Author Archives: Peak innovations Engineering

Threaded Fastener Loosening

A common frustration of threaded fastener suppliers is their customers pointing to their fastener as the cause of their joint loosening problems. Even when the problem is failure from fastener fracture, in the vast majority of instances the fastener meets all specifications and the root cause of their problems is the joint design or assembly process. Furthermore, even when the customer believes the solution lies in altering their installation torque, the end result can still result in a phone call to the fastener supplier because the corrective action may be counter-intuitive. Reducing installation torque for fasteners that fracture in the field can create larger problems when the cause is fatigue failure generated by insufficient clamp load. Likewise, when a joint doesn’t clamp-up sufficiently because the parts are deflecting or yielding under the clamp load, increasing the installation torque is not going to produce a happy ending. While joint design and fastener installation are generally not the responsibility of the fastener distributor, being able to associate common problems with their root causes and solutions helps speed troubleshooting and lends added technical credibility.

While a wide variety of loading profiles can cause fastener loosening, it is understood that forces which lead to slipping of the clamped parts relative to one another will cause the most dramatic losses. The force that resists loosening is generated by friction between the mating threads and between the bolt or nut and the mating part. In the standard bolted joint this resisting force is directly proportional to bolt tension – the greater the elongation of the bolt, the greater the friction force available to resist loosening. Because resistance to loosening decreased bolt elongation, the common occurrence of joint relaxation due to embedment within the joint stack will leave the joint more susceptible to loosening. The following flowchart identifies these three primary means of preventing threaded fastener loosening and lists specific remedies under each of the three headings.

threaded fastener loosening

Written by Dave Archer
Principal Engineer for Peak innovations Engineering

Thinking About the Unthinkable

Fastener Magazine ArticleRecently, I was asked to serve as an expert witness in a case where a catastrophic bolted joint failure led to severe, debilitating injury. The discovery phase, where information is requested and where people are deposed under oath, is a sobering, expensive and time-consuming process for all on its receiving end. I came to realize that, if considered before it was a required activity, product liability can serve as an excellent framework from which to review your processes and decision-making. That is ask yourself the question, “How would I fair if all my business practices and decisions came under critical scrutiny?” And if you are a fastener distributor, as most of you reading this column likely are, this question does apply to you. Supplying components carries certain responsibilities, and the legal process has an ability to cast a wide net when questioning.

Dave Archer

Dave Archer is president of Archetype Joint, LLC, a provider of engineering and testing services focused on joint design and development. Dave founded Archetype Joint in 2004 as a natural progression of his experience in the development of efficient designs, having held senior consulting positions with the founding companies of the design for manufacture and assembly and the lean design movements. Dave previously held design and manufacturing engineering positions with major industrial equipment manufacturers and defense contractors. In addition, he has privded independent design services and has been named in several patents on products successfully introduced into the marketplace.

A member of SME and SAE, Dave holds a bachelors degree in Mechanical Engineering & Applied Mechanics and a master’s degree in Manufacturing Engineering from the University of Rhode Island. He is interested in hearing from your and appreciates your feedback.

The first and most obviously responsibility of the distributor is to deliver to the customer the component that was requested, in all aspects of its specification: size, grade, finish, etc. While no delivery error is desirable, the errors that are not readily detectable can be the most dangerous. For example, while the incorrect nominal diameter or thread pitch probably would be discovered at assembly and not installed, the bolt that is 1/8” too short might not, and that reduction in thread length could compromise the joint. Even bolts that are slightly too long can have the same effect by raising the possibility that installation torque will be reached due to reaching the end of the thread rather than the desired clamp load. Of course, the most insidious errors usually occur when stocking or picking errors are not visually apparent but can have significant consequence on joint integrity. Supplying a washer of a lower grade than intended is a common example. Another less common but potentially dangerous example is supply a conical lug nut with the cone angle incompatible to the wheel’s nut seat. Even supplying fasteners with incorrect finishes can impact joint integrity by changing the torque-tension relationship, resulting in potentially harmful changes in clamp load or fastener elongation. The inventory control software most distributors have incorporated in their operation cuts down on human error, but it doesn’t eliminate it. Utilizing part numbers that integrate a code that provides size/grade/finish allows easier verification. More aggressive strategies, such as totally segregating grades or finishes in different stocking locations, only carrying one finish within a category, or ensuring that different grades or finishes have an obviously different appearance, may appear too extreme at first glance. However, some distributors’ sale profiles, this leaning out could actually benefit the bottom line.
The fact that a distributor may not be involved in the production of the products they sell does not in itself absolve them of legal responsibility if an action involving their application is initiated. Again, a simple proactive action is to consider how you would respond if deposed tomorrow and asked questions such as:

  • How do you choose your suppliers?
  • Have you ever visited your suppliers’ manufacturing facilities?
  • Do you have a copy of their quality management system?
  • How can you verify the product you receive meets the required specifications?
  • Do you have the means of independently?

