Sensors - May 1998 -The Helix Load Cell

A new type of load cell can be used in pairs to measure a pallet load as it is raised by a forklift. Four of these load cells can also be placed under a platform to create a portable weigh scale. In this photo, a zoo employee checks a lemur's weight as it stands on a sheet of plywood.

The Helix
Load Cell

A truly new load cell based on the principle of the wirewound spring can weigh the lion, the lemur, and the pallet load.

Robert W. Bruns, GageTek

eighing of loads in the trucking industry is becoming an increasingly important aspect of freight hauling. Most trucking companies have instituted weight checking programs whereby pallets are check-weighed and corrected invoices are issued for understated load weights. Using platform scales for check-weighing reduces productivity. A driver must take a pallet to the scale, set it down, then pick it up again once the measurement is made. This significantly slows the transfer process. Scales that directly attach the forks to the truck are bulky, heavy, and expensive, and reduce the forklift's capacity. Moreover, they are often damaged by normal forklift use.

Forklifts have lift chains that pass over the hydraulic ram in the mast and are attached to anchor bolts. It would seem a simple matter then to "instrument" a forklift by placing load cells on these anchor bolts below the anchor itself such that the tension of the chains would

Photo 1. For pallet weighing, the load cells are placed on the anchor bolts at the end of the lift chains. By measuring tension on the chains, the pallet load can be determined.

compress them (see Photo 1). Compression-type load cells, rather than tension types, would be the safest way to go because failure of a compressive cell would not affect the original equipment. Should a tensile link fail, on the other hand, the chain would break. We therefore obtained some of these commercially available "load donuts" and tested them.

The results were disappointing. The mounting and loading surfaces needed to be flat and parallel, but a comparison of forklifts revealed that the anchorages were rarely flat and often worn. An additional problem was that the anchor bolts wobbled back and forth as the chain's rollers passed over the cylindrical roller at the top of the mast. This wobble, ~0.060 in., was enough for the loading of the cell to go completely from one side to the other cyclically as the forks were raised. The resulting error was up to 20% of the applied load. A new load cell technology was called for.

The Helical Load Cell
We set out to develop a load cell with these properties:

Insensitivity to off-axis loading
Rugged and tolerant of shock loading and overload
Stops for up to 1000 3 overload
High sensitivity, infinite resolution
Through hole for easy mounting
Low cost

Figure 1. The helical load cell is based on the principle of the wirewound spring.

The first load cell we developed was a helical device constructed from a spring. Although it has been superseded by the Helix load cell, this original unit nonetheless serves to illustrate how the technology works. The helical load cell harnesses the properties of a wirewound spring to correct the deficiencies of conventional compressive load cells (see Figure 1).

A spring works by converting the vertical load force, F_L, to a torsional moment in the wire. This torsional reaction travels through the wire from the top of the helix to the bottom, where it is again converted to a linear

Figure 2. A freebody diagram of the helical load cell shows how the applied force is resolved into a shear and a torsional reaction in the wire. The torsional reaction is measured with shear-type gauges at points A and B.

reaction force, F_R. The helical load cell is insensitive to off-axis loading because of the manner in which the torsional moment propagates around the helix. At any two points diametrically opposed across the helix, the sum of the torsional reactive moments is always a constant, proportional to the applied load, regardless of where that load is applied.

Derivation of Strain Equations. This proportional constant can be derived by looking at the general strain equations at the point of application of a strain gauge (see Figure 2). An imaginary cut at any point in the spring allows the forces to be separated into their constituent components. Standard shear-type strain gauges are placed on the outside of the spring at locations A and B. A force, F, is applied to the top surface of the spring.

The total shear force, , present at gauge A is:

(1)

where:

F = applied force
A = cross-sectional area of the coil
T_A = resisting torsional moment at gauge A
r = radius of the wire constituting the coil
J = polar moment of inertia of the wire

The resisting torsional moment, T_A, at gauge A is, by inspection:

T_A = Fa

(2)

where a is the distance from F, which is the force applied to the centerline of the coil at gauge A.

Combining Equations 1 and 2:

(3)

Likewise, the shear force at B is:

(4)

By wiring the gauge at A with the gauge at B to form a complete Wheatstone bridge, the voltage output is proportional to the sum of the shear forces:

(5)

and

(6)

Since (a+b) is equal to the mean diameter D of the coil:

(7)

(8)

(9)

Thus, the total shear force _TOTAL measured by the two diametrically opposed strain gauges A and B is directly proportional to the loading force F, where the constant of proportionality k is:

(10)

Since the proportionality constant k consists only of the physical parameters of the coil, the total shear, _TOTAL, is completely independent of the position of the load. Loading anywhere along the top surface of the coil produces the same _TOTAL. Likewise, loading outside the diameter of the coil will also result in the same _TOTAL. This load cell is then, theoretically, completely insensitive to off-axis loading.

Photo 2. Testing demonstrates that the load cell's accuracy is not adversely affected by off-axis loading or use on a tilted surface.

If the applied load F is not in line with the two gauges, as shown, then a resultant moment, M, on the base of the load cell results from the requirements of static equilibrium. By placing the strain gauges along the neutral axis of the wire, the strains present at the gauge location due to this moment are equal and opposite on the upper and lower halves of the gauge, and are completely canceled. The bridge output is then still proportional only to the applied load, F.

Testing indicates that even with extreme off-axis loading and upper and lower surfaces subject to tilting of several degrees, the accuracy of the helical load cell typically remains within 0.4% total error (combined nonlinearity, repeatability, and hysteresis) compared with the on-center calibrated condition (see Photo 2).

