UNTHREADED FASTENERS (Hub/shaft assemblies)
Dismountable =Temporary assemblies
A
Positive lock assemblies - torque transmitted by shape
Shear transmitted torque
Keys
Splines
Poligons
Pins
Rotation
B
Retaining ring
Translation
Friction assemblies - torque transmitted by friction
Taper shaft
Taper rings
nov. 2005
1/40
Interference
(press-fitted)
Traian CICONE
KEYS – Generalities I
Prismatic parts, partly mounted in the shaft (in keyseats) and partly in the hub (in keyways),
Parallel key
Shear
transmitted
torque
(square or flat key)
feather key
l
Woodruff key
nov. 2005
b
h
2/40
Traian CICONE
1
KEYS – Generalities II
b
l
b
l
h
Taper key
h
Plain taper key
Gib head taper key
``
HUB
Taper on hub side
HUB
Plain taper key
Thin taper key
SHAFT
SHAFT
Wedging effect
SHAFT
Mt
Mt
Gib-head – dangerous !
Gib-head used to drive out the key
Concave Taper key
HUB
No keyway on shaft !
Concave key
SHAFT
SHAFT
Mt
nov. 2005
3/40
Traian CICONE
PARALLEL KEY on the shaft
Type A key
Threaded blind
holes for end-cap
(washer)
nov. 2005
Type B key
Shaft shoulder
(step)
End-part
shaft
Threaded
centering hole
4/40
Traian CICONE
2
KEYWAYS & KEYSEATS
nov. 2005
5/40
Traian CICONE
PARALLEL KEY - Geometry
h
most used the cheapest
b
standardized function of shaft diameter
l
leff
Type A
leff=l-b
b
h
Type B
b
leff=l
Type C
b
leff=l-b/2
b
leff
l
nov. 2005
6/40
Traian CICONE
3
KEYSEATS - Technology
Parallel keyseat
End-milled, double ended
End-milled, single ended
Plane keyseats
Milling
Disc keyseat
Sled-runner, single ended
Closed (rounded end) keyseats
nov. 2005
7/40
Traian CICONE
PARALLEL KEYS - Stresses
h
Ft
Ft
l
Mt
Ft2
σk
d
b
Mt
SHAFT
leff
σk
Ft1
HUB
t1
t2
Assumptions
Tightly fitted to prevent rolling
nov. 2005
t1 = t 2 = h 2
8/40
Ft1 = Ft 2 = Ft = 2M t d
Traian CICONE
4
PARALLEL KEYS – Shear Stress
h
Shear failure
τs =
Ft
≅
Ashear
2M t
dbl eff
Ft
τa=70-120MPa
b
b
Type A
b
Type B
b
Type C
πb
Ashear = bl eff +
Mt
2
4
h
Ashear = bl eff = bl
Ashear = bl eff +
b
t1 t2
πb 2
8
l
nov. 2005
9/40
Traian CICONE
PARALLEL KEYS – Contact Stress
h
2M t
Ft =
d
Ft
Bearing failure
σk =
Ft
Abearing
=
c
2Mt
4Mt
≅
d (t1 −c)l eff dhl eff
σk
b
Mt
σk
t1 t2
static
σk=100-150MPa
nov. 2005
mobile
σk=20-40MPa
10/40
Traian CICONE
5
PARALLEL KEYS - Design considerations
4M t
dhl eff
Bearing failure
σk ≅
Shear failure
2M t
τs ≅
dbl eff
σ k > 2τ s
h ≅ 0.8b
BUT
σ ak ≈ 1.4τ as
b ≈ 0.25d
from standard
b×h
Given shaft dia, d
l eff >
Bearing failure
prevails
4M t
dhσ ak
leff standard
nov. 2005
11/40
Traian CICONE
Key
Keyway
b
d
b
h
Length
no
mi
nal
Clearance (sliding free)
on shaft N9
fro
m
on hub D10
on shaft N9
Pressed
fit
on hub
D10
on shaft
& hub, P9
±0.0180
-0.015
-0.051
t2 (in the hub)
t1 (in the shaft)
Nominal
Tolerances
Tolera
nces
Nominal
from
up
to
22
30
8
7
18
90
8
30
38
10
8
22
110
10
38
44
12
8
28
140
12
44
50
14
9
36
160
14
50
58
16
10
45
180
16
58
65
18
11
50
200
18
7
65
75
20
12
56
220
20
7.5
4.9
75
85
22
14
63
250
22
9
5.4
85
95
25
14
70
280
25
9
5.4
95
110
28
16
80
320
28
10
6.4
110
130
32
