3.3. hydraulic motor

3.3. Hydraulic motor 2012

Hydraulic and pneumatic control lecture notes by Siraj K.

3.3. Hydraulic motors

3.3.1. Introduction

A fluid power motor is a device that converts fluid power energy to rotary motion and force. The

function of a motor is opposite that of a pump. However, the design and operation of fluid power

motors are very similar to pumps. Motors have many uses in fluid power systems. In hydraulic

power drives, pumps and motors are combined with suitable lines and valves to form hydraulic

transmissions. The pump, commonly referred to as the A-end, is driven by some outside source,

such as an electric motor.

The pump delivers fluid to the motor. The motor, referred to as the B-end, is actuated by this

flow, and through mechanical linkage conveys rotary motion and force to the work. This type of

power drive is used to operate (train and elevate) many of the Navy’s guns and rocket launchers.

Hydraulic motors are commonly used to operate the wing flaps, radomes, and radar equipment in

aircraft. Air motors are used to drive pneumatic tools. Air motors are also used in missiles to

convert the kinetic energy of compressed gas into electrical power, or to drive the pump of a

hydraulic system.

Fluid motors may be either fixed or variable displacement. Fixed-displacement motors provide

constant torque and variable speed. The speed is varied by controlling the amount of input flow.

Variable-displacement motors are constructed so that the working relationship of the internal

parts can be varied to change displacement. The majority of the motors used in fluid power

systems are the fixed-displacement type. Although most fluid power motors are capable of

providing rotary motion in either direction, some applications require rotation in only one

direction. In these applications, one port of the motor is connected to the system pressure line

and the other port to the return line or exhausted to the atmosphere. The flow of fluid to the

motor is controlled by a flow control valve, a two-way directional control valve, or by starting

and stopping the power supply. The speed of the motor may be controlled by varying the rate of

fluid flow to it.

In most fluid power systems, the motor is required to provide actuation power in either direction.

In these applications the ports are referred to as working ports, alternating as inlet and outlet



ports. The flow to the motor is usually Fluid motors are usually classified according to the type

of internal element, which is directly actuated by the flow.

Figure 3.3.1. Actuators classifications

3.3.2. Limited rotation hydraulic motors

Limited rotation actuators, called torque motors, have a wide variety of applications where a

limited specified degree of rotation at the output shaft is required. Rotation is usually limited to

720°. They are used extensively in industry for actuating clamping devices, material handling,

rotating cams for braking mechanisms, tumbling and dumping, positioning and turning, and

many other situations where an economical application of fluid power for limited rotation is

desirable. (Fig. 3.3.2) Vane-type limited actuators apply fluid force to the cross section area of

single or multiple vanes. Rack and pinion type actuators apply fluid force to the cylindrical

chambers which move the rack to drive the pinion gear.



Figure 3.3.2 (a) Rack and pinion limited rotation actuator (courtesy of Flo-Tork, Inc. ); (b) Vane

type limited rotation actuator (courtesy of Bird-Johnson ); (c) Typical applications of limited

rotation actuators (courtesy of Bird-Johnson).



Analysis of torque capacity

The following nomenclature and analysis are applicable to a limited rotation hydraulic motor

containing a single rotating vane:

=RR Outer radius of rotor (in, mm)

=VR Outer radius of vane (in, mm)

=L Width of vane (in, mm)

=p Hydraulic pressure (psi, Pa)

=F Hydraulic force acting on vane (lb, N)

=A Surface area of vane in contact with oil (in2, m2)

=T Torque capacity (in. lb, N.m)

The force on the vane equals the pressure times the vane surface area:

( )LRRppAF RV −==

The torque equals the vane force times the mean radius of the vane:

( ) ( )2

RVRV

RRLRRpT

+∗−=

On arrangement we have

( )22

2 RV RRpL

T −= 3.3.1

A second equation for torque can be developed by noting the following relationship for

volumetric displacement VD:

( )LRRT RV22 −= π 3.3.2

Combining equations (3.3.1) and (3.3.2) yields

π2DpV

T = 3.3.3

3.3.2. Types of hydraulic motors

Continuous rotation actuators, called hydraulic motors, provide sustained rotation in either

direction. Some hydraulic motors are also convertible to serve as hydraulic pumps if a

mechanical drive is applied to the output shaft, but this is not usually recommended without

special provision because of port timing and other internal part arrangements. Vane motors, for



example, have spring loaded vanes, whereas vane pumps usually do not. This is not the case with

axial piston motors, however , which are widely advertised as combination pump-motors.

