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Design of an adjustable roller chain coupling for shafts of different diameters.

Introduction

Shafts are usually available up to 7 meters length in order to avoid inconvenience of their transport [4]. In order to have a greater length, it becomes necessary to join two or more lengths of shafts by mean of some couplings. Couplings and clutches are the devices which are used as a same purpose to transmit torque. But the essential difference between clutch & a coupling is that clutch can be disengaged or engaged at the will of operator, where as coupling is regarded as being fixed. Shaft coupling are used in machinery for a several purposes, the most of common which are listed as follow [4]:-

1. It allows easy disconnection of shafts for repair and maintenance.

2. It tolerates a small amount of misalignment between the connecting shafts.

3. It can prevent transmission of overloading power.

4. Due to flaxible element like rubber that is used, it can modify the shock and vibration characteristics of the drive.

Requirements of Good Shaft Couplings [4]

1. It should be easy to connect or disconnect.

2. It should transmit full torque from one shaft to another shaft without any loss.

3. It should hold the shafts in perfect alignment.

4. It should reduce the transmission of shock loads from one shaft to another.

5. It should have no projecting parts.

Types of Shaft Couplings [1]

Rigid coupling: It is used to connect the shafts which are perfectly aligned. Broadly, following types of rigid coupling are available:-

1. Sleeve or muff coupling.

2. Clamp or split muff or compression coupling.

3. Flange coupling.

4. Marine flange coupling

Rigid couplings do not accommodate misalignment and consequently should not be used indiscriminately.

Flexible coupling: It is used to connect two shafts having both lateral and angular misalignment. Following types of flexible coupling are usually recommended under this category:-

1. Bushed flexible pin coupling.

2. Universal coupling.

3. Oldham coupling.

Flexible coupling allows the slight angular deviation, also permit the axis of the shaft to float or run slightly out of alignment, and in some cases to move end wise, whilst still transmitting torsional moment from the one shaft to the another shaft. Further the use of flexible coupling enables to compensate slightly inaccuracy of workmanship in aligning to the connecting the machine elements.

Limitations of Conventional Couplings

1. The couplings are the essential part of the industrial machines. As we know the shafts of the different diameter are used in an industry for different machines according to the requirement of torque to drive the machine. This requires the wide size range of coupling to be used in that particular industry. Therefore the industry needs many specialized couplings, which adds to cost and, standardization becomes non viable. With wide range of size of the coupling, the requirement of standby couplings to replace the damaged coupling in case of emergency, may further adds to cost

2. Secondly, the conventional couplings could mainly be used for transmitting torque between shafts of same diameter. That mean the shafts which have different diameters are not easy to couple with conventional couplings. For example, if we have two shafts having different diameters say as 35mm and 45mm which are necessary to couple to operate a machine, then none of the conventional coupling will help us to couple these shafts.

3. In the ever growing world the demand of essential commodities such as water, electricity is increasing day by day. As we know, the electric power is generated with the electric generators, which are directly coupled with the engines or the turbines with the help of shaft couplings. Similarly the centrifugal pumps, which used to bring the water out from the earth, these are also coupled to the engines and motors with the help of coupling. As the requirements of water and electricity are increasing, we have to replace the previous generator or pump with a generator or pump of higher power. Thus the replaced pump or generator needs more torque to drive, which causes increase in shaft diameter of pump or generator. Then it becomes a must to purchase another coupling to couple the new pump or generator with the motor or generator or turbines. This will eventually results in discarding the previous coupling, hence adds to the cost of installation.

4. There is abyss use of the devices in the human life which needs torque to operate it. When these devices are manufactured, their testing is done for the required performance. These are tested by coupling it with the testing machine by means of shaft couplings. These devices are manufactured for various specifications according to there use. Thus diameter of the major shaft varies, thus couplings of different sizes respective to diameter of the major shaft are required to fix on the testing machine. This repeated replacement of the coupling with change in product to be tested, causes lot of time consumption and fatigue to the work piece.

Proposed Variable Flange Coupling

Keeping in view, the above mentioned limitations of the conventional coupling, we propose the design of an adjustable roller chain coupling which can be adjusted according to the requirement with regard to the shaft diameter. The major advantage of this variable coupling is that it can be adjusted according to diameter of the shaft. In the conventional coupling the hub and the flange is a one rigid unit, which is manufactured by casting or machining. But in the proposed adjustable roller chain coupling, this unit is separated into two different parts, namely hub and the flange. The flanges are made like the sprockets, and these are joined together by using the combined roller chain (duplex) over these flanges. The use of roller chain in this mechanism accommodates some misalignment between shafts. The hub is further cut into four or three parts, such that these parts look like jaws. These jaws are fixed in the flanges by the means of nuts and bolts, and can be moved radially in the slots losing these nuts and bolts. The radial slots are provided in the flanges to maintain the radial movement of the jaws. However, this creates the problems that jaws do not make full contact due to difference between the curvature of the shaft and the jaws. The solution of this problem is found by flattening the jaws from the internal face on the shaping machine, such that when these are set together, these provide square hole instead of circular hole. In this square hole a square block is fixed in the jaws. This square block has a circular hole in which shaft can be fixed by means of keys or splines. Square blocks of different sizes with different hole diameter can be manufactured for the different shaft diameters. When we have to accommodate a changed diameter shaft situation a suitable block is fitted after adjusting the jaws suitably. A 3D view of the proposed flange coupling is shown in Fig.1, which is designed in the modeling software pro/ENGINEER.