American Fastener JournalThe trend for distributors to provide a wider range of services to their customers from inventory control to application support is quickly becoming a minimum requirement to service even medium-sized accounts. While the application advice may be “free” to the customer, it could be very expensive for the distributor if a claim is made on a product that was influenced by that advice. This can be a particularly tricky situation for distributors because it is rare that all inside and outside personnel who could be asked for application advice have the depth of knowledge to provide educated answers. However, they probably all will want to be helpful. Consciously planning who will provide application support, the extent of that support, and how the interaction will be documented is time well spent.

In closing, while luck certainly plays a role in whether a product liability action visits your door, you can certainly influence your luck by planning and preparation. The difference in deposition testimony between those who have considered the nuts and bolts of legal responsibility and those who haven’t is painfully obvious. I only hope to remind the reader, as I was reminded that these innocuous commodities we deal with every day, which are invisible to most people due to their abundance and their apparent simplicity, are in reality both patent and fickle in their influence and behavior.



Written by Dave Archer
Principal Engineer for Peak innovations Engineering

Comparing the Cost of Securing Sheet Metal Panels

One of the more common fastening tasks for OEMs is attaching cover panels to a fabricated frame. In some cases these panels are designed to be removable, but in most cases they are permanently joined or are fastened by not intended to be removed in normal use. In a cost-reduction study we conducted not long ago, we compared the cost of securing sheet metal panels to a welded tubular frame by various methods. We wanted to expand and generalize that study to make it applicable to a wide range of American Fastener Journal readers. In this article, we compare the cost of fastening or joining a plain sheet panel using the methods listed in Table 1. These methods are not all-inclusive and were selected because they do not require high levels of capital investment in process or material handling equipment. In these cases, comparative costing tends to be function of calculating return on capital investment on equipment whose implementation is too specialized to be considered in an article on costing guidelines.


As a practical necessity, we will need to make several assumptions regarding the component configuration and assembly conditions on which the estimates are based. Because these assumptions will have a significant impact on the cost estimates generated, the results of this study should be thought of as only a starting point for process selection. These assumptions are summarized in Table 2.

Comparative Basis

Before a cost comparison can be undertaken, a fundamental aspect of joint requirements must also be assumed. For each of the joining and fastening methods selected the basis for determining the coverage or pitch needs to be determined. In other words, is the distance between rivets or the percentage full perimeter a bead of adhesive is applied established base on the need to simply hold the panel in place without objectionable gap, or is it a minimum strength requirement? We felt that providing some indication of equivalent strength would be of value and based the estimates on equivalent shear strength.

When used to secure thin panels, it is unlikely that fastening and joining methods will be capable of achieving their full shear or tensile strength before joint failure. This is because deformation of the sheet material either causes the sheet to pull out from under the fastener head, or it puts a bending load on the fastener due to eccentric loading from the inboard side of the panel causing sheet bending. This effect reduces actual performance of adhesives as well because it causes the bond to be loading peel rather than pure shear or tension. We selected shear rather than tensile loading as the basis for comparison as it is probably more common case, and actually loading is closer to what would be expected in theory in comparison to assumption of tensile loading. In order to minimize the over-estimate of each method’s capacity, we selected fastener sized that were on the small end of the range of what might be used for these applications.

Based on the assumptions made in Table 2, the absolute and relative shear strength of the securing methods are shown in Table 3. The column at right shows the quantity of fasteners or tack welds that would be needed to provide the same shear strength for each inch of bond line. Because adhesive isn’t applied on a unit basis, it was decided to use the length of the adhesive bond line as the basis to calculate the quantity of welds or fasteners required to achieve equivalent strength.

Labor Estimates

Based on the assumptions in Table 2 and the relative shear strength of Table 3, the estimated labor required to secure the panels in the two scenarios presented are summarized in Table 4.

Material Cost

The price paid for hardware, adhesive or consumables is, of cours, highly dependent on the annual volume required. For the purpose of this type of comparative study, it is probably more important to be accurate in relative costing as it is in absolute terms. For this reason, all materials were priced at the same national industrial supply company, so the markup is kept consistent. Our experience is that a good estimate for what the low- to mid-volume manufacturer might pay for hardware is to take the retail price from an industrial supply house and discount it by 20%. Using that formula resulted in the material costs shown in Table 5.


We applied a $35/hr labor rate to time estimate in Table 4 and extended the material cost by the required quantities. The tabular cost summaries are shown in Table 6 and graphed in Figure 1 and Figure 2.

Discussion of Results

As seen when comparing Figure 1 and Figure 2, the total costs of the two scenarios are very similar because the quantities required are very similar (25% of the perimeter of a 24” x24” panel is very similar to 50% of a 12” x 12” panel). The epoxy joint does not behave in the same manner because the labor required to prep the panel in the first scenario was the same in all three cases. An important point should be made regarding the equivalent strength assumption. This assumption results in fastener counts higher than would ordinarily be used – up to 82 per panel, as shown in Table 7. Even so, in most cases the fastened joints were more cost-effective due to the higher setup and cleaning cost of adhesives. Had #12 drill screws and ¼” rivets been used, the fastening costs would have been relatively lower still. However, this also points out that bonded joints can achieve very high strength relative to fastened or tack welded joints when they are utilized as intended, with 100% bond coverage. When this level of strength is actually required, a bonded planar joint will generally be more cost-effective than a fastened joint. In fact, if cleaning wasn’t included, the 24” x 24” 100% bonded joint would have bad a lower cost than tack welded joint.

