Building a Sensor to Measure Weight, using a Potential Divider and Wheatstone Bridge.

Physics Sensor coursework 25/04/07 James Ashley-Smith

Deps

Initial Ideas:

Firstly I needed to have an idea of what I would have liked to investigate about sensors, whether it be to evaluate against a ready-made sensor or to build and calibrate a sensor. I decided on building and calibrating a sensor as I feel it would be more creative. Then I brainstormed a couple of ideas to build, for example measuring the speed of water by measuring the time it takes the water to fill a cup, so increasing its weight. Another idea was to build an accurate weighing device that works in two directions, the first the conventional way using gravity and the other using a pulley system to measure the upward pulling force.

I chose the second idea as I felt the first idea would be to long an experiment as it involves more stages of planning. The first idea is very similar as it also measures weight, but has a different specification. In my primary thinking I realised using a potential divider to measure the weight would be accurate and make it easier to involve equipment we have been shown. The first piece of equipment I thought would be a useful item to use was the strain gauge. These measure the strain on a material, in this case a hacksaw blade. The gauge is on top of the blade and when it is bent down the resistance of the gauge increases, where it is bent up it decreases in resistance. I now have my idea and the specific apparatus I need to start planning the experiment.

Planning:

Apparatus:

Power supply

Resistor

Multi-meter

Wires

Weights

G-clamp

Strain Gauge

Diagram of Double-sided Strain Gauge in action

In order to make a sensor that can weigh items, I assumed I needed to make the circuit that would give me a voltage output. I had studied the circuit for a potential divider and so I am familiar with the design. It needs two resistors, I knew one was from the strain gauge and thought the other was for a fixed resistor. At this point I found a double-sided strain gauge, which is useful because it is more sensitive. The two gauges compensate for each other so the output voltage is doubled for a certain strain making the sensor more sensitive. This is ideal for my sensor, as I wanted to make an accurate weighing scale that could measure a 1 g weight difference. I also found that an additional bonus is that the double-sided strain gauge is not affected by temperature. This is because if the temperature of one of the gauges increases then it does so for both so the output voltage does not change. However this is not that relevant for my idea as I will be only measuring small weights and the voltage will be small so the current will not be great enough to heat the gauge by very much. On a broader scale, if the design of my sensor were to be used elsewhere then the bonus might be useful. To finalise my circuit I have decided to use a 5-volt power supply and a digital multi-meter.

When I set up the experiment I had to position the strain gauge where it is most flexed, this is closest to the pivot point. Also I have resolved that placing the weights at the furthest point on the hacksaw blade will increase the leverage on the gauges so they will detect a larger range of strain.

To calibrate the circuit I needed to use set amounts of weights; I used weights increasing from 0 g to 1600 g, increasing by 200 g each time. To prepare for the experiment ahead I needed to find the starting resistance of both gauges and see how much their resistance change with strain. At this point I started the first run of the experiment.

Predictions:

As the weights are added the resistance increases in the top gauge and so the voltage across the top gauge ...

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Predictions:

As the weights are added the resistance increases in the top gauge and so the voltage across the top gauge increases and so decreases across the lower gauge. Therefore I predict that the curve of the graph that is associated with the potential divider circuit, which plots output voltage against the weight, will be a negative curve, because as the gauge is strained the voltage across the top gauge will increase, due to the resistance increasing. With this circumstance the voltage output across the bottom gauge will decrease due to the circuit dividing the voltage. The curve should be close to a straight line, as this would suggest that the voltage decrease would be regular, which obeys Hooks Law.

Development:

After I had taken the first set of results from the potential divider, I found that the sensitivity of the voltage output was not good enough. I was measuring to two decimal places and the range of results was not broad enough. The potential divider sensor could only measure 0.01 V for a change in weight of 800 g giving a resolution of 0.0000125 V/g, which is not accurate enough for the sensor’s specification of (0.01/1) 0.01 V/g. To improve this resolution I had to determine how I could make the sensor more sensitive. I found that in order to measure a smaller change in voltage, I needed a smaller voltage output so I could change scale on the digital Voltmeter. This meant all I needed to do was either turn down the voltage or connect a resistor in series, as this would limit the voltage used for the two gauges. I chose to use a 470Ω resistor as this means if in the future I had time to repeat the results I would not need to reset the voltage output on the supply.

