Chapter4 第4章

4.1 Uses and Characteristics of Shafting

In a machine, power and/or motion from an electric motor or internal combustion engine is transmitted to an output work site, through shafting and couplings. “Shaft” covers numerous variations, such as axles and spindles. The operational loads on a shaft arise from elements mounted on or attached to the shaft.



Most power transmission shafts are cylindrical ones subjected to loads of torque and bending moments. The loading on the shaft can be various combinations of bending (almost always fluctuating); torsion (may or may not be fluctuating)
Some Typical Shafting Configurations
In practice, shaft are often stepped instead of having a constant diameter.
4.2 Potential Failure Modes

Fatigue is a very important potential failure mode for power transmission shafting. Excessive misalignment may induce failure by forceinduced elastic deformation. Critical speed resonance In summary, the main considerations in designing a shaft are strength, using yield or fatigue (or both) as a criterion; deflection; or the dynamics established by the critical speeds.
max
x 2 xy 2
2

max
16 3 M2 T2 d
Sy

From We obtain
2n

16 d3
M 2 T2
1/ 3

32n 2 2 1/ 2 d (M T ) Sy


4.4 Design for Static Loads

The stresses at the surface of a solid round shaft subjected to combined loading of bending and torsion are:
32M 16T x xy 3 3 d d The maximum shear stress is:
32M n d Se
n
1/ 3

4.6 Shaft design procedure
Common ways of fixing elements on shafts
Steps in Developing a Successful Shaft Design




1.Generate a first conceptual sketch for the shaft. 2. Identify potential failure modes (see 4.2). 3. Select a tentative shaft material (see 4.3). 4. Determine the state of stress at each potential critical point 5. Select an appropriate design safety factor 6. Calculate a tentative shaft diameter for each critical section along the length of the shaft. 7. Check deflections and slopes of the tentative strengthbased shaft design, to assure proper function of shaftmounted components. 8. Check critical speed and vibrational characteristics to assure that resonant vibration does not occur.
Useful Experience-based Guidelines




Try to make the shaft as short, stiff, and light as possible. Try to use a straddle-mounted bearing support configuration if possible. Try to place shaft support bearings close to the lateral bending loads on the shaft. Try to avoid the use of more than two support bearings for the shaft. Try to configure the shaft so that stress concentration sites do not coincide with high nominal stress regions. Consider potential failure problems due to excessive deflection or shaft slope at mounting sites for gears, bearings, sprockets, cams, and shaft seals. Specific manufacturing guidelines should be followed wherever possible.



1. Rigid Couplings
(a) and (b) illustrate the geometry of a simple, flange-type, rigid coupling.
(c) a "ribbed" coupling
Consideration in designing a ຫໍສະໝຸດ igid coupling


4.3 Shaft Materials

Candidate materials for power transmission shafting typically should have good strength (especially fatigue strength), high stiffness, low cost, and, in some applications, good wear resistance. Commonly chosen ones are low or medium-carbon steel, such as 10, 20, or 35 steel, low-alloy steels such as 40CrNi, 38CrMoAlA with appropriate heat treatment; QT450-5, QT600-2 for forged shafting; 20, or 20Cr for case-hardening. If conditions such as corrosive environment or elevated temperature are present, materials such as stainless steel, titanium might be required


Both static and fatigue strength are important for designing a shaft subjected to static stresses, completely reversed stresses, and repeated stresses, at the same time.
Chapter 4 Power Transmission Shafting, Couplings, Keys and Splines



4.1 Uses and characteristics of shafting 4.2 Potential failure modes 4.3 Shaft materials 4.4 Design for static loads 4.5 Reversed bending and steady torsion 4.6 Shaft design procedure 4.7 Couplings, keys, and splines
Here, Sy is the yield strength, n is safety factor.
4.5 Reversed Bending and Steady Torsion
32M a d3

16T m 3 d

Experimental evidence shows that bending-fatigue strength is not affected by the existence of torsional mean stress until the torsional yield strength is exceeded by about 50 percent. Then Se a or
4.7 Couplings, Keys, and Splines

Basic design requirements for couplings. Rated shaft torque must be transmitted without slip Premature failure must not be induced in any part of the operating machine. To prevent premature failures, couplings need to accommodate shaft misalignments to which parallel centerline offset, nonparallel (angular) centerlines, or both may contribute.


1. Shear and bearing in the key 2. Shear and bearing in the flange attachment bolts, including the influence of flange bolt preloading and/or bolt bending, if applicable 3. Bearing on the flange at attachment bolt interfaces 4. Shear in the flange at the hub