Some of the most common metallurgical failures we encounter involve rotating shafts. Shaft and journal (the part of a shaft supported by a bearing) failures are very common in the pulp and paper and other machinery intensive industries. We thought it might be useful to offer our readers a review of some of the common causes of rotating shaft failures, as many of these failures could be avoided through appropriate engineering and/or manufacturing choices.
Although sometimes fatigue isn't the mechanism, and a shaft will fail as a result of another mechanism, such as simple overload, this is usually the exception rather than the rule. Overload failures generally result from an unexpectedly high stress condition associated with failure of another component or some abnormal operating condition.
The mechanism of fatigue requires the simultaneous presence of three things: 1) there must be cyclic stresses on the component, 2) those stresses must be tensile in nature, and 3) there must be plastic strain. The process of fatigue is considered to consist of three stages: 1) initial fatigue damage (involving plastic strain) leading to crack initiation, 2) crack propagation that continues until the remaining cross section of a shaft (or other component) becomes too weak to carry the imposed loads, and 3) final sudden fracture (stress overload) of the remaining cross section.
Fatigue failures are insidious because the stresses responsible for crack initiation and propagation are generally much lower than the nominal yield strength of the material; fatigue failures often occur under normal operating conditions and are therefore a big surprise to equipment operators, maintenance personnel, and engineers.
Although fatigue failures in rotating shafts often have similar crack propagation and final failure mechanisms, the root cause of each failure (i.e., the conditions responsible for fatigue crack initiation) can vary markedly from failure to failure.
Fatigue failures in shafts nearly always initiate at the surface, generally at points of mechanical or metallurgical stress concentration that locally increase stresses or reduce the material's fatigue resistance. Mechanical stress risers include small fillets, sharp corners, grooves, keyways, and press/shrink fits. (If it were not for stress concentrations, either those designed into a part or those inadvertently caused during manufacturing, many metallurgical consultants would go hungry!) Manufacturing operations such as forging, machining, plating, cladding, and heat treating can introduce metallurgical defects that initiate failure; these metallurgical defects include hydrogen embrittlement, grinding damage, quench cracks, laps/seams, and weld defects. Another very important factor in fatigue initiation is service-related damage caused by corrosion and wear.
RESIDUAL STRESS INTRODUCTION
As we know, all manufacturing processes introduce residual stress into mechanical parts, which influences its fatigue behaviour and breaking strength and even its corrosion resistance. Few metalworking methods exist which do not produce new stresses. The role of residual stress is therefore very important when designing mechanical parts. Over the last few years, an increasing number of studies have been carried out to understand the effects of residual stress on mechanical performance. This article attempts to present a global approach to including residual stress in expected fatigue life calculations, and the possibility of introducing it into mechanical engineering design offices. We will first present the definitions and origins of residual stress according to production methods. We will then show the beneficial and harmful effects of residual stress on the resistance of structures or industrial components depending on whether they are tensile or compressive. The methods used to include residual stress in calculation of the fatigue life will also be analysed. We will lastly show the problems involved in correctly adapting these modelling techniques for use in design offices and the industrial consequences of taking residual stress into account on quality assurance control procedures.
DEFINITION OF RESIDUAL STRESS
Residual stress is usually defined as the stress which remains in mechanical parts which are not subjected to any outside stresses. Residual stress exists in practically all rigid parts, whether metallic or not (wood, polymer, glass, ceramic, etc). It is the result of the metallurgical and mechanical history of each point in the part and the part as a whole during its manufacture. It exists at different levels, generally divided into three, depending on the scale on which the stress is observed :
* 3rd level stress, on the crystal scale. At this level, the outside limit of the notion of stress is reached. It corresponds to the actions created by all the different types of crystalline defects: vacancies, interstitial compounds, substitute atoms, dislocations, stacking defects, twin crystals and grain joints.
* 2nd level stress, due to the heterogeneity and anisotropy of each crystal or grain in a polycrystalline material. In the presence of mechanical stress (uniform traction of a smooth test specimen, for example), certain grains oriented in the right direction will reach the yield point before others, which results in heterogeneous behaviour when the load is eliminated. The resilience will therefore develop differently or more or less freely according to the grains, thus producing non-nil stresses (2nd level residual stress). However, the average of these stresses, that is, the general resultant along the traction axis, will be nil at the end of the test (1st level residual stress). This type of stress can be measured by X-ray diffraction.
