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motor shaft: Not as simple as it looks, The Electrical Apparatus, Sep 2006 by Nailen, Richard L
A look at the physics behind the behavior of a common motor component

DRIVEN FIRST BY WATER POWER, THEN BY steam, machinery ushered in the Industrial Revolution. Yet the height of that development could not be reached until the technology of steel went far beyond the ancient art of sword-making. Steel has become our most widely used metal-yet also one of the most misunderstood.

Even the steel industry's terminology can be confusing. We find "plain carbon" steel contrasted with "alloy steels"; yet all steel is an alloy, and all contains carbon. Strength, corrosion resistance, and magnetic properties of steel all vary not only with chemical composition but also with the manufacturing method and subsequent heat treatment. Even for such an apparently simple application as the electric motor shaft, steel comes in many varieties, confronting the designer with numerous choices.

Only half a dozen standard steels are in common use for rotating machine magnetic core laminations. For structural and machine parts, however, industry standards recognize dozens of different grades, depending upon the mix of alloying elements (mostly carbon, plus manganese, silicon, phosphorous, and sulfur). Heat treating processes (even "hot rolling" versus "cold rolling") can convert many of these into still others. Choosing the "right" steel for a particular use calls for thorough knowledge of such variations, as well as of the relative ease and cost of fabrication and machining.

Stress and strain are of most concern. Apply enough force to any object and it will break. All materials are subject to some stress limit beyond which failure occurs. Anyone working with rotating machinery knows that shaft breakage is not an uncommon occurrence. What is seldom as well understood is that the stresses developed in an electric motor shaft differ in two important ways from mechanical stress affecting many other machine parts. Those differences account for failure modes that sometimes seem difficult to explain.

Types of stress

First, all motor shafts are subject to combined stress. Forces act on a shaft in three directions simultaneously whenever the motor is running. The most obvious one is gravity. At right angles to the axis of the shaft, the weight of the entire rotating assembly imposes two stresses on the shaft material: a shear stress, acting across the cross-sectional area of the shaft where it is supported by the bearings; and a bending stress in the form of tension along one side of the shaft, compression along the other. If the motor is driving its load through belts, chains, or gears, that imposes an added bending force that may be at any angle from 0° to 180° with the gravitational force. The third stress on any motor shaft driving a load is twisting or torsional shear. The resultant stress does not necessarily act in a plane at right angles to the shaft axis, giving rise to the well-known "45 degree" breakage plane.

A second difference from the loading sustained by many other machine elements is that shaft stress always involves reversal or alternation. For example, although the directions of both gravitational and belt loads are fixed, the shaft is rotating. Natural bending and shear stresses therefore reverse in direction for each revolution of the shaft. In reciprocating compressor and some other machine drives involving cyclic torque swings in the drive train, torsional stress also undergoes periodic variation and sometimes reversal.

Whenever a shaft is subject to rapidly cycling stress, it will eventually fail at a stress magnitude well below what it could sustain indefinitely under a unidirectional, steadily applied force. We call this phenomenon fatigue (Figure 1). Shaft designs must be based on relatively low stress levels associated with fatigue life of the material, rather than the strength limit applicable to a steady load.

That design problem is further complicated by keyways in the shaft, which act as stress concentration or intensifying points, as is also true of steps in shaft diameter. (see "Fillet radius versus shaft stress-not a simple relationship" in EA September 2002.)

Metal fatigue

Fatigue is a characteristic most often associated with duc tile material. Ductility is what allows such materials to "stretch" under applied force. The behavior of steel is characteristic. Under increasing stress, the metal can be stretched or compressed but will return to its original dimensions once the stress is removed. If a tensile stress is increased to the yield point,motor shaft, however, steel abruptly elongates to a level from which it will not return. Even though breakage has not yet occurred, the irreversible dimensional change renders the part unusable.

That behavior is expressed by the "stress-strain curve" for steel, a typical example of which appears in Figure 2. The values of yield stress and ultimate breaking strength will vary with the alloy, but both must be taken into account in design.

Combined stress limits as illustrated in Figure 3 are valid for steady loads. For cyclic loading, the fatigue concept applies; shaft stress must be reduced to what's called the endurance limit-that value well below the yield point for which indefinitely long life can be expected. (see Figure 4.)

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