Hydraulic motors differ from pumps in other respects. Because the case is pressurized from an

outside source, case drains are provided to protect shaft seals (Fig .3.3.3). These may be piped

directly to the low pressure reservoir, or through a crossover check valve arrangement to the

exhaust port of the motor. External drain lines or crossover check valve arrangements are needed

only for series circuits or meter out circuits. This is necessary during reversing, braking, and

other operating conditions which would otherwise subject the case drain to system pressure.

Maximum pressure at the case drain is usually 100-250 psi. Port timing is an additional factor

that may be different between pumps and motors.

Figure 3.3.3. Hydraulic case drain arrangements

Hydraulic motors are available as fixed or variable displacement unit s so that speed variation

with rotation in either direction is possible.

Gear motors

External gear positive displacement motors operate in the reverse manner of their pump

counterparts (Fig. 3.3.4). They are available in sizes to 20 in3 per revolution. Fluid supplied to

the inlet port circulates around the out side of the gear teeth driving both gears, although only

one gear is connected to the motor output shaft. The gear teeth seal where they mesh and

between their ends and the motor housing. Fluid is trapped in cavities formed by the gear teeth

and the motor housing and transported around the out side diameter of the gears to the low

pressure port side of the motor.



Industrial gear motors are the least expensive to manufacture, have overall efficiencies to 90%,

and operate in the speed range of 1000 to 2500 rpm. Recent developments in gear tooth materials

and technology have extended the speed range of gear motors in excess of 20,000 rpm for motor

size s in the 0.063-0.093 in3 per revolution displacement range. Their small size, high speed, and

high power (4-5.5 hp) make these motors ideal for spindle drives in the machine tool industry.

Figure 3.3.4. External gear positive displacement motor

Vane motors

Vane motors operate similarly to vane pumps with the exception that unlike their pump

counterpart s, spring loading is used to insure positive contact between the vanes and the



eccentric cam ring (Fig 3.3.5). Seals, high speed bearings, and case drains also are given special

attention.

Vane motor showing spring loaded vanes

Figure 3.3.5. Vane-type motor.

Fluid entering the motor under high pressure acts against the rectangular surfaces of the vanes

while the chamber volume increases, and then is exhausted as it decreases (Fig. 3.3.6). Balanced



vane motors admit fluid from two ports located 180° apart to reduce side thrusts on the

supporting shaft and bearings, and discharge the fluid 90° later through two similarly located

discharge ports. One piece motor body and cartridge element construction permit interchange to

adapt the unit to a wide variety of flow capacities and ease repair with minimum disassembly and

number of spare parts. Fluid viscosities between 55 and 275 SSU are recommended at normal

operating temperatures of 120°F with a maximum of 180°F. Most vane motors are not

recommended for use with water-based emulsion fire-resistant fluids .

Figure 3.3.6. Balanced vane motor operation (Courtesy of Sperry Vickers)

Piston type motors

Piston motors are the most like their pump counterparts and incorporate only minor changes to

effect the conversion. They are available in both axial and radial designs. In-line-type motors are

similar to pumps and make use of both the fixed displacement swash plate and variable

displacement adjustable yoke. Bent axis motors are available with fixed displacement angles as

well as variable displacement angles. Radial piston motors are used widely in low speed, high

torque applications. Piston motors also operate at the highest efficiencies, speeds, and pressures

available.



