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How to Create a Linearized Math Model of a Hydraulic Motor

Primarily defined as a mechanical actuator, a hydraulic motor is used for converting hydraulic pressure and flow right into angular displacement and torque. The hydraulic motor is the main rotary counterpart of the present hydraulic cylinder as a linear actuator. Broadly stated, these motors are sometimes run on hydropower. However, in modern terminology, the name refers more specifically to the motors using the hydraulic fluid as part of this closed hydraulic circuit within modernized hydraulic machinery.

Create a Linearized Math Model of a Hydraulic Motor
Image Credit: hydraulicspneumatics.com

In some instances, these hydraulic motors are interchangeable with the Hydraulic Pump because of its opposite functionality. But, most of these pumps cannot be widely used as hydraulic motors as they cannot be back driven. The hydraulic motor is designed for working pressure at both sides of the motor, where most of the pumps rely on lower pressure provided from the reservoir at the input side and might leak fluid when abused as a motor.

The types available under hydraulic motors:

These hydraulic motors are widely divided into two fundamental classes. One is the simple rotating systems under gear motors and vane motors. It will include higher rpm and low initial costs. Another one is the plunger and piston ones in radial or axial configurations, which are complex and made using higher quality rotating drive systems. These motors will offer an adjustable transferring ratio.

Hydraulic motor types

Description

Vane motor

It comprises of housing with the eccentric bore. It runs a rotor with vanes in it. The different force causes the rotor to spin in just one direction. A major element is how the tips are machined at the contact point between the motor housing and vane tip.

Gear motor

It comprises two gears, one is the idler gear and another one is driven gear. Higher pressurized oil is ported into one side of gears where it flows around the periphery of gears.

Gerotor motors

These motors are in essence of the rotor with the N1 teeth, which is rotating off-center in stator or rotor with N teeth.

Axial plunger motors

These motors are widely used for higher quality rotating drive systems. The speed will range from 1200 to 1800 rpm and the machine is driven by motors at a lower speed.

Radial piston motors

These motors are primarily available under two major sections. One is piston pushing inward and another one is piston pushing outward.

Mathematical model of the hydraulic motor:

Electrical based hydraulic drives are a common mechanism for automation control and industrial equipment. The drives are here to follow some generalized fluid motion law, as discovered in the 17th and 18th centuries. The basic mechanisms were created for the canals and have evolved over passing time to become major components of the industrial automation.

·         The exact calculating methods to cover up electric hydraulic drive are necessary for multiple industrial systems like in foundry equipment, thermoplastic machinery, and metalworking tools. The mathematical models are used for solving various practical issues.

·         For example, the electric hydraulic drives as modeled on hydraulic equipment designs and computers can be optimized by minimum energy consumption and weight. You can optimize the precision of the machine as well. The models are used for automating hydraulic equipment controlling systems for some parameters like the speed of tools and loads.

Example of ways to create linearized math model:

As an example, you can consider mounting bushing on axles using a hydraulic press. Here, the elastic deformation takes place when metallic parts of the machine and the fluid deform. The deformations help in the increasing volume of fluid passages. In case the pump fails to compensate for changing volume, the speed of the press will decrease. The issue is to determine the response time of changing parameters.

·         The pressurized force F can be properly characterized by equation systems that model hydraulic press. After determining ΔPb from the 2nd equation, it will be substituted with the 3rd equation. Then you have to rewrite the equations using Laplace transform.

·         After that, it is mandatory to find the deviation of hydraulic system pressure after calculating determinants of the Cramer formula. Later, you need to calculate the D1 using Ti substitutions.

·         The roots can be found using a computer. By evaluating these toots, the function of ΔP becomes clear.

The procedure clearly states that elastic deformation works during the transient portion of the pressing applications. The same process can determine the response of the pressure regulators as connected to the hydraulic pump.

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