This web page presents details regarding the design of a strain gage based load cell that can be used, in conjunction with an electronic data acquisition (DAQ) system, for static thrust measurement of a rocket motor. The load cell described here is meant to be relatively simple to make, versatile to design with regard to load capacity, sufficiently accurate for its intended use, and inexpensive. The total cost of a load cell made by this method would typically be no more than $10-20 USD. Of course, the underlying reason for constructing a load cell isn't measured in "dollars and sense", but is part of the fundamental premise of amateur experimental rocketry -- the desire to fabricate, whatever is practical, from scratch.

The type of load cell that is being presented is basically similar to a bending beam type. When a force is applied to the load cell, the beam (or bridge) onto which the strain gage is mounted, is subjected to combined bending and axial compressive stresses. The bending stress is by far the dominant component, hence the term "bending beam". Importantly, the relationship between the applied force and the combined stress in the beam is linear.

The stress in the beam results in corresponding strain of the beam material, and also of the strain gage (which is bonded to the surface of the beam). Strain is defined as change in length divided by the original length. The relationship between stress and strain is linear, related by the Elastic Modulus (E) of the beam material. The electrical resistance of the strain gage is linearly proportional to the strain, with the net result being that the output signal from the load cell is linearly, or directly, proportional to the applied load, simplifying calibration and use of the load cell.

An important feature of the load cell is that total displacement under load is very small. This is significant, as it nearly eliminates unwanted dynamic effects associated with mass and large displacement (e.g. spring) systems.

When I originally came up with the idea of making a load cell, I wanted to simplify the construction as much as possible, while meeting certain criteria. For one thing, a compression load cell is most appropriate for thrust measurement,. Another criterion was to minimize displacement under load, as I had had a problem with my earlier Static Test Rig which had utilized a strain gage mounted on a cantilever beam. The deflection for that system was significant enough under loading such that it proved to be necessary to add a hydraulic damper to eliminate oscillations.

What eventually evolved was the concept shown in Figure 1. The load cell consists of a block of metal (steel, alumininum or brass) with a single hole drilled through it. To generate the required bending strain, a slit is cut on one side to create bending bridge on the opposite side, to which a strain gage is bonded. Two gages mounted side-by-side will provide double the output signal (and thus double the sensitivity and resolution) of a single gage. Mounting of the load cell is achieved by a single bolt which screws into a tapped hole at the base of the load cell.

Figure 1-- Diagram of Load cell

Figure 2-- Determining gage strain

The equation shown in Figure 2 gives the strain at the gage location (e_gage) in terms of the applied load, as well as geometry and the material property of the load cell body. As mentioned in the introduction, the strain is directly (linearly) proportional to the applied load, and is inversely proportional to the body thickness (t) and the elastic modulus (E). In terms of geometry, the defining parameters are the body width (B), hole diameter (D) and the location (b) of the applied load (P). The relationship between geometry and strain is non-linear, in fact, being quite sensitive to the dimension (B - D).

Therefore, it can be seen that there are four geometrical variables that determine the strain of the load cell:

1. Body width (B)
2. Body thickness (t)
3. Hole diameter (D)
4. Location of applied load (b)

• B/3 £ D £ 2B/3
• B £ H £ 1.75B
• B/8 £ t £ B/2
• b ³ B/2

The negative sign indicates that this is compressive stress. The term k is a stress concentration factor obtained from Figure 3, and units of measure are lb. or N. for force, and in. or mm. for dimensions.

        

Figure 3-- Stress concentration factor chart and table of allowable stress

The load cell should be designed such that the maximum body stress under full applied load is approximately half the Yield Stress (Fty) of the body material. This is to ensure that no permanent strain occurs to the load cell which could affect its calibration. Recommended maximum stress values are given in Table 1.

