Machine Design Key 2014(1)

Machine Design

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Machine Design

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- A key is defined as a machine element that is used to connect the

Key

transmission shaft to rotating machine elements like pulley, gear, sprocket, flywheel etc. . Keys are used as temporary fastening of shaft and hub

Functions of Keys ¾ The primary function of the key is to transmit the torque from the shaft to the hub of connecting element or vice-versa ¾ The another function of the key is to prevent relative rotational motion & axial movement (except in case of feather key or splines) between the shaft & the joined m/c elements like gear, pulley etc. Shaft Keyed joint

Consisting of

Hub Key

Keyway is a slot or recess on a shaft and or hub to accommodate a key Machine Design

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Key Drawback ¾ The keyway results in stress concentration in the shaft & the part becomes weak Assembly procedure ¾ For mounting a part at any intermediate location on the shaft,, first the key is firmly placed in the keyway of the shaft & then the hub to be mounted is slide from one end of the shaft till it is fully engaged with the key. ¾ After mounting positioning the hub on the shaft, such that both the keyways are properly aligned, the key is then driven from the end, resulting in a firm joint Manufacturing process for keyways ¾ Keyway is usually cut by vertical or horizontal milling cutter in case of shaft ¾ Keyway is usually cut by slotting machine in case of hub

Materials

Plain Carbon Steels like 45C8, 50C4 etc.

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Types of Keyways

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Key Rectangular sunk key or Flat key

Sunk Keys

Square sunk key Gib- head key

Saddle keys

Parallel Key

Taper key

Hollow Saddle Key Flat Saddle Key

Types of Keys Woodruff key

Special Keys

Feather or kennedy key Round key

Splines

Factors are considered for selecting of the type of key for a given application ¾ ¾ ¾ ¾

Power to be transmitted Tightness of fit Stability of connection Cost Machine Design

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Sunk Key

- Half the thickness of the key fits into the keyway on the shaft & the remaining half in the keyway on the hub - Power is transmitted due to shear resistance of the key. The relative motion between the shaft & the hub is also prevented by the shear resistance of key

Square

Rectangular

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Rectangular Sunk Key - Sunk key with rectangular cross-section, is also called Flat Key d=diameter of the shaft = diameter of the hole in the hub

Usual proportions of dimensions of key

b= width of key

b=

h=height or thickness of key l=length of key

2 d d h= b= 4 3 6

l ≥1.5d

Square Sunk Key - Width & thickness are equal Usual proportions of dimensions of key

b=h=

d 4

l ≥1.5d

Check: Check the dimensions considering mode of failure due to shear & crushing N.B: Flat key has more stability as compared with square key Machine Design

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Dimensions of Square & Rectangular Sunk Keys (in mm) [IS : 2293]

Shaft diameter Above

Upto & including

Key size Width × Height

Keyway depth In shaft

In hub

6

8

2×2

1.2

1

8

10

3×3

1.8

1.4

10

12

4×4

2.5

1.8

12

17

5×5

3

2.3

17

22

6×6

3.5

2.8

22

30

8×7

4

3.3

30

38

10 × 8

5

3.3

38

44

12 × 8

5

3.3

44

50

14 × 9

5.5

3.8

50

58

16 × 10

6

4.3

Machine Design

Parallel Sunk Key

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IS: 2048

- is a sunk key (with rectangular or square cross-section) which is uniform in width as well as height throughout the length of key

Taper Key

IS: 2292

- is a sunk key which is uniform in width but tapered in height - Bottom surface of the key is straight & the top surface is given a taper - Standard taper is 1 in 100 Designation of Parallel Sunk Keys Width × Height × Length Example: A parallel key of width 10mm, height 8 mm & a length 50 mm shall be designated as : Parallel key 10×8 ×50 [IS: 2048] Machine Design

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Taper is provide for following two reasons ¾ When the key is inserted in the keyways of shaft and the hub & pressed, it becomes tight due to wedge action. This ensures tightness of the joint in operating condition ¾ Due to taper, it is easy to remove the key & dismantle the joint As compared with parallel key, taper key has following advantages

¾ The taper surface results in wedge action & increases frictional force & the tightness of the joint ¾ The taper surface facilitates easy removal of the key, particularly with gib head

