The books on this don’t tell engineers all they need to know.
By James G. Skakoon
You’ve probably struggled with an ordinary spring clamp that doesn’t hold very well. The clamping force might have been good with it fully open, so perhaps you added clumsy spacers on the fly to get by. But inadequate force at the start of the clamp’s range is likely the result of a poorly designed spring, and performance improvements for this—and any—device might lie in optimizing a spring’s design.
Textbooks and handbooks show how to calculate load and stress in springs, and modern spring design software speeds the calculations. Advanced handbooks and fabricators offer guidance on the many watch-outs such as stability, fatigue, tolerances, environment, and natural frequency. Despite all of this, your spring clamp still doesn’t hold.
Why? Because neither design software nor spring fabricators tell designers how to select the best spring and the best operating point for their spring assembly. But this article does:
When designing springs, use the smallest possible spring rate, and operate springs at the largest allowable deflection.
But won’t operating a spring near its maximum allowable stress precipitate failure? And why would someone want to do that anyway? Read on to learn why, and no, highly stressed springs will not fail, as long as you follow the otherwise customary design guidelines.
When talking about designing springs, Joe Altstatt of Western Spring Manufacturing in Minnesota, a family-owned spring manufacturer, tells it straight: “You’ve got travel and load. Those two have to come together. If you’re asking for too much of one or the other, then you’re going to be in trouble. Once you’ve determined, OK, I need this much travel and this much load, then go back to a manufacturer and have them validate that it’s a safe operating situation for you.”
Despite textbooks, handbooks, and design software, the occasional
spring clamp still can’t do its job properly.
Even then, according to Altstatt, observing recommended limits for parameters isn’t always enough. “It’s based on your environment,” he said, “and you really never know [if a spring will fail] without a little testing.”
Designing coil springs is unavoidably trial-and-error. You must assume a geometry, calculate the result, adjust the geometry, and recalculate until you are satisfied. This is where a spring program is invaluable. “We use the latest version of the Advanced Spring Design software (ASD 7.0) from the Spring Manufacturers Institute,” said Joe’s son, Alex, who, along with brother Ben, represents the fourth generation in the spring business.
Getting to the (Operating) Point
According to SMI’s Handbook of Spring Design, “Functional requirements are usually expressed as a load at a test position and/or a rate.” The combination of force at a length (linear), or torque at an angle (torsional) is the operating point. This must lie on a spring’s load-deflection curve, which is defined by the familiar Hooke’s Law, F = -K × x, for linear displacement, where F is force, x is deflection, and K is the spring constant.)
Think of designing a spring as selecting a force-deflection curve together with the operating point on that curve, while never exceeding the allowable stress for your material and conditions of use. For example, a torque-limiting slip clutch uses a spring to control release torque. The operating point is the spring’s length when the ball fully nests in its detent hole, and the operating range extends to where the ball is fully disengaged.
In this torque-limiting clutch, the spring’s rate, not just its force, is an important
consideration. A lower spring rate is better in most applications.
In most cases of simple spring design, like this clutch and the spring clamp, it is desirable for the force to remain as close as possible to the operating point force throughout the deflection range. Devices then usually function best. For example, we do not want the force to be many times higher as the clutch disengages; that is why we use a spring. And we want the clamp’s force to be high even when only slightly open.
For the force to remain nearest the initial force when fully deflected, the lowest possible spring rate is required. The lower the spring rate, the less the force will change for a given travel. This implies a “relatively” large initial deflection, something approaching the allowable maximum. Perhaps surprising then, the higher the stress, the better the spring design.
“That more or less says it all,” Joe Altstatt said, “but sometimes our customers get nervous about having high stress in their springs.” But as long as the spring remains below its allowable stress, this won’t be a concern.
More to the (Operating) Point
But there is more. Equally important reasons for a low spring rate and high initial deflection are manufacturability and robustness. Assembly parts’ tolerances, spring dimension tolerances, and force adjustments are all more forgiving with lower spring rates. This is because for a given dimensional deviation, the force varies less with a lower spring rate than with a higher one. (Compare FL vs. FH for the same deviation on the diagram.)
