Clutches. Clutches 885 C H A P T E R

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1 Clutches 885 C H A P T E R 4 Clutches 1. Intoduction.. Types of Clutches.. Positive Clutches. 4. Fiction Clutches. 5. Mateial fo Fiction Sufaces. 6. Consideations in Designing a Fiction Clutch. 7. Types of Fiction Clutches. 8. Single Disc o Plate Clutch. 9. Design of a Disc o Plate Clutch. 10. Multiple Disc Clutch. 11. Cone Clutch. 1. Design of a Cone Clutch. 1. Centifugal Clutch. 14. Design of a Centifugal Clutch. 4.1 Intoduction A clutch is a machine membe used to connect a diving shaft to a diven shaft so that the diven shaft may be stated o stopped at will, without stopping the diving shaft. The use of a clutch is mostly found in automobiles. A little consideation will show that in ode to change geas o to stop the vehicle, it is equied that the diven shaft should stop, but the engine should continue to un. It is, theefoe, necessay that the diven shaft should be disengaged fom the diving shaft. The engagement and disengagement of the shafts is obtained by means of a clutch which is opeated by a leve. 4. Types of Clutches Following ae the two main types of clutches commonly used in engineeing pactice : 1. Positive clutches, and. Fiction clutches. 885

2 886 A Textbook of Machine Design We shall now discuss these clutches in the following pages. 4. Positive Clutches The positive clutches ae used when a positive dive is equied. The simplest type of a positive clutch is a jaw o claw clutch. The jaw clutch pemits one shaft to dive anothe though a diect contact of intelocking jaws. It consists of two halves, one of which is pemanently fastened to the Fig Jaw clutches. diving shaft by a sunk key. The othe half of the clutch is movable and it is fee to slide axially on the diven shaft, but it is pevented fom tuning elatively to its shaft by means of feathe key. The jaws of the clutch may be of squae type as shown in Fig. 4.1 (a) o of spial type as shown in Fig. 4.1 (b). A squae jaw type is used whee engagement and disengagement in motion and unde load is not necessay. This type of clutch will tansmit powe in eithe diection of otation. The spial jaws may be left-hand o ight-hand, because powe tansmitted by them is in one diection only. This type of clutch is occasionally used whee the clutch must be engaged and disengaged while in motion. The use of jaw clutches ae fequently applied to spocket wheels, geas and pulleys. In such a case, the non-sliding pat is made integal with the hub. 4.4 Fiction Clutches A fiction clutch has its pincipal application in the tansmission of powe of shafts and machines which must be stated and stopped fequently. Its application is also found in cases in which powe is to be deliveed to machines patially o fully loaded. The foce of fiction is used to stat the diven shaft fom est and gadually bings it up to the pope speed without excessive slipping of the fiction sufaces. In automobiles, fiction clutch is used to connect the engine to the dive shaft. In opeating such a clutch, cae should be taken so that the fiction sufaces engage easily and gadually bing the diven shaft up to pope speed. The pope alignment of the beaing must be maintained and it should be located as close to the clutch as possible. It may be noted that : 1. The contact sufaces should develop a fictional foce that may pick up and hold the load with easonably low pessue between the contact sufaces.. The heat of fiction should be apidly *dissipated and tendency to gab should be at a minimum.. The sufaces should be backed by a mateial stiff enough to ensue a easonably unifom distibution of pessue. 4.5 Mateial fo Fiction Sufaces The mateial used fo lining of fiction sufaces of a clutch should have the following chaacteistics : * Duing opeation of a clutch, most of the wok done against fictional foces opposing the motion is libeated as heat at the inteface. It has been found that at the actual point of contact, the tempeatue as high as 1000 C is eached fo a vey shot duation (i.e. fo second). Due to this, the tempeatue of the contact sufaces will incease and may destoy the clutch.

3 1. It should have a high and unifom coefficient of fiction.. It should not be affected by moistue and oil.. It should have the ability to withstand high tempeatues caused by slippage. 4. It should have high heat conductivity. Clutches It should have high esistance to wea and scoing. The mateials commonly used fo lining of fiction sufaces and thei impotant popeties ae shown in the following table. Table 4.1. Popeties of mateials commonly used fo lining of fiction sufaces. Mateial of fiction sufaces Opeating Coefficient of Maximum Maximum condition fiction opeating pessue tempeatue ( C) (N/mm ) Cast ion on cast ion o steel dy Cast ion on cast ion o steel In oil Hadened steel on Hadened steel In oil Bonze on cast ion o steel In oil Pessed asbestos on cast ion o steel dy Powde metal on cast ion o steel dy Powde metal on cast ion o steel In oil Consideations in Designing a Fiction Clutch The following consideations must be kept in mind while designing a fiction clutch. 1. The suitable mateial foming the contact sufaces should be selected.. The moving pats of the clutch should have low weight in ode to minimise the inetia load, especially in high speed sevice.. The clutch should not equie any extenal foce to maintain contact of the fiction sufaces. 4. The povision fo taking up wea of the contact sufaces must be povided. 5. The clutch should have povision fo facilitating epais. 6. The clutch should have povision fo caying away the heat geneated at the contact sufaces. 7. The pojecting pats of the clutch should be coveed by guad. 4.7 Types of Fiction Clutches Though thee ae many types of fiction clutches, yet the following ae impotant fom the subject point of view : 1. Disc o plate clutches (single disc o multiple disc clutch),. Cone clutches, and. Centifugal clutches. We shall now discuss these clutches, in detail, in the following pages. Note : The disc and cone clutches ae known as axial fiction clutches, while the centifugal clutch is called adial fiction clutch.

4 888 A Textbook of Machine Design 4.8 Single Disc o Plate Clutch Fig. 4.. Single disc o plate clutch. A single disc o plate clutch, as shown in Fig 4., consists of a clutch plate whose both sides ae faced with a fictional mateial (usually of Feodo). It is mounted on the hub which is fee to move axially along the splines of the diven shaft. The pessue plate is mounted inside the clutch body which is bolted to the flywheel. Both the pessue plate and the flywheel otate with the engine cankshaft o the diving shaft. The pessue plate pushes the clutch plate towads the flywheel by a set of stong spings which ae aanged adially inside the body. The thee leves (also known as elease leves o finges) ae caied on pivots suspended fom the case of the body. These ae aanged in such a manne so that the pessue plate moves away fom the flywheel by the inwad movement of a thust beaing. The beaing is mounted upon a foked shaft and moves fowad when the clutch pedal is pessed. When the clutch pedal is pessed down, its linkage foces the thust elease beaing to move in towads the flywheel and pessing the longe ends of the leves inwad. The leves ae foced to tun on thei suspended pivot and the pessue plate moves away fom the flywheel by the knife edges, theeby compessing the clutch spings. This action emoves the pessue fom the clutch plate and thus moves back fom the flywheel and the diven shaft becomes stationay. On the othe hand, when the foot is taken off fom the clutch pedal, the thust beaing moves back by the leves. This allows the spings to extend and thus the pessue plate pushes the clutch plate back towads the flywheel. When a ca hits an object and deceleates quickly the objects ae thown fowad as they continue to move fowads due to inetia.

