(Autonomous) Shamshabad, Hyderabad-501218.
DESIGN OF MACHINE MEMBERS-I
LECTURE NOTES
by
D.V.RAMANAREDDY ASSISTANT PROFESSO P ROFESSOR R MECHANICAL ENGINEERING DEPARTMENT
UNIT-VII SYALLABUS: SHAFT COUPLING : Rigid couplings – Muff, Split muff and Flange couplings. Flexible couplings –Flange coupling (Modified).
Instructional Objectives: The focus is on blending fundamental development development of concepts with practical specification of components The objectives of the text are to: 1. Cover the basics of machine design, including including the design process, Engineering Engineering mechanics mechanics and and materials, materials, failure prevention under static and variable loading, and characteristics of the principal types of mechanical elements. elements. (PEO 2) 2. Offer a practical approach to the subject through a wide range of real world applications and examples. (PEO 1,2) 3. Encourage readers to link design and analysis. (PEO 2) 4. Encourage readers to link fundamenta f undamentall concepts with practical component specification. (PEO 2) At the end of this lesson, the students should be able to understand: 1. Ability to design of shaft couplings 2. Ability to understand the stresses in design of shaft couplings
DESIGN OF SHAFT COUPLING A coupling is a device used to connect two shafts together at their ends for the purpose of transmitting power. Couplings do not normally allow disconnection of shafts during operation, however there are torque limiting couplings which can slip or disconnect when some torque limit is exceeded. The primary purpose of couplings is to join two pieces of rotating equipment while permitting some degree of misalignment or end movement or both. By careful selection, installation and maintenance of couplings, substantial savings can be made in reduced maintenance costs and downtime. Shaft couplings are used in machinery for several purposes, the most common of which are the following
To provide for the connection of shafts of units that are manufactured separately such as a motor and generator and to provide for disconnection for repairs or alterations. To provide for misalignment of the shafts or to introduce mechanical flexibility. To reduce the transmission of shock loads from one shaft to another. To introduce protection against overloads. To alter the vibration characteristics of rotating units. To connect driving and the driven part
A rigid coupling is a unit of hardware used to join two shafts within a motor or mechanical system. It may be used to connect two separate systems, such as a motor and a generator, or to repair a connection within a single system. A rigid coupling may also be added between shafts to reduce shock and wear at the point where the shafts meet. When joining shafts within a machine, mechanics can choose between flexible and rigid couplings. While flexible units offer some movement and give between the shafts, rigid couplings are the most effective choice for precise alignment and secure hold. By precisely aligning the two shafts and holding them firmly in place, rigid couplings help to maximize performance and increase the expected life of the machine. These rigid couplings are available in two basic designs to fit the needs of different applications. Sleeve-style couplings are the most affordable and easiest to use. They consist of a single tube of material with an inner diameter that's equal in size to the shafts. The sleeve slips over the shafts so they meet in the middle of
the coupling. A series of set screws can be tightened so they touch the top of each shaft and hold them in place without passing all the way through the coupling. Clamped or compression rigid couplings come in two parts and fit together around the shafts to form a sleeve. They offer more flexibility than sleeved models, and can be used on shafts that are fixed in place. They generally are large enough so that screws can pass all the way through the coupling and into the second half to ensure a secure hold.Flanged rigid couplings are designed for heavy loads or industrial equipment. They consist of short sleeves surrounded by a perpendicular flange. One coupling is placed on each shaft so the two flanges line up face to face. A series of screws or bolts can then be installed in the flanges to hold them together. Because of their size and durability, flanged units can be used to bring shafts into alignment before they are joined together. Rigid couplings are used when precise shaft alignment is required; shaft misalignment will affect the coupling's performance as well as its life. Examples: Sleeve coupling A sleeve coupling consists of a pipe whose bore is finished to the required tolerance based on the shaft size. Based on the usage of the coupling a keyway is made in the bore in order to transmit the torque by means of the key. Two threaded holes are provided in order to lock the coupling in position. Sleeve couplings are also known as Box Couplings. In this case shaft ends are coupled together and abutted against each other which are enveloped by muff or sleeve. A gib head sunk keys hold the two shafts and sleeve together
Clamp or split-muff coupling A clamp coupling is different from the sleeve coupling in that the sleeve used in this type is split from one side.The shafts are entered and keyed to this sleeve and then split sides are screwed together.
