How tight is right?

Aug. 23, 2001
Tension, not torque, indicates proper joint tightness.

Dave Miller
RS Technologies Ltd.
Farmington Hills, Mich.


An M-Alpha auditing system from RS Technologies Ltd. checks lug clamp loads on an automobile rim.

A line drawn through two points on the elastic portion of the curve locates the elastic origin.

In this test with a 100 N-m applied torque, the combined under-head and thread friction torque absorbed 80 N-m, leaving about 20 N-m to produce clamp force.


Designers typically qualify clamp force of a bolted joint by the amount of torque applied to fasteners holding it, either as they're tightened or after the fact. The approach may be adequate for many noncritical applications, though results depend strongly on operator technique.

But torque only indicates work done on a joint by an installation tool and not necessarily clamping force. This is because torque must first overcome under-head and thread friction before clamp loads build. In fact, friction can consume up to 95% of applied torque in some cases, leaving just 5% for clamping. For critical applications, also consider (in addition to torque) fastener tension, rotation angle, and friction. Neglecting these items during assembly can lead to loose or broken bolts in the field.

Tension and clamping force
Bolted assemblies act as two springs — the fastener in tension and the bolted components in compression. An elastic joint results when a fastener flexes more than the clamped parts and overcomes resistance to joint compression. Fastener tension is measurable with various devices including strain-gaged bolts, fastener-force washers, or with special ultrasonic boltmeasurement techniques. Though these tools help during research and engineering phases, they're often impractical or too costly for production-level quality control. A simpler yet effective measure of joint load is fastener rotation angle.

Fastener tension is proportional to fastener rotation angle after parts come into firm contact. M-Alpha systems from RS Technologies Ltd., Farmington Hills, Mich., record torque (M), friction, and fastener rotational angle (Alpha) during assembly or residual levels of these metrics in pretightened fasteners. Here's how it works: A computer-controlled dc electric-motor drive inputs to a torque-angle sensor. The sensor output shaft couples to a fastener (bolt portion) to be tested while a research head traps the nut. The research head contains a torque sensor and an axial load cell. The torque sensor indicates frictional loads and the axial cell, clamp force.

Typically — to establish a baseline — there are several tests performed on a joint with similar stiffness and friction qualities. The resulting curves or torque-angle signatures contain four distinct zones, each of which can be analyzed separately.

The rundown or prevailing torque zone comes before the bolt head or nut contacts the bearing area. Prevailing torque is basically thread friction and is often purposely boosted with nylon inserts or deformed threads to prevent unintentional loosening. Additional and undesirable sources of prevailing torque in the rundown zone include frictional drag on the shank or threads from misalignment of parts, chips, contamination, as well as unintended interference from out-of-tolerance threads.

The second curve portion is the alignment or snugging zone. Here, the torque-angle relationship is nonlinear as mating parts draw together and fasteners bend because of nonparallel bearing surfaces. Other factors shaping the curve here include fastener coatings and plating, surface roughness, and deforming threads.

Next is a linear-elastic clamping zone. This portion of the signature is considered most significant of the four because a large portion of tightening energy is transferred from tool to assembly. The curve's linear slope can give an accurate estimate of fastener tension: Draw a line tangent to the curve back to zero torque or to the prevailing torque level. The intersection with the X axis is called the elastic origin. Fastener tension is proportional to fastener rotation angle as measured from the elastic origin to where tightening was stopped in the elastic clamping zone. This allows, without direct measurement, accurate estimates of fastener tension and clamping force.

Finally, the postyield zone begins with an inflection point at the end of the elastic range. Although the shape of this curve portion can indicate fastener yield, it's sometimes more influenced by joint yield. Here, gaskets, relatively soft or plastic clamped components, or yielding threads, all can contribute to total yield.

Applied torque must overcome friction before clamp load builds. In other words, more friction lowers clamp force for a given torque. The type and hardness of materials, surface finishes, plating (thickness, condition, and type), thread percentage or fit, lubricants, and temperatures, all can affect friction. Based on this, some may conclude that a joint with less friction is better. But it is under-head and thread friction that keeps a fastener tight under load. For better holding power, joint friction is often purposely enhanced with a starred washer under the head or a patch or nylon locking device on nut threads.