*Click Here to View/Download a Printable PDF of this Case Study.*

Table 1 Table 2 Table 3 Table 4 Table 5 Table 6 Table 7

Written by Dave Archer
Principal Engineer for Peak innovations Engineering

New Location in Machesney Park, IL

The transition from Archetype Joint to Peak innovations Engineering also brought a change in physical location. We are now proudly located about 1.5 hours west of Chicago in Machesney Park, IL.

Peak Testing Helped Fastener Distributor Save Customer $24,950

solar panelsChallenge:

A fastener distributor had a customer that was using liquid adhesive during the assembly process of gearboxes for solar panel tracking. The adhesive was allowing for variation in clamp load, slow production time, and messy application. The distributor was recommending a pre-applied adhesive patch to replace the liquid adhesive and needed validation testing to compare the two applications. The distributor had an engineering staff and testing capabilities, but the validation testing needed was not available in-house and so the distributor went to Peak innovations Engineering.


Peak provided the validation testing that the fastener distributor needed by using a torque-angle to failure test. The test results showed that the pre-applied adhesive patch provided consistent joint performance, reduced assembly time, had excellent loosening resistance, better quality joint and no mess.


The software at Peak allowed for detailed analysis with minimal time and effort. The fastener distributor would not have been able to do this testing without Peak. The Peak software and capabilities allowed the fastener distributor to get a better understanding of the threshold point for the joints in the gearbox, and ultimately provide their customer with a more confident recommendation.

Going from liquid adhesive to a pre-applied adhesive patch:
• Eliminated application time
• Eliminated application labor cost $22,200
• Eliminated mess
• Reduced chance of warranty issues
• Increase revenue
• Improved consistency of the joint
• Total cost savings to customer: $24,950

Testing Services Provided:

• Torque-angle to failure testing

*Click Here to View/Download a Printable PDF of this Case Study.*

Know Your Customer, Know Your Competition

Every supplier has opinions of their customers and what seems to motivate them to buy. Success in meeting economic goals is always dependent on the accuracy of those views. Following is one view of what makes the product development engineer tick in 2006. Of course the first question is whether engineering or procurement is your real customer. Ultimately, it’s either one or the other, and much more often than not it’s the engineer. However, engineers often abdicate their decision out of apathy or fear, making it appear you’re stuck with a low-bid situation more often than is actually the case. If you’re not sure, just ask engineer. They’ll tell you. There are some good reasons why procurement doesn’t want to you to talk to their engineers without a chaperone.

We’re usually not the best businesspeople. Of course make sure you know whether it’s the engineering manager or procurement that’s the barrier. If is the engineering manager, the observations that follow still apply. Like everyone else, workload is one of the engineer’s biggest complaints. Since in nearly all your interactions you will be saving your customer time or you will be asking your customer to invest time in you, constantly ask yourself which you are doing. For example, every supplier constantly complains they never get in on a program early enough. The most common reason for this is the supplier isn’t bringing enough benefit at that time for engineer to invest time in explaining their needs. Forwarding a drawing or parts list for quotation a few months later is much easier.

peak article diagramA fastener rep needs to have a greater depth of application knowledge than the engineer (or have direct access to it) to get the engineer’s attention. When you consider that there are a limited number of those people at the hundreds of fastener manufacturers, where the fastener is developed and applications validated in test labs, it shouldn’t be surprising that they will be much harder to find at the thousands of companies whose primary function is to sell those fasteners. Of course if you don’t believe that the investment in increased technical support can’t be paid for by increased revenue, the overriding issue is, “How am I going to know the customer will pay for this when they are hammering me for tenths of a cent.” The answer is you won’t. But if you are committed to competing on product and service rather than price, providing quality applications support and testing is the greatest untapped source of competitive advantage in a wide swath of industries between MRO on one end and automotive/aircraft on the other

Partly because of workload and partly due to the relentless short-term focus on next quarter’s results, many engineers are becoming more risk-adverse. If you are getting push-back in trying to place a new application because your contact has technical concerns, to be successful these concerns need to be addressed to his satisfaction, however unreasonable that might appear to be. You need data or hardware as your assurances aren’t addressing his concerns. The most valuable weapons, in decreasing order of effectiveness:

    • Find the same component successfully fielded in the same application. Even if that application is your competitor’s product, this approach has more potential benefit than harm unless the competitor has clear differentiation or pricing advantage. The key is that the customer perceives it as the same application (thus mitigating their risk) as opposed to whether it is the same fastener.
    • Take it upon yourself to test the application, preferably from an independent source. The customer will say it’s OK if you test it yourself. What they won’t tell you is that they will question the credibility of any positive result, largely negating the benefit of your investment. This is particularly true in industries where engineers are not familiar with joint testing. In any case, forward the test procedure to the decision-maker for an informal approval before you get started. =Forwarding it by e-mail requesting an OK in reply is a documented but non-threatening way to make it more difficult for the engineer to ignore or downplay the benefit of positive results.
    • The last resort is to decrease the perceived risk of your product by increasing the perceived risk of any alternative

This is can be effective if make sure you are focusing on the potential customer’s concern; technical risk. Telling him that your competitor’s rep is dumb, never delivers, has a 37 handicap and cheats on his wife might be interesting (and might even be true), but it isn’t going to get you the sale. Neither is relating third party dissatisfaction. Getting existing test results, warranty or recall data, obtaining testimonials from experts such as an independent service organization or commissioning an independent competitive test will all help level the playing field. Forwarding feedback from industry technical forums is an effective means of making your point. Just make sure you run a search to be sure your product isn’t being harpooned in a thread somewhere else on the site.

