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Figure 5.1 shows the geometrical details needed when analysing what happens when a nut is fitted to a bolt and tightened to produce an axial load in the bolt.

Typical values of the friction coefficient for various material combinations and lubrication conditions are given in Table 5.1.

Table 5.1 Typical coefficients of friction, f_t and f_c

Equations 5.3 and 5.4 indicate that for a given bolt diameter and tightening torque, a greater axial load is produced by a fine thread than by a coarse one. After tightening is completed, there will be a residual torque in the bolt, which is given by the expression:

In this condition, the thread is said to be overrunning or overhauling. The limiting case is of interest in the design of power screws, but has no significance in itself where threaded fasteners are concerned. However, it does illustrate that the ratio of unscrewing torque to tightening torque increases, for a given axial load, as the thread helix angle is reduced. In practical terms, this means that a fine thread has better self-locking properties than a coarse one; that is, it is less likely to come undone due to vibration or variable loading.

5.2 Loads And Stresses In Screw Threads

5.2.1 Stresses on Loaded Threads

Conceptually, an axially loaded thread may be imagined to fail by bending or shear at the thread root, or possibly by compressive loading of the loaded flanks (Figure 5.2). In fact, for standard vee-form fastener threads, the second mode of failure is not usually limiting, and the third almost never. The usual failure mode is therefore by bending, although this may not be obvious when examining a stripped fastener, since final gross rupture of the thread may well be by shear.

If the load is applied and the thread dimensions defined as shown in Figure 5.3

The equation for the nominal bending stress is:

For general design of fasteners employing standard vee threads, it is suggested that the critical stresses should be taken as the bending stresses in both the bolt and nut threads, and the tensile core stresses in the various critical sections of the bolt. These stresses may be evaluated and each compared to a value of the material strength, using a safety factor appropriate to the situation.

The values of the stresses calculated using the equations above are purely nominal: no account has been taken of geometrical stress concentrations and the stress has been assumed uniform along the whole loaded length of the thread helix. In practice, both geometrical stress raisers and axial disparity of thread loading are significant, and must therefore be accounted for as indicated below.

5.2.2 Axial Stress Distribution in Loaded Threads

When a bolted joint is assembled and tightened, the bolt is normally loaded in tension and the nut in compression. The bolt thus stretches axially, causing an increase in pitch of the male thread; and the nut compresses, resulting in a reduction in pitch of the female thread. The consequence of these two actions is that the threads near the loaded nut face are forced into much harder contact than the remainder; resulting in a concentration of load, and therefore stress in the thread, in this region - as shown in figure 5.4. Typically, the resulting maximum stress is about three times the nominal stress.

The easiest and most common way to reduce this effect when designing with standard fasteners is to select a material for the nut that it softer than the bolt material. The nut material is chosen so that the highest working stress (based on uniform thread loading) is only slightly below the yield strength. Provided the material is sufficiently ductile, the most heavily loaded nut thread will then yield on application of the load, and permit the remaining threads to do a fairer share of the work. Clearly this method is only practicable if the loading involved can be sustained by the soft nut material, and if the amplitude of any fatigue load at the threads is reasonably small.

5.3 Locking Methods for Threaded Fasteners

In many instances, notably when the fastener is to be pre-loaded (see Sections 3.6 & 4.2), a correctly designed thread will not loosen in service once it has been properly assembled and tightened, even when the bolted joint is subject to vibration or shock loading. Friction at the threads and at the loaded nut and bolt faces resulting from the tensile load in the fastener will be sufficient to prevent loosening, and additional locking devices are neither necessary nor desirable.

However, there are cases in which it is not always possible to maintain loaded contact between the mating threads. This applies particularly where the thread is used as a means of axial adjustment of two components. In such instances, a free-fitting nut will tend to work its way along the bolt, particularly under vibration, and a means of preventing relative rotation of the male and female threads is required. A selection of these is shown in Figure 5.5.

In recent years, mechanical locking methods have given way to anaerobic adhesives, such as 'Loctite', for many applications. The liquid adhesive is applied to one of the threaded components prior to assembly. On assembly, the material fills the clearance between the mating threads and hardens by polymerisation in the absence of air; a reaction which is catalysed by contact with steel but impeded by the presence of oil or grease. These adhesives are available in various strength grades and are cheap, effective and reliable provided the manufacturers recommendations regarding surface preparation and application are strictly observed.