Fixed displacement in-line swash plate motors commonly use nine pistons with the swash plate

at 15° (Fig. 3.3.7). They are available in single or double shaft versions. Reversal of the motor is

accomplished only by reversing the direction of fluid flowing through the motor.

Figure 3.3.7. Fixed displacement in-line piston motor (courtesy of Sperry Vickers).

When used as a motor, hydraulic pressure on the piston create s tangential force s on the angled

swash plate (Fig. 3.3.8). This gives the required turning moment to the shaft. As fluid is directed

to the rotor through the inlet and kidney-shaped port in the valve plate, it imparts a force (F) on

the pistons in line with their axis.

Figure 3.3.8. Vector forces in in-line piston motor (courtesy of Sperry Vickers).



The axial force is resolved into its component angle force s (FI) and (Fz). While the force (F1) is

directed perpendicular to the surface of the stationary swash plate and is not available to

accomplish work, the force (Fz) is in a direction parallel to the surface of the swash plate and so

is free to move down the angled surface imparting motion to the piston group, cylinder block,

and output shaft. Fluid under pres sure is directed to the piston s through the kidney-shaped inlet

port while the piston s are descending the swash plate angle , and directed from the pistons to the

exhaust port as they ascend the swash plate angle.

Variable displacement in-line piston motors differ from fixed swash plate motors in that the

angle of the swash plate is changeable (Fig. 3.3.9). Angles of + 15° and -15° from the center

position are common. Reversal of the motor is accomplished by tilting the yoke over center by

the action of a servo yoke actuating piston or manual control. The torque from variable

displacement motors varies with the change in volume displacement caused by tilting of the

yoke. If the motor receives fluid at constant flow rate from the pump, a decrease in torque is

accompanied by an increase in speed. The fluid horsepower of the motor is constant since the

product of pressure (p) and flow rate (Q) input are constant. Neglecting losses, the horsepower

output is also constant.

252,5

NTBhp

∗=

Figure 3.3.9. Variable displacement in-line piston motor (courtesy of Sperry Vickers).



Increases or decreases in torque resulting from increases or decreases in motor displacement will

be accompanied by inverse decreases or increases in motor output speed. As the angle of the

actuating yoke is reduced to approach 0°, the speed of the variable displacement motor increases.

Further decrease in the angle of the yoke will cause the motor to stall and cause excessive

pressure in the system which must be released to redirect the constant flow provided by the

pump.

3.3.3. Hydraulic motor theoretical torque, power and flow rate

Motors convert fluid energy back into mechanical energy and thus are the mirror image of

pumps. It is not surprising that the same mechanisms are used for both. The typical motor

designs are gear, vane, and piston. Motor performance is a function of pressure. As pressure

increases, leakage increases, speed decreases, and thus the quantity of mechanical energy

delivered to the load decreases. Due to this a hydraulic motor delivers less torque than it should

theoretically. The theoretical torque (which is the torque that a frictionless hydraulic motor

would deliver) can be determined by the following equation developed for limited rotation

hydraulic actuators:

( ) ( ) ( )π2

/3 psiprevinVlbinT D

T

∗=∗ 3.3.4

Using metric units we have

( ) ( ) ( )π2

/3 PaprevmVmNT D

T

∗=∗

Thus, the theoretical torque is proportional not only to the pressure but also to the volumetric

displacement.

The theoretical horsepower (which is the horsepower a frictionless hydraulic motor would

develop) can also be mathematically expressed:

( ) ( )000,63

rpmNlbinTHP T

T

∗∗=

( ) ( ) ( )π2

/3 rpmNpsiprevinVD ∗∗= 3.3.5

In metric units, theoretical power (W)



( ) ( ) ( ) ( ) ( ) ( )π2

///

3 sradNPaprevmVsradNmNTWpowerlTheoretica D

T

∗∗=∗∗=

Also due to the leakage, a hydraulic motor consumes more flow-rate than it should theoretically.

The theoretical flow-rate is the flow-rate a hydraulic motor consume if there where no leakage.

As is the case for pumps, the following equation gives the relationship among speed, volumetric

displacement and theoretical flow-rate.