* 1st level or macroscopic residual stress, affecting a large number of grains or the whole of the mechanical part. It can be measured using gauges, for example, which detect the deformation produced, or X-rays.
These three types of residual stress occur one after the other. It is first level or macroscopic residual stress which is of interest to mechanical engineers and design offices. However, 2nd level residual stress is also very important, since it is an indicator of strain-hardening and damage to the material .
Summary of motor stresses. Most motor failures are caused by a combination of various stresses that act upon the bearings, stator, rotor, and shaft. If these stresses are kept within the design capabilities of the system, premature failure shouldn't occur. However, if any combination of the stresses exceeds the design capacity, the life of the system may be drastically reduced and catastrophic failure could occur.
These stresses are classified as follows:
* Bearing stresses -
Thermal, dynamic and static loading, vibration and shock, environmental, mechanical, electrical
* Stator stresses -
Thermal, electrical, mechanical, and environmental
* Rotor stresses -
Thermal, dynamic, mechanical, environmental, magnetic, residual, and miscellaneous
* Shaft stresses -
Dynamic, mechanical, environmental, thermal, residual, and electromagnetic
For a more detailed summary of these stresses.
LITTLE LEARNING IS A dangerous thing." So said English poet Alexander Pope in 1711; we've probably all heard it. Although not always "dangerous," incomplete knowledge can certainly be misleading. As an example, consider what's sometimes said about the importance of a proper radius or fillet at the point in a machined shaft where diameter changes abruptly (as at a ball bearing shoulder).
Here are a couple of such comments, from literature on motor repair practices:
"A sharp inside corner concentrates the stresses, resulting in a 40% reduction in strength. . . ."
"A shaft with square corners has 60% of the strength of the smaller diameter."
Although both statements attempt to express a basic truth, neither is correct. The extent to which stress is concentrated at a shaft step is no simple percentage but a highly variable number dependent upon four separate conditions:
* The larger diameter adjacent to the step.
The smaller diameter at that point.
* The fillet radius itself.
* Whether the shaft is stressed in bending, in torsion (twisting), or both.
In general, the smaller the radius, and the greater the difference between the two diameters, the greater the stress concentration factor. That factor is the number by which the calculated stress in the smaller of the two diameters must be multiplied to arrive at the actual stress present. This is nothing new. The principles involved were explained in engineering papers 80 years ago
To put these values in perspective, remember that the fatigue strength of a shaft is inversely proportional to the stress imposed. Thus, if strength is reduced to 60% of its theoretical value, the stress is presumably 1/0.6, or 1.66, times that value. The stress concentration factor is 1.66. As Figure 1 shows, for either type of loading, the actual factor may be far above or far below that number, depending upon the various shaft dimensions. A "square corner" would mean a radius of zero. Though impossible in practice, that would obviously result in a stress concentration factor much higher than 1.66.
Stress may be greatly increased at a diameter change even with a seemingly generous radius. For example, suppose a three-inch diameter is stepped down to 2.5", with a 1/4" fillet radius. The value of D/d is 1.20. From the ratio of r/d as 0.25/2.5, or 0.10, the stress concentration factor is 1.4 in torsion, and 1.7 in bending (the ratio of 1.25 for bending versus torsion is fairly typical). In torsion alone, the fatigue strength of the shaft is thus reduced to 1/1.4, or less than three-fourths what it would be without any stress concentration.
If the step in diameter occurs at a bearing fit, the radius as shown in Figure I cannot exceed a value dependent upon the bearing race dimensions. Otherwise, the bearing cannot seat properly. Two solutions have been popular. One is to undercut a larger radius. This is poor practice, because although the D/d ratios involved are small, the corners are essentially square. Stress concentration factors will be needlessly high.
Most motor shafts are designed with large safety margins. Experienced machinists have developed a good feel for appropriate step machining dimensions. However, a better understanding of just how stresses are distributed in stepped shafts can help avoid trouble when components are applied outside their original design conditions.