the natural frequencies of the draft pad is also investigated. As far as the dynamics of draft gear as a part of train-consist is concerned, draft gear 1 v is subjected to maximum travel during acceleration and braking for loaded condition. At the end of braking, a recoil of an amount equivalent to maximum draft gear travel is observed indicating jerks upon braking. In loaded condition, especially during braking the capacity of draft gear 1 is surpassed and it becomes overloaded for values above 35000 ft-lb. Impacting forces on the draft gear are maximum during braking and cross the value of 300 ton while braking a vehicle from a speed of 100 km/h. The capacity of draft gear corresponding to such impacting load exceeds a value of 75000 ft-lb, which is quite above the existing capacity. The exciting frequencies drop to 210 Hz during acceleration and 100 Hz during braking for both wagons under loaded condition. These are the values for which fatigue behaviour of an individual draft pad should be observed as against the current loading frequency of 10 Hz. While considering the dynamics of draft pad and draft gear, it is observed that first five mode shapes of the individual draft pad are dominating the behaviour of each draft pad in the draft gear for all 7 mode shapes of the draft gear. It is also observed that crack parameters like, crack width, crack aspect ratio and crack location/orientation, influence the dynamic behaviour of draft pad. For an individual draft pad, with increase in compressive prestress load, the frequency decreases for the first three modes. However, for the fourth and fifth mode an increase in the frequency is observed with increasing compressive prestress load. For a draft gear, reduction in modal frequency is observed due to presence of crack. This drop in frequency is however governed by the orientation of the crack as well as its location. The drop in the modal frequency of draft gear due to presence of crack with different orientations is totally dependent on the mode shapes of the draft pads. As far as the effect of location of defective pad on natural frequency of draft gear is concerned, except for fourth and seventh mode shape, for all other modes the draft gear frequency drops when defective pad is located adjacent to the housing base plate and top follower. Thus, draft gears with higher capacity are necessary for current maximum speed of 75 km/h and a probable increased speed of 100 km/h. To control the amount of irregular motion during post acceleration period as well as during wagon recoil at the end of braking, an enhanced energy absorption capacity of draft gear is necessary.