Rigid Sleeve Coupling
Suitable for joining any two shafts when flexibility not required Consists of a one piece sleeve, with two set screws Applications include: light to medium duty applications
A Sleeve Coupling consists of a pipe whose bore is finished to the required tolerance based on the shaft size. Based on the usage of the coupling a keyway is made in the bore in order to transmit the torque by means of the key. Two threaded holes are provided in order to lock the coupling in position. Sleeve couplings are also known as Box Couplings. In this case shaft ends are coupled together and abutted against each other which are enveloped by muff or sleeve. A gib head sunk keys hold the two shafts and sleeve together.
These couplings cannot take much misalignment hence are preferred on long shafts which can absorb stress. In sleeve coupling two shafts screw into a single connecting piece. To remove sleeve coupling shaft needs to be moved.
Flexible Coupling: Can take shaft misalignments and are of many types. Some are shown below
Rigid Coupling Flange locked onto each shaft. One flange with recess and the other with matching spigot. Flanges bolted together to form rigid coupling with no tolerance for relative radial, angular or axial movement of the shafts.
Muff Coupling Long cylindrical coupling bored and keyed to fit over both shafts. Split axially and clamped over both shafts with recessed bolts. Rigid coupling for transmitting high torques at high speeds
Pin Coupling As rigid coupling but with no recess and spigot and the Bolts replaced by pins with rubber bushes. Design allows certain flexibility.
Flexible Rubber disc Couping As rigid coupling except that a thick rubber disc bonded between steel plates is located between the flanges. The plates are bolted to the adjacent coupling flanges.
DESIGN
design a pin bushed flexible coupling to draw a pin bush flexible coupling the given data will be dia of shaft d to be joined in mm,power P to be transmitted in kw ,no. of revolution N in rpm,bearing pressure pb in n/mm2,allowable shear stress in shaft,keys,flange t in N/mm2 and allowable stress in pin s. STEP 1. find torque T=(P*60)/(2*3.14*N) in N-m cange it in N-mm by multiplying 1000.
Check suitability of shaft dia by (d')3=[(16*t)/(3.14*t)] if d'
enlarged dia of pin d2= d1+2*step size(3-4) mm assume a brass bush t1=2-3mm and rubber bush t2= 6-8mm so d3 = d2+2*t1+2*t2 STEP 3 hub dia D1 = 1.75*d pin circle dia D2 =3d force per pin f= T*2/(D2*n) STEP 4 From bearing consideration pb=F/(l*d3) find l from above expression. shear stress in pin t= (F*4)/(3.14*d1*d1) STEP 5 Bending moment M = F*(l/2 + e)
select e suitably e= 3-5mm
section modulus Z =(3.14*d1*d1*d1)/32 bending stress = M/Z
C-PROGRAM FOR BUSHED COUPLING #include #include #include #include float arr[20]; float *am(float d1,int d,float T,float pb,float n,float ta) { int d2,t1,t2,d3,e; float a,d0,q,D1,k,F,l,ti,D2,D3,tp,z,M,c,qp,qb,w,t,l1;
- See more at: http://www.bestinnovativesource.com/2012/11/06/sleevecoupling/#sthash.Tu5kJc2j.dpuf
/* Enlarged dia of pin */ d2=d1+2*3; arr[0]=d2; t1=2;
t2=6; d3=d2+2*t1+2*t2; arr[1]=d3;
/* STEP 3*/ D1=1.75*d; D1 = abs(D1)+1;
/* check suitability of hub*/ k=d/D1; k=pow(k,4); ti=(16*T)/(3.14*D1*D1*D1); ti=ti/(1-k); if(ti
/* SHEAR STRESS IN PIN*/
tp=(4*F)/(3.14*d1*d1); arr[6]=tp; /* BENDING MOMENT */ e=4; M=F*((l/2)+e); arr[7]=M;
z=(3.14*d1*d1*d1)/32; arr[8]=z; qb=M/z; arr[9]=qb; /* PRINCIPAL STRESS IN PIN*/ c=(qb*qb)+4*(tp*tp); qp=.5*(qb+sqrt(c));
