Machine Design

➢ Machine design is the subject where we apply the concepts of Engineering mechanics and Strength of materials during the Preproduction process of various machine elements like bearings, gears, brakes, clutches, springs etc. hence this subject is also called as “Design of machine elements”.

Machine Design Syllabus

Keys and Coupling
Welded Riveted Bolted Joints
Clutches, Chain and Belt Drive
Design of Gears
Design of Bearings

Keyed Joint

➢ The key prevents relative rotation between the two parts and may enable torque transmission. For a key to function, the shaft and rotating machine element must have a keyway and a key seat, which is a slot and pocket in which the key fits. The whole system is called a keyed joint.

Key

➢ A key is a piece of metal usually mild steel inserted between the shaft and hub or boss of the pulley to connect these together in order to prevent relative motion between them.
➢ Keys are used as temporary fastenings and are subjected to considerable crushing and shearing stresses.
➢ A key way is a slot or recess in a shaft and hub of the pulley to accommodate a key.
➢ Key is the weakest element among shaft, assembly and key.

Design of Key

➢ As key is weak in both shear and crushing we need to design accordingly.
➢ Let
❖ d = Diameter of shaft,
❖ L = Length of key,
❖ b = Width of key.
❖ t = Thickness of key, and

➢ Let
❖ T = Torque transmitted by the shaft,
❖ Ft = Tangential force acting at the circumference of the shaft,
❖ Ï„ and Ïƒc = Shear and crushing stresses for the material of key.

➢ Considering shearing of the key, the tangential shearing force acting at the circumference of the shaft :

➢ F = Area resisting shearing × Shear stress.
Ft = (L×b)ÔŽ
➢ Torque transmitted by the shaft.
T = Ft ×d/2 = (L×b)ÔŽ×d/2
➢ From above equation we can find the dimensions of the key

➢ Considering crushing of the key, the tangential crushing force acting at the circumference of the shaft :

➢ F = Area resisting crushing × Crushing stress
Ft = (L×t/2)Ïƒc
➢ Torque transmitted by the shaft
T = Ft ×d/2 = (L×t/2)Ïƒc×d/2
➢ From above equation we can find the dimensions of the key.

Types of Keys

1. Sunk Key
Rectangular, Square, Parallel, Gib Head, Feather, Woodruff

3.Tangent Key

4.Round Key

5.Splines

1.Sunk Keys

➢ The sunk keys are provided half in the keyway of the shaft and half in the keyway of the hub or boss of the pulley.
Rectangular sunk key :
➢ A rectangular sunk key is shown in Fig.
➢ The usual proportions of this key are :
➢ Width of key, w = d/4 ;
➢ Thickness of key, t = 2w/3 = d/6
where d = Diameter of the shaft or diameter of the hole in the hub.
➢ It is tapered along length.

Square sunk key :

➢ The only difference between a rectangular sunk key and a square sunk key is that its width and thickness are equal, i.e. w = t = d / 4

Parallel sunk key :

➢ The parallel sunk keys may be of rectangular or square section uniform in width and thickness throughout.
➢ It may be noted that a parallel key is a taper less and is used where the pulley, gear or other mating piece is required to slide along the shaft.

➢ It is a rectangular sunk key with a head at one end known as gib head. It is usually provided to facilitate the removal of key.

Feather key :

➢ A key attached to one member of a pair and which permits relative axial movement is known as feather key.
➢ It is a special type of parallel key which transmits a turning moment and also permits axial movement.
➢ It is fastened either to the shaft or hub, the key being a sliding fit in the key way of the moving piece.

Woodruff key :

➢ The woodruff key is an easily adjustable key.
➢ It is a piece from a cylindrical disc having segmental cross-section in front view.
➢ A woodruff key is capable of tilting in a recess milled out in the shaft by a cutter having the same curvature as the disc from which the key is made.
➢ This key is largely used in machine tool and automobile construction.

➢ Saddle keys fit in the key-way of the hub only; there is no key-way on the shaft.
➢ The power is transmitted by friction between that inner hollow cylindrical face of the key and shaft.
➢ Saddle keys are suitable for light service or in cases where relative motion between shaft and hub is required for adjustment and the key way cannot be provided on the shaft.

Tangent Keys

➢ The tangent keys are fitted in pair at right angles.
➢ Each key is to withstand torsion in one direction only.
➢ These are used in large heavy duty shafts.