5 Clutches 889 The axial pessue exeted by the sping povides a fictional foce in the cicumfeential diection when the elative motion between the diving and diven membes tends to take place. If the toque due to this fictional foce exceeds the toque to be tansmitted, then no slipping takes place and the powe is tansmitted fom the diving shaft to the diven shaft. 4.9 Design of a Disc o Plate Clutch Conside two fiction sufaces maintained in contact by an axial thust (W ) as shown in Fig. 4. (a). Fig. 4.. Foces on a disc clutch. Let T = Toque tansmitted by the clutch, p = Intensity of axial pessue with which the contact sufaces ae held togethe, 1 and = Extenal and intenal adii of fiction faces, = Mean adius of the fiction face, and μ = Coefficient of fiction. Conside an elementay ing of adius and thickness d as shown in Fig. 4. (b). We know that aea of the contact suface o fiction suface =π.d Nomal o axial foce on the ing, δw = Pessue Aea = p π.d and the fictional foce on the ing acting tangentially at adius, F = μ δw = μ.p π.d Fictional toque acting on the ing, T = F = μ.p π.d = πμp..d We shall now conside the following two cases : 1. When thee is a unifom pessue, and. When thee is a unifom axial wea. 1. Consideing unifom pessue. When the pessue is unifomly distibuted ove the entie aea of the fiction face as shown in Fig. 4. (a), then the intensity of pessue, p = π W ( ) ( ) 1

6 890 A Textbook of Machine Design whee W = Axial thust with which the fiction sufaces ae held togethe. We have discussed above that the fictional toque on the elementay ing of adius and thickness d is T =π μ.p..d Integating this equation within the limits fom to 1 fo the total fiction toque. Total fictional toque acting on the fiction suface o on the clutch, T = 1 πμ. p.. d = πμ. p 1 = ( ) ( ) ( ) ( ) πμ. p = πμ 1 W 1 π[ ( 1) ( ) ]... (Substituting the value of p) ( = 1) ( ) μ. W = μ. W. R ( 1) ( ) ( 1) ( ) whee R = = Mean adius of the fiction suface. ( 1) ( ). Consideing unifom axial wea. The basic pinciple in designing machine pats that ae subjected to wea due to sliding fiction is that the nomal wea is popotional to the wok of fiction. The wok of fiction is popotional to the poduct of nomal pessue ( p) and the sliding velocity (V). Theefoe, Nomal wea Wok of fiction p.v o p.v = K (a constant) o p = K/V...(i) It may be noted that when the fiction suface is new, thee is a unifom pessue distibution ove the entie contact suface. This pessue will wea most apidly whee the sliding velocity is maximum and this will educe the pessue between the fiction sufaces. This weaing-in pocess continues until the poduct p.v is constant ove the entie suface. Afte this, the wea will be unifom as shown in Fig Let p be the nomal intensity of pessue at a distance Fig Unifom axial wea. fom the axis of the clutch. Since the intensity of pessue vaies invesely with the distance, theefoe p. = C (a constant) o p = C /...(ii) and the nomal foce on the ing, δw = p. π. d = C π. d = πc. d Total foce acing on the fiction suface, 1 1 W = π Cd= π C[ ] = π C( ) o C = W π ( ) 1 1

7 Clutches 891 We know that the fictional toque acting on the ing, C T = πμ. p.. d = πμ. d = πμ. Cd.....(Q p = C/) Total fictional toque acting on the fiction suface (o on the clutch), T = 1 πμ Cd.. = πμc ( ) ( ) = 1 πμ. C = π μ. C [( 1) ( ) ] = πμ W 1 [( 1) ( ) ]. W ( 1 ). W. R π ( 1 ) whee R = 1 + = Mean adius of the fiction suface. Notes : 1. In geneal, total fictional toque acting on the fiction sufaces (o on the clutch) is given by T = n.μ.w.r whee n = Numbe of pais of fiction (o contact) sufaces, and R = Mean adius of fiction suface ( 1) ( ) = ( 1) ( ) = (Fo unifom pessue)... (Fo unifom wea). Fo a single disc o plate clutch, nomally both sides of the disc ae effective. Theefoe a single disc clutch has two pais of sufaces in contact (i.e. n = ).. Since the intensity of pessue is maximum at the inne adius ( ) of the fiction o contact suface, theefoe equation (ii) may be witten as p max = C o p max = C / 4. Since the intensity of pessue is minimum at the oute adius ( 1 ) of the fiction o contact suface, theefoe equation (ii) may be witten as p min 1 = C o p min = C / 1 5. The aveage pessue ( p av ) on the fiction o contact suface is given by Total foce on fiction suface W p av = = Coss-sectional aea of fiction suface π [( 1) ( ) ] 6. In case of a new clutch, the intensity of pessue is appoximately unifom, but in an old clutch, the unifom wea theoy is moe appoximate. 7. The unifom pessue theoy gives a highe fiction toque than the unifom wea theoy. Theefoe in case of fiction clutches, unifom wea should be consideed, unless othewise stated Multiple Disc Clutch A multiple disc clutch, as shown in Fig. 4.5, may be used when a lage toque is to be tansmitted. The inside discs (usually of steel) ae fastened to the diven shaft to pemit axial motion (except fo the last disc). The outside discs (usually of bonze) ae held by bolts and ae fastened to the housing which is keyed to the diving shaft. The multiple disc clutches ae extensively used in moto cas, machine tools etc. A twin disk clutch

8 89 A Textbook of Machine Design Fig Multiple disc clutch. Let n 1 = Numbe of discs on the diving shaft, and n = Numbe of discs on the diven shaft. Numbe of pais of contact sufaces, n = n 1 + n 1 and total fictional toque acting on the fiction sufaces o on the clutch, T = n.μ.w.r whee R = Mean adius of fiction sufaces = ( 1) ( ) ( 1) ( )... (Fo unifom pessue) = (Fo unifom wea) Example 4.1. Detemine the maximum, minimum and aveage pessue in a plate clutch when the axial foce is 4 kn. The inside adius of the contact suface is 50 mm and the outside adius is 100 mm. Assume unifom wea. Solution. Given : W = 4 kn = 4000 N ; = 50 mm ; 1 = 100 mm Maximum pessue Let p max = Maximum pessue. Since the intensity of pessue is maximum at the inne adius ( ), theefoe p max = C o C = 50 p max We also know that total foce on the contact suface (W ), 4000 = πc ( 1 ) = π 50 p max (100 50) = p max p max = 4000 / = N/mm Ans. Minimum pessue Let p min = Minimum pessue. Since the intensity of pessue is minimum at the oute adius ( 1 ), theefoe, p min 1 = C o C = 100 p min

