Machine Design II Prof

7/30/2019 Machine Design II Prof

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Machine Design II Prof. K.Gopinath & Prof. M.M.MayuramIndian Institute of Technology Madras

Energy ConsiderationIt has been noted that the most common brakes employ friction to transformthe braked system's mechanical energy, irreversibly into heat which is thentransferred to the surrounding environment - Kinetic energy is absorbed during slippage of either a clutch or brake, and this energy appears as heat. If the heat generated is faster than it is dissipated, then the temperature rises. Thorough design of a brake therefore requires a detailed transient thermalanalysis of the interplay between heat generated by friction, heat transferredthrough the lining and the surrounding metalwork to the environment, and theinstantaneous temperature of the surface of the drum as well as the lining. Fora given size of brake there is a limit to the mechanical power that can betransformed into heat and dissipated without lthe temperatures reachingdamaging levels. Temperature of the lining is more critical and the brake size ischaracterized by lining contact area, A.The capacity of a clutch or brake is therefore limited by two factors:1. The characteristics of the material and,2. The ability of the brake to dissipate heat.

Heat Generated In BrakingDuring deceleration, the system is subjected to an essentially constant torqueT exerted by the brake, and in the usual situation this constancy implies constantdeceleration too.

Application of the work or energy principle to the system enables the torqueexerted by the brake and the work done by the brake, U, to be calculated from:-Machine Design II Prof. K.Gopinath & Prof. M.M.MayuramIndian Institute of Technology Madras

U = E = T (2)Where E is the loss of system total energy which is absorbed by the brakeduring deceleration, transformed into heat, and eventually dissipated.The elementary equations of constant rotational deceleration apply, thus whenthe brake drum is brought to rest from an initial speed o :-Deceleration = o2/ 2 (1) = m.t ; m = o/2 =

/t where m is the mean drum speed over the deceleration period.The mean rate of power transformation by the brake over the braking period is:-Pm = U / t = T m ( 3 ) which forms a basis for the selection or

the design of the necessary brake dimensions.The rise in temperature in the lining material is also important as rate of wear isalso a function of the temperature. Further for any lining material, the maximumallowable temperature is also another performance criteria.

Temperature RiseThe temperature rise of the brake assembly can be approximated by the classicexpression,,T E


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C.m

=

Where is temperature T is rise in temperature in oC,C is the specific heat ofthe brake drum material (500J/Kg for steel or Cast Iron) and m is the mass(kg) of the brake parts dissipating the heat into the surroundings.

Though the equation appears to be simple, there are so many variables involvedthat it would be most unlikely that such an analysis would even approximateexperimental results.Machine Design II Prof. K.Gopinath & Prof. M.M.MayuramIndian Institute of Technology Madras

On the other hand the temperature-rise equations can be used to explain whathappens when a clutch or brake is operated frequently. For this reason suchanalysis are most useful, for repetitive cycling, in pin pointing those designparameters that have the greatest effect on performance.

An object heated to a temperature T1 cools to an ambient temperature Taaccording to the exponential relation

Time-temperature relationT T (T T )e (AU/WC)t i a 1 a

=

Where T1 = instantaneous temperature at time t, CA= heat transfer area, m2U= Heat Transfer coefficient, W/(m2.s. C)T1 = Initial temperature, CTa = Ambient temperature, CC - Specific heatt - time of operation, sMachine Design II Prof. K.Gopinath & Prof. M.M.MayuramIndian Institute of Technology Madras

TTt t tCBT

AT

Aa

B C1

T2Time tFigure 3.1.16Figure shows an application of Eq. (a). At time tA a clutching or brakingoperation causes the temperature to rise to T1 at A. Though the rise occurs in afinite time interval, it is assumed to occur instantaneously. The temperature then


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drops along the decay line ABC unless interrupted by another braking operation.If a second operation occurs at time tB, the temperature will rise along the dashedline to T2 and then begin an exponential drop as before. About 5 -10 % of theheat generated at the sliding interface of a friction brake must be transferredthrough the lining to the surrounding environment without allowing the lining to

reach excessive temperatures, since high temperatures lead to hot spots anddistortion, to fade (the fall-off in friction coefficient) or, worse, to degradation andcharring of the lining which often incorporates organic constituentsMachine Design II Prof. K.Gopinath & Prof. M.M.MayuramIndian Institute of Technology Madras

In order to determine the brake dimensions the energy need to be absorbedduring critical braking conditions is to be estimated.