I could now read to three decimal places, this was an improvement giving me sensitivity reading, ranging from 0.002 V to 0.005 V for a change in mass of 200 g. Still this is not sensitive enough, as it gives me a resolution range from 0.00001 V/g to 0.000025 V/g, my targets resolution for this circuit was (0.001/1) 0.001 V/g. To suit my specification I decided to change the design of the circuit so that the resolution was improved. To do this I intended to use a Wheatstone bridge to show the voltage output. These circuits involve four resistors that to start with are balanced, if the resistance in the circuit changes then a potential difference will be shown, which then be countered by the variable resistor. The combination of the three known resistors allows us to determine the fourth value.

P and Q are the gauges; R is the variable resistor that I will adjust every time a weight is added, to keep the sensitive galvanometer reading 0. This indicates a balanced circuit, S is the fixed resistor of value 10 000 Ω to make the circuit more sensitive by decreasing the voltage output, this also means the variable resistor can be changed by 1Ω, so the resolution is 1 Ω in 10 000 Ω.

For this next experiment I decreased the weight change from 200 g each time to 100 g to make use of the extra sensitivity in the circuit. I have designed the circuit as above, because I know that when the gauge is bent down with weights the resistance of the gauge on top of the hacksaw blade will increase and the gauge on the bottom will decrease. This means P increases and Q decreases, as a result R and S need to match this so R increases on a variable resistor and S is kept as a control as it is not needed to change.

Predictions 2:

With the new circuit the results will be different and so a new prediction is required. With the Wheatstone bridge the resistance of the variable resistor will need to increase to counter the increase from the gauge. I predict another influencing factor will be that as the weight increases the difference in resistance change will be smaller. I predict this because I found from the previous experiment that, initially the weights bend the blade and the gauges. Then as the blade becomes more vertical due to considerable weight on the blade, the force from the weights will start to pull the gauges longitudinally and not bend them as much each time an extra weight is added. This means the force bending the blade has been increasing through the experiment, but will not have done so with a regular series between the readings. This is due to the total force being divided into two individual acting forces, one the force bending the blade and the other the force pulling the blade and the gauges. Over all as the masses increase the difference in resistance will be smaller. The effect of this will be that the resolution will be small and so more useful for the sensor, but then for larger masses the resolution will increase as the difference in resistance will be smaller. This would mean the graph, which plots resistance of the variable resistor against the weight will begin low as there will be no load on the blade so no extra resistance, then as more weights are added the resistance will increase as the blade is bent more. I know that the larger the weight the smaller the resistance increase between the readings, this will be shown on the graph by a curve that tends to a line that is parallel to the x-axis.

Results:

Using the Potential divider

As you can see from the graph the metre can not detect the change in voltage to a smaller enough voltage. So the results were repeated with the extra resistor as described above to give more sensitive results.

The results now give a more defined graph that shows that as the mass increases the voltage output decreases, as the voltage across the top gauge has increased. In this potential divider circuit the bottom gauge will therefore have less voltage across it.

Using the Wheatstone Bridge

Analysis:

With the Wheatstone bridge and other experiments complete I must interpret my data so that I can fulfil my aim. My ultimate aim is to be able to weigh an object and find out what its weight is to the nearest gram.

I will start by analysing my results; the potential divider shows me that as the weight increases the voltage output decreases. This agrees with my prediction, but the prediction is based on theory, so in fact the line I have recorded is a curved asymptotic line tending from a steep negative line then dropping to a flat line parallel to the x-axis. This is indicated on the graph, by the curve, which has a starting gradient of 2.5. 10-5 V/g. This is a steep negative gradient, then by 500g the gradient is 6.10 –6 V/g. The line is almost horizontal by 1600g, which show that the voltage change across the Strain gauges is decreasing by a very small value each time a mass is added.