9 Clutches 89 We know that the total foce on the contact suface (W ), 4000 = πc ( 1 ) = π 100 p min (100 50) = 1 40 p min p min = 4000 / 1 40 = 0.17 N/mm Ans. Aveage pessue We know that aveage pessue, p av = Total nomal foce on contact suface W = Coss-sectional aea of contact suface π [( ) ( ) ] = 0.17 N/mm ( ) π[ 100 (50) ] = Ans. Example 4.. A plate clutch having a single diving plate with contact sufaces on each side is equied to tansmit 110 kw at 150.p.m. The oute diamete of the contact sufaces is to be 00 mm. The coefficient of fiction is 0.4. (a) Assuming a unifom pessue of 0.17 N/mm ; detemine the inne diamete of the fiction sufaces. (b) Assuming the same dimensions and the same total axial thust, detemine the maximum toque that can be tansmitted and the maximum intensity of pessue when unifom wea conditions have been eached. Solution. Given : P = 110 kw = W; N = 150.p.m. ; d 1 = 00 mm o 1 = 150 mm ; μ = 0.4 ; p = 0.17 N/mm (a) Inne diamete of the fiction sufaces Let d = Inne diamete of the contact o fiction sufaces, and = Inne adius of the contact o fiction sufaces. We know that the toque tansmitted by the clutch, P T = = = 840 N-m π N π 150 = N-mm Axial thust with which the contact sufaces ae held togethe, W = Pessue Aea = p π [( 1 ) ( ) ] = 0.17 π [(150) ( ) ] = 0.54 [(150) ( ) ]...(i) and mean adius of the contact suface fo unifom pessue conditions, R = ( 1) ( ) (150) ( ) = ( 1) ( ) (150) ( ) Toque tansmitted by the clutch ( T ), = n.μ.w.r (150) ( ) = [(150) ( ) ] (150) ( ) = 0.85 [(150) ( ) ] o (150) ( ) = / 0.85 = and ( ) = (150) = o = 75 mm d = = 75 = 150 mm Ans....(Q n = )

10 894 A Textbook of Machine Design (b) Maximum toque tansmitted We know that the axial thust, W = 0.54 [(150) ( ) ]... [Fom equation (i)] = 0.54 [(150) (75) ] = 9011 N and mean adius of the contact sufaces fo unifom wea conditions, R = = = 11.5 mm Maximum toque tansmitted, T = n.μ.w.r = = N-mm = 811 N-m Ans. Maximum intensity of pessue Fo unifom wea conditions, p. = C (a constant). Since the intensity of pessue is maximum at the inne adius ( ), theefoe p max = C o C = p max 75 N/mm We know that the axial thust ( W ), 9011 = π C ( 1 ) = π p max 75 (150 75) = 5 47 p max p max = 9011 / 5 47 = 0.55 N/mm Ans. Example 4.. A single plate clutch, effective on both sides, is equied to tansmit 5 kw at 000.p.m. Detemine the oute and inne diametes of fictional suface if the coefficient of fiction is 0.55, atio of diametes is 1.5 and the maximum pessue is not to exceed 0.1 N/mm. Also, detemine the axial thust to be povided by spings. Assume the theoy of unifom wea. Solution. Given : n = ; P = 5 kw = 5 10 W; N = 000.p.m. ; μ = 0.55 ; d 1 / d = 1.5 o 1 / = 1.5 ; p max = 0.1 N/mm Oute and inne diametes of fictional suface Let d 1 and d = Oute and inne diametes (in mm) of fictional suface, and 1 and = Coesponding adii (in mm) of fictional suface. We know that the toque tansmitted by the clutch, P T = = = 79.6 N-m = N-mm π N π 000 Fo unifom wea conditions, p. = C (a constant). Since the intensity of pessue is maximum at the inne adius ( ), theefoe. p max = C o C = 0.1 N/mm and nomal o axial load acting on the fiction suface, W =πc ( 1 ) = π 0.1 (1.5 ) = ( )... (Q 1 / = 1.5) We know that mean adius of the fictional suface (fo unifom wea), R = = = 1.15 and the toque tansmitted (T ), = n.μ.w.r = ( ) 1.15 = 0.09 ( ) ( ) = / 0.09 = o = 96 mm and 1 = 1.5 = = 10 mm

11 Clutches 895 Oute diamete of fictional suface, d 1 = 1 = 10 = 40 mm Ans. and inne diamete of fictional suface, d = = 96 = 19 mm Ans. Axial thust to be povided by spings We know that axial thust to be povided by spings, W =π C ( 1 ) = π 0.1 (1.5 ) = ( ) = (96) = 1447 N Ans. Example 4.4. A dy single plate clutch is to be designed fo an automotive vehicle whose engine is ated to give 100 kw at 400.p.m. and maximum toque 500 N-m. The oute adius of the fiction plate is 5% moe than the inne adius. The intensity of pessue between the plate is not to exceed 0.07 N/mm. The coefficient of fiction may be assumed equal to 0.. The helical spings equied by this clutch to povide axial foce necessay to engage the clutch ae eight. If each sping has stiffness equal to 40 N/mm, detemine the dimensions of the fiction plate and initial compession in the spings. Solution. Given : P = 100 kw = W; *N = 400.p.m. ; T = 500 N-m = N-mm ; p = 0.07 N/mm ; μ = 0. ; No. of spings = 8 ; Stiffness/sping = 40 N/mm Dimensions of the fiction plate Let 1 = Oute adius of the fiction plate, and = Inne adius of the fiction plate. Since the oute adius of the fiction plate is 5% moe than the inne adius, theefoe 1 = 1.5 Fo unifom wea conditions, p. = C (a constant). Since the intensity of pessue is maximum at the inne adius ( ), theefoe p. = C o C = 0.07 N/mm and axial load acting on the fiction plate, W =π C ( 1 ) = π 0.07 (1.5 ) = 0.11 ( ) N...(i) We know that mean adius of the fiction plate, fo unifom wea, R = = = 1.15 Toque tansmitted (T ), = n.μ.w.r = ( ) 1.15 = ( )...(Q n = ) ( ) = / = o = 190 mm Ans. and 1 = 1.5 = = 7.5 mm Ans. Initial compession in the spings We know that total stiffness of the spings, s = Stiffness pe sping No. of spings = 40 8 = 0 N/mm Axial foce equied to engage the clutch, W = 0.11 ( ) = 0.11 (190) = 970 N... [Fom equation (i)] Initial compession in the spings = W/s = 970 / 0 = 1.4 mm Ans. * Supefluous data

12 896 A Textbook of Machine Design Engine Radiato Aiflow Fins In ca cooling system a pump ciculates wate though the engine and though the pipes of the adiato. Example 4.5. A single dy plate clutch is to be designed to tansmit 7.5 kw at 900.p.m. Find : 1. Diamete of the shaft,. Mean adius and face width of the fiction lining assuming the atio of the mean adius to the face width as 4,. Oute and inne adii of the clutch plate, and 4. Dimensions of the sping, assuming that the numbe of spings ae 6 and sping index = 6. The allowable shea stess fo the sping wie may be taken as 40 MPa. Solution. Given : P = 7.5 kw = 7500 W ; N = 900.p.m. ; /b = 4 ; No. of spings = 6 ; C = D/d = 6 ; τ = 40 MPa = 40 N/mm 1. Diamete of the shaft Let d s = Diamete of the shaft, and τ 1 = Shea stess fo the shaft mateial. It may be assumed as 40 N/mm. We know that the toque tansmitted, T = We also know that the toque tansmitted (T), P = = 79.6 N-m = N-mm π N π 900 π π = τ 1 ( ds) = 40 ( ds) = ( ds) (d s ) = / = o d s = 1.6 say 5 mm Ans.. Mean adius and face width of the fiction lining Let R = Mean adius of the fiction lining, and b = Face width of the fiction lining = R/4 We know that the aea of the fiction faces, A =πr.b Nomal o the axial foce acting on the fiction faces, W = A p = π R.b.p Ciculating wate...(i)... (Given)

