Stress shaft

Torsional stresses are developed when power is transmitted through shafts. In addition, the tooth loads of gears mounted on shafts create bending stresses. Shaft design, therefore, is based on safe limits of torsion and bending. 

Material Shaft Design Tensile Stress Shaft Design Shear Stress Blade Design Stress ... 

Sophisticated stmctural analysis techniques make it possible to determine both the amount and exact orientation of reinforcement that the product wQl need to meet the critical stresses in actual service. Hybrid reinforcement systems containing different fiber compositions with different properties are being increasingly used. For example, hybrid carbon and glass fiber automotive drive shafts are in commercial use. 

A useful simphfication of the total energy equation applies to a particular set of assumptions. These are a control volume with fixed solid boundaries, except for those producing shaft work, steady state conditions, and mass flow at a rate m through a single planar entrance and a single planar exit (Fig. 6-4), to whi(m the velocity vectors are perpendicular. As with Eq. (6-11), it is assumed that the stress vector tu is normal to the entrance and exit surfaces and may be approximated by the pressure p. The equivalent pressure, p + pgz, is assumed to be uniform across the entrance and exit. The average velocity at the entrance and exit surfaces is denoted by V. Subscripts 1 and 2 denote the entrance and exit, respectively. 

Belts should not be tightened more than necessary, otherwise the drive and the driven shafts will come under torsion and excessive bending moment. The bearings would also be subjected to excessive stresses. 

Note The shaft deflection should not be more lhan 11% of the air gap between the stator and the rotor. For loads that exert more force and torsional stress on the motor shaft and bearings than is permissible, due to the larger width of pulleys which may shift the... 

The stress in the crank shaft is calculated approximately from the power and speed as follows. Bear in mind that approximate calculations of this sort may be in error by up to a factor of 2 - but this makes no difference to the conclusions reached below. Referring to Fig. 16.9 ... 

This stress is only a quarter of the yield stress of a typical structural steel, and the shaft therefore has an ample factor of safety against failure by plastic overload. 

The second failure mode to consider is fatigue. The drum will revolve about once every second, and each part of the shaft surface will go alternately into tension and compression. The maximum fatigue stress range (of 2 x 56 = 112 MPa) is, however, only a quarter of the fatigue limit for structural steel (Fig. 28.5) and the shaft should therefore last indefinitely. But what about the welds There are in fact a number of reasons for expecting them to have fatigue properties that are poorer than those of the parent steel (see Table 28.1). 

Fig. 28.8. Exaggerated drawing of the deflections that occur in the loaded drum. The shaft deflects under four-point loading. This in turn causes the end plates to deflect out of plane, creating tensile (-r) and compressive (-) stresses in the weld.

Expander-compressor shafts are preferably designed to operate below the first lateral critical speed and torsional resonance. A flame-plated band of aluminum alloy or similarly suitable material is generally applied to the shaft in the area sensed by the vibration probes to preclude erroneous electrical runout readings. This technique has been used on hundreds of expanders, steam turbines, and other turbomachines with complete success. Unless integral with the shaft, expander wheels (disks) are often attached to the shaft on a special tapered profile, with dowel-type keys and keyways. The latter design attempts to avoid the stress concentrations occasionally associated with splines and conventional keyways. It also reduces the cost of manufacture. When used, wheels are sometimes secured to the tapered ends of the shaft by a common center stretch rod which is pre-stressed during assembly. This results in a constant preload on each wheel to ensure proper contact between wheels and shaft at the anticipated extremes of temperature and speed. 

Component reliability will vary as a function of the power of a dimensional variable in a stress function. Powers of dimensional variables greater than unity magnify the effect. For example, the equation for the polar moment of area for a circular shaft varies as the fourth power of the diameter. Other similar cases liable to dimensional variation effects include the radius of gyration, cross-sectional area and moment of inertia properties. Such variations affect stability, deflection, strains and angular twists as well as stresses levels (Haugen, 1980). It can be seen that variations in tolerance may be of importance for critical components which need to be designed to a high reliability (Bury, 1974). 

It is required to find the torque without slippage that can be transmitted by a hub that is assembled by an interference fit to a powered shaft. The hub outside diameter D = 070 mm, and the shaft diameter d = 050 mm, as shown in Figure 4.55. The length of the hub is 100 mm. Both hub and shaft are machined from hot rolled steel SAE 1035 with a yield strength Sy A(342,26) MPa (see Table 4.6). Given that the hub is stopped suddenly in service due to a malfunction, and considering only the torsional stresses, what is the probability that the shaft will yield ... 

The radial pressure is not eonstant over the length of the hub, but in faet peaks at the projeeting portions of the shaft whieh resist eompression resulting in an inereased pressure at the ends of the hub, or stress eoneentration. For this reason, fretting fatigue failure may be antieipated when the applied torque is alternating. 

M = applied torque D = shaft diameter L = loading stress. 

Hysteretic whirl. This type of whirl occurs in flexible rotors and results from shrink fits. When a radial deflection is imposed on a shaft, a neutralstrain axis is induced normal to the direction of flexure. From first-order considerations, the neutral-stress axis is coincident with the neutral-strain axis, and a restoring force is developed perpendicular to the neutral-stress axis. The restoring force is then parallel to and opposing the induced force. In actuality, internal friction exists in the shaft, which causes a phase shift in the stress. The result is that the neutral-strain axis and neutral-stress axis are displaced so that the resultant force is not parallel to the deflection. The... 

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