In other words, the flatter the curve, the better. For the spring clutch example, the variation in release torque due to parts’ tolerances is less with a lower spring rate, improving manufacturability. Moreover, the spring’s dimensional tolerances can likely be loosened (e.g. wire diameter, free length, number of coils). Finally, wear and corrosion affect release torque less, improving robustness.
FORCE VS. DEFLECTION FOR DIFFERENT RATE SPRINGS
As the spring rate decreases, so does the force range for an equal deflection range.
As with all rules of thumb, there are exceptions. One is the counterbalance spring for a garage door, where the load changes with door position. Another is a plastic spring that, to avoid stress relaxation, must remain undeflected most of the time, yet provide high force when deflected. For assemblies that have different desired forces at more than one operating point, all of the points must lie on the spring’s curve. In this case, load points are sometimes overspecified. That is why Joe Altstatt always checks that all of the load points for a customer’s spring add up. “A lot of times they don’t,” he said, which requires at least some redesign before the spring can be produced.
But won’t a high-stress spring have a lower life in high-cycle applications? Probably, but this is not as bad as it first seems. Fatigue failure models such as Goodman diagrams account for both mean stress and fluctuating stress. For the same force, a low-rate, high-deflection spring has a higher mean stress compared to a high rate spring, but this is partially offset by a lower fluctuating stress. In any case, you will usually want to use the lowest-rate, highest-deflection design that meets the fatigue life.
Hints of Springs
Remembering a few explicit relationships revealed by the spring equations is helpful when optimizing a spring. For example, to decrease spring rate, increase the number of coils, decrease the wire size, or increase the coil diameter.
So to improve that inferior spring clamp, first add more coils to the spring, then increase the initial angular deflection. The maximum force and maximum stress can still be as before, but the initial force will be higher. If the spring is operating near the maximum allowable stress with the clamp fully open (and it should), you would need larger wire to increase the force throughout the operating range—but don’t forget to also reduce the spring rate.
Here is a final hint: the maximum force a spring can exert is limited by the mass of material in the spring. Once you optimize a spring design, to get more force, you need more mass—and more space. This becomes painfully clear if the space for a spring is already fixed, but the force is inadequate; playing with spring geometry alone won’t help. Another way of saying this is that beyond a certain point, the only way to reduce stress to the allowable limit is to provide more space for the spring. Instead, too many design engineers resort to exotic—meaning costly—solutions. Savvy ones leave extra space in their assemblies just in case, or test early and thoroughly; some do both.
Coil Springs: The Basics
SPRINGS ARE COMMON IN WORKING ASSEMBLIES: return springs, latch springs, clamping springs, detent springs, contact springs. They all store energy and supply force, the functions of a spring.
Most springs are simple wire wound coil springs. Among these, helical compression springs are usually the best choice because they are inexpensive, easy to assemble, and robust. Conical springs can be made to telescope reaching as little as one wire diameter in solid height. Extension and torsion springs need formed ends and are often difficult to assemble, making them less desirable, even if they are still the best solution for some applications (like the spring clamp).
Design engineers can take two different paths to successful coil spring design. The first is to specify an operating point or points and the corresponding loads, then consult a fabricator to create the spring’s geometry. The second is to use a spring program and fully define the spring’s geometry—wire size, free length, number of coils, and so on. Either way, be sure to consider both the operating point load and the optimal spring rate, as this article suggests. And never overlook tolerances, which are difficult to hold close, nor application-specific requirements such as temperature, corrosion resistance, and fatigue.
For more about springs
THE CURRENT HANDBOOK OF SPRING DESIGN is the 2002 edition, which was published by the Spring Manufacturers Institute of Oak Brook, Ill. The institute offers the volume for sale through its Web site, www.smihq.org.
COILED OR MACHINED? A manufacturer of machined springs looks at the advantages offered by conventional wound wire springs and the machined alternative. This month at Mechanical Engineering Magazine Online, www.memagazine.org.
James G. Skakoon, a frequent contributor to Mechanical Engineering, operates Vertex Technology LLC, an engineering design firm in St. Paul, Minn. He has written several books, most recently The Elements of Mechanical Design, published by ASME Press.
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