Calculation of vehicle behavior in traction and braking

Program TSIM in the GENSYS package can be used for studying braking and traction forces.

Brake simulation
Create springs between the bogie and the axles, located at the same place as the brake disks. The property of the springs does not include a stiffness, they only contains a preload force which corresponds to the braking force.

                                                                                        
  func  const  Fbrake=  28553.362
  func  const  Rbrake=  0.235
                                                                 
  coupl p_lin  kdbrakep1=  Fbrake  0.                                   
  coupl p_lin  kdbrakep2= -Fbrake  0.                                   
                                                                                        
  coupl k kdbr_111 axl_111 -Rbrake 0 -ro  bog_11  (aba-Rbrake) 0 -ro  kdbrakep1 esys1 z     
  coupl k kdbr_112 axl_112 +Rbrake 0 -ro  bog_11 -(aba-Rbrake) 0 -ro  kdbrakep2 esys1 z     
  coupl k kdbr_121 axl_121 -Rbrake 0 -ro  bog_12  (aba-Rbrake) 0 -ro  kdbrakep1 esys1 z     
  coupl k kdbr_122 axl_122 +Rbrake 0 -ro  bog_12 -(aba-Rbrake) 0 -ro  kdbrakep2 esys1 z

Traction simulation
Traction simulation is very similar to Brake simulation. However, often the center of two cogwheels in the gearbox are on different heights, why the cog-force will have an angle Theta relative to the horizontal plane. Therefore, it can be more practical to define the traction force with the force-command instead. The cogwheel forces shall have different signs on the two cogwheels.
```
  func  const      Ftrac=   28553.362                  # Total cogwheel force
  func  operp_init FtracX=  cos( theta ) * Ftrac       # Longitudinal component of the cogwheel force
  func  operp_init FtracZ= -sin( theta ) * Ftrac       # Vertical component of the cogwheel force
  force rel_mass1  cogForceW axl_111    -0.235 0.435 -0.65   FtracX 0  FtracZ  0 0 0     # Positive sign on wheelset
  force rel_mass1  cogForceM mot_111 aba-0.235 0.435 -0.65  -FtracX 0 -FtracZ  0 0 0     # Negative sign on motor
```
Theta is the angle relative to the horizontal plane in which the resulting cog-forces are acting.
In this example the pitch point of the cogwheel is defined with the three values (-0.235, 0.435, -0.65) relative to the wheelsets coordinate system lsa_XXX.
Often the motor is defined in the bogie coordinate system lsb_XX, therefore the pitch point for the motor becomes (aba-0.235, 0.435, -0.65).

With the applied traction or braking force the vehicle will accelerate or retardate, and the longitudinal displacements of all masses in the vehicle with respect to the moving coordinate systems lsys will increase or decrease. To avoid too big longitudinal displacements between the vehicle and the moving coordinate systems the user has two possibilities to solve this problem:

Apply a longitudinal force on the coupler of the vehicle, avoiding an acceleration or retardation.

                                        
  force rel_lsys1 coupler_force car_1 0 0 -1.  -Fx 0 0  0 0 0

Regulate the longitudinal position of the esys coordinate system, making the coordinate systems to follow the vehicle.

                                        
  lsys e_reg_xpos esys1 car_1 1. 1.