Energy to be AbsorbedIf t is the time of brake application and m the mean or average angular velocitythen the energy to be absorbed in braking EE = T. m .t = Ek+ Ep+ Eiwhere Ek is the kinetic energy of the rotating system

Ep is the potential energy of the moving systemEi is the inertial energy of the systemEnergy to be absorbed

( )k22 22 1

E 1

2 g1 mv

21 v v

2 g

=

=

=

( )p2

i2 22 1

E mgh hE 1 I

2

1 I


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2

= =

=

=

Frictional MaterialA brake or clutch friction material should have the following characteristics to adegree, which is dependent upon the severity of the service. A high and uniform coefficient of friction. Imperviousness to environmental conditions, such as moisture. The ability to withstand high temperatures together with good thermalconductivity. Good resiliency. High resistance to wear, scoring, and galling.Machine Design II Prof. K.Gopinath & Prof. M.M.MayuramIndian Institute of Technology Madras

Linings

The choice of lining material for a given application is based upon criteria such asthe expected coefficient of friction; fade resistance, wear resistance, ease ofattachment, rigidity or formability, cost, abrasive tendencies on drum, etc. Thelining is sacrificial - it is worn away. The necessary thickness of the lining istherefore dictated by the volume of material lost - this in turn is the product of thetotal energy dissipated by the lining throughout its life, and the specific wear rateRw (volume sacrificed per unit energy dissipated) which is a material propertyand strongly temperature dependent. The characteristics of a typical mouldedasbestos lining material is illustrated in the figure below. The coefficient offriction, which may be taken as 0.39 for design purposes, is not much affected bypressure or by velocity - which should not exceed 18 m/s. The maximum

allowable temperature is 400C. However at this temperature the wear is veryhigh. From a lower wear or higher life point, the maximum temperature shouldnot exceed about 200 oC0 Temperature ( C ) 4000

0.5o

Figure 3.1.17Machine Design II Prof. K.Gopinath & Prof. M.M.MayuramIndian Institute of Technology Madras

Linings traditionally were made from asbestos fibers bound in an organic matrix,however the health risks posed by asbestos have led to the decline of its use.Non-asbestos linings generally consist of three components - metal fibers for

strength, modifiers to improve heat conduction, and a phenolic matrix to bindeverything together.

Brake Design SectionThe braked system is first examined to find out the required brake capacity that isthe torque and average power developed over the braking period. - The brakeis then either selected from a commercially available range or designed fromscratch ff a drum brake has to be designed for a particular system (rather thanchosen from an available range) then the salient brake dimensions may be


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estimated from the necessary lining area, A, together with a drum diameter- toliningwidth ratio somewhere between 3:1 and 10:1, and an angular extent of 100C say for each of the two shoes.

Worked out Example 1An improved lining material is being tried on an existing passenger car drum

brake shown in Figure. Quality tests on the material indicated permissiblepressure of 1.0 MPa and friction co-efficient of 0.32. Determine what maximumactuating force can be applied for a lining width of 40 mm and the correspondingbraking torque that could be developed. While cruising on level road at 100kmph, if it is to decelerated at 0.5g and brought to rest, how much energy isabsorbed and what is the expected stopping distance?Machine Design II Prof. K.Gopinath & Prof. M.M.MayuramIndian Institute of Technology Madras

While cruising on level road at 100 kmph, if it is to decelerated at 0.5g andbrought to rest, how much energy is absorbed and what is the expected stoppingdistance?

