Note: Try to complete tasks 4.1.2, 4.3.1, 4.4.1, 4.4.2, 4.5, and 4.6.1 before coming to the WorkINGLab so that you have more time for the experimental part.

1. Context of the Experiment

This experiment concerns resistive sensors and especially their usage in Wheatstone-bridges. Resistive sensors transmit information by a change in resistance due to external influences such as temperature, bending, light, etc. In the course of this experiment, you will learn, how to measure this change, even if it is very small, and how to compensate for some common errors.

2. Learning Goals of this Experiment

• Know: Wheatstone-bridge and why it is useful

• Abilities: choosing the correct setup for resistive sensors, handling Wheatstone-bridge/multimeter/(oscilloscope)/strain gauges/amplifiers

• Understand: how to compensate for certain errors

3. Literature

[1] Lectures: resistive sensors, electrical measurement technology

[2] Keil, Dehnungsmessstreifen. Wiesbaden: Springer Fachmedien Wiesbaden, 2017.

[3] P. L. Regtien, Hg., Sensors for Mechatronics // Sensors for mechatronics. Amsterdam: Elsevier, 2012.

[4] HBM-homepage: Wheatstone-bridge circuit (German webpage with correct table: https://www.hbm.com/de/7163/die-wheatstonesche-brueckenschaltung-kurz-erklaert/)

Necessary further reading/datasheets:

4. Basics/Fundamentals

Wheatstone-Bridge

To measure small resistances or measure their value very exact, using a measurement bridge is reasonable. One common measurement bridge is the Wheatstone-bridge (fig. 1) that consists of two balanced voltage dividers. One to four unknown resistances are compared to (known) resistances, which leads to a much more exact measurement of the resistances than by purely measuring voltage and current.

Figure 1: Wheatstone-Bridge

Strain-Gauges

In this experiment, you will be using strain gauges in different measurement setups and bridges. A strain gauge basically consists of a metal measurement grid on top of a backing film that is covered by a protective sheet. The metal measurement grid consists of many turns, therefore, it changes its resistance once it is being stretched.

Strain gauges change their resistance as a result of applied strain. The change in resistance in comparison to the nominal resistance equals the k-factor of the strain gauge multiplied by strain:

For calculating the mechanical stress applied, the law of hook with the mechanical stress σ, the elasticity module E and the strain ε can be used:

The Wheatstone bridge can be used in a full-, half- or quarter bridge-setup, using zero, two or three known fixed resistors respectively that have the same resistance as the strain gauges nominal resistance. Using the voltage divider, the following equation can be used for the Wheatstone-bridge

As strain gauges only have small changes in resistance, assume all strain gauges and all other resistors have the exact same nominal value R₁=R₂=R₃=R₄.

Due to the difference voltage being in the range of mV, amplification is necessary. The amplification factor .

From these equations, you can obtain the necessary formula for the experiments tasks for all different bridge setups.

ADCs

In this experiment a HX711-sparkfun 24-bit Analog-to-digital-Converter (ADC) will be used. This device also amplifies the measured signal before converting to digital values. Please read the electrical measurement technology lecture for further information on ADCs.

5. Technical Basics & preparations

• All strain gauges have a nominal resistance of 350 Ohms and a k-factor of 2.

• Build your own Wheatstone bridge using the supplied resistors

  • amplification is necessary, use the sparkfun HX711

General instructions

• Always balance the Wheatstone-bridge anew after you changed the setup!

• The supply voltage is set by the HX711.

• For different bridge setups, it might be necessary to consider the strain you want to measure and its direction/the direction in which the strain gauges are placed in your formula! Superposition of factors might happen.

• Always make sure, the Arduino is set to the correct baud-rate and the port is correctly chosen.

Preparations:

• Gather all the necessary measurement objects and instruments:

  • Sparkfun HX711

  • 350 Ohm resistors

  • Breadboard

  • Cables to connect

  • Arduino Uno & Cable

• Install the Arduino IDE and the packages and download this program:
  

Troubleshooting:

In case you find your sensor reading always a raw value of ~16 mio or 0, check if one of the following errors might have occurred:

• Are all the resistors and cables well-connected? There might be a loose contact.

• Is your USB-cable plugged in? Does your Arduino have power?

• Did you connect the correct Arduino-pins?

• Check with the multimeter, if the Arduino actually outputs 5V.

• Check if your cables are connected to the luster clamp and the strain gauge.

• Do the Breadboard-interconnections work?

- If you can only read a combination of characters, that makes no sense - check if the baud-rate of your program and your serial monitor are the same.

6. Experiment Procedure

4.1 Use the bending beam, but only connect a single strain gauge using the luster terminal. Make sure that you're connecting the longitudinal strain gauge! To see which one is the longitudinal one, try to hold it into the light and check the direction of the strain gauges windings.

4.1.1 Use a multimeter to measure the resistivity change when loading the beam with the the caliper box (which acts as a defined weight) from the drawers assigned to your seat. (for this task a measurement is necessary)

4.1.2 If you had a 10mA current source like in fig. 3, what voltage change would you expect across the strain gauge for a 1‰ strain of the beam (task a)? What voltage change would you need to measure, if you want to resolve the maximum strain of 1‰ to 100 steps (task b)? (for this task you only need to do a calculation, no measurement required)

Figure 3: current source setup

4.2 Now use the breadboard and additional resistors to build the setup from fig. 4, a voltage divider, using the strain gauge instead of R1. Connect the 5V supply of the Arduino to V_s (do not use the laboratory power supply!).