While these observations might provide food for thought on an individual organizational basis, they don’t address the fact that the biggest challenge to the industry comes from outside, not from fastener manufacturers overseas.

Figure 1 is a screen shot of a selection guide on our web site showing potential fastening and joining applications by joint requirement. One of the challenges of the fastener industry is that their products are used in applications were other options are a very viable alternatives. For example, many threaded fasteners are used in joints that are not intended to come apart. Why? Often it’s not because it’s the most cost-effective solution. It is because bolts are familiar, available and don’t require a lot of time or investment to implement. Many people don’t trust bonded joints because they had them fail in the past. Just like 30 years ago everyone had war stories about how the plastic parts in their car cracked and fell off. Do you want all that metal back in your car now? Adhesives, like thermoplastics, can be much more easily modified for specific applications than formed metal, and chemical companies certainly have the budget for customer education and testing. New adhesives that are more insensitive to surface conditions and others with innovative cure mechanisms are making significant inroads.

Consider also that the utility of any attachment method is dependent on the materials and manufacturing process of the components it secures. As more low-density metals and composite are introduced new joint designs will be required because the material properties demand it. At that point it takes just as much effort to look at alternatives as it does to rethink how to make the existing fastener work. I think the solution is for this traditionally fragmented industry is to form coalitions that do more than develop standards. There are some compelling success stories of industry consortiums whose mandate is growing their market through innovation. One of the most impressive has parallels to the fastener industry. What is another product seen as decidedly low-tech, low growth, and so 20th century? How about steel? Yet the UltraLight Steel Auto Body (ULAB) project, funded by a consortium of 33 steel producers, demonstrated through a comprehensive combination of analysis, testing and prototyping that advanced high strength steels could compete quite well with aluminum, magnesium and composites.

Because of this 2002 report, and the knowledge that arose from it, applications that would have otherwise been lost to other materials are still steel. Of course the return on this type of investment can be debated; the industry has survived without it. With that in mind, perhaps it’s appropriate to quote a Chinese proverb, which loosely translated warns, “If you continue on your current path, you’ll get to where you’re going.”

Written by Dave Archer
Principal Engineer for Peak innovations Engineering

Drive Features – How Low Can You Go?

Here in metro Detroit, a popular subject for editorials and panel debate is why it seems the passion America once held for the automobile is in decline. Does the legislation and message coming out of Washington promote the development of appliances on wheels? Are manufacturers too risk-adverse and infested with a “bean-counting” mentality to ignite a passion dormant only through a lack of interesting product to awaken it? While both are undoubtedly true to some degree, it seems that young people in particular have simply a found a new, more seductive love. In truth, even the most dedicated ‘60’s gear head would find it hard to pick up a wrench if he had the world in the palm of his hand. Mustang vs. Camaro? More like I Phone vs. Droid. While internet access, hardware advancements and better software are all prerequisites for the smart phone market, fitting all that functionality in the most usable (i.e. thin) form factor is an equally important factor in their explosive growth.

sdbPackaging products like this is about attention to the smallest detail, including what screw type is used. Further, the screw is itself a study in packaging. Thread size and screw length can be chosen over an almost continuous spectrum, with the thread dimensions standardized in the most applications. On the other hand, choices of head and drive style have greater variation in both performance characteristics and in dimensions relative to standard threads. The drive style should allow easy insertion and not fail during insertion prior to screw shank failure, either within the head or the bit. The limitations to shrinking head diameter, namely crushing the material beneath it or pulling the screw through the hole, are not directly related to the fastener design but to joint requirements. On the other hand, head height is usually dictated largely by the depth of bit engagement required to provide safe driving, and therefore can be a differentiator in screw design.

One drive style, with which many readers are unfamiliar, was developed recently with short bit engagement as a key feature. The Phillips Screw Company developed the Mortorq® Super drive (Figure 1) to check the box on all the features customers want in a drive, but the potential to decrease head height below the that of current head styles is what Phillips believes can provide particular benefit to manufacturers of personal electronics, and other packaging challenges. Shown in Figure 1, the drive geometry was developed with the goal of increasing contact area without increasing the tendency for coating fill. The non-symmetric nature of the contact surface in the tightening and loosening directions is claimed to provide functional benefits.

Mike Abbott, Director of Technical Sales and Licensing, visited our office recently to discuss a possible test program aimed at comparing the capabilities of Mortorq® Super to other competing drive styles in micro-sized screws like #0-80 and #2-56. Just as manufacturing and inserting screws of this size require a combination of incremental and fundamental changes relative to larger sizes, the details of how to measure their capability carries a similar set of challenges.