I have concluded from these results that gravity is a main force on the strain gauges, my method uses the weight from the masses to bend the hacksaw blade. As more masses are added, the blade is bent towards the ground. As the mass’ total increases the blade is made to bend more, so that is starts to become vertical, this means the masses are pulling the blade and not so much bending it any more. The gauges can not detect the longitudinal force so the energy from the masses is lost effectively and now the reading will increase by a smaller amount. This means when using the graph to find a weight of an item it might be difficult due to the scale of the graph, also any errors that might have occurred in the experiment could have significant effects on the resistance reading and therefore the result from the sensor. This could be incorporated into the method of finding an item's weight by using the graph as a calibration chart. I found that the resolution for this potential divider was about 0.000125 V/g. I can read the digital voltmeter to two decimal places so 0.01 V/10 g gives me a target resolution of 0.001 V/g. With respect to the potential divider this is not bad and is only a factor of two powers out, but I found I could do better with a Wheatstone bridge.

When using the Wheatstone Bridge the variables were different it records the resistance of each resistor in the circuit that work to balance the voltage output across a volt-meter to 0. In my circuit I only changed one resistor with a variable dial, not including the strain gauges, so I could in fact record a graph from this resistor and use it to estimate the weight of items. This would solve my problem and this method is commonly use in the rest of the world, the graph is called a calibration graph.

Overall the improvements I made, made the circuit more efficient. To start with the resolution of the potential divider, graph 2 was 0.000125 V/g. With the Wheatstone Bridge, it was initially able to measure a 2 g increase to change the resistance by 1 Ω and with larger forces, this increased to 50 g to change the resistance by 1 Ω. My target resolution for this circuit was for 1g to change the variable resistor by 1Ω as that was the resolution of the variable resistor. This resolution accuracy was small enough to satisfy my aim and make the Wheatstone Bridge the best circuit for the sensor.

Evaluation:

Through the time it took me to complete my aim with several experiments, there are a couple of areas I felt could be improved. Firstly with more time it would have benefited the results, if I were to repeat a single experiment more than once so an average could be taken. It has not really affected my results so far, as the experiments I have completed are continuations of each other so as all the results have followed the path I expected there has been no cause of alarm and few anonymous results. This was lucky as the two strain gauges had systematic errors of about 2 ohmes due to the resistances of each gauge not being equal.

As I progressed through the experiments I found that some of the weights were not quite the same, since I noticed this early on I decided to just use the 100g hooked weights that were provided. By limiting the range of weights used, any inaccuracies with a set of weights were carried through the experiments and so not affect the formations of graphs.

In particular on the potential divider circuit, when I added a small resistance to the circuit, I should have maybe explored the results with more than one value of resistor. This would have checked the results recorded and the effect extra resistance may have on the gauges, however this was not part of my experiment so is not important.

With the Wheatstone bridge circuit there were not enough multi-meters to measure the individual resistance of the two strain gauges through the experiment. This means that in the future I will need to use the same strain gauge in the sensor to measure the weight of items, so the resistance values are the same for a certain weight.

If you look at the graph to the left you can see that it shows the resistance increase between each reading. It starts high because the sensor is more sensitive with lower weights. However as we proceed along the x-axis the average resistance increase does decrease, but in reality the line is not smooth. This could be because of the mild steel the blade was made out of, it might not have bent a uniform distance for one reading, but then for the next reading the blade might have given more and so bent more than the uniform distance. This would explain the little peaks to the graph. This effect might also have been caused by the way the gauge was mounted on the blade. To diminish these results I would have to take repeats and then average them.

In conclusion I have explained all the areas I feel that needed to be explored so I am in a good position to create a better sensor that works according to its aims. In the future in order to make the best sensor, areas such as the material the blade was made out of and different types of gauges should be investigated. I think the gauges I was using were silicon crystal gauges and the blade was mild steel. The effects from these experiments would determine what materials are best for a sensor that measures weight. If I were to redo this experiment I would have taken more repeats.

Reference:

Advancing Physics AS (Jon Ogborn and Mary Whitehouse)

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