( ) ( ) ( )231

/3 rpmNrevinVgpmQ D

T

∗=

3.3.6

Or

( ) ( ) ( )srevNrevmVsmQ DT /// 33 ∗= 3.3.7

3.3.4. Hydraulic motor performance

The performance of any hydraulic motor depends on the precision of its manufactures as well as

the maintenance of close tolerances under design operating conditions. As in the case for pumps,

internal leakage (slippage) between the inlet and outlet reduces the volumetric efficiency of a

hydraulic motor. Similarly, friction between mating parts and due to fluid tolerance reduces the

mechanical efficiency of the hydraulic motor.

Gear motors typically have an overall efficiency of 70 to 75% as compared to 75 to 85% for vane

motors and 85 to 95% for piston motor. Some systems require that a hydraulic motor start under

load. Such system should include a stall torque factor when making design calculations. For

example only about 80% of the maximum torque can be expected if the motor is required to start

either under load or operate at the speed below 500 rpm.

Motor efficiencies

Hydraulic motor performance is evaluated on the same three efficiencies (volumetric,

mechanical and overall efficiencies) used for hydraulic pumps. They are defined for motor as

follows:



1. Volumetric efficiency (ηηηηv)

The volumetric efficiency of a hydraulic motor is the inverse of that for a pump. This is because

a pump does not produce as much flow as it should theoretically, whereas a motor uses more

flow than it should theoretically due to leakage. Thus, we have

A

Tv Q

Q

motorbyconsumedrateflowactual

consumeshouldmotorrateflowltheoretica=

−−

=η 3.3.8

Determination of volumetric efficiency requires the calculation of the theoretical flow-rate,

which is defined for a motor. Substituting the values of calculated theoretical flow-rate and

actual flow-rate (which is measured) in to equation above yields the volumetric efficiency for the

given motor.

2. Mechanical efficiency (ηm)

The mechanical efficiency of a hydraulic motor is the inverse of that for a pump. This is because

due to friction, the pump requires a greater torque than it should theoretical where as a motor

produces less torque than it should theoretically. Thus, we have

T

Am T

T

deliverllytheoreticashouldmotortorque

motorbydeliveredtorqueactual==η

3.3.9

The following equations (3.3. ) and (3.3. ) allow for the calculation of TT and TA, respectively:

( ) ( ) ( )π2

/3 psiprevinVlbinT D

T

∗=∗ 3.3.10


( ) ( ) ( )π2

/3 PaprevmVmNT D

T

∗=∗

( ) ( )rpmN

motorbydeliveredHPactuallbinTA

000,63∗=∗ 3.3.11


( ) ( )sradN

motorbydeliveredwattageactualmNTA /

000,63∗=∗



3. Overall efficiency (ηηηηo)

As in the case for pumps, the overall efficiency of a hydraulic motor equals the product of the

volumetric and mechanical efficiencies.

motortodeliveredpoweractual

motorbydeliveredpoweractualmvo =∗= ηηη

3.3.12

In English units, we have

( ) ( )

( ) ( )1714

000,63gpmQpsip

rpmNlbinT

A

A

o ∗

∗∗

=η

3.3.13

In metric units, we have

( ) ( )( ) ( )smQPap

sradNmNT

A

Ao /

/.3∗

∗=η

3.3.14

Note that the actual power delivered to a motor by the fluid is called hydraulic power and the

actual power delivered to the load by a motor via a rotating shaft called brake power.