19
90
360
32
11
7.4
130
150
36
20
100
400
36
12
150
170
40
22
100
400
40
170
200
45
25
110
450
45
15
200
230
50
28
120
500
50
17
nov. 2005
up
to
Normal fit
+0.036
0
+0.043
0
+0.052
0
+0.062
0
+0.098
+0.040
+0.120
+0.060
+0.149
+0.065
+0.180
+0.080
0
-0.036
0
-0.043
0
-0.052
0
-0.062
12/40
±0.0215
± 0.0260
±0.0310
-0.018
-0.061
-0.022
-0.074
-0.026
-0.088
4.0
3.3
5.0
3.3
5.0
3.3
5.5
3.8
6.0
13
Tolerances
4.3
+0.2
0
4.4
+0.2
0
8.4
+0.2
0
9,4
10,4
+0.2
0
11,4
Traian CICONE
6
PARALLEL KEYS - Design solutions
Key length > Hub width
2 or 3 keys in parallel
non-uniform
pressure repartition
ltot=1.7×l
ltot=2.2× l
nov. 2005
13/40
Traian CICONE
PARALLEL KEYS - Conclusion
Good load capacity
Positive Features
Simple technology
Standardized
Easy and rapid assembly
Easy & accurate calculation
High stress concentration (Kσ ≈ 2÷3)
Shortcomings
Do not ensure centering
Not recommended for frequent axial motion (translation on shaft)
SPECIFICATION
type b × h × l
Example A12×10 ×50
nov. 2005
14/40
Traian CICONE
7
multiple feather keys
nov. 2005
SPLINES
15/40
SPLINES
Traian CICONE
Classifications
SHAPE
rectangular
involute
triangular
Serrations
Straight sided
MOTION
Mobile
nov. 2005
Stationary
16/40
Traian CICONE
8
SPLINES
SPECIFICATION
z×d×D +l
contact length
number of splines
rectangular
Straight sided - SERIES
d
Heavy
D
Medium
Light
Example
8×42 ×46
8×42 ×48
10×42 ×52
b=8mm
b=8mm
b=6mm
nov. 2005
17/40
Traian CICONE
SPLINES
CENTERING
side/flank fit
•Difficult to finish
major (outer) dia fit
•Difficult to finish
•Good for alternate rotation
or frequent shock loading
nov. 2005
minor (inner) dia fit
The cheapest
Easier finishing technology
18/40
Traian CICONE
9
SPLINES - Technology
Broaching ring for
sizing involute or
serrated splines.
De-burring cutter
for removing
burrs/fraise on
external splines
hobbing or milling
broaching
Male `push broach' for
cutting fine internal splines.
 UKAS Calibration
nov. 2005
19/40
Traian CICONE
SPLINES - Stresses
2M t
Ft 1 =
ϕ dm z
b
c×45°
Ft1
D+d
2
ϕ ≅ 0.75
dm ≅
Ft1
dm
d
Mt
D
Non-uniform
load repartition
c×45°
h
b
Shear failure
Ft 1
Ft 1
2M t
=
≅
τs =
Ashear b l ϕ d m z b l
Bearing failure
σk =
nov. 2005
Ft 1
Abearing
=
Ft 1
lh
=
Ft 1
4M t
=
D
−
d

 ϕ d m z l (D − d − 4 c )
− 2c 
l
 2

20/40
Traian CICONE
10
BALL SPLINES
Friction-free linear motion while simultaneous torque transmission
µ=0.005
Straight ground grooves
nov. 2005
21/40
Traian CICONE
NON-CIRCULAR CONNECTIONS - Polygon Assemblies
Generalities
Bearing failure
Worn shaft
High load capacity
Positive Features
Favorable load distribution - length of contact reduced
Reduced backlash
Shortcoming
nov. 2005
Machining
22/40
Traian CICONE
11
POLYGON ASSEMBLIES - Stresses
a0 = a − 2c
a 
1
M t = 4 F1 a*l = 4 σ k max 0 a*l
2
2
l- contact length
c×45°
a
Bearing failure
Mt
12 M
σ k max = 2 t
na0 l
a0
Shear failure - shaft
σk max
a
1
F1 = σ k max 0
2
2
nov. 2005
a* =
2 a0
3 2
23/40
F1
a*
Traian CICONE
PINS – Types & functions
LOCATION
Interference
How can be firmly located a pin?
