Simple transmission#

The Simple transmission block implements a two-axis transmission model.

The operation of the block is described by the following equations (1):

(1)#\[\begin{split} \frac{∆\omega_1}{∆t}=\frac{T_1-K\alpha-D\frac{∆\alpha}{∆t}}{J_1}\\ \frac{∆\omega_2}{∆t}=-\frac{T_2-\frac{1}{N_{gear}}\left(K\alpha+D\frac{∆\alpha}{∆t}\right)}{J_2}\\ \frac{∆\alpha}{∆t}=\omega_1-\ \frac{1}{N_{gear}}\omega_2 \end{split}\]

where:

\(\omega_1\) и \(\omega_2\) - angular frequencies of the first and second axes;

\(T_1\) - Torque on the first axis;

\(T_2\) - Torque on the second axis;

\(K\) - spring constant;

\(D\) - damping factor;

\(J_1\) and \(J_2\) - axes inertia torques;

\(N_{gear}\) - gear ratio;

\(\alpha\) - first axis torsion angle.

1. Properties#

Property	Default value	Description	Units of measurement
First axis moment of inertia	1.0	-	\(kg\cdot m^2\)
Second axis moment of inertia	2.0	-	\(kg\cdot m^2\)
Gear ratio	2.0	-	-
Damping factor	100.0	-	\(N\cdot m\cdot \frac{s}{rad}\)
Spring constant	10000.0	-	\(N\cdot \frac{m}{rad}\)

2. Inputs and outputs#

Parameters	input/output	Description	Units of measurement	Port type
Torque on the first axis	Input	-	\(N \cdot m\)	Rotational motion
Torque on the second axis	Input	-	\(N \cdot m\)	Rotational motion
Angular velocity port	Output	-	\(\frac{rad}{s}\)	Rotational motion

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