MEE2305 Instrumentation and Data Acquisition Lab Notes

LAB 3 - Instrumentation and Data Acquisition Lab

Course Details

• Course Developer: Dr. Kurosh Darvish

• Course: MEE2305 Instrumentation and Data Acquisition Lab

• Subject: Displacement Measurements

• Instructor: Dr. Osman Sayginer

• Department: Mechanical Engineering, Temple University

• Contact: sayginer@temple.edu

Objectives

• Learn about LVDT Sensors

• Learn about wiring of the sensor

• Learn about programming of LVDT to measure the displacement data

• Measure the displacement of the slider and calculate velocity and RPM

LVDT (Linear Variable Differential Transducer)

Concept

• Function: Measures displacement of the iron core moving inside the sensor

  • This non-contact measurement minimizes friction and mechanical loading, ensuring good alignment and reliability.

• Type: Inductive sensor

  • Contains a primary coil with an AC voltage supply, which generates an alternating magnetic field.

  • This magnetic field induces voltages in two secondary coils, which are typically wound symmetrically on either side of the primary coil.

  • The amount of induced voltage in each secondary coil depends on the location of the ferromagnetic core within the sensor. As the core moves, it alters the magnetic coupling between the primary and each secondary coil differentially.

How It Measures Displacement

• At Center: When the core is precisely at the center (or null position), it couples the primary coil equally to both secondary coils. Therefore, the induced voltages in the secondary coils are equal in magnitude and 180 degrees out of phase, resulting in a zero voltage difference across their series-opposing connection.

• At Ends: As the core moves away from the center, it couples more strongly to one secondary coil and less strongly to the other. This causes an imbalance in the induced voltages. The voltage difference is maximized when the core is at either end of its linear range, with the phase of the output voltage indicating the direction of displacement from the null position.

Preparation Steps

1. Check the Location of the LVDT:

   • Mount the crank slider system securely to the table.

   • Ensure that the core moves inside the LVDT smoothly and remains predominantly within the sensor's range of motion. Adjust the sensor's location if necessary. Proper alignment is critical for accurate readings.

2. Determine Wire Connections: Identify and find these wires:

   • Red (Primary A), Black (Primary B), Blue (Jumper), Green (Secondary 1), White (Secondary 2)

Task 1: Resistance Measurements

• Setup: Use Virtual Bench

• Find Resistance of:

  • Primary Coil

  • Secondary Coil (each individually and combined)

• Tasks:

  • Compare values to typical specifications or manufacturer's data.

  • Save values for future reference and troubleshooting.

Wiring of the Sensor

• Instructions: Follow the circuit diagram for connections carefully to ensure proper sensor operation and avoid damage.

• Connect BNC to alligator clips (2x) - typically for connecting to the primary coil and the output.

• Connect two secondary coils together using a blue jumper in a series-opposition configuration to derive the differential output voltage.

• Connect BNC to BNC clips (1x) and a BNC tee connector (1x) for signal monitoring or connection to data acquisition devices.

Test Setup

• Verify Connections: Visually inspect all connections for correctness and ensure they are secure.

• Identify if the sensor is analog or digital. LVDTs are inherently analog devices, providing a continuous voltage output proportional to displacement.

Setting Power Supply

1. Use Virtual Bench as the signal source.

2. Use Function Generator to create the excitation signal.

3. Apply a $2.5\ \text{kHz}$ sinusoidal input to the primary coil. This AC excitation voltage is crucial for the inductive operation of the LVDT. The frequency is chosen to be high enough for good dynamic response but low enough to avoid excessive eddy current losses.

LabView Tasks

• Acquire Signal Practice:

  • Understand the sampling rate, which is the number of samples taken per second. A higher sampling rate generally provides a more accurate representation of the original signal.

  • Identify the duration of data acquisition, which determines the total number of samples collected.

  • Learn about Nyquist frequency and aliasing, which are fundamental concepts in digital signal processing.

  • Determine the minimum sampling frequency required to avoid aliasing.

Nyquist Theorem

• The Nyquist-Shannon sampling theorem states that to accurately reconstruct a continuous-time signal from its samples, the sampling frequency ($f<em>s$) must be at least twice the highest frequency component ($f</em>{max}$) present in the signal. If this condition ($f<em>s \geq 2f</em>{max}$) is not met, aliasing will occur.

• $f<em>s \ / f \ \text{must be } \begin{cases} 2.6 \ 2.0 \ 1.4 \ 0.8 \end{cases} \ \text{Minimum } f</em>s \ \text{required to sample } f \ \text{properly.}$ This notation seems to represent different ratios that might be used in practice or specific scenarios. To avoid aliasing, the general rule is $f<em>s \geq 2f</em>{max}$.

• \text{Sampling Frequency} \geq \text{Nyquist Frequency} \ . The Nyquist frequency is defined as half of the sampling rate ($f<em>{Nyquist} = f</em>s/2$) or, confusingly, as the minimum sampling rate required ($2f<em>{max}$). For clarity, the minimum sampling rate required to avoid aliasing is $2f</em>{max}$.

Task to Measure Frequency

• Discussion Points:

  • How to make the frequency graph smoother by increasing the number of samples or adjusting the spectral resolution settings in the FFT (Fast Fourier Transform) analysis.

  • Relation between amplitude of time signals and frequency signals. The amplitude in the time domain corresponds to the magnitude of specific frequency components in the frequency domain.

