Four-axle vehicle#

The Four-axle vehicle block describes the movement of avehicle with a trailer, taking into account the road profile and the influence of wind.

Forces acting on the vehicle:

traction force (1) :

(1)#\[ F_{\mathrm{т}\mathrm{я}\mathrm{г}}=\frac{M_{1}+M_{2}+M_{3}+M_{4}}{r}\mathrm{\cdot }\mathrm{G}\mathrm{R}\]

where:

\(M_{1}\) - engine torque, [N\(\cdot\)m];

\(M_{2},M_{3},M_{4}\) – torque of auxiliary engines, [N\(\cdot\)m];

\(r\) – carriage wheel radius, [m];

\(GR\) – transmission gear ratio, gearless.

rolling force (2) :

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

where:

\(m_{v}\) - vehicle weight, [kg];

\(g\) – gravity factor, [m/s\(^2\)];

\(\alpha\) – road elevation angle, [rad].

rolling friction force (3) :

(3)#\[F_{\mathrm{т}\mathrm{к}}=k_{\mathrm{т}\mathrm{р}}\mathrm{\cdot }m_{\mathrm{а}}\mathrm{\cdot }g\mathrm{\cdot }\mathrm{c}\mathrm{o}\mathrm{s}\alpha -k_{\mathrm{п}\mathrm{с}}\mathrm{\cdot }V_{\mathrm{с}\mathrm{у}\mathrm{м}\mathrm{м}}\mathrm{\cdot }\left|V_{\mathrm{с}\mathrm{у}\mathrm{м}\mathrm{м}}\right|\]

where:

\(k_{fr}\) – rolling friction coefficient, gearless;

\(k_{lf}\) – lifting force coefficient, [kg/m];

\(\alpha\) – road elevation angle, [rad];

\(V_{\mathrm{s}\mathrm{u}\mathrm{m}\mathrm{m}}=V_{v}+V_{w}\) – sumof vehicle and headwind velocities, [m/s].

adhesion force (4) :

(4)#\[F_{\mathrm{с}\mathrm{ц}\mathrm{е}\mathrm{п}}=k_{\mathrm{в}\mathrm{я}\mathrm{з}\mathrm{к}}\mathrm{\cdot }V_{\mathrm{а}}+F_{\mathrm{т}\mathrm{р}}\mathrm{\cdot }\mathrm{s}\mathrm{i}\mathrm{n}n\left(V_{\mathrm{а}}\right)\]

where:

\(k_{visc}\) – vehicle viscous drag coefficient, [kg/s];

\(F_{fr} \) – rolling friction force, [N];

\(V_v\) – vehicle speed, [m/s].

aerodynamic drag force (5) :

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

where:

\(k_{drag} \) – vehicle drag coefficient, [kg/m];

\(V_{sum}=V_a+V_в \) – sum of vehicle and headwind velocities, [m/s].

braking force (6) :

(6)#\[F_{\mathrm{т}\mathrm{о}\mathrm{р}\mathrm{м}}=\frac{M_{\mathrm{т}\mathrm{о}\mathrm{р}\mathrm{м}}}{r}\mathrm{s}\mathrm{i}\mathrm{n}n\left(V_{\mathrm{а}}\right)\]

where \( М_{brake} \) – brake torque, [N\(\cdot\) m].

Vehicle acceleration calculation (7) :

(7)#\[ a=\frac{F_{\mathrm{т}\mathrm{я}\mathrm{г}}-F_{\mathrm{а}\mathrm{э}\mathrm{р}\mathrm{о}}-F_{\mathrm{с}\mathrm{к}\mathrm{а}\mathrm{т}}-F_{\mathrm{с}\mathrm{ц}\mathrm{е}\mathrm{п}}-F_{\mathrm{п}\mathrm{р}\mathrm{и}\mathrm{ц}}-F_{\mathrm{т}\mathrm{о}\mathrm{р}\mathrm{м}}}{m_{\mathrm{а}}+m_{\mathrm{п}}+\frac{J}{r^{2}}} \]

where:

\(F_{prop}\) – propulsive force, [N];

\(F_{aero}\) – vehicle aerodynamic drag force, [N];

\(F_{roll}\) – vehicle rolling force, [N];

\(F_{tract}\) – traction force of wheels on the road surface, [N];

\(F_{tr}\) – drag force of the trailer, [N];

\(F_{brake}\) – braking force, [N];

\(m_v\) – vehicle weight, [kg];

\(m_{tr}\) – trailer mass, [kg];

\(J\) – nertia moment of all axes, [kg\(\cdot\) m\(^2\)];

\(r\) – carriage wheel radius, [m].

1. Properties#

Property	Default value	Description	Units of measurement
Radius of wheel	0.6	–	m
Inertia moment of axes	200	–	kg \(\cdot\) m\(^2\)
Vehicle mass	15000	–	kg
Trailer mass	0	–	kg
Viscosity resistance coefficient	0	–	kg/s
Lifting force coefficient	0	–	kg/m
Head resistance coefficient	0	–	kg/m
Rolling friction coefficient	0	–	m
Free fall acceleration	9.81	–	m/s\(^2\)

2. Inputs and outputs#

Parameters	Input/Output	Description	Units of measurement	Port type
Car motor torque	Input	–	N \(\cdot\) m	Automation
Additional motor torque 1	Input	–	N \(\cdot\) m	Automation
Additional motor torque 2	Input	–	N \(\cdot\) m	Automation
Additional motor torque 3	Input	–	N \(\cdot\) m	Automation
Climb angle	Input	–	rad	Automation
Headwind speed	Input	–	m/s	Automation
Trailer motion resistance force	Input	Port for connecting an auxiliary motor. The calculationassumes that the load is distributed symmetrically between all axes.	N \(\cdot\) m	Automation
Braking torque	Input	Port for connecting an auxiliary motor. The calculationassumes that the load is distributed symmetrically between all axes.	N \(\cdot\) m	Automation
Gear ratio	Input	Port for connecting an auxiliary motor. The calculationassumes that the load is distributed symmetrically between all axes.	gearless	Automation
Displacement	Output	–	m	Automation
Car speed	Output	–	m/s	Automation
Car acceleration	Output	–	m/s\(^2\)	Automation

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