Trailer with braking system#

The Trailer with braking system block describes the movement ofcarriages attached to the locomotive taking into account slippage, track profile and wind.

Forces acting on each carriage:

rolling force (1):

(1)#\[F_{\mathrm{с}\mathrm{к}\mathrm{а}\mathrm{т}}=m_{\mathrm{в}}\mathrm{\cdot }g\mathrm{\cdot }\mathrm{s}\mathrm{i}\mathrm{n}\alpha\]

where:

$m_c$ – carriage mass, [kg];

$g$ – gravity factor, [m/s$^2$];

$sin\alpha$ – elevation angle, [rad].

rolling friction force (2) :

(2)#\[F_{\mathrm{т}\mathrm{к}}=\frac{k_{\mathrm{т}\mathrm{р}}\mathrm{\cdot }m_{\mathrm{а}}\mathrm{\cdot }g\mathrm{\cdot }\mathrm{c}\mathrm{o}\mathrm{s}\alpha }{r}\]

where:

$K_{fr}$ – rolling friction coefficient, [m];

$\alpha$ – elevation angle, [rad];

$r$ – carriage wheel radius, [m].

adhesion force (3) :

(3)#\[F_{\mathrm{с}\mathrm{ц}\mathrm{е}\mathrm{п}}=F_{\mathrm{т}\mathrm{р}}\mathrm{\cdot }\mathrm{s}\mathrm{i}\mathrm{n}n\left(V_{n}\right)\]

where $V_t$ - train speed, [m].

maximum adhesion force (4) :

(4)#\[F_{\mathrm{с}\mathrm{ц}\mathrm{е}\mathrm{п}.\mathrm{м}\mathrm{а}\mathrm{к}\mathrm{с}}=m_{\mathrm{в}}\mathrm{\cdot }g\mathrm{\cdot }\mathrm{c}\mathrm{o}\mathrm{s}\alpha\]

aerodynamic drag force (5) :

(5)#\[F_{\mathrm{а}\mathrm{э}\mathrm{р}\mathrm{о}}=k_{\mathrm{а}\mathrm{э}\mathrm{р}\mathrm{о}}\mathrm{\cdot }V_{\mathrm{с}\mathrm{у}\mathrm{м}\mathrm{м}}\mathrm{\cdot }\left|V_{\mathrm{с}\mathrm{у}\mathrm{м}\mathrm{м}}\right|+k_{\mathrm{в}\mathrm{я}\mathrm{з}\mathrm{к}}\mathrm{\cdot }V_{\mathrm{с}\mathrm{у}\mathrm{м}\mathrm{м}}\]

where:

$k_{drag}$ – carriage drag coefficient, [kg/m];

$k_{visc}$ – carriage viscous drag coefficient, [kg/m];

$V_{sum}=V_t + V_h$ – sum of train and headwind velocities, [m/s].

Condition of wheels slipping when braking (slip) (6) :

(6)#\[M_{\mathrm{т}\mathrm{о}\mathrm{р}\mathrm{м}}>M_{\mathrm{м}\mathrm{а}\mathrm{к}\mathrm{с}} $ или $ M_{\mathrm{т}\mathrm{о}\mathrm{р}\mathrm{м}}<-M_{\mathrm{м}\mathrm{а}\mathrm{к}\mathrm{с}}\]

where:

$M_{max}$ – maximum wheel torque, [N $\cdo$t m], (7) :

(7)#\[M_{макс}=F_{сцеп.макс}\cdot r = m_в \cdot g \cdot cos (\alpha)\]

$M_{brak}$ – brake torque, [N$\cdot$ m].

Calculation (8) :

(8)#\[\begin{split} F_{\mathrm{т}\mathrm{р}}=\left(\frac{M_{\mathrm{т}\mathrm{о}\mathrm{р}\mathrm{м}}}{r}+F_{\mathrm{с}\mathrm{ц}\mathrm{е}\mathrm{п}}+F_{\mathrm{а}\mathrm{э}\mathrm{р}\mathrm{о}}+F_{\mathrm{с}\mathrm{к}\mathrm{а}\mathrm{т}}\right)\mathrm{\cdot }K_{\mathrm{в}}+F_{\mathrm{т}\mathrm{р}}\\m_{\mathrm{с}\mathrm{ц}}=m_{\mathrm{с}\mathrm{ц}}+m_{\mathrm{в}}\mathrm{\cdot }K_{\mathrm{в}} \end{split}\]

where:

$K_{w}$ – number of wagons in the coupling;

$m_{c}$ – carriage mass, [kg];

$m_{coup}$ – coupling mass, [kg].

1. Properties#

Property	Default value	Description	Units of measurement
Number of wagons in the coupling, gearless	90	–	gearless
Radius of wheel	0.625	–	m
Mass of one wagon	68000	–	kg
Rail friction coefficient	0.12	–	gearless
Wagon head resistance coefficient	0.0	–	kg/m
Wagon viscosity resistance coefficient	32.6	–	kg/s
Rolling friction coefficient	0.0005	–	m
Free fall acceleration	9.81	–	m/s$^2$

2. Inputs and outputs#

Parameters	Input/Output	Description	Units of measurement	Port type
Train speed	Input	–	m/s	Automatics
Brake torque	Input	–	N$\cdot$ m	Automatics
Climb angle	Input	–	rad	Automatics
Headwind speed	Input	–	m/s	Automatics
Train carriage motion resistance force	Input	–	N$\cdot$ m	Automatics
Train carriage mass	Input	–	kg	Automatics
Train carriage motion resistance force	Output	–	N$\cdot$ m	Automatics
Train carriage mass	Output	–	kg	Automatics

In order to see the connection capabilities of the block, you need to go to page Description of block ports