[FIGURE 1 OMITTED]

Design and Stress Analysis

The design of variable flange coupling has been done firstly on basis of the static load. In the design against static load shearing, tensile or crushing failures have been considered. But in the practical situations there are very few applications where only static loads are acting. So, it becomes necessary to design the components against dynamics loads or endurance limit to increase the safety of design or components. While designing against dynamic loads, there are the many factors, which help to make the design safer. Thus, design of this coupling is done for the static as well as dynamic loads. Firstly, we design of the coupling on the basis of static load is given.

Design Against Static Load

A static load is defined as a force which is gradually applied to a mechanical component and which does not change its magnitude and direction with respect to time. The material of all components of the coupling is taken as mild steel, whose mechanical properties are as follow [2]:-

Tensile strength, [f.sub.t] = 175N/[mm.sup.2]

Shearing strength, [f.sub.s] = 105N/[mm.sup.2]

Crushing strength, [f.sub.c] = 230N/[mm.sup.2]

Assuming a factor of safety = 4

Then allowable stresses come out as follow:-

Tensile, [f.sub.t] = 43N/[mm.sup.2]

Shearing, [f.sub.s] = 26N/[mm.sup.2]

Crushing, [f.sub.c] = 57N/[mm.sup.2]

In all the components of the coupling a flange is a weakest part, so firstly it becomes necessary to design the flange for effective strength.

Shearing of Tie

Taking the dimensions as shown

Thickness of flange, t = 8mm

Thickness of tie, b = 6mm

Number of ties, z = 8

Thus, allowable shearing load given by

F = t x b x z x [f.sub.s] = 6 x 8 x 8 x 26 = 9984N

Thus permissible torque

T = 9984 x 50 = 499200Nmm = 499.2Nm

[FIGURE 2 OMITTED]

Bending of Tie

Bending load acting per tie = 9984/8 = 1248N

B.M. acting on tie, Mb = 1248 x 5 = 6240Nmm

Equating with maximum Bending Moment

[f.sub.b] x [b.sup.3]t/12 = 6240

From above [f.sub.b] = 43.33N/[mm.sup.2]

This is not safe

Thus, allowable Bending Moment

[M.sub.b] = [f.sub.b] x [b.sup.3]t/12 = 6192N

Thus allowable bending load on tie is, F = 6192/5 = 1238N

For eight ties, F = 1238 x 8 = 9904N

Therefore, allowable torque changes to

T = 9904 x 50 = 495200Nmm = 495.2Nm

Shearing of Minor Bolts

The bolts which hold the jaws with flange and moves in radial slots are designated as minor blots.

Diameter of bolt, d = 6mm

Number of bolts, z = 12

Thus design equation [PI]/4 x [d.sup.2] x z x [f.sub.s] = 9904

From above [f.sub.s] = 29N/[mm.sup.2]

This is not safe

Thus allowable shear load

F = [PI]/4 x [d.sub.2] x z x [f.sub.s] = 8817N

Thus permissible torque changes to T = 8817 x 50 = 440850Nm = 440.8Nm

Crushing by Minor Bolts

Design equation is

t x d x [f.sub.c] x z = 8817

From above [f.sub.c] = 15.3N/[mm.sup.2]

This is safe

Design of Chain

To select a suitable chain here we have to find the diameter of pin of the chain. On basis of that diameter corresponding chain can be selected.

Permissible torque by keeping in view all the failures, T = 440850Nmm Therefore the total shearing force acting on the periphery F = Permissible torque/Radius of the sprocket = 440850/82 = 5376N

Therefore shearing force acting per pin on the chain

[F.sub.pin] = Total force/ No. of pins or teeth on flange = 5376/50 = 107N

There fore for the safe design [PI]/4 x [d.sub.2] x [f.sub.s] = 107

d = 2.2 or 3mm preferred

Respective to above pin diameter a chain can be selected

[FIGURE 3 OMITTED]

Design Against Dynamics Load

The endurance limit of the material is defined as the maximum value of completely reversing stresses that a standard specimen can sustain for an unlimited number of cycles without fatigue failure. The endurance limit of material is determined from the ultimate tensile strength of materials, using some empirical relations [3].

