LECTURE #28 MOTION CONTROL

Course Name : DESIGN OF MACHINE ELEMENTSCourse Number: MET 214

Machine systems can operate with intermittent motion. Starting and stopping operations can cycle frequently.

Motion control elements permit machine systems to achieve intermittent motion.

Motion Control elements:

• Clutches: Devices used to transmit power on an intermittent basis by connecting and/or disconnecting a driven component to and/or from the prime mover.

– Motor operates efficiently at continuous speeds.– Avoids accelerating and/or de-accelerating the rotor of the motor each time a driven component

of a machine needs to be cycled.• Brakes: Device that absorbs the kinetic energy of a system and thus controls the motion of the system

by slowing down the system and/or bringing the system to rest.

Functions of a clutch:• Connect a rapidly turning shaft to one that is initially stationary.• Cause two shafts to turn at the same speed and to do so in a manner that shock is not produced.• Limit torque that is transmitted or to prevent torque from being transmitted in a reverse direction.

Types of clutches:• Positive contact

– Square Jaw– Spiral Jaw

• Friction clutches– Plate– Cone

Positive Contact Clutches:• Transmits power from the driving shaft to the driven shaft by means of jaws or teeth.

Advantagesa) No slip operationb) Develop very little heat since they do not depend on frictionc) Generally lighter and less costly than a friction clutch of similar torque capacity

Disadvantagesd) Cannot be engaged at high speedse) Shock accompanies engagement at any speedf) When both driven and drive shafts are at rest, some relative motion may be required to engage.

Disc clutch:

Disc ClutchTransmits torque from the input shaft to the output shaft due to the friction force developed between the two plates or discs.Input disc is free to move axially along the shaft but is splined, or keyed to shaft so disc will rotate with shaft.The friction force that can be transmitted depends on axial force developed between discs.

Axial force can be applied in several ways.1. Mechanical means

a) Leversb) Springsc) linkages

2. Hydraulic or pneumatic3. Electro-magnetic means

Advantages4. Very little shock during engagement due to slippage5. Can be used for high speed engagements.Disadvantages6. Slippages not suitable for applications that require positive transmission7. wear

If the discs or plates used in the clutch are relatively flexible, it is possible to obtain relatively uniform pressure on the friction surfaces when the actuating forces presses the disc together.If the plates are relatively rigid, the wearing of the friction surface is approximately uniform after an initial wearing-in has taken place.When analyzing the clutch, either the assumption of uniform wear or uniform pressure must be made. A conservative approach is to design with the assumption of uniform wear.wear may be assumed to be directly proportional to pressure and velocity at a particular point on the plate of the clutch. Recall velocity is proportional to the radius.AccordinglyUniform wear implies local pressure P times r is constant.

Where Wear Proportionality Constant Local Pressure radius to arbitrary point on disc

Under the assumption of uniform wear, the product of pressure and radius is a constant

Whereproportionality constant

Accordingly the maximum pressure must occur at the minimum radius.K=pr = pmax ri => p=pmax

*W kP r

W

kPr

*W

P r kk

k

Note: If disc or plates used in clutch are relatively flexible, it is possible to obtain relatively uniform pressure on the friction surfaces.Alternatively, if the plates are rigid, the wearing of the plates is relatively uniform after an initial wearing of the friction surface.

Since W and k both are constants

ir

r

Since pr=k, as r increases then p decreasesAlternatively as r decreases, p increases.

Solving for P from the above equation

Pressure varies from a max at to a minimum at where Outer Radius

For the case of uniform wear, the following relationship exists between the activation force and the pressure existing at

The torque that can be transmitted by a disc type of clutch can also be related to the activating force.For the case of uniform wear. The frictional torque for the elemental annular area must be integrated over the area of the dics.

r

rPP imax

ir or or

P r

Actuating force = force pressing the two discs togetherActuating force is normal to the friction surface. It can be obtained by multiplying the pressure between the friction surfaces by the area of the surfaces – since pressure varies with ri we must integrate to obtain F.

