MECH 2410 Machi Ma chi ne Desig Desig n
Lectur e 7 Sha Shaft ft Design
1
Content Shaft Layout Shaft Design Procedure Associated Parts Design Des ign Procedure
Keys
Couplings
2
1
Shaft and Axels
Shaft is a rotating member and it provides axis of rotation for gears, pulley, flywheels, cranks, sprockets. Axels are non rotating rotating member, member, carries no torque torque and it is used to support rotating wheels.
3
Example: Gear Gear Bo x
4
2
Shaft Sizing Considerations Stress Analysis In design it is usually possible to locate the critical areas, size these to meet the strength requirements, and then size the rest of the shaft to meet the requirements of the shaft-supported elements. Deflection and Slope They are a function of inertia. Inertia is a function of Geometry. For this reason, shaft design allows a consideration of stress first. Then, after tentative values for the shaft dimensions have been established, the determination of the deflections and slopes can be made.
5
Example: Drawing
3
Shaft Layout: Shoulder It allows precise positioning Support to minimize deflection. In cases where the loads are small, positioning is not very important, shoulders can be eliminated.
7
Shaft Layout: Bearing In most cases, Only two bearings should be used in most cases. Load bearing components should be placed next to the bearings to minimize the bending due to large forces. Shafts should be kept short to minimize bending and deflection.
8
4
Shaft Layout: Mounting Elements
Shaft Layout: Mounting Elements
10
5
Shaft Layout: Mounting Elements Spacer
11
Shaft Layout: Transmit Power Keys
6
13
Shaft Layout: Transmit Power Spline
7
Shaft Layout: Transmit Power Pulley
15
Shaft Layout: Transmit Power Coupling - Rigid
F
T
Dbc / 2 F
As d
2T
T
2
N ( d / 4)
2
Dbc N ( d / 4)
8T
Dbc N d
16
8
Shaft Layout: Transmit Power Coupling - Flexible
17
Shaft Layout: Transmit Power Coupling - Flexible
18
9
Shaft Layout: Transmit Power Coupling – Universal Joint
19
Shaft Design Procedure Determine the rotational speed of the sha ft Determine the power or the torque to be transmitted by the shaft Determine the design of the power-transmitting components or other devices that will be mounted on the shaft, and specify the required location of each device Specify the location of bearings to support the shaft
The reactions on bearings supporting radial loads are assumed to act at the midpoint of the bearings
If thrust (axial) loads exist in the shaft, you must specify which bearing is to be designed to react against the thrust load
Bearings should be placed on either side of the power-transmitting elements if possible to provide stable support for the shaft and to produce reasonably well-balanced loading of the b earings
The bearings should be placed close to the power-transmitting elements to minimize bending moments
The overall length of the shaft should be kept small to keep deflections at reasonable level
20
10
Shaft Design Procedure Propose the general form of the geometry for the shaft, considering how each element on the shaft will be held in position axially and how p ower transmission from each element to the shaft is to take place.
21
Shaft Design Procedure
22
11
Shaft Design Procedure Determine the magnitude of torque that the shaft sees at all points. It is recommended that a torque diagram be prepared. Determine the forces that are exerted on the shaft, both radially and axially. Resolve the radial forces into components in perpendicular directions, usually vertically and horizontally. Solve for the reactions on all support bearings in each plane. Produce the complete shearing force and bending moment diagrams to determine the distribution of bending moments in the shaft.
Spur Gear Forces Directions of the forces are essential for the accurate analysis of stress in a shaft.
12
Shaft Desig n
When vertical shearing force is the only significant loading
When bending stress is repeated and reversed as the shaft rotates, but the torsional shear stress is nearly uniform
sn'
snC m C st C R C s
sn:
endurance Strength sn’: effective endurance strength Kt: stress concentration factor Cm: material factor, Cst: type of stress factor CR: desired reliability factor, Cs: Size factor
25
Stress Concentration Factor, Kt
Retaining Ring Grooves: Kt = 3. Then add 6% to determine the nominal size for the shaft. www.efatigue.com/constantamplitude/stressconcentration/
13
Shaft Design Procedure Select the material from which the shaft will be made, and specify its condition: cold-drawn, heat-treated, and so on. As indicated in Table 2– 9, suggested steel materials for shafts are plain carbon or alloy steels with medium carbon content, such as SAE 1040, 4140, 4340, 4640, 5150, 6150, and 8650. Good ductility with percent elongation above about 12% is recommended.
Shaft Design Procedure Determine the ultimate strength, yield strength, and percent elongation of the selected material. Determine an appropriate design stress, considering the manner o f loading (smooth, shock, repeated and reversed, o r other). Analyze each critical point of the shaft to determine the minimum acceptable diameter of the shaft at that point in order to ensure safety under the loading at that point. In general, the critical points are several and include those where a change of diameter takes place, where the higher values of torque and bending moment occur, and where stress concentrations occur. Specify the final dimensions, surface finishes, tolerances, geometric dimensioning details, fillet radii, shoulder heights, keyseat dimensions, retaining ring groove geometry, and other details for each part of the shaft, ensuring that the minimum diameter dimensions are satisfied.
14
Exampl e 12-1
Design the shaft shown. It is to be machined from SAE 1144 OQT 1000 steel. The shaft is part of the drive for a large blower system supplying air to a furnace. Gear A receives 200 hp from gear P. Gear C delivers the power to gear Q. The shaft rotates at 600 rpm. DA = 20.00 in, DC = 10.00 in. Pressure angle = ϕ = 20°
Exampl e 12-1 Material properties: sy = 83000 psi, su = 118000 psi, percent elongation is 19%. Using Figure 5–8, we can estimate sn = 42000 psi.
15
Exampl e 12-1 Km = Kst = 1.0, Cs = 0.75, CR = 0.81 s′ n = snCsCR = (42 000)(0.75)(0.81) = 25500 psi
Exampl e 12-1
16
Exampl e 12-1
17
36
18
Exampl e 12-1
Key Design Process Design Shaft, specify the diameter Select the key size from the given table. For diameter 6.5 in or less, use square key. For diameter greater than 6.5 in, use rectangular key Specify key material, usually ANSI 1020 CD steel. Determine yield strength of the material Determine the minimal length. If the length is longer than hub length, select higher strength material or multiple keys Select the actual length of the key, make sure key seat does not run into other parts Complete the design of shaft and keyway in the hub
38
19
Key si ze vs. Shaft Diameter
39
Keys: N = 3 for r egular indu strial applications
Shearing Stress
F
T
d
Compression Stress
D / 2 F
As
2T
T
( D / 2)WL
0.5S y / N
F
DWL
d
Ac
4T
T
( D / 2) L( H / 2)
DLH
S y / N 40
20
Spline
41
Spline Design
T 1000 N
( D 2
2
d )
8
N: number of splines The society of Automotive Engineering (SAE) specifies the torque capability for splines is based on the limit of 1000 psi bearing stress on the sides of the splines
42
21
