Rotary friction#

The Rotary friction block simulates friction between two rotating bodies having a common rotation axis. The inertia moments of bodies are not taken into account.

The input and output port receive the angular velocity signal in [rad/s] (see Fig. 1 below), both transmit torque in [N \(\cdot\) m].

This block implements the “Integrator with reset” friction model, in which static friction depends on the accumulated angle of rotation between bodies, when overcoming the threshold angle, the friction model goes into sliding mode, Fig. 2 :

Moment_from_angle — Fig. 2 Dependence of friction torque on accumulated relative angle#

The relative angular velocity is calculated by the formula (1):

(1)#\[\Delta \omega=\omega_1-\omega_2\]

where:

\(\omega_1\) - is the angular velocity of the left port, [rad/s];

\(\omega_2\) - is the angular velocity of the right port, [rad/s].

A negative angular frequency shall be applied to the right port for co-directional rotation.

At \( heta_{отн.}< heta_{порог.}\) (2) :

(2)#\[T_{трение}=с_{жестк.}\cdot \theta_{отн.}+с_{вязк.}\cdot \Delta \omega\]

where:

\( heta_{rel.}\) - is the accumulated angle of rotation between bodies, [rad];

\(с_{visc}\) - coefficient of resilient friction (specified in block properties).

Hardness \(с_{hard}\). is determined by the formula (3):

(3)#\[с_{жестк.}=cmd \cdot \frac{T_{статич.}}{\theta_{порог.}}\]

When \( heta_{отн.}\geqslant heta_{порог.}\) the model switches to sliding mode at rest relativity, in which only sliding friction is taken into account (4) :

(4)#\[T_{трение}=sign(\Delta \omega)\cdot T_{скольж.}\]

The accumulated angle is reset in sliding mode.

Important

Note that the static moment cannot exceed the sliding moment and their values cannot be negative.

1. Properties#

Property	Default value	Description	Units of measurement
Couloumb friction torque	5.0	-	N \(\cdot\) m
Stiction friction torque	5.0	-	N \(\cdot\) m
Stiction angle	0.2	-	deg
Stiction stiffnes	1000.0	-	N \(\cdot\) m/(rad/s)

2. Inputs and outputs#

Parameters	Input/Output	Description	Units of measurement	Port type
Angular velocity	Input	-	rad/s	Rotational motion
Command signal	Input	-	-	Automation
Torque	Output	-	N \(\cdot\) m	Rotational motion

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