Interdisciplinary laboratory exercises for the design and construction of an LVDT position measurement system

Englund, Richard B

Abstract

This paper describes a series of laboratory exercises for engineering technology (ET) students in courses involving instrumentation and measurement. The exercises involve the design and construction of a linear variable differential transformer (LVDT) position measurement system. A unique feature of this series is that it requires participation from both mechanical and electrical ET students. Exercises include winding of transformer coils, determination of coil properties, fabrication of the core, assembly of the LVDT, construction of a personal computer-based signal conditioner, and determination of system linearity. Efforts required to complete these exercises are roughly divided between mechanical and electrical students.

Introduction

The LVDT is a well-established displacement transducer that allows accurate measurement of position. Consisting of a transformer with a single primary winding, two balanced secondary windings (series opposed), and a moveable core as shown in figure 1, the LVDT may be used either in static or in dynamic applications such as vibration or materials testing. The transducer’s primary winding is excited by a sine wave that is typically in the kHz range, and there is usually a phase difference between the primary and secondary signals.1,2

There are two general styles of LVDTs: four-wire and five-wire versions. The five-wire design includes an additional wire that represents the connection point, or center tap, for both secondary windings, allowing the voltage at both windings to be computed relative to the center tap. In comparison, the four-wire LVDT does not include a center tap. The signal at the output terminals of a four-wire LVDT is the difference between the two secondary windings. In either version, the output signal should be converted into a form that the user can interpret and analyze, and signal conditioners are often used for this task.

An important consideration for LVDT signal conditioners is linearity. Ideally, the relationship between the position of the LVDT core and output voltage of the signal conditioner should be linear. However, both the LVDT and signal conditioner can introduce nonlinearities into the system.

This paper will describe how students in different programs can collaborate in the design and manufacture of a complete LVDT position measurement system. Students in a mechanical engineering technology (MET) course in instrumentation and measurement construct an LVDT as part of a laboratory exercise, and students in an electrical engineering technology (EET) course in control systems design and implement a signal conditioner and determine linearity for the constructed system. Further, the shared application is consistent with the objectives of both courses. One objective of the MET course is the general understanding and application of sensors. In the EET class, course objectives require students to “identify the different parts of a control system” and to “build both parts of, and an entire, control system in the laboratory.” The exercise gives EET students practical experience in building sensor electronics, which is integral to the design of feedback control systems. This exercise would also be suitable for a EET instrumentation and measurements course.

Most EVDTs operate at frequencies above 60 Hz and are more sensitive at even higher frequencies.2 However, existing literature generally docs not discuss the effect of saturation on the coils or describe reduced magnetic coupling at low excitation frequencies. These effects could be investigated further in a series of experiments, but this paper only attempts to arrive at a configuration that functions acceptably for instrumentation class exercises. This configuration, which does not represent an optimum system, is based upon an iterative design. Students used a variety of different configurations to construct EVDTs, specifically, different combinations of primary and secondary turns, coil lengths, and core diameters. This paper describes the LVDT configuration that performed best.

LVDT Construction

The integrated exercise began by introducing MET students to fundamental EVDT components, namely, primary and secondary windings, the moveable core, and a signal conditioning system. A schematic diagram helped students construct a simple EVDT.2 EVDTs are configured by winding magnetic wire around a nonmagnetic cylindrical form such as a soda straw, with a ferromagnetic slug such as a nail used for the movable core. A soda straw form and nail core can function as an EVDT, but coil windings can partially collapse the straw and restrict motion of the core, so this type of EVDT is not as sensitive as one made of better components.

To improve the quality and sensitivity of the EVDT, each MET laboratory group was provided with a 5-inch-long section of aluminum tubing with a 0.33-inch outside diameter and a 0.015-inch wall thickness. In general, aluminum tubing is inexpensive and readily available. The primary and secondary coils, which were constructed from 30-gauge varnished copper magnet wire, were each 1 inch in length. Plastic washers were glued to the outside of the aluminum tube at 1-inch intervals to separate the coils. Students were instructed to make 600 turns on the primary winding and 900 turns on the secondary winding. Coils were wound on general purpose engine lathes operating at a speed of approximately 100 revolutions per minute, with a Starrett 104 revolution counter attached to the end of the tube to count the turns. Each coil was wound independently, and a tape marker was used to label the start and end of the coil for later addition of leadwires.

The EVDT core was constructed from a 0.25-inch diameter cold drawn, low carbon steel rod (AISI 1020 CD). For an EVDT with 1-inch coils, a 2-inch-long core was cut from the rod and deburred, and a shallow 5/64-inch diameter hole was drilled into the center of one end of the core. A 5-inch-long section of 1/16-inch diameter nonmagnetic stainless weld rod (AISI 308) was glued into the hole with two-part epoxy.