3.3.5. Hydrostatic transmissions

Hydrostatic drive

Introduction

The hydrostatic drive is a fluid drive which uses fluid under pressure to transmit engine power to

the drive wheels of the machine. Mechanical power from the engine is converted to hydraulic

power by a pump-motor team. This power is then converted back to mechanical power for the

drive wheels. The hydrostatic drive can function as both a clutch and transmission. The final

gear train can then be simplified, with the hydrostatic unit supplying infinite speed and torque

ranges as well as reverse speeds. There two basic types of hydraulic transmissions:

• Hydrodynamic

• Hydrostatic



Figure 3.3. 10 Hydrostatic drives

Figure 3.3.11 Basic type of hydraulic transmissions

Figure 3.3.12 shows one piston for the pump and one for the motor. To provide a pumping action

for the pistons, a plate called a swashplate is located in both in the pump and motor. The piston



against the swashplates. The angle of the swashplates (figure 3.3.12) can be varied so that the

volume and pressure of oil pumped by the pistons can be changed or the direction of oil flow

reversed.

Figure 3.3.12 Two connected cylinders with swashplates

A pump or motor with a movable swashplate is called a variable-displacement unit. A pump or

motor with a fixed swashplate is called a fixed displacement unit. Figure 3.3.13 shows a variable

displacement pump driving a fixed displacement motor. As the pump pistons rotate, they move

across the sloping face of the swashplate, sliding in and out of their cylinder bores to pump oil

out. The more the pump swashplate is tilted, the more oil it pumps with each piston stroke and

faster it drives the motor.



Figure 3.3.13 Variable displacement pump driving fixed displacement motor

Pressure results whenever the flow of a fluid is resisted. The resistance may come from

acceleration of the machine or normal load. The motor swashplate is at a fixed angle so that the

strokes of its pistons are always the same. Thus its speed of rotation can not be changed except

as it is driven faster or slower by the pump oil. The point to remember now is that a given

volume of oil forced out of the pump will cause the motor to turn at a given speed. More oil will

speed up the motor; less oil will slow it down. The pump is driven by the machine’s engine and

so is linked to the speed set by the operator. It pumps a constant stream of high-pressure oil to

the motor.

Since the motor is linked to the drive wheels of the machine, it gives the machine its travel

speed. Only three factors control the operation of a hydrostatic drive:

• Rate of oil flow-gives the speed

• Direction of oil flow-gives the direction

• Pressure of oil-gives the power

Control of these three factors is infinite, giving endless selections of speed and torque in a

hydrostatic drive. The pump-motor team is the heart of the hydrostatic drive, although the

complete hydraulic system (figure 3.3.14) also includes a reservoir to supply the oil, a filter to

remove dirt, and a cooler to remove excess heat from the oil.



Figure 3.3.14 Complete system for a hydrostatic drive (closed hydraulic loop)

Basically however, the pump and motor are joined in a closed hydraulic loop; the return line

from the motor is joined directly to the intake of the pump, rather than to the reservoir. The

charge pump simply supplies the oil, drawing it from the resorvoir.

Types of hydrostatic drives

Displacement is the quantity of fluid which a pump can move (or motor can use) during each

revolution. It is directly related to the horsepower output of the drive. (Horsepower is a

combination of torque x speed.) As you have already learned, pumps and motors can have a

fixed dispacement or variable displacement. Four pump-motor combinations are possible:

1. Fixed displacement pump driving a fixed displacement motor.

2. Variable displacement pump driving a fixed displacement motor.

3. Fixed displacement pump driving a variable displacement motor.

4. Variable displacement pump driving a variable displacement motor.

The point tor remember is that for each combination the output power must equal the input

power minus negligible power losses. Let’s look at each combination (figure 3.3.15).

No. 1 circuit is like a gear drive; it transmits power without altering the speed or horsepower

between the engine and the load. A constant input speed and torque gives a constant output



horsepower. If either the speed or torque is increased holding the other constant the output

horsepower will increase.

Since the pump flow is variable in No. 2 circuit, the output speed is variable and torque output is

constant for any given pressure. This circuit gives variable speed and constant torque.

Output speed in No. 3 circuit is varied by changing the motor displacement. For constant power

input if the motor displacement decreases, output speed increases but output torque drops.

No. 4 circuit is the most flexible and expensive of the circuits but also the most difficult to

control. It is capable of operating like any of the above combinations.

Figure 3.3.15 Pump-motor combinations for hydrostatic drives

3.3. hydraulic motor

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