/* KEY DIMENSIONS*/ w=d/4; w=abs(w)+1; t=d/6; t=abs(t)+1; l1=1.5*d; l1=abs(l1)+1; printf("\n\n\t principle stress in pin =\t%fN/mm2",qp); arr[10]=qp; printf("\n\n\t n=%f",n); printf("\n\n\t d1=\%fmm",d1); printf("\n\n\t D1=\%fmm",D1); printf("\n\n\t ti=\t%fN/mm2",ti); printf("\n\n\t Hub is safe"); printf("\n\n\t d2=%dmm",d2); printf("\n\n\t d3=\t%dmm",d3); printf("\n\n\t D2=\t%f",D2); printf("\n\n\t Force per pin =\%fN",F); printf("\n\n\t l=\%fmm",l); printf("\n\n\t shear stress in pin =\t%fN/mm2",tp);
printf("\n\n\t bending moment =\t%fN-mm",M); printf("\n\n\t section modulus =\t%fmm3",z); printf("\n\n\t STRESS =\t%fN/mm2",qb); printf("\n\n\t width of key =%fmm",w); printf("\n\n\t thickness of key =\t%fmm",t); printf("\n\n\t length of key =\t%fmm",l1); printf("\n\n\n"); return arr; } main() { clrscr(); float farr[20]; int d,p,N,b,d2,t1,t2,d3,e,i; float T,n,d1,a,d0,pb,ta,q,D1,k,F,l,ti,D2,D3,tp,z,M,c,qp,qb; printf("\n\n\t\t DESIGN OF PIN BUSHED FLEXIBLE COUPLING"); printf("\n\n\n\t enter the dia of pipe to be joined in mm=\t"); scanf("%d",&d); printf("\n\n\t enter the power to be transmitted in kw=\t"); scanf("%d",&p); printf("\n\n\t enter the rpm of the shaft =\t"); scanf("%d",&N); printf("\n\n\t enter the bearing pressure in N/mm2=\t"); scanf("%f",&pb); printf("\n\n\t enter the allowable shear stress in shaft,keys ,flange =\t"); scanf("%f",&ta); printf("\n\n\t enter the allowable stress in pin =\t"); scanf("%f",&q); /* To find the torque*/ T=(p*60000)/(2*3.14*N); T=(T*1000); printf("\n\n\t torque produced =\t%fN-mm",T); /* Suitability of shaft dia*/ a=(16*T)/(3.14*ta); d0=pow(a,.33333); d0=fabs(d0)+1; if (d0
d0=d; printf("\n\n\t d0=%fmm",d0); } else printf("\n\n\t Dia is not secure"); /* No. of pins */ n=(0.02*d)+5; if(abs(n)-n==0) i=abs(n); else { n=abs(n)+1; i=abs(n)+1; } if(i%2==0) n=n; else n=n+1; printf("\n\n\t no. of pins =\t%f",n); /* Pin dia*/ d1=(0.5*d)/sqrt(n); b=abs(d1)+1; d1=abs(d1)+1; if(b<10) printf("\n\n\t The value of d1 is =\t%fmm",d1); else { if(b%2==0) printf("\n\n\t The value of d1 is =\t%fmm",d1); else { d1=d1+1; printf("\n\n\t The value of d1 is =\t%dmm",d1); } } qp=0; //farr[20] = am(d1,d,T,pb,n,ta); memcpy(farr,am(d1,d,T,pb,n,ta),sizeof(am(d1,d,T,pb,n,ta))); if (arr[10] > q)
{ for(int i=0;arr[10]>q;i++) { printf("\n\n*********************************************************" ); printf("\n\n*********************************************************" ); printf("\n\n\t ITERATION NO.%d",i+1); d1=d1+2; memcpy(farr,am(d1,d,T,pb,n,ta),sizeof(am(d1,d,T,pb,n,ta))); } } getch(); return 0; }
DESIGN OF SLEEVE COUPLING
Sleeve coupling is also known as muff coupling and is the type of rigid coupling. This coupling is made of cast iron and has hollow cylinder. In order to avoid misalignment, the internal diameter of sleeve coupling is the same as the shaft has. Gib-head key is used to connect two shafts which mean that sleeve coupling along with gib-head key is treated as the power transfer medium from one shaft to other shaft. The dimensions of sleeve coupling is as following External diameter of sleeve = D = 2d + 13 mm Length of sleeve = L = 3.5d where in the above expressions, d is the internal diameter of sleeve or the diameter of shaft. If we are doing a job in the industry and our boss told us to design sleeve coupling then there are some designing parameters which w ill help us to design sleeve coupling. These parameters are following
Design for sleeve Design for key
Design for sleeve
