7 Torque Control of Preload
7.3 THINGS THAT AFFECT THE TORQUE–PRELOAD RELATIONSHIP
Now let’s take a closer look at some of the many factors which affect the amount of initial preload we get when we tighten a fastener. Many of these factors were included in our discussion in Chapter 6—and in the block diagram of Figure 6.28—but we’ll consider them at greater length now, and will add some new ones!
7.3.1 VARIABLESTHATAFFECTFRICTION
The coefficient of friction is very difficult to control and virtually impossible to predict. There are some 30 or 40 variables that affect the friction seen in a threaded fastener [30]. These include such things as
Inclined plane (10%) Thread
friction (40%)
Nut friction
(50%)
FIGURE 7.2 Relative magnitudes (typical) if the three reaction torques oppose the input torque applied to a nut.
Hardness of all parts Surface finishes Type of materials
Thickness, condition, and type of plating, if present
The type, amount, condition, method of application, contamination, and temperature of any lubricants involved
Speed with which the nut is tightened Fit between threads
Hole clearance surface pressures Presence or absence of washers Cut versus rolled threads
A word about the last item, cut versus rolled threads. Ron Winter of Tennessee Eastman has presented data showing the results he obtained by tightening separate groups of bolts: one group having cut threads, the other rolled threads. The bolts with rolled threads achieved a higher average preload for a given torque, and the bolt-to-bolt preloads were less scattered than the bolts with cut threads. Since a lower average and more scatter are characteristic results for any effect which increases thread friction, I assume that this item should be included in the above list.
In any event, you can see that there are many factors that affect friction, and therefore preload. Some of these factors can be controlled to some degree—but complete control is impossible.
Together, all of the factors listed above determine what I call ‘‘control accuracy,’’ the ability of the variable we’ve selected for control—in this case, torque—to create the thing we’re after, which is always preload. As far as torque is concerned, conventional wisdom—
and much experience—suggests that a given torque will create a given initial preload with a scatter of +30% in a large group of as-received bolts.
7.3.2 GEOMETRICVARIABLES
Friction is often cited as the only villain in the torque–preload equation, but that is not the case. Although we think we know the pitch of the threads, or the half-angle, or the effective contact radii between parts, in practice we have surprising variations in all of these things.
The bolt is not a rigid body. It is a highly stressed component with a very complex shape and severe stress concentrations. The basic deformation is usually elastic, but there are always portions of the bolt—for example, in thread roots and the like—which deform plastically, altering geometric factors rtand pitch.
The face of the nut is seldom exactly perpendicular to the axis of the threads. Holes are seldom drilled exactly perpendicular to the surface of the joint, so contact radius rnis usually unknown. Some experiments indicate that these factors can introduce even more uncertainty than does friction.
The Bolting Technology Council (now Committee F16.96 of the ASTM) sponsored a research study of the torque–preload relationship [29]. The study was done at E´ cole Poly-technique in Montreal. The purpose of the study was to find an economically viable way to conduct bolting experiments, the problem being that very large numbers of variables are often going to affect results.
Eleven variables that were believed to have a significant impact on the torque–preload relationship were selected for the E´ cole Polytechnique study. Taguchi methods were used to statistically design the experiment. The variables chosen included ‘‘perpendicularity.’’
Some bolts were tightened against parallel joint surfaces; others were tightened against joints having a 58 taper. Results of the experiment, which were confirmed by a second round, showed that perpendicularity affected the amount of preload achieved for a given torque more than did any other variable—including whether or not a lubricant had been applied to the threads and nut face.
7.3.3 STRAINENERGYLOSSES
All of the above variables are at least visible in the long-term equation. There are other sources of error, however, to which this torque–balance equation is blind. When we tighten a nut, we do work on the entire nut–bolt–joint system, as we saw in Chapter 2. Part of the input work ends up as bolt stretch or friction loss, as suggested by the long-form equation; but other portions of the input work end up as bolt twist, a bent shank, nut deformation, and joint deformation. The ‘‘true’’ relationship between input torque and bolt preload, therefore, must take these outputs into account, as we attempted to do in Equation 2.29. In one extreme case, for example, if the threads gall and seize, input torque produces just torsional strain and no preload at all. The long-form equation would suggest that all is lost in thread friction torque for this situation (infinite coefficient of friction in the threads). This isn’t true, but thread friction torque is a twist component, so the equation doesn’t lie. It’s just that the result is strain energy, not heat. In fact, I don’t mean to imply that the torque–balance equation is incorrect. It does, indeed, describe the action and reaction torques on the system correctly. But you will get into trouble if, as is common, you then add, ‘‘every part of the input energy which is not converted to preload must end up as friction loss because the equation shows only preload or friction terms.’’