13 Clutches 897 and toque tansmitted, T = μ W.R.n = μ (π Rb.p) R.n R π = μ π R p Rn. = μ. R. pn....(ii) 4 Assuming the intensity of pessue (p) as 0.07 N/mm and coefficient of fiction ( μ) as 0.5, we have fom equations (i) and (ii), π = 0.5 R 0.07 = R... (Q n =, fo both sides of plate effective) R = / = o R = 11. say 114 mm Ans. and b = R / 4 = 114 / 4 = 8.5 mm Ans.. Oute and inne adii of the clutch plate Let 1 and = Oute and inne adii of the clutch plate espectively. Since the face width (o adial width) of the plate is equal to the diffeence of the oute and inne adii, theefoe, b = 1 o 1 = 8.5 mm...(iii) We know that fo unifom wea, mean adius of the clutch plate, R = 1 + o 1 + = R = 114 = 8 mm...(iv) Fom equations (iii), and (iv), we find that 1 = 18.5 mm and = mm Ans. 4. Dimensions of the sping Let D = Mean diamete of the sping, and d = Diamete of the sping wie. We know that the axial foce on the fiction faces, W =π R.b.p = π = 149. N In ode to allow fo adjustment and fo maximum engine toque, the sping is designed fo an oveload of 5%. Total load on the spings = 1.5 W = = N Since thee ae 6 spings, theefoe maximum load on each sping, W s = / 6 = N We know that Wahl's stess facto, K = 4 C = = C 4 C We also know that maximum shea stess induced in the wie (τ), 8 Ws C = K = 1.55 = π d π d d d = 5697 / 40 = 1.56 o d =.68 mm We shall take a standad wie of size SWG 8 having diamete (d) = mm Ans. and mean diamete of the sping, D = C.d = = 4.84 say 4.4 mm Ans.

14 898 A Textbook of Machine Design Let us assume that the sping has 4 active tuns (i.e. n = 4). Theefoe compession of the sping, 8 Ws. C. n δ = = = 6.0 mm Gd (Taking G = N/mm ) Assuming squaed and gound ends, total numbe of tuns, n' = n + = 4 + = 6 We know that fee length of the sping, L F = n'.d + δ δ = = 1. mm Ans. LF 1. and pitch of the coils = = = 6.64 mm Ans. n Example 4.6. Design a single plate automobile clutch to tansmit a maximum toque of 50 N-m at 000.p.m. The outside diamete of the clutch is 50 mm and the clutch is engaged at 55 km/h. Find : 1. the numbe of evolutions of the clutch slip duing engagement; and. heat to be dissipated by the clutch fo each engagement. The following additional data is available: Engine toque duing engagement = 100 N-m; Mass of the automobile = 1500 kg; Diamete of the automobile wheel = 0.7 m; Moment of inetia of combined engine otating pats, flywheel and input side of the clutch = 1 kg-m ; Gea eduction atio at diffeential = 5; Toque at ea wheels available fo acceleating automobile = 175 N-m; Coefficient of fiction fo the clutch mateial = 0.; Pemissible pessue = 0.1 N/mm. Solution. Given : T = 50 N-m = N-mm ; N = 000.p.m. ; d 1 = 50 mm o 1 = 15 mm ; V = 55 km/h = 15. m/s ; T e = 100 N-m ; m = 1500 kg ; D w = 0.7 m o R w = 0.5 m ; I = 1 kg-m ; T a = 175 N-m ; Gea atio = 5 ; μ = 0. ; p = 0.1 N/mm 1. Numbe of evolutions of the clutch slip duing engagement Fist of all, let us find the inside adius of the clutch ( ). We know that, fo unifom wea, mean adius of the clutch, R = = = and axial foce on the clutch, W = p.π [( 1 ) ( ) ] = 0.1 π [(15) ( ) ] We know that the toque tansmitted (T ), = n.μ.w.r = π [(15) ( ) ] [ ] = 0.45 [ ( ) 0.5 ( ) ] Solving by hit and tial, we find that = 70 mm We know that angula velocity of the engine, ω e =πn / 60 = π 000 / 60 = 10 ad / s and angula velocity of the wheel, ω W = Velocity of wheel V = = 15. = 4.7 ad / s Radius of wheel Rw 0.5 Since the gea atio is 5, theefoe angula velocity of the clutch followe shaft, ω 0 = ω W 5 = = 18.5 ad / s

15 Clutches 899 We know that angula acceleation of the engine duing the clutch slip peiod of the clutch, Te T α e = = = 150 ad / s I 1 Let a = Linea acceleation of the automobile. We know that acceleating foce on the automobile, T a 175 F a = = = 500 N R 0.5 We also know that acceleating foce (F a ), 500 = m.a = 1500 a o a = 500 / 1500 = 0. m/s Angula acceleation of the clutch output, Acceleation Gea atio 0. 5 α 0 = = = 4.7 ad/s Radius of wheel 0.5 We know that clutch slip peiod, Δt = ω0 ωe = = s α α 4.7 ( 150) 0 e Angle though which the input side of the clutch otates duing engagement time (Δt) is 1 θ e = ω e Δ t + αe ( Δt) = ( 150) (0.055) = 11. ad and angle though which the output side of the clutch otates duing engagement time (Δt) is θ 0 = ω 0 Δt + 1 α 0 (Δt) = (0.055) = 1 ad Angle of clutch slip, θ = θ 0 θ e = = 0.68 ad We know that numbe of evolutions of the clutch slip duing engagement θ 0.68 = = = 0.11 evolutions Ans. π π Heat to be dissipated by the clutch fo each engagement We know that heat to be dissipated by the clutch fo each engagement = T.θ = = 170 J Ans. Example 4.7. A multiple disc clutch has five plates having fou pais of active fiction sufaces. If the intensity of pessue is not to exceed 0.17 N/mm, find the powe tansmitted at 500.p.m. The oute and inne adii of fiction sufaces ae 15 mm and 75 mm espectively. Assume unifom wea and take coefficient of fiction = 0.. Solution. Given : n 1 + n = 5 ; n = 4 ; p = 0.17 N/mm ; N = 500.p.m. ; 1 = 15 mm ; = 75 mm ; μ = 0. We know that fo unifom wea, p. = C (a constant). Since the intensity of pessue is maximum at the inne adius ( ), theefoe, p. = C o C = = 9.55 N/mm A twin-disk clutch

16 900 A Textbook of Machine Design and axial foce equied to engage the clutch, W =πc ( 1 ) = π 9.55 (15 75) = 99 N Mean adius of the fiction sufaces, R = = = 100 mm = 0.1 m We know that the toque tansmitted, T = n.μ.w.r = = 59 N-m T π N 59 π 500 Powe tansmitted, P = = = W = 18.8 kw Ans Example 4.8. A multi-disc clutch has thee discs on the diving shaft and two on the diven shaft. The inside diamete of the contact suface is 10 mm. The maximum pessue between the suface is limited to 0.1 N/mm. Design the clutch fo tansmitting 5 kw at 1575.p.m. Assume unifom wea condition and coefficient of fiction as 0.. Solution. Given : n 1 = ; n = ; d = 10 mm o = 60 mm ; p max = 0.1 N/mm ; P = 5 kw = 5 10 W; N = 1575.p.m. ; μ = 0. Let 1 = Outside adius of the contact suface. We know that the toque tansmitted, P T = = = N-m = N-mm π N π 1575 Fo unifom wea, we know that p. = C. Since the intensity of pessue is maximum at the inne adius ( ), theefoe, p max = C o C = = 6 N/mm We know that the axial foce on each fiction suface, W =πc ( 1 ) = π 6( 1 60) = 7.7 ( 1 60)...(i) Fo unifom wea, mean adius of the contact suface, R = = = We know that numbe of pais of contact sufaces, n = n 1 + n 1 = + 1 = 4 Toque tansmitted (T), = n.μ.w.r = ( 1 60) ( )... [Substituting the value of W fom equation (i)] =.6 ( 1 ) 81 4 ( 1 ) = = o 1 = mm Ans. Example 4.9. A multiple disc clutch, steel on bonze, is to tansmit 4.5 kw at 750.p.m. The inne adius of the contact is 40 mm and oute adius of the contact is 70 mm. The clutch opeates in oil with an expected coefficient of 0.1. The aveage allowable pessue is 0.5 N/mm. Find : 1. the total numbe of steel and bonze discs;. the actual axial foce equied;. the actual aveage pessue; and 4. the actual maximum pessue. Solution. Given : P = 4.5 kw = 4500 W ; N = 750.p.m. ; = 40 mm ; 1 = 70 mm ; μ = 0.1 ; p av = 0.5 N/mm