Grooved & knurled pin Grooved & ribbed pin
Taper pin
nov. 2005
24/40
Traian CICONE
12
PINS – Types & functions
Unique tolerance
for the “shaft” –
φ8h7
Interference
Dowell pins
Close running fit
φ8D7/h7
Centering
φ8M7/h7
Interference fit
nov. 2005
25/40
Traian CICONE
PINS – Types & functions
Elasticity
Slotted spring pin
Spiral spring pin
nov. 2005
26/40
Traian CICONE
13
PINS – Types & functions
ARTICULATION
Dowell pin
Retaining ring
Clevis pin
Groove
Cotter pin
nov. 2005
27/40
Traian CICONE
PINS - Failure mode
Axial
location
nov. 2005
28/40
Traian CICONE
14
PINS for articulations
Pin loading in a cylindrical articulation
F
σk1
σk1
σk2
dp
l1
l2
l1
F/2
σ k1 =
Bearing pressure
F
< σ ak
2 d p l1
F
σ k2 =
< σ ak
d pl 2
τs =
Shear stress
nov. 2005
F/2
F /2
π d 2p 4
< τ as
29/40
Traian CICONE
Transverse Pin (Cylindrical cross-pin)- torque transmitting
D−d
F1 = σ k1
dp
2
Uniform pressure distribution
x1 =
PIN/HUB -
PIN/SHAFT Triangular pressure distribution
Moment equilibrum
Shear stress
x2 =
d
3
F2
F1
Ft
σk2
1
d
F2 = σ k 2 max d p
2
2
dp
σk2
M t = 2 F2 x2 = 2 F1 x1
σ k 2 max =
Bearing pressure
σk1
d+D
4
σ k1 =
Ft
6M t
d 2d p
(
F1
F2
σk1
Mt
D
4M t
D −d2 dp
2
d
)
4M t
Ft
τs =
=
2
π d p 4 π d d p2
Ft =
2M t
d
ASSUMPTIONS
Press-fitted in the hub
Sliding-fit in the shaft
nov. 2005
30/40
Traian CICONE
15
Longitudinal Pin (Pin Key ) - torque transmitting
Pin tightly fitted
dp
Ft
d
Ft
leff
Mt
Mt
Uniform pressure distribution
Bearing pressure
F
σk =
Ft
4M t
=
l eff d p 2 d d p l eff
2M
t
t
Shear stress τ s = d l = d d l
p eff
p eff
nov. 2005
31/40
Traian CICONE
RETAINING RINGS - Assemblies
External retainer ring
nov. 2005
32/40
Traian CICONE
16
RETAINING RINGS - Assemblies
Internal retaining ring
nov. 2005
33/40
Traian CICONE
RETAINING RINGS
Internal & External
External
Internal
• Also known as snap rings.
• Provides a removable shoulder to lock components on shafts or in bores.
• Made of spring steel, with a high shear strength.
• Stamped, bent-wire, and spiral-wound.
• Standardized (ring & groove) function of shaft/bore diameter.
nov. 2005
34/40
Traian CICONE
17
RETAINING RINGS - Installation
Installation and assembly pliers
nov. 2005
35/40
Traian CICONE
RETAINING RINGS & CIRCLIPS
nov. 2005
36/40
Traian CICONE
18
RETAINING RINGS
nov. 2005
37/40
Traian CICONE
RETAINING RINGS - Stresses
σk =
Bearing pressure
ring
Shear stress
Fa
π d1s
τs =
Fa
Fa
πdg
g
s
F
a
shaft τ s = π d n
1
m
n
d1
d
Bending
d2
1
1
M
=
−
EI z d 2 + b d + b
2
2
M = Wzσ b
nov. 2005
I z = Wz
b
2
d − d2 ≈ b
d (d + b ) ≈ d
2
b
d 
2
σ b ≅ E  <
38/40
σY
2
most important
Traian CICONE
19
RETAINING RINGS - Design considerations
from standard
Given shaft dia, d
Check
or catalogue
• ring & groove dimensions
• maximum thrust load supported, Fmax
Fmax > Fa
Stress concentration (Kσ ≈ 1.8÷2.2)
For low thrust forces some other simple solutions are available
(setscrews + collars)
nov. 2005
39/40
Traian CICONE
Axial Location
Hitch Pins
Collar & setscrew (grub screws)
Internal
nov. 2005
40/40
Traian CICONE
20