DC Motor with Backlash

1 Standard Modelica Library Components

1.1 Simulation of DCMotorCircuit

2 Modelica.Mechanics.Rotational.ElastoBacklash

2.1 Description

This element consists of a backlash element connected in series to a spring and damper element which are connected in parallel. The spring constant shall be non-zero, otherwise the component cannot be used.
In combination with components IdealGear, the ElastoBacklash model can be used to model a gear box with backlash, elasticity and damping.
The parameters are:

Name Default Description

b 0 Total backlash [rad]

c 1.e5S pring constant (c > 0 required) [N.m/rad]

phi_rel0 0 Unstretched spring angle [rad]

d 0 Damping constant [N.m.s/rad]

2.2 Source Code

2.3 Simulation of DCMotorCircuitBackClash

For comparison we define a model with less mass in inertia2 (J=1), no damping d, and weaker string

constant c, to show more even more dramatic backlash phenomena

2.4 SimpleElastoBacklash

Most properties of the elastic transmission with backlash, both continuous and discrete, are represented in the partial model SimpleElastoBacklash below. This is a typical hybrid mode switching model, with the finite state automaton represented by the equations for the Boolean variables backward, forward and slack and the conditional equation for the torque tau having different right hand side expressions in the three operationg modes.

The ElastoBacklash model consists of a backlash element connected in series to a spring and damper element, which are connected in parallel (Figure 13-90). This is a slight extension compared to the previous SimpleElastoBacklash model since we have introduced a damping element with a damping constant d. The damping element contributes to the torque tau equation by the expression d*w_rel that is nonzero provided d is nonzero. The spring constant must be nonzero, otherwise the model cannot be used. Another extension compared to the simple model is that a constant bEps for minimum backlash has been introduced. The backlash behavior of the model is available only if abs(b) > bEps, since if b is too small or zero, numeric problems with too many generated state events will occur. The following ElastoBacklash model is from the Modelica standard library version MSL3.2.1, Mechanics.Rotational.Components package, but slightly reformatted to increase readability.