Transcript
7. MEASUREMENT OF THE MECHANICAL STRESS
Measurement objectives: 1. Measure the static characteristic (transfer function) of the sensor of mechanical stress on an elastic beam / cantilever as a dependence of the output voltage of a tensometric bridge on the displacement of the beam end. 2. Compute the change of the resistance of the tensometer (strain-gauge) and the relative elongation ∆l/l for the highest displacement of the beam. 3. Determine the dynamic properties of the beam from 15 to 30 Hz. 4. Observe the impact of the disturbing signal (“noise”) on the output voltage of the synchronous demodulator and diode rectifier.
Measurement procedure: Initial configuration a) For beam in an idle position, the strain gauge bridge should be balanced (an the output voltage zero). It is necessary to set the real as well as imaginary component of the bridge output voltage to zero before the measurement. This can be done using the variable resistor and variable capacitor placed at the front panel of the mechanical device for zero beam displacement. Use an oscilloscope connected to the pin Tenzo_Out and digital voltmeter at the output for the measurement. b) For the unbalanced bridge (non-zero displacement of the beam), set the phase of the synchronous detector so that the output signal is of the whole-wave rectified shape, i.e. just like after diode rectifier (observe at the pin SD). Then release the beam.
7.1. Measurement of the characteristic of the tensometer (strain-gauge) sensor Set the displacement from 0 to 5 mm with a step of 0.5 mm using the controlling screw. The displacement is indicated at the mechanical measurement device. Measure the level of the DC voltage at the output of the device. Put the results into a table and draw a graph.
7.2. Relative elongation Compute the relative elongation value ∆ l/l of the strain-gauge element for the highest displacement measured in the step 1. Useful relation:
Here
K R0 ∆l/l
∆R ∆l =K⋅ R0 l is the deformation sensitivity constant, in our case K = 2.03 is the nominal strain-gauge resistance, R0 = 120 Ω is the relative elongation
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The total current flowing through the strain-gauge bridge is 5 mA and the gain of the preamplifier is 10 000x, the gain of other parts is approx. 1x. There are four active straingauge elements connected into the bridge.
7.3. Dynamic properties of the beam a) Unload the beam so that it can freely move and is not restricted by the controlling screw. Ask the teacher to displace the free end of the beam (approx. 1 cm) using a pencil and release it. The beam vibrates at the frequency of natural damped oscillations. Use the oscilloscope to record the voltage waveform at the output of the device (BNC connector ‘Output’). This waveform corresponds to the oscillations of the beam. Compute the damping coefficient, logarithmic damping decrement and the resonance frequency of the oscillating beam.
Useful physical relations:
A(t ) = A0 ⋅ e Amplitude of damped oscillations δ is the damping coefficient.
−δ ⋅t
The logarithmic damping decrement is defined as
Λ = ln
A(t 0 ) A ⋅ e −δ ⋅t0 = ln 0 −δ ⋅(t0 +T ) = δ ⋅ T A(t 0 + T ) A0 ⋅ e
The solution of the differential equation of the damped oscillations for the damping b > ω0, where ω0 is the resonance circular frequency, is in the form
y = A0 ⋅ e −δ ⋅t ⋅ sin(ω1 ⋅ t + ϕ ) , where δ ϕ
is the damping coefficient, is the initial phase and
ω1 = ω 02 − δ 2 is the frequency of the damped oscillations (ω0 = resonant freq.). b) Connect the DC voltage of +5V from the laboratory supply to the electromagnet’s driving circuit. Connect the rectangular signal from the Hewlett-Packard generator’s SYNCH output (the upper BNC) to the “TTL” clamp. By tuning the frequency of the driving pulses and by observing the beam vibrations and the output signal of the device try to find the resonance (adjustment may be very sensitive). Compare the measured value to the value computed in the previous step.
