There are two the most widely used types of freight railway bogies: Y25 bogies and three-piece bogies. The popularity of these bogies is caused by the cheapness of their production and maintenance.
The models of these bogies were created in Universal Mechanism. Models were described according to multibody approach, where mechanical systems are presented as a set of rigid bodies, joints and force elements. These models were verified and now they are applied for solving various practical problems: investigation of freight wagon dynamics, safety problems, wear of wheel and rail profile and so on.
Y25 bogie and its analogues are widely used in Europe. This bogie has only primary suspension which connects side frame and wheelsets.
The UM model of the bogie includes 15 rigid bodies: frame, 4 axle-boxes, 4 spring holders, 4 pushers, and 4 wheelsets and has 50 d.o.f. More than 40 force elements are applied for the description of the bogie suspension, different structural components and contact interactions. In particular, springs of the suspension are modeled by viscoelastic force elements with bilinear stiffness. Y25 bogie. Click to enlarge Special force elements are used for modeling Lenoir links, the center pivot, side bearings, interactions of the pusher with the spring holder and the axle-box, and the axle-box with friction surfaces of the bogie frame that allows taking into account dynamical properties of these elements in details.
Also the modification of Y25 bogie model was developed which has independently rotating wheels.
Freight wagons with three-piece bogies are widely used around the world in practice of heavy haul railway operations. The so-called 18-100 model of the three-piece bogie is the standard bogie used in freight wagons of the Russian Railways.
The following models of freight wagons with three-piece bogies were simulated with the help of UM: open wagon, hopper and tank truck. The main difference of these models in contrast to similar models is introducing friction wedges in the model as free bodies with six degrees of freedom (d.o.f.). Friction wedges interact with a side frame and a bolster by means of the point-plane contact model. A linear viscous-elastic model is used for the normal force in this contact model and stick-slip motion with two-dimensional friction in the tangent plane. UM model of the three-piece bogie allows all clearances between the bolster, wedges, side frames and wheelsets. Such model is more accurate one for simulation of the dynamic behavior of wedges, axle-boxes and pivots. Models of the wagons include 19 rigid bodies: car body, 2 bolsters, 4 side frames, 8 friction wedges, and 4 wheelsets and have 110 d.o.f.
- to show derailment and wheel climb processes.
For adequate simulation of the three-piece bogie it is necessary to introduce in the model a number of contact force elements which lead to stiff equations of motion [1, 2]. Such contact force elements are introduced in the bogie model between wheelsets and side frames, between wedges in the friction system, between the bolster and side frames, and in the pivot unit between the bolster and the car body. Real contact parameters are so high that it leads to a sharp decrease of a step-size and an increase of time efforts. In order to accelerate the simulation process analytical solutions for elements of Jacobian matrices of force elements were obtained and implemented in UM. It made the simulation of freight wagons several times faster.
Bringing 6-d.o.f. wedges with contact force elements in the multibody model significantly increases adequacy and accuracy of the model. Numerical and field experiments showed that using simplified analytical functions (without 6-d.o.f. wedges) for the simulation of the contact interaction with friction in the mathematical model of the three-piece bogie had low accuracy.
In order to test the developed multibody model of the three-piece bogie series of numerical experiments were done by "State United Enterprises URALVAGONZAVOD", Russia. Experiments were done as follows. The pivot is loaded with the vertical force. After that side frames are loaded with the horizontal opposite forces. The turning angle of the bolster, the shift of side frames and shifting forces were measured. A comparison of numerical and experimental results showed good qualitative and quantitative coincidence. Maximum difference of the square of the hysteresis loop was 12 %.