The torques are only cam action or friction torques, but what this means from an energy distribution standpoint is not revealed by the torque equation.
7.3.4 PREVAILINGTORQUE
Another factor not included in the long-form equation is prevailing torque: the torque required to run down a lock nut which has a plastic insert in the threads, for example. The insert creates interference between nut and bolt threads, and thereby helps the fastener resist vibration. The torque required to overcome this interference doesn’t contribute to bolt stretch. It might be considered an addition to the thread friction component of torque, but it is a function of the design of the lock nut, and of the materials used, as well as the geometry, so it’s best handled as a separate term, as suggested below:
Tin¼ FP
P 2pþ mtrt
cos bþ mnrn
þ TP (7:3)
where TP¼ prevailing torque (lb-in., N mm), and all other terms were defined earlier.
Note that the prevailing torque is not a function of preload, the way all the other terms are. Note too that prevailing torque may not be a constant; it may change as the lock nut is run farther down the bolt, or is reused.
7.3.5 WEIGHTEFFECT
Heavy or misaligned joint members resist being pulled together. This may not affect the torque–preload relationship, but it will reduce the amount of input torque, which ends up as clamping force between joint members.
7.3.6 HOLEINTERFERENCE
If the hole is undersize or misaligned it will take some effort merely to pull the bolt through the hole. This, too, can reduce the amount of torque available to create bolt preload.
7.3.7 INTERFERENCEFITTHREADS
If threads are damaged, or if they’re designed to have zero clearance, it can take some torque to run the nut down on the loose bolt.
7.3.8 THEMECHANIC
Lest we forget, there are people involved here too. The results we get for a specified torque will depend very much on whether or not the person using the wrench has been well trained, knows what he’s doing, cares about doing it right, can reach the bolts easily, can see the dial gage on his wrench, etc. The operator can be a more important factor than all of the others combined.
7.3.9 TOOLACCURACY
We must also remember that tools aren’t perfect. They will produce a requested torque with some tolerance or error, depending upon their construction, the accuracy with which the gage reports their output, how recently they have been calibrated, etc.
7.3.10 MISCELLANEOUSFACTORS
There are many other factors that have been found to have some effect on the torque–preload relationship. Joseph Barron of the Newport News Shipbuilding Co. reported on a situation in which a regular hex nut, being used without a washer in an oversized hole, dug into the surface of the joint ‘‘like a plow.’’ That would drive the nut factor through the roof. Many other, more common, factors have been identified, which have generally a smaller effect than the ones listed above. Some years ago, for example, R. Stewart of the Wright-Patterson Air Force Base gave me a list of 75 variables, which they had found had a statistically significant impact on the torque–preload relationship [30]. The list included most—but not all—of the factors listed above, plus things like type, thickness, and consistency of plating; the type of bolt head; the treatment of the hole, hole finish, hole concentricity, hole size, countersunk angle; gaps; burrs; type of wrench used to tighten the bolts; whether it was torqued from head or nut ends; number of times the bolt and nut had been used; number, type, and size of the washers used if any; etc. The list ended with item 76: ‘‘Any combination of the above.’’
The E´ cole Polytechnique study mentioned above also included, as test variables, such factors as lubricant, grade of bolt, type of wrench used, whether or not the fastener was covered with rust, whether or not it was plated, the number of times it was tightened, full versus partial thread engagement, and the stiffness of the joint in which the bolts were tightened. All were found to have some effect on the amount of preload achieved for a given torque, but most had a relatively—and sometimes surprisingly—small effect. Corro-sion, joint stiffness, and amount of thread engagement were expected to have a fairly large effect, for example, but did not.
Since each of the effects listed above is itself affected by many secondary variables, you can see that literally hundreds of factors can influence the results when we tighten a single bolt. As we saw in the last chapter, additional factors—such as elastic interactions—further complicate our lives when, as usual, we tighten not just one but a group of bolts.