# Fixed-Displacement Motor (External Efficiencies)

Fixed-displacement hydraulic motor with externally specified mechanical and volumetric efficiencies

Pumps and Motors

## Description

The Fixed-Displacement Motor (External Efficiencies) block represents a fixed-displacement hydraulic motor with both mechanical and volumetric efficiencies provided through the external physical signal ports. Hydraulic losses are implemented as a leakage between hydraulic ports, while mechanical losses are introduced through the friction imposed on the driving shaft. Both the leakage and the friction are determined by the efficiency values. The ideal hydraulic motor is described with the following equations:

${q}_{id}=D\cdot \omega$

${T}_{id}=D\cdot p$

where

 qid Ideal volumetric flow rate p Pressure differential across the motor D Displacement ω Angular velocity Tid Ideal torque

When accounting for mechanical and hydraulic losses, the flow rate through the motor is increased by the leakage value

${q}_{leak}=D\cdot \omega \cdot \left(1-{\eta }_{V}\right)$

and output torque becomes lower due to mechanical losses simulated with the friction torque

${T}_{FR}={T}_{id}\cdot \left(1-{\eta }_{M}\right)$

where

 qleak Leakage flow through the motor ηV Volumetric efficiency TFR Friction torque ηM Mechanical efficiency

For numerical stability purposes, the friction torque is implemented as

${T}_{FR}={T}_{id}\cdot \left(1-{\eta }_{M}\right)\cdot \mathrm{tanh}\left(4\frac{\omega }{{\omega }_{th}}\right)$

where ωth is the threshold angular velocity, a parameter that specifies how steeply the `tanh` function changes in the vicinity of zero velocity.

Connections A and B are hydraulic conserving ports associated with the motor inlet and outlet, respectively. Connection S is a mechanical rotational conserving port associated with the motor shaft. Physical signal ports EV and EM import volumetric and mechanical efficiencies, respectively. Use a separate block to compute these efficiencies. The block positive direction is from port A to port B. This means that the flow rate flowing through the motor from A to B rotates the shaft in positive direction, and positive pressure differential $p={p}_{A}-{p}_{B}$creates positive torque at the motor shaft.

## Basic Assumptions and Limitations

• Fluid compressibility is neglected.

• Hydraulic loss is simulated as leakage through the motor.

• Mechanical loss is represented with the friction torque applied to the motor shaft.

## Dialog Box and Parameters

Displacement

Motor displacement. The default value is `5e-6` m^3/rad.

Threshold velocity

This parameter specifies how steeply the `tanh` function changes in the vicinity of zero velocity. It is introduced to avoid sharp change in the friction torque. The default value is `0.001` rad/s.

## Ports

The block has the following ports:

`A`

Hydraulic conserving port associated with the motor inlet.

`B`

Hydraulic conserving port associated with the motor outlet.

`S`

Mechanical rotational conserving port associated with the motor shaft.

`EV`

Physical signal port that imports the motor volumetric efficiency.

`EM`

Physical signal port that imports the motor mechanical efficiency.