17 1. Total numbe of steel and bonze discs Let n = Numbe of pais of contact sufaces. We know that the toque tansmitted by the clutch, P T = = = 57. N-m = N-mm πn π 750 Fo unifom wea, mean adius of the contact sufaces, R = = = 55 mm Clutches 901 and aveage axial foce equied, W = p av π [( 1 ) ( ) ] = 0.5 π [(70) (40) ] = 60 N We also know that the toque tansmitted (T ), = n.μ.w.r = n = n n = / =.87 Since the numbe of pais of contact sufaces must be even, theefoe we shall use 4 pais of contact sufaces with steel discs and bonze discs (because the numbe of pais of contact sufaces is one less than the total numbe of discs). Ans.. Actual axial foce equied Let W ' = Actual axial foce equied. Since the actual numbe of pais of contact sufaces is 4, theefoe actual toque developed by the clutch fo one pai of contact suface, T T ' = = = 14 5 N-mm n 4 We know that toque developed fo one pai of contact suface (T '), 14 5 = μ.w '.R = 0.1 W ' 55 = 5.5 W ' W ' = 14 5 / 5.5 = N Ans.. Actual aveage pessue We know that the actual aveage pessue, W p' av = = = 0.5 N/mm Ans. π[ ( ) ( ) ( ) ( ) 1 ] π[ ] 4. Actual maximum pessue Let p max = Actual maximum pessue. Fo unifom wea, p. = C. Since the intensity of pessue is maximum at the inne adius, theefoe, p max = C o C = 40 p max N/mm We know that the actual axial foce (W '), = πc ( 1 ) = π 40 p max ( 70 40) = 7541 p max p max = / 7541 = 0.45 N/mm Ans. Example A plate clutch has thee discs on the diving shaft and two discs on the diven shaft, poviding fou pais of contact sufaces. The outside diamete of the contact sufaces is 40 mm and inside diamete 10 mm. Assuming unifom pessue and μ = 0., find the total sping load pessing the plates togethe to tansmit 5 kw at 1575.p.m.

18 90 A Textbook of Machine Design If thee ae 6 spings each of stiffness 1 kn/m and each of the contact sufaces has won away by 1.5 mm, find the maximum powe that can be tansmitted, assuming unifom wea. Solution. Given : n 1 = ; n = ; n = 4 ; d 1 = 40 mm o 1 = 10 mm ; d = 10 mm o = 60 mm ; μ = 0. ; P = 5 kw = 5 10 W; N = 1575.p.m. Total sping load Let W = Total sping load. We know that the toque tansmitted, P T = = = N-m π N π 1575 = N-mm Mean adius of the contact suface, fo unifom pessue, ( ) ( ) ( ) 1 10 (60) R = = = 9. mm ( ) ( ) ( ) 1 10 (60) and toque tansmitted (T ), = n.μ.w.r = 4 0. W 9. = 11 W W = / 11 = 15 N Ans. Maximum powe tansmitted Given : No. of spings = 6 Contact sufaces of the sping = 8 Wea on each contact suface = 1.5 mm Total wea = = 10 mm = 0.01 m Stiffness of each sping = 1 kn/m = 1 10 N/m Reduction in sping foce = Total wea Stiffness pe sping No. of spings = = 780 N and new axial load, W = = 57 N We know that mean adius of the contact sufaces fo unifom wea, R = 1 = = 90 mm = 0.09 m and toque tansmitted, T = n. μ W. R = = 6 N-m T π N 6 π 1575 Powe tansmitted, P = = = 10 7 W = 10.7 kw Ans Cone Clutch A cone clutch, as shown in Fig. 4.6, was extensively used in automobiles, but now-a-days it has been eplaced completely by the disc clutch. It consists of one pai of fiction suface only. In a cone clutch, the dive is keyed to the diving shaft by a sunk key and has an inside conical suface o face which exactly fits into the outside conical suface of the diven. The diven membe esting on the feathe key in the diven shaft, may be shifted along the shaft by a foked leve povided at B, in ode to engage the clutch by binging the two conical sufaces in contact. Due to the fictional esistance set up at this contact suface, the toque is tansmitted fom one shaft to anothe. In some cases, a sping is placed aound the diven shaft in contact with the hub of the diven. This sping

19 Clutches 90 holds the clutch faces in contact and maintains the pessue between them, and the foked leve is used only fo disengagement of the clutch. The contact sufaces of the clutch may be metal to metal contact, but moe often the diven membe is lined with some mateial like wood, leathe, cok o asbestos etc. The mateial of the clutch faces (i.e. contact sufaces) depends upon the allowable nomal pessue and the coefficient of fiction. Fig Cone clutch. 4.1 Design of a Cone Clutch Conside a pai of fiction sufaces of a cone clutch as shown in Fig A little consideation will show that the aea of contact of a pai of fiction suface is a fustum of a cone. Fig Fiction sufaces as a fustum of a cone. Let p n = Intensity of pessue with which the conical fiction sufaces ae held togethe (i.e. nomal pessue between the contact sufaces), 1 = Oute adius of fiction suface, = Inne adius of fiction suface, R = Mean adius of fiction suface = 1 +, α = Semi-angle of the cone (also called face angle of the cone) o angle of the fiction suface with the axis of the clutch, μ = Coefficient of fiction between the contact sufaces, and b = Width of the fiction sufaces (also known as face width o cone face).

