Keys
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Keys connect functional parts of
mechanisms and machines, allowing moving parts
to transmit power or to locate parts relative to each
other.
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OBJECTIVES OF THIS CHAPTER
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1. Describe several kinds of keys and their
complete geometries.
2. Specify a suitable size key for a given size shaft.
3. Specify suitable materials for keys.
4. Describe splines and determine their torque
capacity.
5. Describe several alternate methods of fastening
machine elements to shafts.
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Types of keys
Round
Kennedy
Woodruff
Square
Cross Section
of Roll Pin
Flat
Tapered pin
Gib-head key
Involute 10 spline
Standard straight 8 spline
Parallel keys.
Key and keyseat applied
to a gear and shaft
Radiused
Chamfered
Square key, Rectangular key
•Radiused keyseats and chamfered keys is used to reduce the
stress concentrations.
•The use of parallel keys, taper keys, gib head keys, pin keys,
and Woodruff keys are used to provide special features of
installation or operation.
•Keyseats in shafts are machined with either an end mill or a
circular milling cutter, producing the profile or sled runner
keyseat.
Dimensions for parallel keyseats
D  D2 W 2
Y
2
Chordal height
S  D Y  H / 2
T=D-Y+(H/2)+C
Depth of shaft
keyseat
Depth of hub keyseat
C = Allowance: + 0.12mm clearance for parallel keys - 0.05mm
interference for taper keys
D = Nominal shaft or bore diameter.
H = Nominal key height,
W = Nominal key width,
Y = Chordal height
Cylindrical and Taper Keys
Cylindrical and Taper keys are designed to be inserted from the end of
the shaft after the hub is in position rather than installing the key first.
The taper extends over at least the length of the hub, and the height, H,
measured at the end of the hub. This design gives a smaller bearing area
on the sides of the key.
Gib head key
Gib head key has a tapered geometry inside the hub that is the same as
that of the plain taper key. The extended head provides the means of
extracting the key from the same end at which it was installed. This is
very desirable if the opposite end is not accessible to drive the key out.
Key types.
(a) Plain taper key (b) Alternate plain taper key
(c) Gib head taper key
Pin Keys
The pin key is a cylindrical pin placed in a cylindrical groove in
the shaft and hub. Lower stress concentration factors result from this
design as compared with parallel or taper keys. A close fit between the
pin and the groove is required to ensure that the pin does not move and
that the bearing is uniform along the length of the pin.
Woodruff Keys
Where light loading and relatively easy assembly and disassembly are
desired, the Woodruff key should be considered. The circular groove in
the shaft holds the key in position while the mating part is slid over the
key.
Selection and Installation of Keys and Keyseats
•The key and the keyseat for a particular application are designed after
the shaft diameter is specified .
•With the shaft diameter, the size of the key is selected from Table 1.
•The key material are specified, and the requirements then be computed.
•The length of a key is specified to be a substantial portion of the hub
length of the element in which it is installed to provide for good
alignment and stable operation.
• Square cut keys are used with the sled-runner-type keyseat.
•The key is sometimes held in position with a set screw in the hub over
the key. Axial location of the assembly provided by shoulders,
retaining rings, or spacers.
MATERIALS FOR KEYS
Keys are most often made from
low-carbon,
higher-carbon steel,
cold-drawn steel,
heat-treated steels
that having an ultimate tensile strength of 420 MPa , a yield
strength of 352 MPa , and a 15% elongation. The actual
material, guaranteed strength of key stock and good ductility
used in critical applications
STRESS ANALYSIS TO DETERMINE KEY LENGTH
There are two modes of potential failure for keys transmitting power:
(1) shear across the shaft/hub interface and
(2) compression failure due to the bearing action between the sides
of the key and the shaft or hub material.
•The reaction force of the hub back on the key then
produces a set of opposing forces that place the key in
direct shear over its cross section, WL. The magnitude
of the shearing force is F = T/(D/2)
•The shearing stress is
•In design, the shearing stress equal to a design stress in shear
for the maximum shear stress theory of failure:
(N - design factor, sy – yield strength ) The required length
of the key is
•The failure in bearing is related to the compressive stress on
the side of the key, the side of the shaft keyseat, or the side of
the hub keyseat.
•The area in compression is A = L* (H/2). The failure occurs
on the surface with the lowest compressive yield strength.
A design stress for compression as σd = sy/N
•The compressive stress is
The required length of the key for this mode of failure:
In typical industrial applications, N = 3 (design factor)
Design Procedure for Parallel Keys.
1. Specify the actual diameter at the location of the keyseat.
2. Select the size and type of the key from standard table.
3. Specify the material for the key.
4. Determine the yield strength of the materials for the key, the shaft, and
the hub.