Round Keys

➢ The round keys are circular in section and fit into holes drilled partly in the shaft and partly in the hub.
➢ They have the advantage that their keyways may be drilled and reamed after the mating parts have been assembled.
➢ Round keys are usually considered to be most appropriate for low power drives.

Splines

➢ Sometimes, keys are made integral with the shaft which fits in the keyways broached in the hub.
➢ Such shafts are known as splined shafts.
➢ These shafts usually have four, six, ten or sixteen splines.
➢ The splined shafts are relatively stronger than shafts having a single keyway.
➢ The splined shafts are used when the force to be transmitted is large in proportion to the size of the shaft as in automobile transmission and sliding gear transmissions.

Joints or Fastenings

➢ A fastener or fastening is a component that mechanically joins or affixes two or more objects together to give desired strength or shape to the machine or structure.

The fastenings (i.e. joints) may be classified into the following two groups :

Joints

Permanent Fastenings

The permanent fastenings are those fastenings which can not be disassembled without destroying the connecting components. The examples of permanent fastenings in order of strength are soldered, brazed, welded and riveted joints.

Temporary fastenings

The temporary or detachable fastenings are those fastenings which can be disassembled without destroying the connecting components. The examples of temporary fastenings are screwed, keys, cotters, pins and splined joints.

Riveted Joint

➢ A rivet is a short cylindrical bar with a head integral to it. The cylindrical portion of the rivet is called shank or body and lower portion of shank is known as tail.
➢ The rivets are used to make permanent fastening between the plates such as in structural work, ship building, bridges, tanks and boiler shells.
➢ The riveted joints are widely used for joining light metals.
➢ Rivets are generally specified by Nominal diameter.

Method of Riveting

➢ When two plates are to be fastened together by a rivet the holes in the plates are punched and reamed or drilled and riveted as shown in figure :

➢ The snap heads are usually employed for structural work and machine riveting.

➢ The pan heads have maximum strength, but these are difficult to shape.

➢ The counter sunk heads are mainly used for ship building where flush surfaces are necessary.

➢ Mushroom Head Rivets are used for aircraft, and these rivets are often created using Aluminium alloys, titanium and nickel-based alloys.

Riveted Joints

Type of Lap Joints

➢ Single rivet lap joint
➢ Double rivet lap joint with chain arrangement
➢ Double rivet lap joint with Zig-Zag arrangement

Type of Butt Joint

➢ Single riveted butt joint with single and double cover plate
➢ Double riveted butt joint with single and double cover plate (chain arrangement)
➢ Double riveted butt joint with single and double cover plate (Zig-Zag arrangement)

Lap Joints:

➢ The plates that are to be joined are brought face to face such that an overlap exists.
➢ Single rivet lap joint :
➢ Double rivet lap joint with chain arrangement
➢ Double rivet lap joint with Zig-Zag arrangement

Butt Joints:

➢ In this type of joint, the plates are brought to each other without forming any overlap. Riveted joints are formed between each of the plates and one or two cover plates.
➢ Single riveted butt joint with single and double cover plate :
➢ Double riveted butt joint with single and double cover plate (chain arrangement) :
➢ Double riveted butt joint with single and double cover plate (Zig-Zag arrangement)

Important terms used in riveted joints

Pitch:

➢ This is the distance between two centers of the consecutive rivets in a single row. (usual symbol p)

Back Pitch:

➢ This is the shortest distance between two successive rows in a multiple riveted joint. (usual symbol pt or pb )

Diagonal pitch:

➢ This is the distance between the centers of rivets in adjacent rows of zigzag riveted joint. (usual symbol pd )

Strength of riveted joint

➢ Strength of a riveted joint is evaluated taking all possible failure paths in the joint into account.

Tearing of the plate :

➢ If the force is too large, the plate may fail in tension along the row. The maximum force allowed in this case is :
Pt = Ïƒt(P-d)t
➢ Strength of a riveted joint is evaluated taking all possible failure paths in the joint into account. Here :

Ïƒt = allowable tensile stress of the plate material
p = pitch
d = diameter of the rivet hole
t = thickness of the plate

➢ The rivet may shear as shown in figure. The maximum force withstood by the joint to prevent this failure is.

➢ For lap joint and single strap butt joint :
Ps = ÔŽ(Ï€/4 d2)

Here :
ÔŽ = allowable shear stress of the rivet material
d = diameter of the rivet hole.