The ultimate tensile strength of mild steel with 0.2% carbon [2], [S.sub.ut] = 420N/[mm.sup.2] Then endurance limit is given by relation [3], [S.sub.e1] = 0.5x [S.sub.ut] = 210N/[mm.sup.2] Above relationship is based on the 50% reliability [3] Endurance limit is further modified using following relation [3] [S.sub.e] = [S.sub.e1]x[K.sub.a]x[K.sub.b]x[K.sub.c]x[K.sub.d] In above relation [3] [K.sub.a] = surface factor [K.sub.b] = size factor [K.sub.c] = reliability factor [K.sub.d] = modified factor All the components are machined, there fore [3] [K.sub.a] = 0.81 Reliability is 50% for all components, there fore [3] [K.sub.c] = 1 Assuming that factor of safety is = 4 [K.sub.b] and [K.sub.d] are depending on the components

Shearing of Flange Tie

Modified endurance limit is given by [S.sub.e] = [S.sub.e1]x[K.sub.a]x[K.sub.b]x[K.sub.c]x[K.sub.d] (1) Stress concentration factor [3], [K.sub.t] = 2.1 Notch sensitivity [3], q = 0.7 Now using relation [K.sub.f] = q ([K.sub.t] - 1) + 1 Then, [K.sub.f] = 1.77 And [K.sub.d] is given by = 1. [K.sub.f] = 0.55 Value of size factor [3], [K.sub.b]=0.85 Then from (1), Se = 79.52N/[mm.sup.2] There fore, [f.sub.t] = 79.52/4 = 19.88N/[mm.sup.2] = 19N/[mm.sup.2] Using maximum shear stress theory [3], [f.sub.s] = 0.5x [f.sub.t] =9.5N/[mm.sup.2] Number of ties = 8 Now permissible shear load on tie, F = txbxzx[f.sub.s] = 8x6x8x9.5 = 3648N Thus allowable torque, T = 3648x50 = 182400Nmm = 182.4Nm

Bending of Tie

Bending load per tie, F = 3648/8 = 456N Bending moment acting, [M.sub.b] = 456x5 = 2280N Equating with maximum allowable bending moment i.e. [f.sub.b] x [b.sup.3.sub.t]/12 = 2280 and [f.sub.b] = 15.8N/[mm.sup.2] This is safe

Shearing of Minor Bolts

Diameter of bolts = 6mm Value of size factor [3], [K.sub.b] = 1 The bolts are notch less, assuming [K.sub.d] = 1 Therefore using (1), [S.sub.e] = 170N/[mm.sup.2] So, [f.sub.t] = 170/4 = 42N/[mm.sup.2] And [f.sub.s] = 0.5x [f.sub.t] = 21N/[mm.sup.2] Total shearing load on bolts, F = 3648N [PI]/4x[d.sup.2]xzx[f.sub.s] = 3648 [f.sub.s] = 10.7N/[mm.sup.2] This is safe

Crushing by Minor Bolts

Design equation is txdx[f.sub.c]xz = 3648 [f.sub.c] = 6.3 N/[mm.sup.2] This is safe

Design of chain

To select a suitable chain here we have to find the diameter of pin of the chain. On basis of that diameter corresponding chain is preferred Diameter of pin from static load design = 3mm Value of size factor [3], [K.sub.b] = 1 The pins are notch less, assuming [K.sub.d] = 1 There fore using (1), [S.sub.e] = 170N/[mm.sup.2] So, [f.sub.t] = 170/4 = 42N/[mm.sup.2] And [f.sub.s] = 0.5x [f.sub.t] = 21N/[mm.sup.2] Permissible torque by keeping in view all the failures, T = 440850Nmm Therefore the total shearing force acting on the periphery F = Permissible torque/Radius of the sprocket = 182400/82 = 2224N Therefore shearing force acting per pin on the chain [F.sub.pin] = Total force/No. of pins or teeth on flange = 2224/50 = 45N There fore for the safe design [PI]4xd2x[f.sub.s] = 45 d = 1.65mm

But to make the design common to both situations on static and dynamics loading a chain with 3mm pin can be preferred

Conclusion

The demand for the proposed adjustable roller chain coupling could be wide for the industrial machines to solve the problems mentioned in the paper. The proposed adjustable flange coupling has bee designed for an arbitrary chosen set of parameters. It can sustain a torque up to 440Nm, when subjected to static loads, and a torque of 180Nm under dynamic loads.

References

[1] Sharma C. S. and Purohit K., Machine design ( Prentice-hall of India, 2003)

[2] Sharma P.C. and Aggarwal D.K., Machine design (S.K. Kataria Publications, 2006)

[3] Bhandari V.B., Design of machine elements (Tata McGraw-Hill Publications, 2003)

[4] Khurmi R.S. and Gupta J.K., Machine design ( S. Chand Publications, 2006)

[5] Tsubaki U.S., Power transmission components division ( Roller Chain Couplings)

Sandeep Singh, Balraj Singh and Harpreet Singh Department of Mechanical Engineering B.B.S.B. Engineering College, Fatehgarh Sahib, 140407, Punjab, India E-mail: mechmehal@gmail.com, hnr97@yahoo.com
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Author:Singh, Sandeep; Singh, Balraj; Singh, Harpreet
Publication:International Journal of Applied Engineering Research
Article Type:Report
Geographic Code:1USA
Date:Nov 1, 2008
Words:2686
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