Written by Dave Archer
Principal Engineer for Peak innovations Engineering

Dissecting the Nut Factor

A Riddle, Wrapped In a Mystery, Inside an Enigma

It is recognized that we measure torque when tightening threaded fasteners only because measuring bolt tension, the more important quantity, is much more difficult. The relationship between the torque applied to a fastener and the tension created from the resulting bolt elongation is most commonly described by T = F*K*D where T is torque, K is the nut or friction factor (nut factor for this article), D is the bolt diameter and F is the bolt tension or preload. Less common is a discussion of how this equation was derived, in particular the origin of the nut factor. Because this single variable K determines the critical torque-tension relationship, the factors that cause its value to vary about 300% across a range of common applications aren’t clear. Examining the sources and relative sensitively of these factors is the subject of this column.

The nut factor, as defined in the above equation (often called the short form relationship), is in reality fudge factor not derived from engineering principles but instead arrived at experimentally to make the equation valid. Various published torque-tension test procedures call for tensioning a threaded fastener in a controlled manner while monitoring both torque and tension. At the specified torque or tension, the nut factor is calculated by inserting T, D and F in the short form equation and solving for K.

Given this rather unsophisticated origin, one may be surprised to know that there are a number of published torque-tension relationships derived from engineering principles. They produce similar results to one another and take the general form T=F*X, where X is a placeholder for a series of terms containing variables of fastener geometry and friction coefficients. Three of the most widely-used examples are shown below. While at first glance they may appear to be quite different from one another, they are actually different forms of the same relationship and produce the same results.



To understand what factors influence the relationship between torque and tension we’ll review the variables contained in these equations and quantify their relative influence. The Motosh equation is easiest to understand for most people so we’ll base our discussion in it’s format. Each term within the bracket calculates a length that when multiplied by the force generated by bolt tension (Fp) results in a torque. So each term is a reaction torque that resists the input torque Tin, and their sum must be equal to the input torque. The first term produces the clamp load due to the inclined plane produced by the thread pitch.

The second term is the resisting torque caused by thread friction, and the last term is a similar resting torque caused instead by friction between the nut or head face (which ever is rotated) and the mating surface. Therefore the value of each term indicates the relative influence of the variables in each term. For example, solving for an M12-1.75 flange head screw with 0.15 friction coefficients produces values of 0.28 N-m, 0.93 N-m and 1.35 N-m for each kN of tension. This breaks out to 10.9%, 36.3% and 52.8% of the 2.56 N-m total, and illustrates the common comment that “only about 10-15% of input torque goes toward stretching the bolt”.

How do our design decisions influence the torque-tension relationship? To answer that, Figure 1 shows the effect of doubling the value of each variable in the short form equation while holding the others fixed. It shows that if the thread friction coefficient was doubled while the other variables remained the same, the bolt tension generated for the same installation torque would decrease about 28%. While friction coefficients occur on a continuous spectrum, the dimensions of standard fasteners and accompanying clearance holes tend to be discrete. To illustrate, Figure 1 also contains three points showing the effect of the following design alternatives; replacing a fine pitch thread with a standard pitch, replacing a hex head with a hex flange head, and replacing a close diameter clearance hole with a large diameter hole.

For example, replacing a hex head fastener with a hex flange head (but not changing friction coefficients, thread pitch or hole diameter) increases the bearing diameter by about 35% which in turn will cause bolt tension to be reduced by about 8% for a given torque. While these values vary a bit with fastener size, the relative importance of each variable will remain the same.


We are sometimes asked the question. “If we perform a torque-tension test with a particular fastener diameter to calculate nut factor, do those results apply to other diameters, assuming all other conditions are the same?” In fact the nominal diameter is separated from the nut factor in the short form equation for just that reason, so that test results can be scaled to other fastener sizes. Is this an assumption based on engineering principles? Actually, it is only approximation as none of the terms in the long form equations contain the nominal diameter as a variable. Therefore the accuracy of using the nominal fastener diameter D as a means of applying a constant nut factor across all fastener sizes is dependent on whether the effected variables in the long form equations vary in direct proportion to the nominal diameter. The answer is shown in Figure 2 where the long-form equation is solved for standard pitch metric hex head cap screws with constant and equal coefficients of friction.

The traces, normalized at M10-1.5, show a 4.2% maximum deviation between the short and long form equations, decreasing as the friction coefficients increase. The variable with the greatest relative deviation from nominal diameter through the range of fastener sizes is the thread pitch, as the pitch is somewhat arbitrarily selected, while dimensions of the thread form and the clearance hole diameter are all directly tied to nominal diameter. Because the first term containing the pitch diameter does not contain a friction coefficient, as friction increases the relative importance of pitch is decreased, and therefore the fact that pitch does not vary directly with nominal diameter has less impact on the result of the torque-tension calculations.

Therefore, holding all else constant, applying a nut factor that was calculated at one diameter across a range of fastener sizes is a reasonable assumption. For best results the weighted mean diameter of the fasteners on which the nut factor will be used should be the basis of testing. In reality, most organizations apply nut factors across a greater set of conditions. For example, fasteners may not have the same head style or clearance hole diameter. When a constant nut factor is applied to joints where geometry variables other than nominal diameter are changing, calculated deviations of 15% can occur between short and long form equations even for standard geometries.