Gib- head Key

IS: 2293

- It is a rectangular sunk key with a head at one end & taper at top surface to facilitate removal At large end,

b=d/4; h=(2/3).b=d/6 Machine Design

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Machine Design

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Gib Head Key

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- Is a key that fits in the keyways of the hub only

Saddle Key

- There is no such keyway on the shaft Hollow Saddle Key

- Fits in a keyway in the hub & the bottom of the key is concave shaped to match the circular/curve surface of the shaft Flat Saddle Key

Hollow Saddle Key

Flat Saddle Key

- Fits in a keyway in the hub & the bottom of the key sits on the flat surface machined on the shaft

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Saddle Key ¾ Friction between shaft, key & hub prevents relative motion between the shaft & the hub. Therefore power is transmitted by means of friction ¾ Saddle keys are suitable for light duty & low power transmission as compared with sunk keys ¾ The resistance to slip in case of flat saddle key is slightly more than that of hollow saddle key. Therefore flat saddle key is slightly superior to hollow saddle key as far as power transmitting capacity is concerned Sunk Key -There is no possibility of the key to slip

around the shaft. -It can be used in medium & heavy duty applications - It is necessary to cut keyways both on the shaft & the hub. Cost is more

Saddle Key -Is liable to slip around the shaft when subjected to heavy torque -It can not be used in medium & heavy duty applications -Requires keyway only on the hub Cost is less Machine Design

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Feather Key

- Is a parallel sunk key that is fixed either to the shaft or to the hub & that permits relative axial movement between them - There is a clearance fit between the key & the keyway in the hub. - The hub is free to slide over the key, at the same time, there is no relative rotational movement between the shaft & the hub - It transmits torque & permits some axial movements of hub

N.B: It is an alternative to splined connection Machine Design

Woodruff Key

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- is a piece from cylindrical disc having segmental cross-section (in the form of an almost semi-circular disk of uniform thickness)

- Keyway in the shaft is in the form of a semi-circular recess with the same curvature as that of the key. The bottom portion of the key fits into circular keyway in the shaft. - The projecting part fits in the keyway in the hub - Once placed in position, the woodruff key tilts & aligns itself on the shaft

The key is largely used on tapered shafts in Automobile & machine tool construction Machine Design

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Woodruff Key

Advantages ¾ Can be used on tapered shaft because it can be aligned by slight rotation in the seat ¾ The extra depth of key in the shaft prevents its tendency to turn over the shaft

Disadvantages ¾ The extra depth of keyway in the shaft increase stress concentration & reduces its strength ¾ The key does not permit axial movement between the shaft & the hub

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Round Key - are circular in section & fit into holes drilled partly in the shaft & partly in the hub - Sometimes the tapered pin is held in tapered holes

It has the advantage that their keyways may be drilled after the mating parts have been assembled

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Splines

- Splines are keys that are made integral with the shaft. Such shafts are known as Splined Shaft - These types of shafts usually have 4, 6, 10 or 16 splines - They are used when there is a relative axial motion between the shaft & the hub and are also used when the force to be transmitted is large in proportion to the size of the shaft as in Automobile transmission & sliding gear transmission. - These types of shafts usually have 4, 6, 10 or 16 splines - Manufacturing Method: Splines are cut on the shaft by Milling the hub by Broaching

Machine Design

Straight Sided Splines

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- Used in gear shifting mechanism in Automobile gear boxes & machine tool gear boxes - Stub teeth with pressure angle 30°

Types of Splines

- Are specified by module

Involute Splines

- Greater strength - Are used in applications where it is important to keep overall size of assembly as small as possible

Serrations

Machine Design

- Used as interferance joint 28

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Design of Sunk Keys Step 1

- Function: Key is used in transmitting torque from a shaft to a hub.

Step 2

Forces acting on a sunk key

The following two types of forces act on the key:

ƒ Forces due to fit of the key in its keyway. These forces produce compressive stresses in the key which are difficult to determine its magnitude and distribution. ƒ Force (P) due to the torque transmitted by the shaft. - The distribution of the forces along the length of the key are not uniform because the forces are concentrated near the torque-input end. Therefore, the stresses are not uniform along the key in the axial direction. - The non-uniformity of distribution is caused by the twisting of the shaft within the hub. Assumption

¾ Forces due to fit of the key are neglected. ¾ The distribution of forces along the length of key is uniform. Machine Design

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Forces acting on Key P’ D P

A P

B C

P’

- The transmission of torque from the shaft to the hub results in two equal & opposite forces denoted by P. - The torque (T) is transmitted by means of a force P acting on the left surface (AC) of the key. - The equal & opposite force (P), acting on the right surface (DB) of the key is reaction of the hub on the key.