Generally, a load cell will be designed based on available (on-hand) material, to minimize the amount of metal cutting. For example, the design might be based on an available bar of aluminum, which needs only to be cut to the required length. Therefore, it is only necessary to drill the two holes, cut the slot, and file the vee notch. Particular care should be taken with regard to the body hole. The location should be accurately marked out, then drilling should be done by drilling a series of progressively larger holes, to ensure that the location does not "shift" while drilling.
The vee notch is important because it precisely determines the load application point. Load should therefore be applied to the load cell with a corresponding vee shaped device. For the prototype load cell, I initially used a shallow hole rather than a vee notch. This did not work nearly as well, as the load bearing surface around the hole tended to shift, leading to inconsistent results.
The bottom mounting hole should be drilled at approximately mid-width, then tapped to the desired thread size. The slot is simply cut with a hacksaw, and the vee notch is made with a file after accurately marking the location.

The strain gage is mounted at the location shown in Figure 1. If two gages are used, they are mounted side-by-side. The gage is to be mounted with the grid lines running parallel to the long edge, as shown in Figure 1. The gages are bonded with cyanoacrylate or epoxy adhesive (epoxy is easier and perhaps more reliable). It is important to lightly sand the bonding surface with 600 or finer grit sandpaper, then to clean the surface with acetone or lacquer thinner.

It is highly recommended to use a strain gage with lead wires attached. The strain gages that I purchased did not have lead wires, rather, only a pair of solder pads, which were very tiny. Soldering the lead wires (I used 30 AWG wire-wrap wire) onto the pads could only be accomplished with the aid of a illuminated magnifier lamp. The strain gages which I used were OMEGA SG-3/350-LY43 (Cost=$45 USD pkg. of 10). A similar type, but with lead wires attached, would be KFG-5-120-C1-11L1M2R (Cost=$59 USD pkg. of 10). After bonding, the strain gage is covered with a protective layer of epoxy, immersing a portion of the lead wires, as well.

To test the concept, I decided to build a prototype load cell using a small block of 6061 aluminum alloy that I came across in my metal stores. Having need for a load cell of 250 lb. (1100 N.) capacity, I determined hole diameter, hole location, and load application point to achieve this goal, based on the dimensions of the block.
Dual strain gages were used for greater resolution.
The finished product is shown in Figure 4, with the design data shown in Table 2.
The maximum deflection under full load was measured with a "feeler" gage, and found to be a mere 0.0035 inch (0.09 mm).

Figure 4-- 250 lb. capacity dual-gage load cell

Table 2-- Design data for prototype load cell

The method used in calibrating the prototype load cell was similar to that used for calibrating the Hydraulic Load Cell. A 32 inch (80 cm.) lever arm was used to amplify an applied load of known magnitude. The applied load consisted of a container of water of known mass which was suspended at the end of the lever arm. An amplifier circuit was used to measure the resistance change of the strain gages as an increasing amount of weight was applied. The setup for the calibration test is shown in Figure 5, and the results of the test are shown in Figure 6.

An alternate method of calibration that is simple and accurate would be to employ a Hydraulic Load Cell to precisely meter the force applied to the strain gage load cell.

Figure 5-- Calibration setup for prototype load cell

Figure 6-- Calibration curve for the prototype load cell

In order to verify the design methodology, a number of 3-D finite element method (FEM) models were made of various configurations and capacities, utilizing a solid modeler software package. A typical model consisted of more than 1000 tetrahedron elements, with stress/strain results obtained by use of a NASTRAN solver. An example is shown in Figure 7, illustrating the stress contours.

Comparison of predicted gage stress was in good agreement with the FEM models. Prediction of maximum body stress tended to be conservative by about 10 percent.

Click for more details

Figure 7-- Verification FEM model of a 1000 lb. (4.45 kN.) capacity load cell. Stress range is shown, red is highest stress

To greatly ease the design process, an Excel spreadsheet was created. The user simply need enter the desired load capacity, the basic dimensions of the load cell body, and the material. Subsequently, the hole diameter, hole location, and load application point may be chosen such that the maximum body stress does not exceed the values recommended in Table 1. An interactive pictorial of the load cell aids the design process. An example of the spreadsheet appearance is given in Figure 8.

Figure 8-- Sample Excel spreadsheet

---

Link to download Excel spreadsheet:
LOADCELL.XLS