chine Design II Prof. K.Gointh & Prof...yurm Drum Brkes Among the vrious tyes of devices to be studied, bsed on their rcticl use, the discussion will be limited to Drum brkes of the following tyes which re minly used in utomotive vehicles nd crnes nd elevtors. Drum Brke Tyes: Rim tyes with internl exnding shoes Rim tyes with externl contrcting shoes Internl exnding Shoe The rim tye internl exnding shoe is widely used for brking systems in utomotive lictions nd is generlly referred s internl shoe drum brke. The bsic roch lied for its nlysis is known s long-rigid shoe brke nlysis. Long rigid Shoe Anlysis A schemtic sketch of single shoe locted inside rotting drum with relevnt nottions, is shown in the figure below. In this nlysis, the ressure t ny oint is ssumed to be roortionl to the verticl distnce from the hinge in, the verticl distnce from the hinge in, which in this cse is roortionl to sine of the ngle nd thus, dsin sin Since the distnce d is constnt, the norml ressure t ny oint is just roortionl to sinθ. Cll this constnt of roortionlity s K Indin Institute of Technology drs
chine Design II Prof. K.Gointh & Prof...yurm Figure 3..4 Thus = Ksin It the mximum llowble ressure for the lining mteril is mx then the constnt K cn be defined s K = = sin sin mx mx Indin Institute of Technology drs
chine Design II Prof. K.Gointh & Prof...yurm mx = sin sin mx The norml force dn is comuted s the roduct of ressure nd re nd the frictionl force s the roduct of norml force nd frictionl coefficient i.e. f dn. By integrting these over the shoe length in terms of its ngle the brking torque T, nd other brke rmeters re comuted. To determine the ctuting force F, the moment equilibrium bout the ivot oint is lied. For this we need to determine the moment of the norml force N nd moment of the frictionl force bout the ivot oint. oment of the norml force is equl to the norml force times its moment rm bout the ivot oint. From the figure it is cler tht the moment rm in this cse is equl to d sin Θ where d is the distnce between the drum center nd ivot center N =.b.r.d.d sin = b..r.d.sin.d mx = b.d.r. sin d sin mx b.d.r N = ( ) (sin sin ) sin 4 On similr lines the moment of friction force is comuted ( ) F = f..b.r.d r d sin mx = f.b.r. sin ( r dsin ) d sin mx Indin Institute of Technology drs
chine Design II Prof. K.Gointh & Prof...yurm ( ) ( n ) f.mx. b.r d f = r cos cos sin si sin The ctuting force F is determined by the summtion of the moments of norml nd frictionl forces bout the hinge in nd equting it to zero. Summing the moment bout oint O gives F = N ± f c where, N nd f re the moment of the norml nd frictionl forces resectively, bout the shoe ivot oint. The sign deends uon the direction of drum rottion, (- sign for self energizing nd + sign for non self energizing shoe)where the lower sigh is for self energizing shoe nd the uer one for self deenergizing shoe. The rection forces re determined by lying force summtion nd equilibrium R x = dn.cos+ df.sin = b.r. cos d+ f b.r. sin d mx mx = b.r. sin cos d+ f b.r. sin d sin sin mx mx ( ) ( ) mx.br mx = ( ) sin sin ± f sin sin sin 4 The equtions cn be simlified nd ut s br R x = (A fb) sin br R y = (B± fa) F sin x Indin Institute of Technology drs
chine Design II Prof. K.Gointh & Prof...yurm Where ( ) A = sin sin B = ( ) sin sin 4 The brking torque T on the drum by the shoe is of the frictionl forces f. dn times the rdius of the drum nd resulting eqution is, T = f.b..r.d.r = fbr mx sin d sin fd r (cos cos ) T = sin T Double Shoe Brkes Twin Shoe Brkes Behvior of single shoe hs been discussed t length. Two such shoes re combined into comlete rcticl brke unit, two being used to cover mximum re nd to minimize the unblnced forces on the drum, shft nd berings. mx If both the shoes re rrnged such tht both re leding shoes in which self energizing re reviling, then ll the other rmeters will remin sme nd the totl brking torque on the drum will be twice the vlue obtined in the nlysis. Indin Institute of Technology drs
chine Design II Prof. K.Gointh & Prof...yurm However in most rcticl lictions the shoes re rrnged such tht one will be leding nd the other will be triling for given direction of drum rottion If the direction of drum rottion chnges then the leding shoe will become triling nd vice vers. Thus this tye of rrngement will be eqully effective for either direction of drum rottion. Further the shoes cn be oerted uon using single cm or hydrulic cylinder thus rovide for ese of oertion One leding shoe & one triling Two Leding shoe Figure 3..5 However the totl brking torque will not be the twice the vlue of single shoe, if the sme norml force is lied or creted t the oint of force liction on both the brke shoes which is the norml rctice s they re ctuted using common cm or hydrulic cylinder. Indin Institute of Technology drs
chine Design II Prof. K.Gointh & Prof...yurm This is becuse the effective contct ressure (force) on the triling shoe will not be the sme, s the moment of the friction force ooses the norml force, there by reducing its ctul vlue s in most lictions the sme norml force is lied or creted t the oint of force liction on the brke shoe s noted bove Consequently we my write the ctul or effective ressure reviling on triling shoe ' F. =. ( n + f ) Resulting eqution for the brking torque T f.w.r. B = (cos -cos )( sin + ') below Some ictoril illustrtions of the utomotive drum brkes re resented Figure 3..6 Indin Institute of Technology drs
chine Design II Prof. K.Gointh & Prof...yurm Figure 3..7 Oblong Cm Actutor Leding shoe Triling shoe Rotting Drum Pivot oint(fixed xis) The ntomy of the single leding shoe drum Brke Animtion Indin Institute of Technology drs
chine Design II Prof. K.Gointh & Prof...yurm Figure 3..9 Externl Contrcting Shoe The sme nlysis cn be extended to drum brke with externl contrcting tye of shoes, tyiclly used in elevtors nd crnes. A schemtic sketch of s single shoe locted externl to the rotting drum is with ll relevnt nottions is shown in the figure below. Indin Institute of Technology drs
chine Design II Prof. K.Gointh & Prof...yurm X Figure 3.. Corresonding contct geometry is shown in the figure The resulting equtions for moment of norml nd frictionl force s well s the ctuting force nd brking torque re sme s seen erlier. For convenience they re reroduced here gin ( ) fb r cos cos T = sin F = N ± f c br N = ( ) (sin sin ) sin 4 Indin Institute of Technology drs
chine Design II Prof. K.Gointh & Prof...yurm ( ) fbr d f = r cos cos (sin sin sin ) TWIN SHOE BRAKES As noted erlier for the internl exnding shoes, for the double shoe brke the brking torque for one leding nd one triling shoe cted uon common cm or ctuting force the torque eqution develoed erlier cn be lied. i.e T f.w.r. B = (cos -cos )( sin + ') Indin Institute of Technology drs