# Hydraulic Motor

Fixed-displacement hydraulic motor

Pumps and Motors

## Description

The Hydraulic Motor block represents a positive, fixed-displacement hydraulic motor of any type as a data-sheet-based model. The key parameters required to parameterize the block are motor displacement, volumetric and total efficiencies, nominal pressure, and angular velocity. All these parameters are generally provided in the data sheets or catalogs. The motor is represented with the following equations:

`$q=D·\omega +{k}_{leak}·p$`
`$T=D\cdot p\cdot {\eta }_{mech}$`
`${k}_{leak}=\frac{{k}_{HP}}{\nu \cdot \rho }$`
`${k}_{HP}=\frac{D\cdot {\omega }_{nom}\left(1-{\eta }_{V}\right)\cdot {\nu }_{nom}\cdot {\rho }_{nom}}{{p}_{nom}}$`
`$p={p}_{A}-{p}_{B}$`

where

 `q` Flow rate through the motor `p` Pressure differential across the motor `pA,pB` Gauge pressures at the block terminals `T` Torque at the motor output shaft `D` Motor displacement ω Output shaft angular velocity `kleak` Leakage coefficient `kHP` Hagen-Poiseuille coefficient ηV Motor volumetric efficiency ηmech Motor mechanical efficiency ν Fluid kinematic viscosity ρ Fluid density ρnom Nominal fluid density `pnom` Motor nominal pressure ωnom Motor nominal angular velocity νnom Nominal fluid kinematic viscosity

The leakage flow is determined based on the assumption that it is linearly proportional to the pressure differential across the motor and can be computed by using the Hagen-Poiseuille formula

`$p=\frac{128\mu l}{\pi {d}^{4}}{q}_{leak}=\frac{\mu }{{k}_{HP}}{q}_{leak}$`

where

 `qleak` Leakage flow `d, l` Geometric parameters of the leakage path μ Fluid dynamic viscosity, μ = ν.ρ

The leakage flow at `p` = `pnom` and ν = νnom can be determined from the catalog data

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

which provides the formula to determine the Hagen-Poiseuille coefficient

`${k}_{HP}=\frac{D\cdot {\omega }_{nom}\left(1-{\eta }_{V}\right)\cdot {\nu }_{nom}\cdot {\rho }_{nom}}{{p}_{nom}}$`

The motor mechanical efficiency is not usually available in data sheets, therefore it is determined from the total and volumetric efficiency by assuming that the hydraulic efficiency is negligibly small

`${\eta }_{mech}={\eta }_{total}/{\eta }_{V}$`

The block hydraulic positive direction is from port A to port B. This means that the flow rate is positive if it flows from A to B and rotates the output shaft in the globally assigned positive direction. The pressure differential across the motor is determined as $p={p}_{A}-{p}_{B}$, and positive pressure differential accelerates the shaft in the positive direction.

## Basic Assumptions and Limitations

• Fluid compressibility is neglected.

• No loading on the motor shaft, such as inertia, friction, spring, and so on, is considered.

• Leakage inside the motor is assumed to be linearly proportional to its pressure differential.

## Dialog Box and Parameters

Motor displacement

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

Volumetric efficiency

Motor volumetric efficiency specified at nominal pressure, angular velocity, and fluid viscosity. The default value is `0.92`.

Total efficiency

Motor total efficiency, which is determined as a ratio between the mechanical power at the output shaft and hydraulic power at the motor inlet at nominal pressure, angular velocity, and fluid viscosity. The default value is `0.8`.

Nominal pressure

Pressure differential across the motor, at which both the volumetric and total efficiencies are specified. The default value is `1e7` Pa.

Nominal angular velocity

Angular velocity of the output shaft, at which both the volumetric and total efficiencies are specified. The default value is `188` rad/s.

Nominal kinematic viscosity

Working fluid kinematic viscosity, at which both the volumetric and total efficiencies are specified. The default value is `18` cSt.

Nominal fluid density

Working fluid density, at which both the volumetric and total efficiencies are specified. The default value is `900` kg/m^3.

## Global Parameters

Parameter determined by the type of working fluid:

• Fluid kinematic viscosity

Use the Hydraulic Fluid block or the Custom Hydraulic Fluid block to specify the fluid properties.

## 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 output shaft.