LITERATURE: Technical Articles

Verifying Coupling Torsional Stiffness Ratings to Maximize Servo Positioning Speed and Accuracy

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 are very frequently used in servo and motion control systems. No other design does an equivalent job of providing high torsional stiffness while accommodating significant misalignments between powertrain components. They're frequently specified to compensate for assembly misalignments, bearing wear, vibration and thermally-induced dimensional changes.

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, that are approaching the practical limitations of the torsional stiffness of bellows couplings.

While it's never been more important to designers to know how much torsional stiffness they're really working with, they often don't have access to coupling torsional stiffness data that's consistent from one manufacturer to the next. Published stiffness ratings can vary widely depending on test methods, 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.

To put a real face on the issue, engineers at Gam, Chicago, IL devised a coupling stiffness testing method and conducted a set of side-by-side tests.

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.

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

The fixture is designed to allow the application of known masses at a known moment arm, allowing computation of applied torque. The dial indicator allows measurement of angular displacement. 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. Table 1 provides information on the couplings and rated torque values for the coupling tests covered in this report.

Table 1: Couplings Tested for Torsional Stiffness

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 and 45.17 kg, depending on the published ratings of the couplings. The couplings were tested to rated torque values except where noted.

Calculating Torsional Stiffness From the Tests

Torsional stiffness is a measurement of torque per angular displacement, and may be expressed as follows:

Ct = Torsional Stiffness (Nm/rad)
Ct = M/Y
Where: M = Torque (Nm) and Y = Angular Displacement (rad)

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 2 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.

Table 2: Averaged Torsional Stiffness Testing Results for 12 Bellows Couplings

It's important to stress that these results are based only on the test fixture and methodology described here. Results may be affected by as much as 5 to 10% 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 heads-up when engineering a motion device whose ultimate performance relies heavily on overall stiffness.

The watchword, 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.