7.4. Selective properties of synchronous detector Connect the disturbing voltage from the generator to the appropriate connector of the device and observe the voltage levels at the output of the device. Verify that the synchronous detector is sensitive only to the odd multiples of the switching frequency (i.e. the frequency of the bridge bias signal). Connect the voltmeter and the oscilloscope to the output of the
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measurement chain. You will see the beats at the frequencies corresponding to the odd harmonics of the reference signal (i.e. 5, 15, 25… kHz) on the oscilloscope. The diode rectifier does not have these selective properties; the output voltage at whichever frequency is proportional to the arithmetic (rectified) mean value of the signal. Disturbances therefore influence the output at all frequencies.
Device description Mechanical part A flexible steel beam is mounted at one of its ends at a holder. Four pieces of wire strain-gauges are placed at the beam’s surface and connected into a Wheatstone bridge. The free end of the beam may be moved by a screw. The displacement is measured by a precise position meter, which has the outer scale divided by 0.01 mm (one turn = 1 mm). The small scale is divided by 1 mm. The range of the measurement can be up to 10 mm. The beam can also be displaced by an electromagnet. The TTL control pulses are led to the clamps on the right side of the device. The power driver of the electromagnet is supplied with a voltage of 5 V from the laboratory voltage source. In the front left part of the device are placed the variable resistor and the variable capacitor, which serve for balancing the bridge to zero offset.
Electrical part The electrical part is placed on a separated board. The whole measurement chain is described by the block diagram (see below) and some of its nodes are connected to the clamps so that the function of the device can be observed easily.
Circuitry description The microcontroller PIC16F84 programmed as a generator of two square signals at the frequency of 5kHz is the heart of the synchronous detector circuit. The phase between the two signals can be tuned. The phase control knob is connected to the microcontroller using Schmitt’s flip-flop circuits. The first rectangular signal from the generator is filtered by a sixth-order low-pass filter to obtain a sine waveform, which is amplified and led through a resistor to the measurement bridge supply. The voltage from the measurement diagonal of the bridge is amplified by an AC coupled instrumentation amplifier. After the amplification, the signal is led to the inputs of the rectifiers. There are two rectifiers and it is possible to compare the function of the uncontrolled (diode) rectifier (also known as a mean value converter) and the controlled rectifier, which works as a switched synchronous detector. This synchronous detector is controlled by the second signal generated by the microcontroller. The phase of the control signal can be changed in order to compensate the phase shift of the bridge output signal. Switch SW4 selects which of the two rectifiers is connected to the output of the device. The disturbing signal is led to the inputs of the rectifiers using a summation amplifier.
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Description of the inputs and outputs frq1_square frq1_sin SD_Ctrl Tenzo_Out AddC SD RD Output Disturb signal TenzoIn TenzoOut1,2
1th signal generated by the microcontroller, TTL, 5kHz the same signal after the 6th order Low Pass filter, sine, 5kHz control signal for the synchronous detector output signal of the instrumentation amplifier input signal of the rectifiers output of the synchronous detector output of the diode rectifier total output the connector of the disturbing signal identical to frq1_sin diagonal voltage of the bridge Generator 1 - 100Hz TTL
Power supply 5V
Cantilever
Screw Wheaston Bridge
R
Additive circuit - Sčítací obvod Cantilever - vetknutý nosník Diode rectifier - Diodov ý usměrňovač Disturbing signal - Rušivý signál Low pass filter - Filtr dolní propust Instrumentation OpAmp - Přístrojový zesilovač Strain Gauge - Tenzometr Phase control by incremental opto-coupler - Řízení fáze inkrementálním optickým čidlem Power supply - Zdroj napájení Switching type detector - Řízený (synchronní) usměrňovač
C
Generator 1Hz - 25kHz
Interface connector to strain gauges
Interface connector to board
+15V
Disturbing signal
0V
-15V
Diode rectifier Instrumantation OpAmp
Additive circuit
SW4
Switching type (synchronous) detector
Output 2nd order Low pass filter - 60Hz
5 kHz TTL Phase control by incremental optocoupler
TTL
6th order Low pass filter - 5,5kHz TTL
5 kHz TTL
Generator
GND
Reset SW2
frq1_square
frq1_sin
SD_Ctrl
4
Tenzo_Out AddC
SD
DR
GND
Power supply ± 15 V
