Testing Coupling Torsional Stiffness to Maximize Servo Positioning Speed and Accuracy

Can there be a significant difference between a coupling's published and measured torsional stiffness?

An Independent Study Using a Consistent Test Method Reveals the Answer. Read On...

With today's increasing reliance on faster servo systems for motion control, even small variations in the stiffness of a powertrain can significantly affect positioning accuracy or constrain cycling speeds. While many factors may be involved, a very important one is the stiffness of the couplings used to connect moving machine components.

Metal bellows couplings like the GAM units we produce are very frequently used in servo and motion control systems. The metal bellows design offers a very high level of torsional stiffness that designers recognize as among the best available. At the same time, metal bellows couplings are capable of accommodating significant misalignments between powertrain components. In fact, no other coupling style balances these two design requirements so well. So it's no surprise they're so frequently specified to compensate for assembly misalignments, bearing wear, vibration and thermally induced dimensional changes.

Figure 1: Test Fixture for Measuring Torsional Stiffness of Bellows Couplings
Test Fixture for Measuring Torsional Stiffness of Bellows Couplings

Higher Cycling Speeds and Accuracy Requirements Increase Torsional Stiffness Demands

Today's motion control systems are operating at unprecedented speeds, with extremely rapid start/stop cycling and directional changes. Consequently, designers are running up against the practical limitations of the torsional stiffness of bellows couplings — unusual 10 years ago but increasingly common today.

Having arrived at the far end of the stiffness spectrum, it's never been more important for designers to know how much torsional stiffness they're really working with and how far it can be pushed. As we at Gam have worked in this area, we've come to recognize that designers often don't have access to coupling torsional stiffness data that's consistent from one manufacturer to the next. Different manufacturers' published stiffness ratings can vary widely depending on the test methods they use, and may even be overstated.

Conversely, the ability to make direct comparisons between competing products would allow the designer to select the optimum coupling for a given application. This report is devoted to describing a stiffness testing method and the sometimes surprising results it yielded.

A Test Fixture to Measure Torsional Stiffness

The test fixture shown in Figure 1 was designed to accommodate many sizes of couplings. An independent testing firm was used to ensure objectivity and credibility.

To conduct tests, one end of a bellows coupling is attached to the fixed housing indicated in the drawing. The opposite end of the coupling is attached to a freely moving beam moment arm capable of being loaded with various weights.A dial indicator attached to the fixed and freely moving ends is used to measure the coupling's torsional deflection under varying loads. The fixture measures the coupling's overall stiffness, including the end hubs and the bellows.

Four coupling models from each of three manufacturers were tested; two sets of measurements were taken for each coupling. Each set of measurements involved tests with between five and seven weights of different masses applied to the beam moment arm; masses ranged between 4.54 kg and 45.17 kg, depending on the published ratings of the couplings. The couplings were tested to rated torque values except where noted. Table 1 provides information on the manufacturers, model numbers and rated torque values for the coupling tests covered in this report.

Table 1: Couplings Tested for Torsional Stiffness

Test 1.



Part Number

Rated Torque

A Gerwah AKN 60 60 Nm
B GAM KP-60 60 Nm
C R&W BK2-60/83 60 Nm

Test 2.



Part Number

Rated Torque

A Gerwah AKD 150 150 Nm
B GAM KM-170 170 Nm
C R&W BK2-150/107 150 Nm

Test 3.



Part Number

Rated Torque

A Gerwah AKN 150 150 Nm
B GAM KP-170 170 Nm
C R&W BK2-150/95 150 Nm

Test 4.*



Part Number

Rated Torque

A Gerwah AKD 500 500 Nm
B GAM KSD-550 550 Nm
C R&W BK3-500/100 500 Nm

*Couplings for Test 4 were tested to 170Nm

Comparing Measured and Published Torsional Stiffness Ratings

An example of the values calculated from the measurement tests is provided in Table 2, displaying results for one test set on a GAM KP-60 bellows coupling. At the bottom of the table, note that an average value is shown for measured torsional stiffness, based on testing conducted with the different masses indicated in the “Test Mass” column.  There is also an average value provided for the ratio of measured to published torsional stiffness for the coupling. 

While there isn't space in this report to provide detailed test results for all 12 couplings tested, a full data set is available upon request. However, Table 3 highlights the most critical data set in this report. It shows the percentage of each coupling's published torsional stiffness rating that was actually measured in these tests. Each reported percentage is a composite number obtained from between 10 and 14 individual torsion tests on a coupling.

Of course, we'd like to stress that these results are based only on the test fixture and methodology we've described
here. Results may vary as a result of fixture design and how the operator set up and performed the actual test runs.

What these numbers really tell us is that there can be some very significant differences between published and measured torsional stiffness values when a consistent test method is used for comparison. For the designer, that should serve as a caution when engineering a motion device whose ultimate performance relies heavily on overall stiffness. 

The watch-word, of course, is “test for yourself.” If you establish a set of evaluation protocols that faithfully model the performance needs of your designs, then you can be confident you're getting the overall stiffness and system performance you intended. That's important when you're pushing all of your components and the design itself to the limits.

Table 3: Averaged Torsional Stiffness Testing Results for 12 Bellows Couplings

Test No.


Part Number

Average Measured Stiffness as a percentage of published stiffness

1A Gerwah AKN 60 58.6
1B GAM KP-60 92.2
1C R&W BK2-60/83 49.8

2A Gerwah AKD 150 65.1
2B GAM KM-170 89.8
2C R&W BK2-150/107 48.9

3A Gerwah AKN 150 69.1
3B GAM KP-170 90.1
3C R&W BK2-150/95 44.2

4A Gerwah AK 500 81.7
4B GAM KSD-550 90.5
4C R&W BK3-500/110 35.1

Greater Stiffness Translates Into Faster Cycling in a Real-World Motion Control Example

What might these results mean in a real-world motion control setting? We see one example from one of our customers using GAM bellows couplings in a motion control application in a printed circuit board drilling machine.

The machine uses bellows couplings to connect servomotors and lead screws used to position a 30 x 36-inch table in X and Y axes. Moving masses are in the range of 700 to 1000 pounds. Previous coupling designs had worked well, with no positioning accuracy problems. But design goals for upgrading the machine placed a premium on powertrain stiffness.

The customer tested many different couplings, and the results pointed to the superior stiffness of GAM bellows couplings. In combination with a number of other design changes to increase overall system stiffness, the GAM couplings helped the customer achieve a settling time frequency response as much as 50% better than previous models. And that improvement in positioning time lead to an 8 to 12% improvement in machine throughput.

Download a PDF of this information
Browse GAM couplings