3003000

R=1250

100.950 50300 05

AUTOMOTIVE DOUBLE SHOE BRAKE0

5

30

F F120 Pin Pin 1200

30086.6

Figure 3.1.18Analysis based on leading shoea2 2

P 1 MPa f 0.32 a 187.5 mm

b 40 mm 900 d = 100 +86.1 max

= = =

= =

= 99.99 100mm

50 1200 r =125 mm 1 2

= =Machine Design II Prof. K.Gopinath & Prof. M.M.MayuramIndian Institute of Technology Madras


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( )

( )a 2 1n 2 1a

6 -3 3n

p rd 1

M (sin 2 sin 2 )

sin 2 4

10 *40*10 *125 *10 * 0.1 115 1

= * sin 240 sin10

1 2 180 4

1

=40*125*0.1 1.003- 1.03

4

M 631.459 N.mb

=

=

Mf fs.ibn.rpm r(cos 1 - cos 2) - d2(sin2 2 - sin2 1) a0.32*40*10-3 *125*10-3 *106 0.125(cos5 - cos120 ) - 0.04(sin2 120 - sin2 5 )

Mf 224.85 N -m

=

=


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=

F*a=MN MfF Mn Mf631.459 224.85 2174.3N

a 0.187 Max. actutating force

= = =

2 a( ) aB1 2

a n f3 2 6

B

B

p F

T fbr cos cos ) 1

sin M M

T 0.32 * 40 *10 * (0.125) *10 (Cos5 Cos120) 1 406.609856.36

T 441.329 N-m=

+

+

= + =

Running at 100 kmph =100*5/8= 27.7 m/sMachine Design II Prof. K.Gopinath & Prof. M.M.MayuramIndian Institute of Technology Madras

U= 27.7 m/sDeceleration =0.5*9.8=4.92 22

2V U 2aS

0 (27.7) 2*( 4.9) *SS 27.7 78.29 m

2*4.9

=

=

= =

E T. av.t

441.329 1 27.7 . 78.242 0.125 27.7

138206138.2KJ

=

= =

=


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Worked out example 2A spring set, hydraulically released double shoe drum brake, schematicallyshown at Fig 2 is to be designed to have a torque capacity of 600 N.m underalmost continuous duty when the brake drum is rotating at 400 rpm in eitherdirection. Assume that the brake lining is to be molded asbestos having a

friction coefficient of 0.3 and permissible pressure of 0.8 MPa. The width of thebrake shoe is to be third of drum diameter and the remaining proportion's are asshown in figure.0

1 41

30 6 0 693

30

=

== =

a . D

b D

d . D .

cos

DMachine Design II Prof. K.Gopinath & Prof. M.M.MayuramIndian Institute of Technology Madras

Double block brake

9030

1.4 D

0.6 D

Figure 3.1.19Determine the required brake drum diameter, width of the lining and the springforce required to be set.0

a 1.4D

b 1 D

3d 0.6D 0.693D

cos30

=

=

= =Machine Design II Prof. K.Gopinath & Prof. M.M.MayuramIndian Institute of Technology Madras


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( )

( ) ( )( ) ( )1

1

6

3NaJ

2 2a 1 2 263

0.8*10 * 1 D* D * 0.6028D. sin(210 ) sin 30

3 2 4 4

M 92373.3D *1.035P brfM r a cos sin d

1

P brf r cos cos d sin sin2

0.8*10 * D * D * 0.3 D 1.225 0.6928 0.866

3 2 2 212500D

1

= ==

=

= =

a' N Fa a

N F

aa

P 'for the trailing shoeM M

P P

M MP 95606.36 12500

95606.36 12500


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0.7687P

= + = + =

Torque due to trailing and leading shoe=

( )( )2 2

1 1

aa2

a aa

2a a 1 2

a

fdN.r

P sinf.r .rd .b

sinfbr P sin d P ' sin d

sin

fbr . P P ' . cos cos

sin

=

=

= +

= +

( )total


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263

0.3* D * D

3 4 1.7687 *0.8*10 cos15 cos1.5

1

43324 DT 600 Nm

Therefore D 240.14mm

= =

=

=

Machine Design II Prof. K.Gopinath & Prof. M.M.Mayuram

Indian Institute of Technology Madras

Actuating force due to spring2F MN MF 83106 * 0.240 3423.22N

1.4 *D 1.4

= = =

Actuating force =3423.22 NLiving width D

3

80.04 mm

=

=__

Machine Design II Prof

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