Construction Figure 10.1: Jaw clutches

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Erik Rose
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CHAPTER TEN FRICTION CLUTCHES The wod clutch is a geneic tem descibing any one wide vaiety of devices that is capable of causing a machine o mechanism to become engaged o disengaged.

Disc o Plate Clutches. Cone clutches 3. Centifugal clutches Figue 0.: Jaw clutches 0.

1 CHAPTER TEN FRICTION CLUTCHES The wod clutch is a geneic tem descibing any one wide vaiety of devices that is capable of causing a machine o mechanism to become engaged o disengaged. Clutches ae of thee main types:. Positive o jaw clutches, Figue 0.. Fiction clutches 3. Hydaulic clutches The fiction clutches of the following types ae impotant fom the subject point of view:. Disc o Plate Clutches. Cone clutches 3. Centifugal clutches Figue 0.: Jaw clutches 0. Plate Clutches In a plate clutch, the toque is tansmitted by fiction between one o moe pais of co-axial annula faces maintained in contact by axial thust (foce. Both sides of each plate ae nomally effective, so that a single-plate clutch has two pais of sufaces in contact, Figue Constuction Figue 0.: Single-plate clutch The basic components of plate clutch ae, Figue 0.3:. inne plates: which ae fiction discs connected to the diving shaft so that they ae feely to slide axially in inne gooves, as shown in Figue 0.3b - -

2 . oute plates: which ae fiction discs connected to the diven shaft so that they ae feely to slide axially in oute gooves, as shown in Figue 0.3c 3. toggle mechanism: which is a mechanism used to apply axial thust (foce on the plates, so that they ae maintained in contact duing engagement of the clutch Inne disc Oute disc 0.. Numbe of pais in contact (n If the oute and inne discs have two sides of fiction mateial (i.e. two effective sides then: If n = oute discs no., n = inne discs no. n = n + n = n + n - If n = 3, n = 4, n = = 6 pais n = pais in single plate clutch (a (b Inne disc Toggle mechanism 0..3 Maximum tansmitted toque: Let Fiction mateial,, R: Oute, inne and mean adius of fiction faces in the disc espectively. (c Oute disc W Axial thust (nomal foce between fiction faces of discs applied by toggle mechanism (by spings. T Maximum tansmitted toque fo no slipping to be occued. Figue 0.3: Plate clutch - -

3 P Pessue intensity between fiction faces duing clutch engagement. µ Coefficient of fiction of contact sufaces. Conside the ing element of one suface of contact: The diffeential aea of ing element is da = π d The diffeential nomal foce is dw = π P d The total foce: W = π Pd The diffeential fiction foce is df = µ dw Then the toque in the ing element is dt = df = µpπ d The total maximum toque fo no slipping is T = πµ P d 0..4 Theoies used in the analysis of Fiction clutch. Unifom pessue theoy This theoy is applicable fo new clutches, in which the pessue intensity between fiction faces is assumed to be constant. P = constant W = π P W = π P( d P T = πµ P d P

4 fo one suface of contact T = 3 3 π P( * n 3 µ fo n pais of suface of contact o in tems of W: 3 3 ( T = µ W * n 3 ( fo n pais of suface of contact. Unifom wea theoy This theoy is applicable fo old clutches, in which the wea in the fiction mateial is assumed to be constant i.e. wea = constant but wea α pessue * velocity, velocity = ω*, ω = constant P* = c whee c is any constant and W = π c d W = π c( T = πµ c d P min P max T = πµ c( o ( T = µ W * n + fo n pais of suface of contact - 4 -

5 o T = µ W R* n Example : A single plate clutch, with both sides effective, has oute and inne adii 50 mm and 00 mm espectively. The maximum intensity of pessue at any point in the contact suface is not to exceed 0. Mpa. If µ = 0.3, detemine the powe tansmitted by a clutch at a speed 500 pm. Since the maximum intensity of pessue is at the inne adius, theefoe fo unifom wea, P max * = c c = 0. x 0 6 x 0. = 0000 N/m Axial foce: W = π.c( - = 34.6 N 34 N Toque tansmitted: T = µ.π.c ( - *n = N.m Powe: Powe = T.ω = * (π*500/60 = 6.7 kw Hosepowe tansmitted = 6700/746 = 8.7 h.p 0..5 Adjustment of toggle mechanism Toggle mechanism is used to apply the equied nomal foce (W. This mechanism consists of links and spings, in which links used to contol the engagement o disengagement of the clutch. Duing engagement, the links ae in position so that the sping is compessed to apply a nomal foce W, but duing disengagement, the links ae in position so that the sping is with thei fee length. Let s = sping numbe - 5 -