2o

a

i

rF p rdr

r max 2

oo

i

rrp rdrr

r max2

o

i

rrp dr

r max2 [ ]

o

i

i

rr p r

r max2 [ ]i o ir p r r

2 2max 0[ ] 2 [ ]

o o

f i i

i i

r rT rF dr r f p rdr fr p r r

r r

max 0 0[ ][ ]i i iT fr p r r r r 0[ ]

2

a iF f r rT

f=coefficient of friction

Brake and Clutch Material Properties

MaterialMaximum Drum Temperature, 0F

Coefficients of friction, f

Maximum Allowable

Pressure, psiMetal on metal 500-600 0.25 200-250

Wood on metal 200 0.2-0.3 50-90

Leather on metal 150-200 0.3-0.4 15-40

Molded Blocks 500-600 0.25-0.5 100-150

Asbestos on metal in oil

500 0.35-0.45 50-150

Sintered metal on cast iron in oil

450 0.2 400

Example : A single plate disc clutch, with both sides effective, is to be used in an automobile. The friction material that the clutch is made of has a coefficient of friction of 0.3 and a maximum allowable pressure 15 psi. If the outside radius of the clutch is 10 in., and the inside radius is 8 in., determine the torque that can be transmitted and the actuating force required of the springs.

Solving for torque on a single side

Torque transmitted for 2 sides

Actuating force required to transmit torque.

Wear rating: The previous relationships concerning the torque that can be transmitted by a clutch involved the mean radius of the disc. The area of the disc did not influence torque.Several different combinations of and can produce the same but different areas. Although the different combinations of and lead to the same and therefore are capable of transmitting the same level of torque, the difference in the areas will effect the rate at which the disc wears and/or the amount of power that can be accommodated with a specified wear rate.

1T

12 2TT

aF

or ir mRor ir mR

Where Wear rating Area of friction surfacePower transmitted by frictional surfaces of discs

Note: for frequent applications, a conservative rating for average service for infrequently used brakes allowed to cord some what between applications

Where amount of torque that can be transmitted by clutch/ brake angular velocity of disc

Wheren = speed of rotation in rpm

A

PWR f

WR

AfP

2/04. inhpWR 2/10. inhp2/40. inhp

ff TP

fT

000,63

nTP ff

Two approaches are available for establishing the torque requirement demanded from a clutch and/or brake.

1)

where Conversion factor for units Power of prime mover Speed of prime mover rpm Service factor based on application Torque level required from clutch

2a)where

Mass moment of inertia of load presented to motorangular acceleration rad/sec2

For constant α, α=∆ / ∆t

w= angular speed rads/secequation 2 may be rewritten:

2b)

n

CPkT

CPnkT

mJT

mJ

t

JT m

Equation 2b enables the designer to relate the torque required to produce a change in rotational speed ∆ in a given amount of time ∆t,Equation 2b enables the designer to assess the impact of time to start and/or time to stop on the requirements of the clutch.

GivenExample :

Calculate Torque T required to accelerate inertia with specifications given above.

T=

sec50.2

550

0

473.2 2

t

rpmn

n

ftslugJ

f

i

m

Energy Absorption/ Heat DissipationWhen using a clutch to accelerate an object or a brake to stop a rotating object, heat is generated due to friction. Heat is transferred from the clutch and/or brake to the surroundings and equilibrium temperature is established.Temperature of components can effect life time.The energy to be absorbed or dissipated by the unit on operational cycle is equal to the change in kinetic energy of the components being accelerated or stopped.

where energy absorbed or dissipated Mass moment of inertia Initial Angular velocity

Final Angular velocity Change in Kinetic energy

22

2

1fimJKEE

EmJi

KEf

Cone Clutch:Cone clutches have the advantage of being able to transmit a larger torque than disc clutches with the same outside diameter and actuating force.The reason for this capability is the increased frictional area and the wedging action that takes place.Cone clutches find their widest use in relatively low peripheral speed applications.

Cone clutch analysis

0 XF

0sincos' NFFa

sincos NfNFa

sincos' NFFa

)cos(sin fNFa

cossin f

FN a

Assuming the friction force is isotropic and acts at the mean radius

Substituting for N from above expression

Compute the axial force required for a cone brake if it is to exert a braking torque of 50 lb-ft. The mean radius of the cone is 5.0 in. Use f=.25. Try cone angles of 100, 120 and 150

α Fa

100

120

150

20 i

m

rrR

mf fNRT

cossin f

RfFT maf