SimHydraulics^®

Hydraulic Motor - Simulate fixed-displacement hydraulic motor

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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:

where

`q`	Flow rate through the motor
`p`	Pressure differential across the motor
`p_A,p_B`	Gauge pressures at the block terminals
`T`	Torque at the motor output shaft
`D`	Motor displacement
ω	Output shaft angular velocity
`k_leak`	Leakage coefficient
`k_HP`	Hagen-Poiseuille coefficient
η_V	Motor volumetric efficiency
η_mech	Motor mechanical efficiency
ν	Fluid kinematic viscosity
ρ	Fluid density
`p_nom`	Motor nominal pressure
ω_nom	Motor nominal angular velocity
ν_nom	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

where

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

The leakage flow at p = p_nom and ν = ν_nom can be determined from the catalog data

which provides the formula to determine the Hagen-Poiseuille coefficient

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

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 , and positive pressure differential accelerates the shaft in the positive direction.

Basic Assumptions and Limitations

The model is based on the following assumptions:

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.

Global Parameters

Fluid kinematic viscosity: The parameter is determined by the type of working fluid selected for the system under design. 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.