**Textboo**k **on Hydraulic Motor (In the SI Units**)

**by Joji Parambath**

The textbook presents information on the types, constructional features, working, and essential terms and definitions of semi-rotary actuators and hydraulic motors. Many solved, and unsolved numerical exercise problems are given in the textbook. The book uses the SI system of units.

**Textbook on Hydraulic Rotary Actuators (In the English Units)**

**by Joji Parambath**

Please click on the images to go to the book link of Amazon.com

Some critical factors relevant to the operation and applications of every hydraulic motor is its operating pressure, displacement, flow rate, input power, output power, torque output, and efficiency.

**Operating Pressure (P)**

It is the pressure in a hydraulic system that overcomes all resistances in the system, which includes both useful work and losses. The rated pressure of a hydraulic motor is the maximum pressure, which the manufacturer recommends for the motor.

**Motor Displacement (V _{D})**

It refers to the volume of the system fluid required for turning the output shaft of a motor through one revolution. Some of the units of motor displacement are m^{3}/rev or lit/rev or cc/rev or in^{3}/rev.

**Q _{T} = V_{D}(m^{3}/rev) x n (rps)**

**Theoretical Flow Rate (Q _{T})**

It is the quantity of the system fluid that must flow through a motor per unit of time, provided there is no leakage in the system. The flow rate is commonly measured in m^{3}/s or lpm. The equation for the theoretical flow rate (Q_{T}) of the hydraulic motor is as follows:

**Slippage in Hydraulic Motors**

It is the internal leakage of the system fluid that passes through the unintended paths of a motor, without performing any useful work. As the slippage in the hydraulic motor increases, more and more available flow intended for doing the useful work is lost, leading to the loss of power in the motor.

**Theoretical Torque (T _{T}), **

**Hydraulic Motor**

Theoretical torque of a hydraulic motor is a function of the motor’s displacement and the differential pressure across the motor. The theoretical figures represent the torque available at the motor shaft, assuming no mechanical losses.

**Theoretical Torque, T _{T} (Nm) = V_{D} (m^{3}/rev) x ΔP (Pa) /2π**

**Breakaway (Starting) Torque** of a hydraulic motor is the rotary force required for turning a stationary load connected to the motor.

**Running Torque** of a hydraulic motor refers to the torque required to run a load connected to the motor. Remember, the running torque of the hydraulic motor changes whenever there is a variation in the associated system pressure.

**Stalling Torque** of a running hydraulic motor is the torque needed to stop the motor to a standstill.

**Actual Torque (T _{A}), **

**Hydraulic Motor**

It is the torque which a motor develops to drive the attached load alone. It is equal to theoretical torque minus the torque losses on account of any friction in the motor.

**Input Power (P _{in}), Hydraulic Motor**

**Input Power (Watt) = P (Pa) x QA (m ^{3}/s)**

**Output Power (P _{out}), **

**Hydraulic Motor**

**Output power, (Watt) = T _{A} (Nm) x ω (rad/s)**

**Motor Efficiency**

Two basic types of efficiencies are identified for the motor. They are: (1) Volumetric efficiency, and (2) Mechanical efficiency. Overall efficiency can, then, be derived from these two types of efficiencies.

**Volumetric Efficiency (η _{v}) **of the hydraulic motor is the ratio of the theoretical flow rate responsible for developing the actual motor speed to the total flow rate consumed by the motor, including the leakage in the motor.

**Volumetric efficiency, η _{v }= Theoretical flow rate (Q_{T}) / Actual flow rate (Q_{A})**

**Mechanical efficiency (η _{m}) **of the hydraulic motor is the ratio of the actual torque delivered by the motor to the theoretical torque of the motor. The hydraulic motor produces less torque than it should theoretically, due to the frictional losses in the motor.

**Mechanical efficiency, η _{m }= Actual torque (T_{A}) / Theoretical torque (T_{T})**

**Overall Efficiency (η _{o}) **of the hydraulic motor is the ratio of the ‘brake’ power delivered by the motor to the hydraulic power delivered to the motor. It is also the product of its volumetric efficiency and its mechanical efficiency and is expressed mathematically as:

** η _{o} =η_{v }x η_{m}**

Joji Parambath

Director

Fluidsys Training Centre Pvt Ltd

Bangalore, India