First assumption for the designing of sleeve coupling is that the shaft on which we are installing coupling is hollow.
The torque transmission by hollow section of the shaft is as following T = (π /16) x τc x (D4 – d4)/D Where in the above expression, T is the torque transmission, τ c is the allowable shear stress. Usually we consider cast iron for sleeve and taken allowable shear stress equal to 14 MPa. Design for key
The basic designing parameter for the designing of gib-head key is same but there are some other consideration as well because both are necessary for the transmission of torque like the length of key should be equal to the length of sleeve. For the sake of installation, we divide coupling into two parts, therefore the length of the key in each shaft should be as following l = L / 2 = 3.5d/2 After designing the length of key, next step is to check shear and crushing stresses. Therefore torque transmission with key is
T = l x w x τ x d/2
if we consider shear stress
T = l x t/2 x σc x d/2
if we consider crushing stress
BUSHED-PIN FLEXIBLE COUPLING The modified form of rigid flange coupling is the bushed pin flexible coupling and the bolts used to joint both parts of coupling are called pins. This coupling is somewhat different in terms of general construction as compare to other couplings. It has both different flanges, 5 mm clearance between flanges, absence of any rigid connection and main focus to drive is on leather or compressible rubber bushes. The main modification in rigid coupling is on to reduce bearing pressure on leather or rubber bushes and to make sure that its value doesn’t increase from 0.5 N/mm2. To maintain this pressure, engineers increase pin size and pitch circle diameter.
Bearing load on pins = W = pb x d2 x l x n where in the above expression, p b is the bearing pressure, d 2 is the bush diameter, l is the bush length in flange and n is the number of pins. Torque transmission by coupling = T = W x n x ( D1 / 2 ) In order to reduce bending stresses, the threaded portion of the pin is tapping fit and its length is as small as possible so that all shear stress acts during application effect unthreaded portion of the pin. Direct shear stresses = τ = W / [(π/4)d12]
FLANGE COUPLING Flange coupling is actually the combination of two flanges mounted on opposite shafts. These flanges are made of cast iron. The reason behind using cast iron is its ability to resist vibrations and it is also cheap as compare to other metals. Each flange uses separate key to mount on its shaft. On one flange of the coupling, we have projected portion and it fits into the body of other flange. This type of arrangement help engineer to maintain process because it gives us accurate alignment. The reason behind their accurate alignment is not only the fitting of projected portion but also due to the tightening of both flanges by using bolts and nuts combination. This type of construction enable engineer to use flange coupling in heavy duty applications. There are three types of flange coupling
Unprotected type flange coupling Protected type flange coupling Marine type flange coupling
Unprotected type flange coupling
In this type of coupling, we use two keys, one is attached to the boss of the flange and the other one is the counter sunk key. Both flanges are coupled by using bolts which are three, four or six in numbers. Both keys are attached to the shaft at right angle. The reason behind this arrangement is to share the weakness of the shaft caused by the presence of keyways.