6 k = sping stiffness (N/m = compessive deflection in the sping (m W = k* *s (N 0..6 Won layes Duing opeation of the clutch, the pai of sufaces of contact ae subjected to mechanical wea, then the thickness of the plates will deceases and the compessive deflection in the spings of toggle mechanism will elaxed, then the change in the thickness of plates will be equal to the elaxation in the spings. Let t = the change in the thickness of plates l = laye thickness won due to mechanical wea t = *n*l If W epesent the change in nomal foce W = k*t*s Example : A plate clutch has thee discs on the diving shaft and two discs on the diven shaft. The outside and inside diamete of the contact sufaces ae 40 mm and 0 mm espectively. Assuming unifom pessue and µ = 0.3; find the total sping load pessing the plates togethe to tansmit 3 kw at 575 pm. If thee ae 6 spings each of stiffness 3 kn/m and each of contact sufaces has won away by.5 mm, find also the maximum powe that can be tansmitted, assuming unifom wea. ω = π*575/60 = 64.9 ad/s Toque, T = powe/ω = 3000/64.9 = N.m Fo unifom pessue: 3 3 ( T = µ W * n; W = 45N 3 ( s = 6 spings; n = 3+- = 4 pais of contact, i.e. Thee ae 8 layes in contact - 6 -

t = *4*.5*0-3 = 0.0 m = 0 mm W = k*t*s = 3000 * 0.0 * 6 = 780 N New axial load W new = 45 780 = 465 N Fo unifom wea; T = n*w new *R*µ = 4*465*0.09*0.3 = 50. N.m Maximum powe tansmitted = T * ω = 50.

7 t = *4*.5*0-3 = 0.0 m = 0 mm W = k*t*s = 3000 * 0.0 * 6 = 780 N New axial load W new = = 465 N Fo unifom wea; T = n*w new *R*µ = 4*465*0.09*0.3 = 50. N.m Maximum powe tansmitted = T * ω = 50. * 64.9 = 8.83 kw 0. Cone Clutch 0.. Geomety: = D/ oute adius = d/ inne adius R = cuent adius α = semi-angle of cone S = width of conical suface R = mean adius R = ( + /, S = ( - *cosecα W 0.. Maximum tansmitted toque: Conside an element of width (d*cosecα along the width of cone: N = nomal foce between fiction sufaces P = pessue intensity between contact sufaces F = fiction foce between contact sufaces W = axial componenent on the nomal foce - 7 -

8 T = maximum tansmitted toque dn = P*πd*cosecα dw = dn*sinα dw = P*πd α N W = π Pd W df = µ*dn = µp*πd*cosecα and dt = *d = µp*π d*cosecα T = πµ *cosecα * P d fo unifom pessue theoy: Pessue distibution afte wea W = πp( T = ( µ W *cosecα * 3 ( 3 3 Pmax fo unifom wea theoy: W = πc( T = µ W * R cosecα whee c = P max * 0..3 Minimum applied axial foce fo no slipping (F a : While applying axial foces, some of them consumed in esisting the tangential fiction suface, as shown F = µ*n F ta = µ*n*cosα (axial component of F but N = W/sinα F ta = µw*cotα F=µN α F ta =µncosα α N W - 8 -

9 Requied axial foce: F a = W + F ta = W*(+µ*cotα Example 3: A cone clutch of the following specification R = 0.4 m; ω = 300 pm; S = m; α = 6 ; µ = 0.8; P max = 7 kn/m Find: a maximum powe fo no slipping; b minimum axial load equied fo maximum powe to hold the clutch in engagement. R = ( + / and S = ( - *cosecα = m, and = m c = P max * = 7000* = N/m W = πc( = N T = µ W * Rcosecα = N. m Powe = T*ω = 300.6*(π*300/60 = kw Requied axial foce is: F a = W + F ta = W*(+µ*cotα = 6.36 kn 0.3 Centifugal Clutches: A centifugal clutch consists of a numbe of shoes, which can move in adial guides and bea on the inside of an annula im, Figue 0.5. The oute sufaces of the shoes ae coveed with a fictional mateial, and as the speed ises, the centifugal foce on the shoes causes them to tansmit powe by fiction to the im