These comparisons using nut factor in relative to the long form relationships may imply that these impressive-looking equations produce the “right” answer due to their fundamental correctness. This is in fact not true, as there assumptions and approximations inherent in their derivation. However the potential error of these assumptions pale in comparison to the variation that exists in real world joints. As an example, Figure 3a shows the result of torque-tension testing on the bench-top setup and controlled test conditions specified by published test methods. Even though all fasteners and bearing materials are the same for each test, and are actually swapped out for fresh ones, there is approximately 10% variation within the group. According to both the short and long-form equations there should be no variation at all. Figure 3b shows a similar graph generated from in-torque-tension testing.

Using ultrasonic pulse-echo techniques bolt tension can be measured real-time in the actual joint without altering joint characteristics. The graph shown reflects the dynamic torque-tension relationships of single assembly with a circular six bolt pattern. The variation inherent in how components actually fit to one another adds another source of torque-tension variation on top of the variation seen in the bench top test. The variation in Figure 3a is primarily due to the fact that the friction coefficients for each sample were in reality not identical. The extreme 60% variation seen in Figure 3b occurred because the joint configuration magnified the effect of imperfect contact. This results in changes to both the geometry and friction variables.


These examples illustrate why the relationship between torque and tension can only be accurately determined through testing, where both the mean and distribution about that mean can be determined.

While the nut factor K is the most popular means of quantify the torque-tension relationship in the U.S., in Europe or within organizations that design strictly to ISO or DIN standards, the long-form equations are utilized. Because separating thread and head friction significantly limits the test equipment that can be used, and eliminates the potential for in-joint testing with actual components, it is common to make the assumption that both under-head and friction coefficients are equal (ISO 16047 estimates a 1%-2% error for this assumption).

Using ISO designations, the long-form equivalent of K is shown below to the left of short-form arranged to solve for K. The VDI/DIN designation for µtot is µges Because the terminology used when describing µtot and K are similar (friction factor, friction coefficient), errors are sometimes made by unknowingly substituting one for the other. As shown in Figure 2, to arrive at het same result the value of K is approximately 35% greater than µtot.

In summary, the ability to predict the tension in a threaded fasten for a given torque input is largely a function of understanding the friction present between mating surfaces containing relative motion. Only testing can accurately determine these friction conditions, which are so sensitive to component variation that only in-joint testing can determine the relationship when controlling bolt tension is critical. Organizations calculating the nut factor K in testing may want to consider the simplified long-form equations (friction coefficients assumed equal) for greater sensitivity over a range applications, particularly when more than nominal diameter is expected to vary.

Written by Dave Archer
Principal Engineer for Peak innovations Engineering

Calibration Techniques for Ultrasonic Tension Measurement

The fundamentals of using ultrasonic pulse-echo technology for bolt strain measurement, detecting change in the time required for a pulse of energy to travel the length of the fastener after elongation, can be performed with very good resolution and repeatability. The challenge is utilizing this core capability in a manner such that the resulting calculation of boll tension is also accurate and repeatable. Traditionally, the primary barriers to this have been in three areas maintaining a stable bolt-sensor interface where the pulse passes into and out of the fastener, accounting for the influence of temperature on the measurement, and providing an accurate means of converting a given change in the pulse’s time-of-flight (TOF) to usable units of tension or load.

The last is generally refined to as calibration. Recent developments that affix the sensor to the fastener, leaving the bolt-sensor interface a fixed and permanent condition, have largely solved the interface instability problems associated with separate sensors and liquid coupling. Temperature management and compensation remains a challenge to varying degree for both ultrasonics and other measurement techniques. As issues and solutions to temperature management are very application-dependent they won’t be covered in this article. In general the desire is simply to minimize temperature differentials and gradients. Conversely, the means of effectively converting TOF to tension can be discussed in manner that is widely applicable and will thus be the subject of this article. An attempt will be made to address both experienced and novice practitioners.


We will compare the effectiveness of common calibration methods for use in both the elastic and plastic range of elongation. These methods are summarized in Table l.


In all these four methods as a fastener under calibration is increasingly loaded, both the TOF of the ultrasonic pulse and the load required to produce the elongation (and increase the TOF) are monitored. A series of load/TOF data pairs are produced for each sample, and once all samples have been calibrated regression analysis is run to predict the bolt tension for a given TOF Figure I illustrates the relationship between bolt elongation and the resulting bolt tension. Line A-B-C represents the behavior of a bolt loaded into yield, with permanent elongation occurring after point B. While this trace is often produced by pulling the bolt in a tensile tester, compressing a load cell by rotating the bolt into a nut member produces the same effect.

Finally, since the change in TOF is directly proportional to elongation, line A-B-C also represents the response of an ultrasonic sensor as measured by TOF. As most bolted joints are designed for bolt load to remain within the elastic range (Line A-B), it is common to calibrate within this range only and produce a simple linear estimate for Load vs. ATOF. These linear calibrations can also be used to measure tension in bolts that have been permanently elongated by taking the installed tension measurement, fully loosening the bolt and measuring the residual ” tension” due to permanent elongation and then subtracting this residual value from the initial reading. Because a linear relationship between TOF and load treats all changes in TOF the same, a given increase in elongation produces the same estimate of increased load in all situations.