The material of unprotected flange coupling is cast iron and general dimensions of the shaft of hub is as following External diameter of hub = D = 2d Length of hub = L = 1.5 d Pitch circle diameter of bolts = D1 = 3d Flange external diameter = D2 = D1 + (D1 – D) = 4d Flange thickness = tf = 0.5d
Number of bolts = 3 in case of diameter upto 40 mm = 4 in case of diameter upto 100 mm = 6 in case of diameter upto 180 mm
Protected type flange coupling
In this type of coupling, we increase the protection of nuts and bolts by flanges itself. Main reason for doing this is to save worker for any mishap. The only parameter that changes from unprotected type flange coupling is the thickness of circumferential flange as 0.25d.
Marine type flange coupling
In this type, we actually forged flange couplings rather than attaching through key and attach both parts of coupling using tapered headless bolts. The general dimensions of this flange coupling is as following
Flange thickness = d / 3 Bolt taper = 1 in 20 to 1 in 40 Pitch circle diameter = D1 = 1.6 d External diameter of flange = Ds = 2.2 d
COMPRESSION COUPLING Compression coupling is also known as split muff coupling or clamp coupling. For the ease of installation, this coupling is made into two parts and both are joined by using bolts. For the manufacturing of muff part of the coupling, we use cast iron but the bolts used to join these two parts are made of mild steel. Depending upon the process requirement and the size of coupling, we can use two, four or six bolts. This coupling can be used for heavy duty operation with moderate speed. The main advantage of using this coupling is that we don’t need to change the position of shafts when we are assembling or disassembling coupling.
The general dimensions of compression coupling are following Diameter of sleeve = D = 2d + 13 mm Length of sleeve = L = 3.5d where in the above expression, d is the diameter of shaft. During working of compression coupling, our main torque transmission medium is the key and the friction between muff and shaft. The designing parameters of compression coupling are following Design of muff
In order to start the designing of muff, we assume that the torque transmission shaft is hollow The torque transmission is as following T = (π /16) x τc x (D4 – d4)/D where in the above expression, T is the torque transmission, τ c is the allowable shear stress. Design for key
With compression coupling, we use gib-head key. Next step is to take the length of key equal to muff. In order to provide ease, we use coupling in two parts, therefore half of the key is installed in one part and half in other part.
l = L / 2 = 3.5d/2 Next we have to check shear and crushing stresses produced inside key. Therefore torque transmission with key is T = l x w x τ x d/2
if we consider shear stress
T = l x t/2 x σc x d/2
if we consider crushing stress
Design of clamping bolts
In order to know the designing of clamping bolts, we know about the force exerted by each bolt, therefore F = π x db2 σt where in the above expression, d b is the diameter of bolt and σ t is the allowable tensile stress according to the material of bolt. Force exerted by bolts on each side of shaft F = π x db2 σt x n/2 where in the above expression, n is the number of bolts installed in the coupling. In order to know the pressure on the shaft, we consider the force which bolts exerts by clamping coupling per projected area of the coupling p = Force / Projected area p = [π x db2 x σt x n/2] / [(L x d)/2] where in the above expression, L is the length of muff. Since friction is treated as the medium to transfer torque, therefore F = μ x Pressure x Area = μ x p x (πd/2) x L F = μ x [{π x db2 σt x n/2} / {(L x d)/2}] x (πd/2) x L F = μ x (π2 /8) x db2 σt x n
