What’s Wrong With My Bolts?
EP Editorial Staff | April 16, 2018
Investigations of two real-world mysteries help explain why bolts can be too loose or too tight.
By Randall Noon, P.E.
Preventing bolts from becoming too loose and discouraging personnel from over-tightening them can prove to be challenging. These two true stories and details about the physics that determine whether a bolt is properly installed will help you solve your own bolting mysteries. Names, of course, have been changed to protect the innocent.
Let’s start with Acme Power Co. After several years of good service, its diesel-engine-generator set began to exhibit bolting issues. During a maintenance teardown and reassembly, several bolts were found to have loosened after only about a week of running time. A check of the quality-assurance (QA) records from the previous engine reassembly and follow-up interviews with maintenance personnel revealed that, in every case, the problem bolts had been tightened to the requisite torque specification. There was no reason to doubt this.
Apex Industries Co. was also dealing with bolting issues. Its problem, though, wasn’t loose bolts, but rather those that were too tight.
Bolt threads in some of the company’s equipment were found to be galled, stripped, and, in some cases, showing cracks between the bolt heads and shanks. A check of QA records and personnel interviews confirmed that the bolts had been tightened as specified—and no more than that. There was no mistake about this.
In each of these situations, the same bolts were being reused on the respective machinery. Furthermore, both companies verified that all problem bolts were original with the equipment. No incorrect substitutions had been made. So, what was going on?
Most machine designers go to a lot of trouble to ensure that the torque-tightening specifications for a particular bolted joint are sufficient to, among other things, keep a bolt from loosening, backing off, breaking, galling, and having threads stripped. Occasionally, however, after a machine has been disassembled and reassembled a few times, bolt problems begin to occur—even when torque-tightening specifications are meticulously followed.
In the process of tightening to create a clamping force, a bolt is stretched. This causes a tensile stress to be developed across the bolt shank. For the bolt to function as desired, the designer requires it to be stretched until it has reached a certain amount of tensile stress.
Tensile stress is best determined by actually measuring the elongation in the loaded portion of the bolt as it is tightened. Elongation is a direct measure of material strain that can readily be converted into a stress number by Hooke’s Law. This method, though, requires access to both ends of the bolt, accurate instrumentation, a skilled person, and a bit of time. As such, this method isn’t amenable to normal maintenance work.
The more common way of determining and setting the clamping force in a bolted joint is to measure the torque applied to tighten the bolt. Tightening torque is directly related, at least algebraically, to the amount of tensile stress created in the bolt and is readily measured with a calibrated torque wrench. For reasons that will be explained later, the error associated with this method, however, can be as high as +/-30%. (That’s why, in some structural applications, torque tables are not allowed.)
While the torque measurement itself is relatively easy to accomplish with good accuracy, the actual clamping force resulting from the tightening torque can be significantly higher or lower than the desired clamping force. Of course, the whole point of the design is to obtain the correct clamping force.
Equation 1 is commonly used to determine how much torque is needed to accomplish a certain clamping force in a bolted joint. Observe that there are two main components in the equation (see italicized text underneath the equation):
• the amount of torque needed to overcome friction between the engaged threads as the bolt is stretched
• the amount of torque needed to overcome friction between the bolt collar and the mating surface under the bolt collar.
T = applied tightening torque
F = clamping force
dp = pitch diameter of bolt
µ = coefficient of friction of bolt and material in the threaded area
µc = coefficient of friction between the bolt collar and the material
α = radial angle of the thread
λ = thread lead angle
Of all the factors in Equation 1 that are needed to determine the necessary tightening torque, only two are actually variable: the overall coefficient of friction between the engaged threads and the overall coefficient of friction between the bolt collar and the material surface.
The other factors in Equation 1, such as thread pitch diameter, thread lead angle, collar diameter, and thread radial angle, are automatically determined by the choice of bolt.
In most cases for UNC and UNF bolts, for example, the value for the radial angle α is 30 deg., so
cos 30 deg. is 0.866. If, say, there are 12 threads/in.
on a bolt, then tan λ is 1/12 or 0.0833. Likewise, if there are 8 threads/in., tan λ is 0.125, and so on. With this information in mind, we can see that, when otherwise identical bolts are compared to each other, Equation 1 can be simplified as Equation 2 below (if there are 12 threads/in. and the radial angle is 30 deg.)
K = (0.5m + 0.036)/(0.866 – 0.0833µ) + 0.625µc = torque coefficient
d = nominal bolt diameter
F = clamping force
T = applied torque
Equations 1 and 2 show the importance of the bolt-collar component. It’s not unusual for, perhaps, 40% of the required tightening torque to be due to the friction between the bolt collar and the bolted material, and 60% due to the friction between the engaged threads.
For a bolt with 12 threads/in. and a radial angle of 30 deg., Fig. 1 shows a plot of the coefficient of friction µ versus the resulting torque coefficient K. The plot assumes that the engaged threads and the bolt-collar contact area have the same coefficient of friction, i.e., µ = µc . Be aware, however, that while this may often be the case, it isn’t always so.