- It is observed that force (P) on left surface ‘AC’ and its equal & opposite reaction ‘P’ on right surface DB is not in same plane. Therefore, forces P’ (=P) act as resisting couple preventing the key to roll in the keyway. - The exact location of force (P) on surface (AC) is unknown.

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Forces acting on Key Engineers commonly assume that the entire torque is carried by a tangential force (P) located at the shaft surface. T : Torque transmitted by the shaft (N-mm). P : Tangential force acting at the circumference of the shaft (N). d : Diameter of the shaft (mm). T

T = P× P=

d 2

2T d

Designation of Parallel Sunk Keys Width (b) × Height (h) × Length (l) Machine Design

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Design Analysis Due to the power or torque transmitted by the shaft, the key may fail due to shearing or crushing. Design of sunk key is based on two criteria:

ƒ Failure due to shear. ƒ Failure due to crushing.

T

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Design Analysis Failure due to Shear A

- Shear failure will occur in plane AB.

B

Area resisting shearing: As = b×L T

Shear stress induced in plane AB = τ

τ=

P P = As b × L

τ=

2T ≤ [τ ]key d.b.L

L≥

2T d.b.[τ ]key

L= Effective length of the Key

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Design Analysis Failure due to Crushing - Crushing failure will occur on surface AC or DB. Area resisting crushing: Ac =L×h/2

D A

Crushing stress induced = σc P P σc = = Ac L × h 2

σc = L≥

4T d.h.L

B

C

≤ min. of ( [σc]key, [σc]shaft, [σc]hub)

4T d.h.[σ c ]min

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Design Analysis Main Steps in Design Analysis of Key Step 1

- Either shaft diameter (d) is given or estimate shaft diameter (d).

Step 2

- Select width×height of the key from IS 2293:1963 (Data Book)

Step 3

- Calculate force acting on key.

Step 4

- Calculate effective length of the key (L) based on two design criteria (shear failure & crushing failure) & recommend larger of the above two dimensions.

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Prob#1: It is required to design a sunk key for fixing a gear on a shaft (made of plain C-steel 50C4) of 25 mm diameter. The shaft is transmitting 10 KW power at 720 RPM to the gear (made of same material of shaft). The drive is subjected to medium shocks for which a service factor of 1.5 is to be considered. The key is made of steel 45C8 and factor of safety is 3. Solution

Diameter of the shaft (d)=25 mm Power transmitted by the shaft (Pow)=10 KW. N=720 RPM Pow =

2π NT0 60 × 10000 ; T0 = = 132.63 N − m = 132630 N − mm 2π × 720 60

T = Cs T0 = 1.5 × 132630 N − mm = 198943.6 N − mm Material of the key

Plain C-steel: 45C8, Yield stress Syt=380 MPa, Factor of safety=3

Allowable tensile stress [σt]key=Syt/FOS=127 N/mm2, Allowable shear stress [τ]key=0.5×[σt]key=63 N/mm2, Allowable crushing stress [σc]key=1.25×[σt]key=158 N/mm2, Machine Design

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Material of shaft & hub Plain C-steel: 50C4, Yield stress Syt=460 MPa, Factor of safety=3

Allowable tensile stress [σt]s=Syt/FOS=153 N/mm2, Allowable crushing stress [σc]s=1.25×[σt]s=191 N/mm2. Selection of width×height of the key from IS 2293:1963 (Data Book) For shaft diameter d=25 mm: width (b) × height (h)=8×7 Width of the key (b) =8 mm; Height of the key (h)=7 mm. Failure due to Shear

Shear stress induced in plane AB = τ P P 2T 2T ; τ= τ= = ≤ [τ ]key ; L ≥ ⇒ L ≥ 31.58 mm As b × L d.b.L d.b.[τ ]key

Failure due to Crushing

P P = Ac L × h 2 4T L≥ d.h.[σ c ]min

Crushing stress induced = σc

σc =

σc =

⇒

4T d.h.L

≤ min. of ( [σc]key, [σc]shaft, [σc]hub)

L ≥ 28.78 mm

Effective length of the key=32 mm

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