The basic elastic torque-tension equation helps analyze friction:

where: = torque (lb-in.), K = nut factor (typically 0.03 to 0.35), D = nominal diameter (in.), and F = force (lb). The expression applies only to the linear elastic region of the torque-angle curve and is solved for K, given torque and force. The K factor combines three other factors:

K = K1 + K2 + K3
where K1 = geometric function of fastener diameter and thread pitch, K2 = thread friction, and K3 = function of under-head friction and surface contact area.

Published tables of K factors cover various combinations of materials, surface finishes, plating, coatings, and lubricants. However, experience has shown them to be highly unreliable for a specific fastener and assembly. It's often better to do a more detailed analysis of under-head and thread friction factors when designing special fasteners or when solving a particular design problem. Methods such as the German standard DIN 946 help estimate these friction coefficients. Still, it is best to supplement calculations with torque-angle experiments. The first step is to separate frictional torque from input torque. Large swings in friction levels may indicate problems in the assembly process, especially with torque tools or methods. Impulse tools, for instance, have wider torque scatter than tools with torque-angle or yield-point control.

Another issue is tool rotational speed. Excessive speeds may trigger stick-slip action and torque peaks that are unrelated to clamp load. Tools momentarily seeing specified torque levels can power down before fasteners are fully tightened. Tool rotational speed is just one of 200 different factors that may affect bolt tension for a given torque. The good news is, a formal design review can help identify such issues before production begins. A review may include design analysis, experimental testing, and assembly testing.

There are several design analysis methods to predict joint reliability ranging from simple algebraic formulas to complex functional analysis. The German standard VDI 2230 introduced in 1977 (revised 1988, 1998) is considered one of the better ways to determine joint stress. The VDI standard is built into numerous software products, the most complete of which is SR1 from Hexagon Industrial Software in Kirchheim, Germany. SR1 is distributed in North America by RS Technologies. SR1 figures crucial joint stresses and safety factors based on geometry, estimates of friction, loads, and on assembly tool scatter.

Consider a cap head screw joining a hydraulic piston and steel connecting rod. SR1 produces a CAD-compatible assembly drawing and a table of inputted and calculated data including dimensions, loads, friction, and safety factors. The VDI standard says acceptable safety factors are 1.0 or greater. The analysis in this case showed all safety factors to be satisfactory except for that evaluating thread strip at yield. The 0.93 value means it's possible to strip threads when the fastener is taken near yield. This would be especially important when a tool applies inconsistent torque levels. This type of analysis can identify suitable installation tools and help users select fasteners in terms of size, grip length, and tensile strength.

After design analysis comes experimental testing. Assemble joints in a rig capable of measuring applied torque, fastener rotation angle, clamp loads, and under-head and thread or prevailing torque. Joints should accurately reflect features of actual hardware such as plating and surface finishes, and thread geometry. To better predict real-world behavior, friction coefficients derived from experiment are fed back into the simulation.

The assembly testing step fixtures actual assemblies and records torque-angle signatures. The signatures are correlated to those obtained from experiment. This helps eliminate contributions from the test equipment itself. But more importantly it provides a baseline for torque-angle analysis of production joints. Data include prevailing torque in the rundown region, cold work done on parts being brought into alignment, boundaries of the linear elastic clamping zone, and possible joint yield and fastener embedment. The torque-angle and tension-angle coefficients are then calculated. The statistical scatter of these coefficients brackets the range for subsequent torque-angle (joint tension) audits.

Putting M-Alpha to the test

M-Alpha is used to measure residual clamping forces on automobile wheel rim joints subjected to heat cycling from track tests. A residual torque audit of a wheel joint still hot from testing adds a 9° audit angle to the existing 16°clamp angle for a total of 25° at 66 lb-ft. A release audit of the same wheel conducted at room temperature shows that as the joint cools, residual torque decreases slightly but the clamp angle remains unchanged, indicating no loss of clamp load.

Yet another residual (release) torque audit on a similar joint but at elevated temperature with a clamp angle of 18° and a 10° audit angle, gives a total angle of 28° at 45 lb-ft. The release audit at an elevated temperature broke away at a slightly lower 40 lb-ft but at the same 28° release angle. This says that clamp load remains unchanged despite a lower torque. This analysis shows that joint temperature has relatively no effect on clamp loads, and primarily impacts friction and slope of the torque-angle curve, provided no additional torque is applied to the joint.

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