20 904 A Textbook of Machine Design Conside a small ing of adius and thickness d as shown in Fig Let dl is the length of ing of the fiction suface, such that, dl = d cosec α Aea of ing = π. dl = π.d cosec α We shall now conside the following two cases : 1. When thee is a unifom pessue, and. When thee is a unifom wea. 1. Consideing unifom pessue We know that the nomal foce acting on the ing, δw n = Nomal pessue Aea of ing = p n π.d cosec α and the axial foce acting on the ing, δw = Hoizontal component of δw n (i.e. in the diection of W) = δw n sin α = p n π.d cosec α sin α = π p n..d Total axial load tansmitted to the clutch o the axial sping foce equied, and p n = 1 ( 1) ( ) p d p p 1 W = π n.. = π n = π n = π p n [( 1 ) ( ) ] W ( ) ( ) π 1 We know that fictional foce on the ing acting tangentially at adius, F = μ.δw n = μ.p n π.d cosec α Fictional toque acting on the ing, T = F = μ.p n π.d cosec α =π μ.p n cosec α. d Integating this expession within the limits fom to 1 fo the total fictional toque on the clutch. Total fictional toque, T = = 1 1 πμ. pn. cosec α. d = π μ. pn cosec α ( 1) ( ) πμ. pn cosec α...(i)

21 Clutches 905 Substituting the value of p n fom equation (i), we get ( ) ( ) W 1 T = πμ cosec α π[ ( 1) ( ) ] ( = 1) ( ) μ. W cosec α ( 1) ( )...(ii) Fig Foces on a fiction suface.. Consideing unifom wea In Fig. 4.7, let p be the nomal intensity of pessue at a distance fom the axis of the clutch. We know that, in case of unifom wea, the intensity of pessue vaies invesely with the distance. p. = C (a constant) o p = C / We know that the nomal foce acting on the ing, δw n = Nomal pessue Aea of ing = p π.d cosec α and the axial foce acting on the ing, δw = δw n sin α = p π.d cosec α sin α =π p. d C = π. d = π Cd.... C Q p = Total axial load tansmitted to the clutch, 1 1 π Cd. = π C = π C ( ) W = [ ] 1 W o C = π ( 1 ) We know that fictional foce on the ing acting tangentially at adius, F = μ.δw n = μ.p π.d cosec α... (iii)

22 906 A Textbook of Machine Design A mammoth catepilla dump tuck fo use in quaies and open-cast mines. Fictional toque acting on the ing, T = F = μ.p π.d cosec α = μ C π.d cosec α = πμ.c cosec α d Integating this expession within the limits fom to 1 fo the total fictional toque on the clutch. Total fictional toque, 1 T = πμ. C cosec α d = πμ. C cosec α ( 1) ( ) = πμ. C cosec α Substituting the value of C fom equation (iii), we have W ( 1) ( ) T = πμ cosec α π ( ) = μ. W cosec α = μ WR cosec α...(iv) whee R = 1 + = Mean adius of fiction suface. Since the nomal foce acting on the fiction suface, W n = W cosec α, theefoe the equation (iv) may be witten as T = μ W n R...(v) The foces on a fiction suface, fo steady opeation of the clutch and afte the clutch is engaged, is shown in Fig. 4.8 (a) and (b) espectively. 1

23 Clutches 907 Fom Fig. 4.8 (a), we find that = b sin α and R = o 1 + = R Fom equation (i), nomal pessue acting on the fiction suface, W p n = [( 1) ( ( ) ] = W 1 ) ( 1 ) = W π π + π Rb. sin α o W = p n π R.b sin α = W n sin α whee W n = Nomal load acting on the fiction suface = p n πr.b Now the equation (iv) may be witten as T = μ ( p n π R. b sin α) R cosec α = π μ.p n R.b The following points may be noted fo a cone clutch : 1. The above equations ae valid fo steady opeation of the clutch and afte the clutch is engaged.. If the clutch is engaged when one membe is stationay and the othe otating (i.e. duing engagement of the clutch) as shown in Fig. 4.8 (b), then the cone faces will tend to slide on each othe due to the pesence of elative motion. Thus an additional foce (of magnitude μ.w n cos α) acts on the clutch which esists the engagement, and the axial foce equied fo engaging the clutch inceases. Axial foce equied fo engaging the clutch, W e = W + μ.w n cos α = W n. sin α + μ W n cos α = W n (sin α + μ cos α) It has been found expeimentally that the tem (μ W n.cos α) is only 5 pecent effective. W e = W n sin α μ W n cos α = W n (sin α μ cos α). Unde steady opeation of the clutch, a decease in the semi-cone angle (α) inceases the toque poduced by the clutch (T ) and educes the axial foce (W ). Duing engaging peiod, the axial foce equied fo engaging the clutch (W e ) inceases unde the influence of fiction as the angle α deceases. The value of α can not be deceased much because smalle semi-cone angle (α) equies lage axial foce fo its disengagement. If the clutch is to be designed fo fee disengagement, the value of tan α must be geate than μ. In case the value of tan α is less than μ, the clutch will not disengage itself and axial foce equied to disengage the clutch is given by W d = W n ( μ cos α sin α) Example The contact sufaces in a cone clutch have an effective diamete of 80 mm. The semi-angle of the cone is 15 and coefficient of fiction is 0.. Find the toque equied to poduce slipping of the clutch, if the axial foce applied is 00 N. The clutch is employed to connect an electic moto, unning unifomly at 900.p.m. with a flywheel which is initially stationay. The flywheel has a mass of 14 kg and its adius of gyation is 160 mm. Calculate the time equied fo the flywheel to attain full-speed and also the enegy lost in slipping of the clutch. Solution. Given : D = 80 mm o R = 40 mm ; α = 15 ; μ = 0. ; W = 00 N ; N = 900.p.m. o ω = π 900/60 = 94.6 ad/s ; m = 14 kg ; k = 160 mm = 0.16 m Toque equied to poduce slipping of the clutch We know that the toque equied to poduce slipping of the clutch, T = μ WR cosec α = cosec 15 = 97 N-mm = 9.7 N-m Ans.

24 908 A Textbook of Machine Design Time equied fo the flywheel to attain full-speed Let t = Time equied fo the flywheel to attain full speed fom the stationay position, and α = Angula acceleation of the flywheel. We know that mass moment of inetia of the flywheel, I = m.k = 14 (0.16) = kg-m We also know that the toque ( T ), 9.7 = I α = α α = 9.7 / = 5.87 ad / s and angula speed (ω), 94.6 = ω 0 + α.t = t = 5.87 t... (Q ω 0 = 0) t = 94.6 / 5.87 =.64 s Ans. Enegy lost in slipping of the clutch We know that angula displacement, ω 0 + ω θ = Aveage angula speed time = t = = ad Enegy lost in slipping of the clutch, = T.θ = = 1591 N-m Ans. Example 4.1. An engine developing 45 kw at 1000.p.m. is fitted with a cone clutch built inside the flywheel. The cone has a face angle of 1.5 and a maximum mean diamete of 500 mm. The coefficient of fiction is 0.. The nomal pessue on the clutch face is not to exceed 0.1 N/mm. Detemine : 1. the face width equied, and. the axial sping foce necessay to engage the clutch. Solution. Given : P = 45 kw = W; N = 1000.p.m. ; α = 1.5 ; D = 500 mm o R = 50 mm ; μ = 0. ; p n = 0.1 N/mm 1. Face width Let b = Face width of the clutch in mm. We know that toque developed by the clutch, P T = = = 40 N-m = N-mm π N π 1000 We also know that toque developed by the clutch (T ), =π. μ. p n. R.b = π (50) b = 7855 b b = / 7855 = 54.7 say 55 mm Ans.. Axial sping foce necessay to engage the clutch We know that the nomal foce acting on the contact sufaces, W n = p n πr.b = 0.1 π = 8640 N Axial sping foce necessay to engage the clutch, W e = W n (sin α μ cos α) = 8640 (sin cos 1.5 ) = 90 N Ans. Example 4.1. Detemine the pincipal dimensions of a cone clutch faced with leathe to tansmit 0 kw at 750.p.m. fom an electic moto to an ai compesso. Sketch a sectional font view of the clutch and povide the main dimensions on the sketch.