The inaccuracy of Equations 1 and 2 with respect to torque and its resulting clamping force occurs because the two coefficients of friction can vary significantly due to, among other things:
• less than full contact between engaged surfaces
• degree of surface roughness between the mating surfaces
• presence of a lubricant
• non-presence of a required lubricant
• wrong lubricant
• surface dirt
• surface corrosion
IN THE FIELD
Coefficients of friction (COFs) aren’t usually measured in the field during maintenance work—and torque specifications aren’t then re-computed based upon the newly measured COFs prior to tightening a bolt. A bolt’s COF is generally assumed.
When the initial torque-versus-clamping-force computation is done, the designer typically assumes the mating surfaces are smooth and clean, and that the machined surfaces are within the usual manufacturing tolerances. In other words, the designer assumes that the coefficients of friction match those listed in a COF bolt reference table.
If any lubricant is specified, the designer also assumes that the correct lubricant is evenly spread over all the contacting surfaces in such a thickness as to match his “COF with lubricant” values in a reference table.
Bear in mind, though, that reference-table numbers are typically an average of many tests. That means the values are statistical in nature. Any one specific COF bolt test can differ from the next one—and differ from the average of the lot that was tested.
Further, field conditions don’t always match conditions under which testing was done to prepare the COF reference table. This is especially true after bolts have been in service for a time, frequently tightened and loosened, and exposed, when not in use, to various conditions.
Consider, for example, the differences between non-lubricated and lubricated installations of the same bolt. If a steel-on-steel dry COF of 0.20 is assumed for the threads and collar, and the bolt has 12 threads/in., then the torque coefficient K in Equation 2 computes to 0.285.
If, on the other hand, a lubricant is applied to the threads and bolt collar so that the COF between surfaces is 0.15, then the torque coefficient computes to 0.224.
To achieve the same clamping force in the same bolted joint, the non-lubricated bolt requires 27% more tightening torque than its lubricated counterpart.
Conversely, if the same tightening torque is used in both cases, the non-lubricated bolt will have only 79% of the clamping force of that of the lubricated bolt. This reduced amount of clamping force may then be sufficiently low enough to allow the bolt to loosen when vibrations are present.
Now consider what occurs when old bolts are reused. Compare an old bolt, that has surface rust, adhesive chemical remnants, or otherwise has become discolored due to surface corrosion, to a new bolt. In most cases, the COF of the old bolt will be higher than that of a “fresh from the box” new one. If a new, non-lubricated bolt, for example, has a COF of 0.2, the corresponding K torque coefficient is 0.285. If a rusted or discolored version of the same bolt has a COF of 0.3, the corresponding K torque coefficient is 0.41 (refer to Fig. 1).
If a rusty or discolored bolt is tightened to the same torque specification intended for a new bolt, Equations 1 and 2 indicate that the resulting clamping force in the rusty or corroded bolt will be about 30% less than the clamping force produced with a new bolt.
Thus, the rusty bolt will result in a looser clamping force than the designer specified. As a result, it may be able to back off/loosen if the applied vibrations occurring in service are sufficient.
Remember the original problem with the loose bolts in Acme Power’s diesel-engine-generator set? Personnel had installed them without lubrication, as prescribed by the manufacturer. They also ensured there was no residual lubrication on the threads and collars by wiping them with soft, white, cotton cloths—every time. And, as noted previously, they were careful to torque the bolts as specified.
Unfortunately, each time the equipment was disassembled, the bolts were stored in a bucket in a hot, humid area. Over time, their exterior surfaces developed a visible patina, something that could have been easily detected by comparing the old bolts to those fresh from the box.
Further, the thread and collar mating surfaces had become roughened as the bolts were repeatedly tightened and loosened. Close inspection of these surfaces with a 20X hand lens found that the mating surfaces of the old bolts were pitted and abraded. They no longer looked like the smooth surfaces of new bolts.
In other words, the COF had increased such that the resulting tensile stress preload in the bolt was below design requirements. When the engine operated, the alternating vibratory forces were sufficient to cause some of the bolts to loosen.
As for Apex Industries’ problem of overly tight bolts, the OEM had specified that the bolts be installed dry, i.e., without lubrication. That’s why Apex personnel had been consistent in cleaning the bolts with alcohol and wiping the threads and collars with clean cotton cloths prior to reassembly.
Observations of maintenance work had found that during disassembly, the crew used various penetrating oils and lubricants to remove the bolts and prevent galling. Unfortunately, while the bolts themselves were thoroughly cleaned of residual lubricant before they were re-used, no one considered that penetrating lubricant might still remain in the bolt holes.
Despite the fact that the bolts had been cleaned, the mating female threads within the bolt holes were still lubricated by the penetrating oil that had been silently collecting in the bottom of the holes. As a bolt was tightened, that residual lubricant spread onto its previously cleaned threads.
In the end, when a bolt was tightened to the specified torque, the resulting clamping force was higher than the design value—and some of the bolts were damaged. EP
Randall Noon is a registered professional engineer and author of several books and articles about failure analysis. He has conducted root-cause investigations for four decades, in nuclear and non-nuclear power facilities. Contact him at firstname.lastname@example.org.