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Figure 4.2 sets out the principal steps in designing a bolted joint to sustain fatigue loading. As with the chart at Figure 3.1, users should exercise thought and judgement as they proceed, and some of the steps may need to be iterated several times before a satisfactory solution is obtained.

4.1 Relationship of Fluctuating Loading to Static Loading

It should be noted that Figure 4.2 is essentially an extended version of Figure 3.1 and the extension to the flowchart is concerned with establishing that the bolts have a satisfactory life expectancy. Consequently, most of the early references on the flow chart refer back to Section 3.0. Section 4.0 is concerned, therefore, with guidance on the aspects of fatigue. In order to understand the issues with respect to fluctuating loads, the user is referred back to Section 3.6.1 which should be studied as far as Equations 3.7. The implications of these equations are shown in Figure 4.1. Thus by designing the joint members to be very stiff and the bolt to be resilient and applying a high preload to the bolt so that the joint faces do not separate, a high cyclic external load is 'convertedč to a high steady load on the bolt, upon which is superimposed a very small cyclic load. In this condition, the bolt is much less liable to fatigue failure than if it were subjected directly to the external cyclic load.

4.2 Benefits of Pre-loading the bolt
As a rough indication, the alternating tensile stress that can be sustained by a standard nut and bolt of medium grade steel with machined threads is about 55 N/mm² , based on the core cross sectional area at the bolt thread root. A superimposed mean tensile stress does not greatly alter this value, provided the material yield strength is not exceeded. As we shall see presently, good detail design and the application a pre-load to the bolt by a controlled initial tightening of the nut can allow much of an externally applied fatigue load to by-pass the bolt, and be felt as a reduction in the clamping load on the joined components. For this reason, it is beneficial to apply as high a pre-load as practicable to a bolted joint subject to fatigue. A high pre-load will also help prevent the nut from loosening, by providing a large friction torque to oppose its movement relative to the bolt and mating face of the joint.

Figure 4.2 Flow chart for dynamically loaded bolted joints

4.3. Fatigue strength calculations

Comparison of stresses in the bolted assembly with realistic working values of fatigue strength should be made at all critical sections. As a general rule, this should include the threads in both the bolt and nut, the bolt shank and thread core diameters and the bolt head fillet. Other sections may have to be checked in specific cases.

Details of the procedures and analysis involved in designing against fatigue are set-out in detail in the SEED Engineering Design Procedural Guide ŒShaft with Fluctuating Loads' by W J Beswarick No. MPT 6.2 (ISBN 0 948 673 087) available from SEED Publications Ltd.

It is suggested that a maximum value of preload, Pmax, is made equivalent to a nominal stress at the minimum bolt cross-section of 85-90% of the bolt material yield strength is a good initial choice. The resulting working stresses at all critical points must then be checked against an appropriate fatigue strength, using the Goodman diagram*. It may prove necessary to reduce the preload if the working stress range is high, but it should be noted that a large safety factor is unnecessary, since the Goodman diagram is conservative at high values of mean stress. A safety factor of around 1.2 might be adequate in critical cases.

4.3.2 Stress Concentration in Threads

Any thread comprises a series of notches which act as geometrical stress concentrations which reduce the fatigue strength of the material.

Table 4.2 gives a guide to the fatigue strength reduction factor, K_f, for various thread forms and materials. The figures quoted include an allowance for the notch sensitivity and surface finish of the thread. It will be noted that the reduction in strength is less serious for formed threads (i.e. threads produced by thread-rolling or fluteless tapping) than for machine-cut threads. This is due to the better surface finish obtained and the beneficial effect of the residual compressive stresses resulting from the forming process; a benefit which is largely negated if any post-forming heat treatment or chemical plating is carried out.

Table 4.2 Working fatigue strength reduction factors (K_f) for standard vee threads