➢ For Double strap butt joint :

Ps = 2ÔŽ(Ï€/4 d2)
Here :
ÔŽ= allowable shear stress of the rivet material
d = diameter of the rivet hole

➢ If the bearing stress on the rivet is too large the contact surface between the rivet and the plate may get damaged so the maximum force allowed is

Pc = Ïƒc(Ï€d)t
Here : Ïƒc = allowable bearing stress between the rivet and plate material

Strength of Solid plate (Plate without hole)

Here :

p = pitch
t = thickness of the plate

Efficiency of Joint :

➢ Efficiency of the single riveted joint can be obtained as ratio between the minimum of (Pt, Ps and Pc) and the load carried by a solid plate without rivets.

Efficiency of joint = Pt ,Ps, Pc
Ïƒt P t

Here : Ïƒt = allowable tensile stress of the plate material
p = pitch
d = diameter of the rivet hole
t = of the plate

Imperial Formula for Diameter :

➢ When thickness of the plate (t) is more than 8 mm, Unwin’s formula is used,

d = 5t

Welded Joint

➢ Welding is a very commonly used permanent joining process.
➢ A welded joint has following advantages :
1. Compared to other type of joints, the welded joint has higher efficiency. An efficiency > 95 % is easily possible.
2. Since the added material is minimum, the joint has lighter weight.
3. It is less expensive

Types of Welded Joints

1.Lap or fillet Joints

➢ Single Transverse Lap Joint
➢ Double Transverse Lap Joint
➢ Parallel Lap Joint

2.Butt Joint

➢ Square Butt Joint
➢ V Butt Joint
➢ Double V Butt Joint

➢ Plug Joint

➢ Joggled Welded Joint

Lap or fillet joint:

➢ Obtained by overlapping the plates and welding their edges. The fillet joints may be single transverse fillet, double transverse fillet or parallel fillet joints.
➢ Obtained by overlapping the plates and welding their edges. The fillet joints may be single transverse fillet, double transverse fillet or parallel fillet joints.
➢ Obtained by overlapping the plates and welding their edges. The fillet joints may be single transverse fillet, double transverse fillet or parallel fillet joints.

Butt joint:

➢ Formed by placing the plates edge to edge and welding them. Grooves are sometimes cut (for thick plates) on the edges before welding.
➢ Plain and butt welds may be used on materials up to approximately 25 mm thick.

Important Question on these topics

1.The key will fail in which of the following manner?
(A) Shearing
(B) Crushing
(C) Both crushing and shearing
(D) None of these

2.For a key to be equal strong in shearing and crushing, the width of the key, assuming that the allowable crushing stress is twice the allowable shear stress, should be
(A) 2.5 times its thickness
(B) 2 times its thickness
(C) 1.5 times its thickness
(D) Equal to its thickness

3.Which of the following key transmits power through friction resistance only?
(B) Barth key
(C) Kennedy key

4.A key made from a cylindrical disc having segmental cross section, is known as
(A) Woodruff key
(B) Feather key

5.Rivets are generally specified by
(B) Thickness of plates to be riveted
(C) Length of rivet
(D) Nominal diameter

6.The main part of the rivet does not involve which of the following part?
(B) Shank
(D) Tail

7.The distance between the centres of the rivets in adjacent rows of zigzag riveted joint is known as ________ .
(A) Pitch
(B) Back pitch
(C) Diagonal pitch
(D) Diametric pitch

8.The thickness of a boiler plate is 16 mm, the diameter of rivet used in the boiler joins is
(A) 24 mm
(B) 28 mm
(C) 10 mm
(D) 20 mm

9.The shear strength, tensile strength and compressive strength of a rivet joint are 100 N, 120 N and 150 N respectively. If strength of the unriveted plate is 200 N, the efficiency of rivet joint is:
(A) 60%
(B) 75%
(C) 80%
(D) 50%

10.The shearing strength of a rivet in 50 N/mm2. if the diameter of the rivet is doubled, then its shearing strength will be:
(A) 100 N/mm2
(B) 200 N/mm2
(C) 50 N/mm2
(D) 300 N/mm2

11.In the tearing efficiency of a riveted joint is 60%, then ratio of rivet hole diameter to the pitch of rivets is ______ .
(A) 0.2
(B) 0.33
(C) 0.4
(D) 0.5

12.The types of failure involved in the analysis of the riveted joints are?
1. Shear failure of rivet
2. Tensile failure of the plate
3. Crushing failure of the plate

13.Which of the following statements are is correct for the analysis of the riveted joints?
(A) 1 and 2 only
(B) 2 and 3 only
(C) 1, 2 and 3 only
(D) 1 and 3 only

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