Fig 1.
Schematic of the wheel-mounted disc and brake caliper with pads.
The braking force is generated by squeezing the wheel using two pads. The braking force of the pad is controlled by the pneumatic pressure Pc of the brake cylinder via a lever mechanism with a pivot at rc. The braking force is released by the spring installed inside the brake cylinder.
Fig 2.
Measured and curve-fitted friction coefficients between the brake disc and the pad.
The left portion of the figure shows the variation of the friction coefficient due to the temperature change at a friction speed of 9.6 m/s, and the right portion of the figure shows the variation of the friction coefficient due to the friction speed change at a temperature of 50°C.
Table 1.
Parameter Values for the Variable Friction Coefficients of a Railway Vehicle Considered in This Paper.
Fig 3.
Schematic of the vehicle dynamic model.
We assume the train runs on rails arranged in a straight line without any curves; thus, each mass is modeled as having plane motion with 3 DOF, i.e., longitudinal, vertical and pitch motions. Moreover, we assume that the wheels are always in contact with the rails so that the wheelset motions can be represented by only two independent variables: x and θ. Therefore, a vehicle including a carbody, two bogies and four wheelsets is represented by 17 motion DOF.
Fig 4.
Free-body diagram of a wheelset and the shape of the contact patch.
The wheel-rail contact is modeled by an elastic rolling contact in which the leading part of the oval contact patch is an adhesion area and the trailing part is a slip area. In the adhesion area, there is no slip velocity, but in the slip area, there is a relative velocity between the wheel and the rail.
Table 2.
Parameter Values for a Wet Condition of a Wheel-Rail Contact Model of the Target Vehicle.
Fig 5.
Schematic configuration of the brake HILS system.
Vehicle dynamics were simulated in real-time using a high-speed dSPACE unit, and the four wheel speeds simulated by the dSPACE unit interfaced with the actual brake hardware through the signal conditioner and the BOU. The braking force measured by the load cells was delivered as feedback to the dSPACE unit to compute the wheel speeds at the next sampling instant.
Fig 6.
The signal flow and interfacing of the brake HILS system.
There are two host computers: one computer is for the dSPACE unit in which the vehicle dynamics are simulated in real-time, and the other computer is for the control unit in which brake force is calculated and the wheel slide is detected and protected. The braking force is generated by the pneumatic brake device according to the output signals of the control unit.
Fig 7.
Picture of the brake HILS system developed in our laboratory.
The red device on the upper side of the picture is a portable air compressor used to deliver power to the mechanical brake unit. The wheel and the brake caliper are installed on the floor (the center of the picture), the BOU and the dSPACE unit are placed on the table (the right side of the picture), and four WSP valves and four white reservoirs corresponding to piping and cylinder volumes are placed on the vertical panel (the bottom of the picture).
Table 3.
Target Vehicle Parameter Values.
COG implies the center of gravity.
Fig 8.
HILS system experimental results for various wheel speeds and axle loads.
(A) The circumferential speeds of four wheelsets during emergency braking. (B) The axle loads of four wheelsets during emergency braking.
Fig 9.
Friction coefficients between the disc and pad during emergency braking of the HILS system.
The variable friction coefficient at the initial and final stage of braking is greater than the friction coefficient at the intermediate stage due to the low temperature of the brake materials and due to the low friction speed.
Fig 10.
HILS results for the tangential brake forces on the disc during emergency braking.
The depression of the blue solid line at approximately 4 s is due to releasing the brake force for the readhesion from the wheel slide by opening the WSP valve of the sliding wheelset. The gree dotted line corresponds to the braking force using a constant friction coefficient in which no wheel slide is simulated during braking even if wheel slide actually occurs.
Fig 11.
Adhesion coefficient as a function of creepage.
Greater brake force due to the variable friction coefficient requires greater adhesion coefficient in the wheel-rail contact for no wheel slide, but the achieved adhesion coefficient is less than the required limit value as shown in the blue dash-dot line, and thus, wheel slide occurs.
Fig 12.
Experimental results of the HILS system for the adhesion forces.
The blue solid line and the green dotted line correspond to the adhesion force as functions of the creepage and of time for the case using the variable friction coefficient and the constant friction coefficient, respectively.