Therefore, when the actual relationship between elongation and load follows Line B-C, the ultrasonic system with linear calibration will incorrectly predict load along Line B-C2. However, the final TOF will be the same in both cases. When loosened, the bolt’s elastic elongation is relieved by following the same path as during the elastic phase of tightening: Line C-D (parallel to Line A-B). The residual “tension” displayed on the ultrasonic measuring system will be Point D2, based on the TOF at Point D. This differential load, represented by Line D-D2, is equal to the differential load represented by Line C-C2 as the lines are of equal length. Subtracting load D2 from the value at Point C2 yields the connect value: Point C.

Some users with the capability for non-linear calibration use it for all applications whether or not the bolt is to be permanently elongated although the capability for nonlinear calibration is not available in all measurement systems. So the calibration method that will be used for given application is not always a given, particularly considering the fact that both tensile and torque based loading methods are possible.

This is the motivation for comparing the effectiveness of the four options summarized in Table 1. TEST PROCEDURE The approach taken was to generate calibration files using the four combinations of regression fit and elongation, then tighten a series of bolts in a load cell and compare the ultrasonic tension calculated using each of the four calibrations to the output from the load cell. The load cell would be considered the control, and deviation from the load cell would be considered measurement 9rTor.

The equipment used in the test is summarized in Table 2. Class 8.8 bolts were chosen for convenience, but all the trends shown here are applicable to other property classes. As noted, the setup used to conduct the comparison test is the same one used for the torque calibration. To enable the most direct comparison of linear and non-linear calibration, the linear calibration was not created with an independent set of samples, but rather the series of data pairs generated over the full range of elongation into yield was cropped so that just the points recorded in the elastic range remained.



The results of comparing load cell tension to tension calculated from the four forms of ultrasonic calibrations are summarized in Table 3a thru 3d. Each table covers a different measurement scenario. Table 3a is a compilation of intermediate measurements, all within the elastic range, taken at the most common design targets the bolt tension. The three subsequent tables are the final tension readings for bolts elongated into yield. The difference between Table 3b and 3c is how far into the plastic range the bolt was elongated. Table 3d is unique in that for all other cases the bolt, nut and washer used for the comparative test were the same used for calibration. The results shown in Table 3d reflect use of a plain finish nut rather than the zinc-plated nut used in all other cases. In all tables variation is defined as the absolute value of the difference in ultrasonic tension relative to load cell tension.



The difference in tension calculated by linear torque and tension calibrations were approximately 0.170. This reinforces our past experience that in the elastic range either elongation method can be equally accurate. It may seem odd that the non-linear calibrations resulted in about three times the deviation when the linear calibrations were derived directly from them. The reason is shown in Figure 2. Even when using 5th order regression, the portion of the calibration covering the proportional elastic range deviates from linear. While the tensile method of calibration allows use of cal bolts for testing as the contact surfaces are unaltered, one tends to need more care in establishing grip length in tensile calibration due to the nature of the tooling. This is particularly true as grip length decreases. To approximate the small increase in stiffness of advancing the bolt during torque calibration we set the grip length for tensile calibration sort of calculated value by 10/0 of the thread pitch (half the rotation assuming it was 72o from threshold). Where possible, it is desirable to simulate actual thread engagement as this influences bolt stiffness, and therefore calibration. .

The three tests conducted in the plastic range highlight the advantages and disadvantages of each calibration. First, the tension-based nonlinear results show greater deviation than those which are torque-based. The reason for this is also the reason that the non-linear calibrations perform poorly in Table 3d. In both cases the limit of the proportional elongation is reduced by the addition of torsional stress. This is illustrated in Figure 3 highlighting the area around yield of three tension-angle traces recorded on the torque test cell. The three traces are the calibration and primary test hardware (nut factor K=0.164), the plain nut used only in the Table 3d test (K=0.184), and a third set tested for this illustration only (K=0.273). If the trace from a pure tensile pull were added, the proportional limit would be still higher than that for the primary test hardware. Fortunately, because actual fastener proof loads are often l5% to 20% higher than minimum requirements, finishes with reasonably low nut factors result in proportion limits above minimum proof. The increasingly indistinct deviation from proportionality that occurs with increasing tensional stress should be kept in mind when analyzing torque-angle or tension-angle traces, as it can be mistaken for the onset of embedment. .

Another finding of the measurements into yield is that the process of using linear calibrations and subtracting the permanent elongation from the as-tightened tension results in accurate measurement, particularly when plastic elongation is short. We have found that best results are obtained recording the residual value immediately after loosening. The fastener continues to contract a small amount for a period thereafter in what appears to be a recovery mechanism rather than being temperature-related. . lt is important to point out that using nonlinear calibration for measurement in the plastic range other than for the initial tension after tightening can be very inaccurate. For example, any tension relaxation after tightening into yield would follow Line C-D in Figure l. However the relaxation predicted by the non-linear calibration would be underestimated, following the same Line B-C used for estimated increasing tension. If service loads were to further increase permanent elongation it is not assured that Line B-C would be followed. Because the torsional stress is removed, recovery from relaxation could instead follow a parallel path resulting from extending the higher proportional limit due to pure tensile stress. Within limits, subtracting the residual elongation from the linear calibration measurement can still be used in these situations.