  • Differences between Time Domain and Frequency Domain. The time domain displays how a signal changes over time, while the frequency domain displays the distribution of signal energy across different frequencies.

  • Units for x-axis and y-axis. In the time domain, the x-axis is time (e.g., seconds) and the y-axis is amplitude (e.g., volts). In the frequency domain, the x-axis is frequency (e.g., Hz) and the y-axis is magnitude (e.g., volts or dB).

dB Measurement Task

1. Define dB: A decibel ($dB$) is a logarithmic unit used to express the ratio of two values of a power or root-power quantity. It is commonly used in acoustics, electronics, and control theory to express ratios of signal power or amplitude. The formula for power ratio is $dB = 10 \log<em>{10}(P</em>2/P<em>1)$ and for root-power (voltage/current) ratio is $dB = 20 \log</em>{10}(V<em>2/V</em>1)$.

2. Understand the unit of dB: It is a dimensionless unit, but often referenced to a specific absolute power (e.g., $dBm$ for mW, $dBuV$ for $\mu V$).

3. Clarify the significance of dB: It allows for the representation of very large or very small ratios in a more manageable numerical range, making it easier to compare signals with vastly different magnitudes. It also models human perception of sound and light, which is logarithmic.

4. Know the order of magnitude for peak calculations: For example, an increase of 20 dB means the power ratio increases by a factor of $100$, or the voltage ratio by a factor of $10$.

5. Examples:

   • $20\ \text{dB}$ corresponds to a voltage ratio of $10:1$.

   • $40\ \text{dB}$ corresponds to a voltage ratio of $100:1$.

   • The examples given (20 dB corresponds to 1 ohm, 40 dB corresponds to 2 ohm) are generally not how dB is applied to resistance directly in this context unless it's part of a specific power calculation in a circuit. Typically, dB relates to power or voltage ratios. For resistance, it might imply a ratio change in impedance related to a power change, but this phrasing can be misleading without further context.

Tone Measurements Task

1. Define amplitude, frequency, phase, and tone. Amplitude is the maximum displacement or distance moved by a point on a vibrating body or wave measured from its equilibrium position. Frequency is the number of cycles or vibrations per unit of time. Phase describes the position in time or space of a point on a waveform cycle. A tone is an audible sound characterized by its pitch, duration, intensity, and timbre, often associated with a single dominant frequency.

2. Compare amplitude and phase shifts for two instruments or two different points in a system to understand signal propagation and delays.

Calculating Phase Shift

• Perform tasks to find the primary frequency, amplitude, and phase for both the primary (excitation) coil and the secondary (output) coils.

• Assess if primary and secondary frequencies are equal within a tolerance. Ideally, the LVDT is a linear transducer, so the output frequency should match the input excitation frequency. Any significant deviation could indicate system issues or non-linearities.

Calibration of LVDT

• Sorting and Copying Data:

  • Select and sort calibration data, which typically involves known displacement values versus measured output voltages.

  • Paste into Excel sheets or other data analysis software.

• Graphing Methods:

  • Ensure data shows a V-shape (or two linear segments with opposite slopes originating from the null point) when plotting output voltage magnitude versus core displacement. This characteristic shape confirms proper LVDT operation. Repeat measurements if necessary to obtain a clean V-shape.

  • Discuss physiological implications and how data impacts design of systems where LVDTs are integrated. For example, understanding linearity and range limitations for specific applications.

Regression Analysis in Calibration

1. Each of the following outputs should be reported from the regression analysis, which helps define the LVDT's transfer function:

   • R-square values: A statistical measure representing the proportion of variance in the dependent variable that is predictable from the independent variable(s). It indicates how well the regression model fits the observed data.

   • Intercepts: The value of the dependent variable when the independent variable is zero (i.e., the output voltage at the null position).

   • X Variable coefficients (slopes): These represent the sensitivity of the LVDT, defined as the change in output voltage per unit of displacement.

   • Lower and upper values of slope: These define the linear range and sensitivity at positive and negative displacements from the null point, which ideally should be very similar in magnitude but opposite in sign.

Final Steps for Lab Report

1. Explain how LVDT operates, detailing the inductive principle and differential voltage output.

2. Describe how cables were connected, referencing the circuit diagram and specific wire functions.

3. Discuss topics around sampling rate, Nyquist frequency, and aliasing effects, and their importance in accurately capturing the LVDT's analog signal.

4. Analyze the effect of sampling rates on data acquisition by showing examples of how improper sampling can lead to distorted or inaccurate data and how to choose an appropriate rate.

The sampling rate is the number of samples taken per second, where a higher rate generally provides a more accurate representation of the original signal.

The duration of data acquisition determines the total number of samples collected.

Regarding the Nyquist Frequency, it is defined either as half of the sampling rate ($f_{Nyquist} = f_s/2$) or, more consistently within the Nyquist Theorem, as the minimum sampling rate required to accurately reconstruct a signal, which is twice the highest frequency component present in the signal ($2f_{max}$).

Aliasing occurs if the sampling frequency ($f_s$) is not at least twice the highest frequency component ($f_{max}$) present in the signal (f_s < 2f_{max}). It leads to a misrepresentation of the original signal.

The minimum sampling frequency required to avoid aliasing is at least twice the highest frequency component ($2f_{max}$) present in the signal. In general, a higher sampling rate is recommended as it provides a more accurate representation of the original signal.