In elasticity, stress concentration refers to the phenomenon of localized stress increases within an object, typically occurring at locations where the object's shape changes abruptly, such as notches, holes, grooves, and areas with rigid constraints. Stress concentration can lead to fatigue cracks and static fracture in parts made of brittle materials. The maximum stress at a stress concentration point, known as the peak stress, depends on factors such as the object's geometry and the loading method. The locally increased stress decreases rapidly with increasing distance from the peak stress point. Because the peak stress often exceeds the yield strength, causing stress redistribution, the actual peak stress is often lower than the theoretical peak stress calculated using elasticity principles.
For motor products, when the shaft has different cross-sectional dimensions, stress will concentrate at the point of abrupt change in cross-sectional area, which is the weakest point of the entire shaft. To improve this phenomenon, fillets are used at the points of abrupt change in cross-sectional area to transition and improve the overall strength of the shaft.
For shaft components subjected to alternating bending and torsional stresses (such as stepped shafts and crankshafts), their working capacity is typically determined by their ability to resist fatigue failure caused by alternating stresses. Practice has shown that fatigue failure often occurs at stress concentration points during operation, specifically at the transition corners of shaft components. Therefore, various measures are frequently employed in shaft structural design to reduce stress concentration and ensure the shaft's fatigue strength. The main measure to reduce stress concentration on a shaft is to increase the radius of the transition arc at the corner; generally, design specifications stipulate that the radius of the transition arc should not be less than 0.05 times the shaft's diameter.
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Measures to reduce and avoid stress concentration
To avoid damage to materials or components caused by stress concentration, the following measures are mainly taken in engineering:
● Surface strengthening. Treatments such as shot peening, rolling, and nitriding can improve the fatigue strength of material surfaces.
● Avoid sharp corners. Replace sharp corners with rounded corners and appropriately increase the radius of the transition arc for better results;
● Improve the shape of the part. A shape with a gradually changing radius of curvature is beneficial to reducing the stress concentration factor. The ideal approach is to use a streamlined profile or a hyperbolic profile, the latter of which is easier to apply in engineering.
● Local reinforcement at the edge of the hole: Using a reinforcing ring or making local thickening at the edge of the hole can reduce the stress concentration factor. The degree of reduction is related to the shape and size of the hole, the shape and size of the reinforcing ring, and the type of load.
● Appropriately select the location and direction of the opening: The location of the opening should avoid high stress areas as much as possible, and the stress concentration factor should be increased due to the mutual influence between the holes. For elliptical holes, the major axis should be parallel to the direction of the external force, which can reduce the peak stress.
●Increase the stress in the low-stress area, reduce the thickness of the part in the low-stress area, or add notches or round holes in the low-stress area to make the transition of stress from the low-stress area to the high-stress area more gradual.
● Utilizing residual stress: When the peak stress exceeds the yield limit, unloading will generate residual stress. Reasonable utilization of residual stress can also reduce the stress concentration factor.
Stress mitigation measures adopted in the design phase
At abrupt changes in size, the absence of fillet transitions can lead to an infinite increase in stress during finite element analysis. In fact, in structural design, there are some basic design principles to reduce stress concentration factors, which are briefly described below:
Modify shape
● Fillets: Sharp corners are absolutely prohibited in structural components. Theoretical analysis shows that when the radius of curvature of a fillet approaches zero, its stress concentration factor approaches infinity. Replacing sharp corners with fillets effectively mitigates stress concentration.
● Streamlined design. For tension or compression members with variable cross-sections, a streamlined transition can make the stress in the member more uniform, thus avoiding stress concentration.
● Elliptical holes. While ensuring the normal operation of the component, changing a round hole to an elliptical hole can often improve the component's strength.
Stress control methods during drilling
● Stress concentration factors should be selected in areas of low stress. For example, when drilling holes, avoid placing them on sections with the greatest bending moment; also, avoid placing them near edges.
● Consider whether there will be interference between the hole and the parent material, leading to increased stress. If the hole is located very close to the edge, the stress concentration problem will be exacerbated.
● When drilling long holes, choose a hole whose long axis is aligned with the long side of the substrate to reduce stress.
● Adding more holes near the machined holes will also reduce the stress coefficient.
● Removing a certain thickness of material from the top and bottom of the hole reduces the stiffness of that area, thus mitigating stress concentration. In these diagrams, the last case has the lowest stress concentration factor.
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