Like any single test that is intended to predict a much wider set of conditions, the key question for these results is how widely and reliably can they be applied. Our experience is that the trends and relative accuracy is representative of most applications. The absolute accuracy is less certain. As noted, because the control test setup was the same used to calibrate the torque calibration, variation was essentially a test of calibration repeatability. The 170 accuracy achieved here is achievable over a range of typical applications, but can be compromised by short grip lengths, fastener materials and certain geometries. An estimate of a lower accuracy limit might be 570 with some exceptions. Both non-linearity and slope variation tend to be effected. Poor repeatability with good linearity tends to point to tooling issues that can usually be rectified.

As another point of comparison, we performed a similar test in the elastic range using linear tensile calibration to determine measurement uncertainty for ISO:17025 certification. The result was an expanded uncertainty of 0.816% with a coverage factor of 2. Even for applications at lower limits of calibration accuracy, because it is only commercially available means by which bolt tension may be measured without functional change to the fastener or the joint members, ultrasonic measurement is still highly effective relative to alternative techniques. Finally, while hardware and software advancements have reduced operator impact and the need for interpretation that were typical of early ultrasonic use, the measuring system and the person using it are still influential.


Written by Dave Archer
Principal Engineer for Peak innovations Engineering

Bolted Joint FAQs

Two of the most commonly asked questions about fasteners are “When should fine-thread fasteners be used?” and “is it preferable to apply torque to the nut rather than the bolt head?” Many different factors influence those decisions, but here are some basic answers to both questions.


For a given fastener diameter, as thread pitch decreases, a bolt’s tensile strength increases because the stress area (the smallest cross-section in the threaded portion of the bolt), becomes larger. This increase is approximately 12 percent for standard pitch differentials and since the helix angle of the thread decreases with finer thread pitch, resistance to vibrational loosening will improve somewhat. The reason is analogous to a snow sled requiring more effort to get moving as a hill becomes flatter. On the other hand, finer threads increase the potential for cross threading and take more time to insert, because they require more turns Still, it could be argued that the pros outweigh the cons, so why are fine threads not more popular? Many of the obstacles to more widespread use ale nontechnical.

First, the combination of fine and course threads in an assembly or maintenance environment invariably leads to cross-use are, and the resulting problems are usually disruptive and expensive. Other’, more isolated disadvantages can be availability and higher part cost In many cases, the option was simply never considered. So, when should fine-thread fasteners be used? The most obvious answer is in applications where weight and size are the overriding drivers in engineering decisions. For example, aircraft engines use fine thread fasteners exclusively because the increased strength in the same size and weight outweighs all other considerations’.

Some manufacturers are missing an opportunity for product improvement with fine-thread fasteners. Good applications are highly engineered products in low to moderate production volumes, where power density, weight or size is critical. Keep in mind that using higher capacity fasteners does not automatically result in realizing their benefits. Joint testing and manufacturing capability are needed to ensure that their benefits are actually realized.


In a through-bolted joint, it is generally preferable to turn the nut rather than the bolt head, a key reason is the effect of bolt torsion. When a threaded fastener is tensioned by rotation of either the nut or the fastener itself, torsional stress is created in its shank.  How this impacts the nut vs. head question can be illustrated with a hypothetical application that magnifies the influence of bolt torsion. Imagine 0.25-inch (M6) stainless steel bolts being used to clamp together two steel plates each 2 inches thick.

If the bolt head were turned and the nut restrained, one could imagine that the combination of a long slender bolt and high thread friction would cause the bolt to twist significantly as torque is applied in fact, the bolt would fail well before the clamp loud predicted by the bolt’s tensile strength could be achieved, due to this high torsional stress being added to the tensile stress created by bolt elongation. Remember that the published strength of fastener materials is based on pure tensile loading. The combination of torsion and tension lowers the bolt’s capacity. If the bolt head were instead restrained and the nut rotated, this joint configuration would still result in a high level of torsional stress, though not as great as in the first example, because the torque is applied more directly to the threads-the nut does not “wind up” like the bolt. However, by changing key variables, such as relative friction at the interfaces or the bolt’s length to-diameter ratio, the relationship between input torque and resulting clamp load can be varied significantly, to the point where turning the head or nut yields effectively the same result.

So, why is turning the nut preferable? Because, turning the nut removes the portion of torsional stress and stored energy created by applying the torque remotely from the threads at the bolt head. This, in turn, results in more predictable and potentially higher clamp loads. Torsional stress reduces the bolt tension that can be achieved during tightening in all applications, not just this extreme example. Fortunately, this loss is often offset by the fact that fasteners are generally 10 percent to 20 percent stronger than minimum specifications. As a point of reference, we have seen bolts yield during tightening at clamp loads lower than calculated by minimum proof load when the nut factor (K factor) is approximately 0.18 or greater.

Written by Dave Archer
Principal Engineer for Peak innovations Engineering