5. Compute the minimum required length of the key based on shear and
bearing stress. The larger of the two computed lengths governs the
design. The computed length must be less than the hub length.
6. The key should extend over all or a substantial part of the length of
the hub. The keyseat should not run into other stress raisers such as
shoulders or grooves.
8. Complete the design of the keyseat in the shaft and the keyway in the
hub. Standard should be consulted for standard tolerances on
dimensions for the key and the keyseats.
Details for proposed design
of key and keyseats
Hub section at keyseat
Shear and Bearing Areas for Woodruff Keys
B = nominal diameter of the cylinder of
which the key is a part
W = width (thickness) of the key
C = full height of the key
ds = depth of the keyseat in the shaft
Shear area =As
Bearing Area
Ac shaft = 0.5 { G(B/2) - L[(B/2) -ds }
Ac hub = 0.5 {J(B/2) - F[(B/2) - C] } -Ac shaft
G = (π/180)B cos-1 {2[(B/2) - ds]/B}
J= (π/180)B cos-1{2[(B/2) – C]/B}
L  2 d s (B  d s )
 2W d s ( B  d s )
SPLINES
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A spline is a series of axial keys machined into a shaft, with
corresponding grooves machined into the bore of the mating part
(gear, sheave, sprocket, and so on).
• The splines perform the same function as a key in transmitting torque
from the shaft to the mating element.
• The advantages of splines over keys are:
1. A more uniform transfer of the torque and a lower loading on a
given part of the shaft/hub interface result.
2. Splines are accurately machined to provide a controlled fit between
the mating internal and external splines. The surface of the spline is
often hardened to resist wear and to facilitate its use in applications in
which axial motion of the mating element is desired.
3. Splines can be either straight-sided or involute. The involute form is
preferred because it provides for self-centering of the mating element
and because it can be machined with standard hobs used to cut gear
teeth.
Straight-Sided Splines
•Straight splines are made according to the specifications of the Standard
and contain 4, 6, 10, or 16 splines version, D - major diameter, d -minor
diameter, W - spline width, and h - spline depth. There are standard
tables
•The permanent fit, A, is used when the mating part is not to be moved
after installation.
•The B fit is used if the mating part will be moved along the shaft
without a torque load.
•When the mating part must be moved under load, the C fit is used.
The torque capacity for SAE splines is based on the limit of 6895 kPa
bearing stress on the sides of the splines, from which the following
formula is derived:
T=25400NRh (SI)
where N = number of splines
R = mean radius of the splines (mm)
h = depth of the splines (mm)
INVOLUTE SPLINES
(a) Side-fit spline
(b) Major diameter fit spline: Note
chamfer on tips of external spline teeth
Involute splines are typically made with pressure angles of 30°, 37.5°, or
45°. The major diameter fit produces accurate concentricity between the
shaft and the mating element. In the side fit, contact occurs only on the
sides of the teeth, but the involute form tends to center the shaft in the
mating splined hub.
Length of Splines. Common designs use spline lengths from 0.75D to
1.25D, (D is the pitch diameter of the spline). If these standards are used,
the shear strength of the splines will exceed that of the shaft on which
they are machined.
Metric Module Splines.
The dimensions of splines made to metric
standards are related to the module, m, where m=D/Z (mm)
Z is the number of teeth in standards describing metric splines.
Pitch diameter D = mZ, Circular pitch p= πm, Basic tooth thickness
t= πm/2
Standard Modules. There are 15 standard modules:
0.25; 0.50; 0.75; 1.00; 1.25; 1.50; 1.75; 2.00; 2.50; 3; 4; 5; 6; 8; 10.
METHODS OF FASTENING ELEMENTS TO SHAFTS
Pinning
(a) Cylindrical pin
(b) Taper pin
The shear stress in the pin is
4T

2
mZd
T = 2F(D/2) = FmZ, or F = T/D.
d is the pin diameter.
(c) Spring pin
Keyless Hub to Shaft Connections
Locking assembly applied to a gear
Polygon Hub to Shaft Connection
Three-sided P3 external
profile
Four-sided PC4 external profile
Set Screws
A set screw is a threaded fastener driven radially through a hub to
bear on the outer surface of a shaft. The point of the set screw is flat,
oval, cone-shaped, cupped
Taper and Screw
Press Fit
Making the diameter of the shaft greater than the bore diameter of mating
element results in an interference tit. The resulting pressure between the
shaft and the hub permits the transmission of torque at fairly high levels,
depending the on the degree of interference.
Molding
Plastic and die cast gears can be molded directly to their shafts. Often
the gear is applied to a location that is knurled to improve the ability to
transmit torque. A modification of this procedure is to take a separate
gear blank with a prepared hub, locate it over the proper position on a
shaft, and then cast zinc into the space between the shaft and the hub to
lock them together.