4.2.1 Measure the voltage with the multimeter across the strain gauge for both the unloaded and loaded beam. What is the difference in voltage between loaded and unloaded beam? Hint: you can even measure at the screws of the luster terminal as they are in contact with the clamped wires (fig. 6).

Figure 4: voltage divider

4.3 Set up the strain gauge in circuit 3 (fig. 5) as a quarter-bridge with the strain gauge as R₁. Use the Arduino and the Sparkfun HX711-board for connecting the bridge-circuit to your PC as in Fig. 5.

Now use the HX711-datasheet and the Arduino-program. Find the scaling factor to convert your measured value to Volts with these next steps!:

4.3.1 a) The setup uses a 24-bit amplifier/ADC. Give the maximum digital value we can expect from this amplifier/ADC in a decimal number.

b) Which maximum differential input voltage can the HX711 stand? Which minimum differential input voltage can the HX711 stand? - check the datasheet, the configuration can be found in the Arduino code.

c) Use your results from a) and b) to calculate the resulting mV/digit for the whole measurement range! (The number of digits are split up over the whole input Voltage range.)

d) Give the ADC-value for the 0mV differential input voltage (in decimal digits). Hint: you need the value for 4.3.1 a).

4.3.2 Insert your value for zeroMVinput and your value for mV/digit into the Arduino code. You will need to provide those values in Vips later. 💾 (Please insert your code where the comments mention it and then uncomment those parts!)

Execute the Arduino-program. Pick the correct port and open the serial monitor. Make sure the baud-rate is set correctly! (Check the “Serial.begin(…);” statement.

Set the calibration value to set the zero balance: For this, you need to know the ADC-value for the 0mV input. Then try to achieve a reading "Result in digits" as close to this value as possible, by entering a's or z's to the serial monitor.

Now your program is ready for measuring!

4.4 Quarter-Bridge

4.4.1For this setup (quarter-bridge), give the equation for the voltage V_d. What happens if R₁ changes?

4.4.2 What voltage change would you measure for a 1‰ strain at 5V supply voltage?

4.4.3 Measure both the unloaded and loaded beam. What is the voltage difference between loaded and unloaded beam?

4.5 If you used a hairdryer to heat up the setup (quarter-bridge), could this setup compensate temperature differences?

Prepare the connection of your Arduino and HX711 at your seat before you go to the teststand.

Go to the force-teststand and open the Matlab App for Experiment 4. Enter your matriculation number and the number of the Experiment Kit you are working with. Then enter your values for 4.1.1 and 4.2.1. All values and calculations for 4.1.2, 4.3, 4.4, 4.5, 4.6.3 and 4.6.4 will need to be supplied to vips later. After entering the values for 4.1.1 and 4.2.1, conduct task 4.6 with the teststand!

4.6 Set up the strain gauge in circuit 4 (fig. 10) as a half-bridge with the strain gauges as R₁ and R₃. Use the luster terminal to connect both strain gauges accordingly.

4.6.1 For this setup, give the equation for the voltage V_d!

4.6.2 Record the measurements for the loaded beam, if your setup is working. If your setup is faulty, please use 10mV as Vd for the following calculations.

4.6.3 Use the hairdryer to heat up the setup (slightly, max. 10 seconds) and record the measurements for the loaded beam again. Compare! Can this setup compensate temperature differences?

4.6.4 Calculate the longitudinal stress you applied in 4.6.2!

Fig. 10: wheatstone-bridge

7. Evaluation of Experiment Results

App

VIPS

The following values should be entered to vips in Stud.ip. Please note that only 30 minutes are available for entering values in vips, after which the vips entry is automatically terminated. The test is only to hand in the final values, so be prepared and have all values ready and at hand!

1. Matriculation number

2. If you had a 10mA current source like in fig. 3, what voltage change would you expect across the strain gauge for a 1‰ strain of the beam?
   unit: [V]
   relevant section: 4.1.

3. If you had a 10mA current source like in fig. 3, what voltage change would you need to measure, if you want to resolve the maximum strain of 1‰ to 100 steps?
   unit: [V]
   relevant section: 4.1.

4. Give the ADC-value for the 0mV input.
   unit: [none]
   relevant section: 4.3.

5. How many mV/digit does the Arduino measure when using the HX711 as ADC?
   unit: [mV/digit]
   relevant section: 4.3.

6. What voltage change would you measure for a 1‰ strain at 5V supply voltage in a quarter-bridge setup?

   unit: [V]
   relevant section: 4.4.

7. What voltage did you measure in the quarter-bridge setup? Type the voltage difference between loaded and unloaded beam!

   unit: [V]
   relevant section: 4.4.

8. Can the setup from task 4.5 compensate temperature?
   select from:
   - yes
   - no
   relevant section: 4.5.

9. Can the setup from task 4.6 compensate temperature?
   select from:
   - yes
   - no
   relevant section: 4.6.

10. Calculate the stress you applied in task 4.6.2
    unit: [MPa] or [N/mm²]
    relevant section: 4.6.