Refining a Spring
While using a spring resulted in a good compression load cell, the design had several drawbacks. Attaching a cover was difficult, as was strain relief. Residual stresses remaining from the winding process had to be removed before calibration. Threaded ends had to be welded on for tension applications.

Figure 3. In this exploded view of the Helix load cell, the circular sensing element is shown with the strain gauges attached.

A spring is also a shape without symmetry about any point, making casting impossible. Available shapes and sizes were limited by the spring winding process itself, rather than the possible forms. So the basic geometry of the spring had to be refined.

Our "spring," cut or cast from stainless steel, became a flat, circular sensing element in the center of the Helix load cell, augmented by strain gauges (see Figure 3). This design is easy to cast, has low residual internal stress, easily accommodates threaded ends for tension, and, for a given capacity, is smaller than the helical load cell. Both types are shown in Photo 3.

Photo 3. The helical and Helix load cells are manufactured in a variety of configurations and capacities. Those shown here range from 3000 lb. to 10,000 lb. capacities.

The active portion of the Helix load cell is the sensing element. An applied force travels from one end of the element to the other. The only function of the top and bottom disks is to provide surfaces for applying the load. The cube configuration of one of the load cells in the photo is possible because the general formulas applicable to this type of load cell are independent of shape. The configuration of the sensing element is unimportant, as long as it completes a 180� change in direction while propagating the loading force, and the gauges are set in diametric opposition to each other. This condition is always met when the line drawn between the gauges is perpendicular to the tangent of the direction of the element at the point of application of the gauges. The combined torsion from each gauge adds to a constant that is proportional to the load and to F x D, where D is the distance between the neutral axes at the point of application of the strain gauges. As with the helical load cell, this constant is independent of load placement. Controlling Sensitivity and Capacity
The distance between the strain gauges, which is the effective diameter, along with the diameter of the sensing element control the load cell's sensitivity. This can be useful when tailoring a load cell to a particular application. The sensing element can have a very long effective diameter and still be

Figure 4. The Helix configuration can take any shape, as illustrated by this "load cube." The sensing element can be seen within the block and, with strain gauges placed as shown, retains the same strain characteristics of the original wirewound spring.

sensitive to very small loads. Likewise, a less sensitive load cell can be constructed by shortening the effective diameter. Generally speaking, the capacity of the Helix load cell is increased by increasing the element's diameter while decreasing the effective diameter of the load cell.

The Helix load cube (see Figure 4) is constructed to maximize the load for a given size, and has been cut from a solid block of material by slotting. Strain gauges are attached to opposite sides of the sensing element. The through hole has been eliminated, allowing a maximum cross-sectional size of sensing element with a minimum effective diameter. Thus a 10,000 lb. load cell fits into a cube 1.5 in. wide and 1.3 in. tall. Mounting holes can also be drilled and tapped in the upper and lower load bearing surfaces.

Photo 4. Helix load cell capacities vary with the thickness of the wire and the diameter of the unit. The wire load cell in the rear has a capacity of 1000 g.

Photo 4 shows Helix load cells of various ranges. The low-capacity unit used for the wire scale has a sensing element with a large effective diameter. A loading platform and base are attached directly to the ends of the sensing element. This simple scale has a capacity of 1000 grams and is insensitive to the weight's position on the loading surface. Shock and Overload
All helical and Helix load cells have the same ancestor, the spring. Overload stops are intrinsic when the load cell is built such that the spring is compressed to solid at overload. This is accomplished by controlling the spring's pitch, or the slot width in the Helix load cell. By matching the slot width of the Helix load cell to its capacity, the cell is compressed

Photo 5. The load cells and related equipment are easily transported in a carrying case for on-site weighing of horses and other bulky objects. The digital readout unit is mounted on the tripod for convenient viewing.

to solid at capacity and a 10-100 x overload rating can be achieved without damaging the cell or overstressing the strain gauges.

The Helix load cell's natural compliance reduces shock. Impulse is the product of acceleration and time—the more the Helix load cell compresses, the greater the increase in the temporal component with a corresponding decrease in the peak acceleration. It withstands rough handling—in one year of placing these load cells on forklifts, not one has failed from shock or overload.

Applications
Four load cells can be configured into a compact portable scale (see Photo 5) that can work with virtually any platform and perform equally well on dirt or concrete. The Sacramento Zoo uses the scale to weigh its collection of animals. Exotic animals are rare and valuable, and tracking their weight is an important part of determining and documenting their health history. Nonaggressive animals such as lemurs or tortoises can be weighed directly on the floor of their cages. Lions and other big cats can be readily weighed while anaesthetized during physical examinations (see Photo 6). The zoo

Photo 6. A lion, considerably less docile than the lemurs, is weighed while under anesthesia for other medical checkups. The adhesive tape keeps an O2 apparatus in place during the exam.

has also undertaken to build false flooring in feeding and transfer areas so that when a weight is wanted, the Helix load cells can be placed beneath that flooring. The giraffe could then be weighed any time it is feeding, or the tigers as they walk between the outdoor viewing area and the indoor holding facility.

For Further Reading
Joseph Shigley. 1963. Mechanical Engineering Design, McGraw-Hill:284-289.

Robert W. Bruns is President, GageTek, 11470 Sunrise Gold Circle #3, Rancho Cordova, CA 95742; 916-853-1265 fax 916-853-1465, bbruns@gagetek.com