10 Spings ae fitted to keep the shoes clea of the im at low speeds and thus allow the moto to gain speed befoe taking up the load. Let: n = numbe of shoes Rim F c = centifugal foce on each shoe Housing F s = inwad foce on each shoe exeted by sping R = inside adius of im µ = coefficient of fiction between im and shoe k = sping stiffness (constant m = mass of one shoe = adius of shoe's mass cente Net outwad foce (adial foces: Shoe Figue 0.5: Centifugal clutch Beam sping F n = F c F s whee F s = k. and F c = m..ω Fiction foce on im: F f = µ*( F c F s = µ* F n fo one shoe Tansmitted toque: T sh = F f.r = µ.r.( F c F s fo one shoe The total fiction toque is: The T = n * T sh = n.µ.r.( F c F s shoes begin to move towad the im. citical speed ω c : that speed at which At citical speed F c = F s F c = F s = m..ω c ω c = (F c /m

11 Example 4: A centifugal clutch of the following specification; m= kg, = 0.5m, k= 50kN/m, = 0.0m, µ = 0.3, ω =60ad/s, R =0.9m, and n = 3. F s = k. = 500 N F c = m..ω = 080 N F n = F c F s = 580 N T = n.µ.r. F n = 99. N.m Powe = T*ω = 99. * 60 = 5.9 kw Example 5: In a cone clutch, the contact sufaces have an effective diamete of 75 mm. The semi-angle of the cone is 5. µ = 0.3. Find the toque equied to poduce slipping of the clutch if the axial foce applied is 80 N. This clutch is employed to connect an electic moto, unning unifomly at 000 ev/min, with a flywheel, which is initially stationay. The flywheel has a mass of 3.5 kg and its adius of gyation is 50 mm. Calculate the time equied fo the flywheel to attain full speed and the enegy lost in the slipping of the clutch. ω = π* 000/60 = 04.7 ad/s J = mass * k = 3.5 * 0.5 = kg m T = µ W * R cos ecα = 0.3* 80* cos ec5 o = 7.84 N Fo the flywheel, T = J*α 7.84 = * α α = ad/s Time taken, t = ω / α = 04.7 / = sec Let θ m and θ f be the angles tuned though by the moto and flywheel espectively befoe slipping ceases. Then θ m = ω * t = 04.7 * = ad - -

12 Since the flywheel acceleates unifomly fom est to 000 ev/min θ f = ½θ m =.84 ad Wok done by moto = T * θ m Wok done on flywheel = T * θ f Wok lost in fiction = T (θ m - θ f = 7.84 ( = 665. J Example 6: Figue 0.6 shows one of the fou shoes of a centifugal clutch. The contact suface is 60 mm adius and the fiction foce is µs, whee S is the esultant of the nomal foces on the suface and µ = 0.5. The cente of gavity is 5 mm fom the contact suface. The clutch is to commence engagement at 500 ev/min. If it is to tansmit 0 kw at 750 ev/min, calculate the coesponding value of S and find the mass of each shoe and the pessue of the beam sping on the adjusting scew. If the sping has a stiffness of 70 kn/m, find the powe tansmitted at 750 ev/min when the shoes have won mm, if not adjusted. Radius of c.g. of shoe, = 60 5 = 35 (mm ω = π*n/60 = 0.047*N (ad/s Centifugal foce on each shoe, F c = mω = m*(π*n/60 Figue 0.6 * 0.35 = m N (N At 750 ev/min, T = powe / ω = 0000 / (0.047*N = 0000 / (0.047*750 = (N.m The total fiction toque, T = n * µ * S * R 55 = 4 * 0.5 * S * 0.6 S = (N When the shoe makes contact with the im, the sping foce emains constant as the speed ises and is theefoe equal to the centifugal foce at 500 ev/min. S = F c F s 594 = m m

13 m = (kg Pessue on beam sping at 750 ev/min = sping foce at 500 ev/min = *3.446* 500 = 75 (N When shoe weas mm, incease in sping foce = * 0.00 = 340 (N new sping foce = = 65 (N New centifugal foce = * ( π*750/60 * ( = 9.6 (N S = = 97.6 (N Powe = 0 * 97.6 / 594 = 6.7 (kw Example 7: Establish a fomula fo the maximum toque tansmitted by a single plate clutch of intenal and extenal adii and if the limiting coefficient of fiction is µ and the axial sping loading is W. Assuming that the pessue intensity on the contact faces is unifom. Apply this to detemine the time equied to acceleate a counteshaft of otating mass 500 kg and adius of gyation 00 mm to the full speed of 50 ev/min fom est though a single plate clutch of intenal and extenal adii 5 mm and 00 mm taking µ as 0.3 and sping load as 600 N. Fo the fist pat of the question see page 3 above. ( T = µ W 3 ( 3 3 *n; ω = π*50/60 = 6. ad/s J shaft = M*k = 500 * 0. = 0 kg m - 3 -