25 Clutches 909 Assume : semi-angle of the cone = 1 1 ; μ = 0. ; mean diamete of cone = 6 to 10 d whee d is the diamete of shaft; allowable nomal pessue fo leathe and cast ion = to 0.1 N/mm ; load facto = 1.75 and mean diamete to face width atio = 6. Solution. Given : P = 0 kw = 0 10 W; N = 750.p.m. ; α = 1 1 ; μ = 0. ; D = 6 to 10 d ; p n = to 0.1 N/mm ; K L = 1.75 ; D/b = 6 Fist of all, let us find the diamete of shaft (d). We know that the toque tansmitted by the shaft, T = P KL = 1.75 = N-m π N π 750 = N-mm We also know that the toque tansmitted by the shaft (T ), π π = τ d = 4 d = 8.5 d (Taking τ = 4 N/mm ) d = / 8.5 = o d = 4. say 50 mm Ans. Fig. 4.9 Now let us find the pincipal dimensions of a cone clutch. Let D = Mean diamete of the clutch, R = Mean adius of the clutch, and b = Face width of the clutch. Since the allowable nomal pessue ( p n ) fo leathe and cast ion is to 0.1 N/mm, theefoe let us take p n = 0.1 N/mm. We know that the toque developed by the clutch ( T ), =πμ. p n. R.b = π R R = 0.04 R... (Q D / b = 6 o R / b = 6 o R / b = ) R = / 0.04 = o R = 50 mm and D =R = 50 = 500 mm Ans. Since this calculated value of the mean diamete of the clutch (D) is equal to 10 d and the given value of D is 6 to 10d, theefoe the calculated value of D is safe. We know that face width of the clutch, b = D / 6 = 500 / 6 = 8. mm Ans. Fom Fig. 4.9, we find that oute adius of the clutch, b = R + sin α = 50 + sin 1 = 59 mm Ans.

26 910 A Textbook of Machine Design and inne adius of the clutch, b 8. 1 = R sin α = 50 sin 1 = 41 mm Ans. 4.1 Centifugal Clutch The centifugal clutches ae usually incopoated into the moto pulleys. It consists of a numbe of shoes on the inside of a im of the pulley, as shown in Fig The oute suface of the shoes ae coveed with a fiction mateial. These shoes, which can move adially in guides, ae held against the boss (o spide) on the diving shaft by means of spings. The spings exet a adially inwad foce which is assumed constant. The weight of the shoe, when evolving causes it to exet a adially outwad foce (i.e. centifugal foce). The magnitude of this centifugal foce depends upon the speed at which the shoe is evolving. A little consideation will show that when the centifugal foce is less than the sping foce, the shoe emains in the same position as when the diving shaft was stationay, but when the centifugal foce is equal to the sping foce, the shoe is just floating. When the centifugal foce exceeds the sping foce, the shoe moves outwad and comes into contact with the diven membe Centifugal clutch with thee discs and fou steel float plates. and pesses against it. The foce with which the shoe pesses against the diven membe is the diffeence of the centifugal foce and the sping foce. The incease of speed causes the shoe to pess hade and enables moe toque to be tansmitted. Fig Centifugal clutch Design of a Centifugal Clutch In designing a centifugal clutch, it is equied to detemine the weight of the shoe, size of the shoe and dimensions of the sping. The following pocedue may be adopted fo the design of a centifugal clutch. 1. Mass of the shoes Conside one shoe of a centifugal clutch as shown in Fig Let m = Mass of each shoe, n = Numbe of shoes,

27 = Distance of cente of gavity of the shoe fom the cente of the spide, R = Inside adius of the pulley im, N = Running speed of the pulley in.p.m., ω = Angula unning speed of the pulley in ad / s = π N / 60 ad/s, ω 1 = Angula speed at which the engagement begins to take place, and μ = Coefficient of fiction between the shoe and im. We know that the centifugal foce acting on each shoe at the unning speed, *P c = m.ω. Since the speed at which the engagement begins to take place is geneally taken as /4th of the unning speed, theefoe the inwad foce on each shoe exeted by the sping is given by 9 1 Clutches 911 Fig Foces on a shoe of a centifugal clucth. P s = m ( ω ) = m ω = m. ω 4 16 Net outwad adial foce (i.e. centifugal foce) with which the shoe pesses against the im at the unning speed 9 7 = Pc Ps = m. ω. m. ω. = m. ω and the fictional foce acting tangentially on each shoe, F = μ (P c P s ) Fictional toque acting on each shoe = F R = μ (P c P s ) R and total fictional toque tansmitted, T = μ (P c P s ) R n = n.f.r Fom this expession, the mass of the shoes (m) may be evaluated.. Size of the shoes Let l = Contact length of the shoes, b = Width of the shoes, R = Contact adius of the shoes. It is same as the inside adius of the im of the pulley, θ = Angle subtended by the shoes at the cente of the spide in adians, and p = Intensity of pessue exeted on the shoe. In ode to ensue easonable life, it may be taken as 0.1 N/mm. l π We know that θ = o l =θ. R = R...(Assuming θ = 60 = π / ad) R * The adial cleaance between the shoe and the im is about 1.5 mm. Since this cleaance is small as compaed to, theefoe it is neglected fo design puposes. If, howeve, the adial cleaance is given, then the opeating adius of the mass cente of the shoe fom the axis of the clutch, 1 = + c, whee c is the adial cleaance, Then P c =m.ω 1 and P s = m (ω 1 ) 1

28 91 A Textbook of Machine Design Aea of contact of the shoe = l. b and the foce with which the shoe pesses against the im = A p = l.b.p Since the foce with which the shoe pesses against the im at the unning speed is (P c P s ), theefoe l.b.p = P c P s Fom this expession, the width of shoe (b) may be obtained.. Dimensions of the sping We have discussed above that the load on the sping is given by 9 P s = m. ω. 16 The dimensions of the sping may be obtained as usual. Example A centifugal clutch is to be designed to tansmit 15 kw at 900.p.m. The shoes ae fou in numbe. The speed at which the engagement begins is /4th of the unning speed. The inside adius of the pulley im is 150 mm. The shoes ae lined with Feodo fo which the coefficient of fiction may be taken as 0.5. Detemine: 1. mass of the shoes, and. size of the shoes. Solution. Given : P = 15 kw = W; N = 900.p.m. ; n = 4 ; R = 150 mm = 0.15 m ; μ = Mass of the shoes Let m = Mass of the shoes. We know that the angula unning speed, ω = πn π = 900 = 94.6 ad / s Since the speed at which the engagement begins is /4 th of the unning speed, theefoe angula speed at which engagement begins is ω 1 = ω= 94.6 = 70.7 ad / s 4 4 Assuming that the cente of gavity of the shoe lies at a distance of 10 mm (0 mm less than R) fom the cente of the spide, i.e. = 10 mm = 0.1 m We know that the centifugal foce acting on each shoe, P c = m.ω. = m (94.6) 0.1 = 1066 m N and the inwad foce on each shoe exeted by the sping i.e. the centifugal foce at the engagement speed, ω 1, P s = m(ω 1 ) = m (70.7) 0.1 = 600 m N We know that the toque tansmitted at the unning speed, P T = = = 159 N-m π N π 900 We also know that the toque tansmitted (T ), 159 = μ (P c P s ) R n = 0.5 (1066 m 600 m) = 70 m m = 159/70 =.7 kg Ans.

