Accounting for lost motion

Jan. 11, 2007
Backlash and deflection are critical factors when designing mechanical control cables.

Werner Steuernagel
Vice President — Engineering
Cable Manufacturing & Assembly Co.
Bolivar, Ohio

Edited by Kenneth Korane

Mechanical control cables feature either a solid-wire or wire-cable core housed within a conduit. They provide a simple and reliable method to activate throttles, latches, and other mechanisms.

Backlash is the lost motion caused by clearance between the core OD and conduit ID, and is present in both push and pull modes.

Deflection is lost motion from elastic strain in tension and compression.

Input load factors provide general guidelines regarding friction in a system.

Mechanical control cables provide a simple, lightweight, economical, and reliable way to activate throttles, latches, gas springs, electromechanical devices, and many other mechanisms. They're widely used in office furniture, recreational vehicles, lawn mowers, and medical devices, as well as adjustable seats in cars and planes.

The basic design features a movable core — either a solid-wire or braided wire-rope cable — that's free to travel axially inside a conduit. Actuating a lever or similar device at one end of the cable assembly produces output force and motion at the other end.

Solid-core controls are generally used to transmit force in both push and pull directions. The ends of solid wires can be formed to eliminate the need for separate fittings and terminations. But the solid wire requires large bend radii and simple routing to avoid kinks, drag or surface friction, and permanent set. All push-pull controls have greater load capacity in tension than compression — they can pull more than they can push.

In some cases stiff, small-diameter wire-rope cables can be used in push-pull applications, provided push loads are light and the cable and conduit are carefully matched. However, these so-called flexible-core controls are usually found on pull-pull controls that transmit tensile force in both directions. For high-load, push-pull applications, specially designed wire cores are available which maintain high flexibility yet permit loads to 100 lb.

In general, more-flexible conduits and cores provide greater routing freedom and smaller bend radii in restricted installations. They often feature return springs, which maintain specified loads on the cables and return mechanisms to their original position after activation.

Engineers should consider parameters such as load, routing, friction, stretch, permanent set, lost motion, temperature, environment, and exposure to contaminants when specifying cables. Here's a look at these critical factors.

Load factors. For push-pull controls, the cable assembly's rated working loads should be in the pull or tension mode. Push, or compression, loads should be ≤50% of pull loads. Reducing the push load minimizes a core's tendency to displace the conduit and, more importantly, reduces the potential for the unsupported core outside the conduit to kink, bend, or distort.

Base maximum pull-pull working loads on the cable's minimum breaking strength, plus a safety factor. Also consider the conduit's resistance to deflection and compressive forces, and cable-assembly end-fitting selection. High loads and cycles can cause the cable to stretch and wear through the conduit liner. Core and conduit must remain as originally routed for an assembly to function properly.

Travel. Experts recommend 5-in. maximum travel for most light and medium-duty push-pull applications. This minimizes lost motion and potential for the core to buckle. Use even shorter travel lengths with small-diameter cores.

Travel in pull-pull applications has fewer restrictions and can generally exceed 5 in. However, if the core is subject to hostile environments, minimize the stroke to limit exposure outside the conduit.

Perhaps the least-understood design factor is lost motion. All push-pull controls lose some motion between input and output sides when applying a load to the system. Lost motion increases with higher loads, more bends, and longer assembly lengths. It can be overcome by designing over travel into the system at the input or output ends, or both.

Lost motion results from deflection and backlash.

Backlash is caused by the clearance between the core OD and conduit ID, and is present in both push and pull operating modes. It is proportional to the number and length of bends in the installed assembly, and the clearance between core and conduit. Calculate backlash B using:

B = X R2/180 X R1/180

where R1 = centerline of core in tension (no load); R2 = centerline of core in compression (no load); and X = total angular degrees of bend in the routing.

Deflection comes from elastic strain caused by tension and compression loads on the control. Calculate deflection ΔL as:


where F = average force, or one-half output load + one-half input load; L = length of active inner core; A = core cross-sectional area; and E = the core's modulus of elasticity.

Note that actual deflection of a control in compression may vary from calculated values based on the column strength of the core and conduit and the buckling potential. And lost-motion calculations assume the control is securely mounted on the ends and the conduit is firmly held in its routed position.

Lost motion is also a factor in pull-pull controls. They typically have little backlash because they operate under tension. However, these controls are subject to the same deflection factors as push-pull controls. And routing always affects the travel length. In some cases, lost motion can be accurately calculated. In others, installing a prototype in the system to confirm correct design length and travel is highly recommended.

Efficiency. The conduit, core, and number of bends, as well as relative friction between core and conduit, determine a push-pull control's efficiency. Depending on the materials, good practice is a 2 to 10-in. minimum bend radius. Estimate the minimum bend radius by multiplying the core diameter by 100.

Bends in the system create friction and reduce efficiency. Estimate frictional effects from:

I = P f

where I = actual input load; P = output load; and f = input load factor, found in the accompanying graphic. Percent efficiency is then determined from:

η= (P/ I) 100.

In pull-pull controls, cable cores generate more friction than solid-wire cores. Most cable controls use 1 X 19 cable because it has a relatively smooth OD and is more flexible than solid-wire cores. For applications requiring more flexibility, specify 7 X 7 cable. However, with 7 X 7 cable, higher loads reduce efficiency and can subject the liner to undue wear and damage.

Proper alignment and mounting also help increase efficiency and cycle life and reduce working loads. In cases where a lever arm moves, mount the control to minimize angular deflection of the core. If possible, specify a fitting or assembly that rotates at the mounting point.

Conduit and core selection
Most applications use braided, reinforced conduits. Braided conduit is generally coated with polypropylene (relatively stiff) or nylon (more flexible and heat resistant). The accompanying tables list some common conduit designs and offer core recommendations for various applications.

All conduit and core combinations should include a reasonable clearance between the conduit ID and core OD. For most light and medium-duty pull-pull applications, a 0.015 to 0.025-in. clearance is recommended. Note that decreasing the clearance to minimize the effects of lost motion can dramatically increase operating forces.

Cable Manufacturing and Assembly Co.,

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