14 Fo the given data: T = N m T = J * α α = / 0 =.98 ad/s t = ω / α = 6. /.98 = 8.79 sec Example 8: A fiction clutch is to tansmit 0 kw at 3000 pm. It is to be of single plate type with both sides of the plate effective, the axial pessue being limited to be 0.09 N/mm. If the extenal diamete of the fiction lining is.4 times the intenal diamete, find the equied dimensions of the fiction lining. Assume unifom wea conditions. The coefficient of fiction may be taken as 0.3. Powe = T * ω T = 0000 * 60/π*3000 = 3.83 N m Dimensions of fiction lining: Let and extenal and intenal adii of fictional lining We know that fo unifom wea conditions, p max * = c c = 0.09 * 0 6 * Total load tansmitted to the fiction lining, W = π * c ( = π * 0.09 * 0 6 * (.4 = T = nµwr 3.83 = * 0.3 * * (.4 + / 3 = *0-3 and = m = mm =.4 * = 8.46 mm - 4 -

15 Example 9: An engine developing 45 kw at 000 pm is fitted with a cone clutch built inside the flywheel. The cone has a face angle of.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. N/mm. Detemine. the axial sping foce necessay to engage the clutch, and. the face width equied. ω = π*000/60 = 04.7 ad/s We know that toque developed by the clutch, T = powe / ω = / 04.7 = 49.7 N m 430 N m. Axial sping foce necessay to engaged by the clutch, T = µwr cosec.5 W = 430 / (0.*0.5*cosec.5 = N. Face width equied, Let b = Face width We know that nomal pessue on the clutch face, p = W / (π * R * b * sin α b = / (π * 50 * 0. * sin.5 = mm Example 0: A centifugal clutch has fou shoes, and tansmits 5 kw at 900 pm. The speed at which the engagement beings is ¾th of the unning speed. The inside adius of the pulley im is 50 mm and the cente of gavity of the shoe lies at 0 mm fom the cente of the spide. The shoes ae lined with im fo which the coefficient of fiction may be taken as 0.5. Detemine. Weight of the shoes, and. Size of the shoes, if angle subtended by the shoes at the cente of the spide is 60 and the pessue exeted on the shoes is 0. N/mm

16 The unning speed; ω = π*900/60 = 94.5 ad/s The engagement speed; ω = ¾ ω = 70.7 ad/s The toque at unning speed; T = powe / ω = 5000 / 94.5 = 59.5 N m. Weight of the shoes; Let m = weight of the shoes in kg, We know that the centifugal foce acting on each shoe F c = m * * ω = m N And the inwad foce on each shoe exeted by the sping i.e. the centifugal foce at the engagement speed ω, F s = m * * ω = 599.8m N Fictional foce acting tangentially on each shoe, F f = µ(f c F s = 0.5(065.97m 599.8m = 6.54m Tansmitted toque: T sh = F f * R = 6.54 * 0.5 = 7.48m N fo one shoe The total fiction toque is: T = n * T sh = 4 * 7.48m =70m N m = 59.5 / 70 =.76 kg. Size of the shoe, l = contact length of shoes in mm, b = width of the shoes in mm, θ = angle subtended by the shoes at the cente of the spide in ad, p = pessue exeted on the shoes in N/mm l = θ * R = 60 * (π/80 * 50 = mm p = (F c F s / l*b b = ( m m/.* = 67.5 mm - 6 -

17 Example : A centifugal clutch has fou shoes which slide adially in a spide keyed to diving shaft and make contact with the intenal cylindical suface of a im keyed to the diven shaft. When the clutch is at est, each shoe is pulled against a stop by a sping to leave a adial cleaance 5 mm between the shoe and the im. The pull exeted by the sping is then 500 N. The mass cente of the shoe is 60 mm fom the axis of the clutch. If the intenal diamete of the im is 400 mm, the mass of each shoe is 8 kg, the stiffness of each sping is 50 kn/mm and the coefficient of fiction between the shoe and the im is 0.3; find the powe tansmitted by the clutch at 500 pm. ω = (π*500/60 = 5.36 ad/s = + = = 65 mm = 0.65 m F c = m ω = 8 * 0.65 * (π*500/60 = N F s = * 0 3 * = 750 N F n = F c F s = = N Total fictional toque, T = n * µ * F n * R = 4 * 0.3 * * 0. = N m Powe tansmitted = T * ω = * 5.36 = 3605 Watt = kw - 7 -

Clutches. Clutches 885 C H A P T E R

Clutches. Clutches 885 C H A P T E R 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