29 Clutches 91. Size of the shoes Let l = Contact length of shoes in mm, and b = Width of the shoes in mm. Assuming that the ac of contact of the shoes subtend an angle of θ = 60 o π / adians, at the cente of the spide, theefoe π l = θ. R = 150 = 157 mm Aea of contact of the shoes A = l.b = 157 b mm Assuming that the intensity of pessue ( p) exeted on the shoes is 0.1 N/mm, theefoe foce with which the shoe pesses against the im = A.p = 157b 0.1 = 15.7 b N...(i) We also know that the foce with which the shoe pesses against the im = P c P s = 1066 m 600 m = 466 m = = 1058 N...(ii) Fom equations (i) and (ii), we find that b = 1058 / 15.7 = 67.4 mm Ans. Special tailes ae made to cay vey long loads. The longest load eve moved was gas stoage vessel, 8.8 m long. EXE XERCISE CISES 1. A single disc clutch with both sides of the disc effective is used to tansmit 10 kw powe at 900.p.m. The axial pessue is limited to N/mm. If the extenal diamete of the fiction lining is 1.5 times the intenal diamete, find the equied dimensions of the fiction lining and the axial foce exeted by the spings. Assume unifom wea conditions. The coefficient of fiction may be taken as 0.. [Ans. 1.5 mm ; 106 mm ; 1500 N]

30 914 A Textbook of Machine Design. A single plate clutch with both sides of the plate effective is equied to tansmit 5 kw at 1600.p.m. The oute diamete of the plate is limited to 00 mm and the intensity of pessue between the plates not to exceed 0.07 N/mm. Assuming unifom wea and coefficient of fiction 0., find the inne diamete of the plates and the axial foce necessay to engage the clutch. [Ans. 90 mm ; 75 N]. Give a complete design analysis of a single plate clutch, with both sides effective, of a vehicle to tansmit kw at a speed of 800.p.m. allowing fo 5% oveload. The pessue intensity is not to exceed 0.08 N/mm and the suface speed at the mean adius is not to exceed 000 m/min. Take coefficient of fiction fo the sufaces as 0.5 and the outside diamete of the sufaces is to be 1.5 times the inside diamete. The axial thust is to be povided by 6 spings of about 4 mm coil diamete. Fo sping mateial, the safe shea stess is to be limited to 40 MPa and the modulus of igidity may be taken as 80 kn/mm. [Ans. 10 mm ; 80 mm ;.658 mm] 4. A multiple disc clutch has thee discs on the diving shaft and two on the diven shaft, poviding fou pais of contact sufaces. The oute diamete of the contact sufaces is 50 mm and the inne diamete is 150 mm. Detemine the maximum axial intensity of pessue between the discs fo tansmitting kw at 500.p.m. Assume unifom wea and coefficient of fiction as A multiple disc clutch employs steel and bonze discs having oute diamete 00 mm and inne diamete 00 mm. Fo a coefficient of fiction of 0., find the axial pessue and the powe tansmitted at 750.p.m., if the nomal unit pessue is 0.1 N/mm. Also find the axial pessue of the unit nomal pessue, if this clutch tansmits kw at 1500.p.m. [Ans N ; kw ; 0.04 N/mm ] 6. A multiple disc clutch has adial width of the fiction mateial as 1/5th of the maximum adius. The coefficient of fiction is 0.5. Find the total numbe of discs equied to tansmit 60 kw at 000.p.m. The maximum diamete of the clutch is 50 mm and the axial foce is limited to 600 N. Also find the mean unit pessue on each contact suface. [Ans. 1 ; 0.04 N/mm ] 7. An engine developing kw at 1000.p.m. is fitted with a cone clutch having mean diamete of 00 mm. The cone has a face angle of 1. If the nomal pessue on the clutch face is not to exceed 0.07 N/mm and the coefficient of fiction is 0., detemine : (a) the face width of the clutch, and (b) the axial sping foce necessay to engage the clutch. [Ans. 106 mm ; 1796 N] 8. A cone clutch is to be designed to tansmit 7.5 kw at 900.p.m. The cone has a face angle of 1. The width of the face is half of the mean adius and the nomal pessue between the contact faces is not to exceed 0.09 N/mm. Assuming unifom wea and the coefficient of fiction between the contact faces as 0., find the main dimensions of the clutch and the axial foce equied to engage the clutch. [Ans. R = 11.4 mm ; b = 56. mm ; 1 = 118. mm ; = mm ; W e = 917 N] 9. A soft cone clutch has a cone pitch angle of 10, mean diamete of 00 mm and a face width of 100 mm. If the coefficient of fiction is 0. and has an aveage pessue of 0.07 N/mm fo a speed of 500.p.m., find : (a) the foce equied to engage the clutch; and (b) the powe that can be tansmitted. Assume unifom wea. [Ans N ; 10.4 kw] 10. A cone clutch is mounted on a shaft which tansmits powe at 5.p.m. The small diamete of the cone is 0 mm, the cone face is 50 mm and the cone face makes an angle of 15 with the hoizontal. Detemine the axial foce necessay to engage the clutch to tansmit 4.5 kw if the coefficient of fiction of the contact sufaces is 0.5. What is the maximum pessue on the contact sufaces assuming unifom wea? [Ans. 414 N ; 0.16 N/mm ]

31 Clutches A soft suface cone clutch tansmits a toque of 00 N-m at 150.p.m. The lage diamete of the clutch is 50 mm. The cone pitch angle is 7.5 and the face width is 65 mm. If the coefficient of fiction is 0., find : 1. the axial foce equied to tansmit the toque;. the axial foce equied to engage the clutch;. the aveage nomal pessue on the contact sufaces when the maximum toque is being tansmitted; and 4.the maximum nomal pessue assuming unifom wea. [Ans. 764 N ; 1057 N ; N/mm ; N/mm ] 1. A centifugal fiction clutch has a diving membe consisting of a spide caying fou shoes which ae kept fom contact with the clutch case by means of flat spings until incease of centifugal foce ovecomes the esistance of the spings and the powe is tansmitted by the fiction between the shoes and the case. Detemine the necessay mass and size of each shoe if.5 kw is to be tansmitted at 750.p.m. with engagement beginning at 75% of the unning speed. The inside diamete of the dum is 00 mm and the adial distance of the cente of gavity of each shoe fom the shaft axis is 15 mm. Assume μ = 0.5. [Ans kg ; l = mm ; b = 10 mm] Clutches, bakes, steeing and tansmission need to be caefully designed to ensue the efficiency and safety of an automobile QUE UEST STIONS 1. What is a clutch? Discuss the vaious types of clutches giving at least one pactical application fo each.. Why a positive clutch is used? Descibe, with the help of a neat sketch, the woking of a jaw o claw clutch.. Name the diffeent types of clutches. Descibe with the help of neat sketches the woking pinciples of two diffeent types of fiction clutches. 4. What ae the mateials used fo lining of fiction sufaces? 5. Why it is necessay to dissipate the heat geneated when clutches opeate? 6. Establish a fomula fo the fictional toque tansmitted by a cone clutch. 7. Descibe, with the help of a neat sketch, a centifugal clutch and deduce an expession fo the total fictional toque tansmitted. How the shoes and spings ae designed fo such a clutch?