A single fixture, composed of a finely threaded vertical adjusting screw and a clamp to hold the LVDT above the screw, was constructed to calibrate the LVDT system. The core stem rests on the screw and rotation of the screw raises the core in the coils. The screw has twenty threads per inch, resulting in a vertical movement of 0.050 inches per revolution. This configuration is particularly helpful when shorter coils and operating ranges are chosen. Various other parameters can also be investigated, such as different core materials, heat treatment conditions, and different core diameters.

The finished LVDT and eore assembly, shown in figure 2, was then given to the EET control systems students for development of the signal conditioning system.

LVDT Signal Conditioner Development

The senior-level EET students were required to build the signal conditioner for the constructed LVDT system. The goal of signal conditioning is to construct a signal in a practical form for the user. For this exercise, the signal conditioner must convert the two output voltage signals from the LVDT secondary windings to a display of core position. Students were given the option of building the signal conditioner in hardware or in LabVIEW, a graphical programming language that has been widely adopted as the standard for data acquisition, instrument control, and analysis.3 External analog signals can be captured by a personal computer equipped with a data acquisition card, and students can then use LabVIEW to build a program that converts the digitized signal to an output based on core position. These EET students were already proficient in LabVIEW, having taken an instrumentation course in their junior year. Each laboratory group decided to build the signal conditioner in LabVIEW, primarily because the hardware version required eight operational amplifiers, which would be difficult to implement without significant troubleshooting. The block diagram for the hardware implementation of the signal conditioner is shown in figure 3.

The general technique used for signal conditioning is the ratiometric method, which states that the difference in amplitude between the two secondary waveforms is divided by the sum of the two waveforms,1

where Va is the output waveform from one secondary of the LVDT, Vb is the output waveform from the other secondary of the LVDT, and Vo is the resultant output of the ratiometric approach. This method works for five-wire LVDTs assuming the value of Va + Vb remains constant throughout the operational range, but it does not work for four-wire LVDTs because Va and Vb are rectified signals that require a reference to the common ground. One benefit of the ratiometric approach is that the students do not need to correct for any phase shifts due to the transformer. The hardware implementation shown in figure 3 results in the calculation of Va – Vb. While not a true ratiometric calculation, this value is still functional, especially since it is assumed that the value of Va + Vb remains constant throughout the operational range of the LVDT.1

To drive the primary side of the LVDT, EET students constructed a simple circuit to generate square waves with a 50% duty cycle and a frequency of approximately 1 kHz, as shown in figure 4. For simplicity, only operational amplifiers and passive components with supply voltages of + or -12 VDC were used. The circuit shown in figure 5 acts like a bandpass filter for the inputted square wave. Students adjusted the potentiometers until the output of the power operational amplifier waveform closely resembled a sine wave at approximately 1 kHz, an excitation frequency that was selected to provide better sensitivity and efficiency for the LVDT.1 Careful tuning of the potentiometers helped reduce distortion. An alternative to this iterative approach is to generate a sine wave with a function generator chip.4 The signal was then provided to the primary winding of the LVDT.

Sufficient current is required to generate the magnetizing flux within the transformer. The power operational amplifier used in this circuit was rated up to 325 mA, but approximately 100 mA was adequate for this laboratory exercise.5 The LVDT secondary signals were then downloaded through a data acquisition card into the computer. Most student groups performed a simple rectification of the signals by searching for the peak amplitude of each secondary waveform.

The LabVlEW program, commonly called a virtual instrument or VI, for the signal conditioner is shown in figure 6. The resulting front panel, which is used to operate the program, is shown in figure 7. This panel is interactive, and students can see the position meter move as the core position is adjusted. In addition, students can adjust parameters such as the scan rate of the analog-to-digital data acquisition card. As seen in both of these figures, a small amount of software coding was required to develop the signal conditioner.

After confirming the operation of the signal conditioner, the EET students measured the change in output of the conditioner as the LVDT core moved. First, students moved the core to a position that corresponded to the zero or null point inside the LVDT. At this point, the contributions of the two secondary windings are equal. Using the ratiometric approach, the signal conditioner output shown on the LabVlEW front panel is zero. Once this null point was defined, students then moved the core in predefined increments, noting the change in output as read by the signal conditioner. The hardware configuration during the measurement process is shown in figure 8.

The EET students then met with the instructor to analyze the data collected from the signal conditioner. First, the instructor and students determined the most linear portion of the data by graphing it in a spreadsheet program. A sample graph is shown in figure 9, in which the effects of moving the core past its linear range are clearly seen. The instructor demonstrated how to perform a linear regression on the data with a built-in function in the spreadsheet program. The resultant best fit linear system was then compared with the collected data to determine the average and maximum percent deviation for each point of measurement, as shown in table 1.

As shown in table 1, the average percent deviation for all groups was 2.84%, with an average maximum deviation from linearity of 5.92%. Results depended upon where the students considered the LVDT to be linear. This procedure gave students the opportunity to judge their results subjectively, as will be required of them in professional practice. Once the students completed their LabVIEW development of the signal conditioner, one of the EET laboratory groups agreed to demonstrate their system to the MET class to show how a reasonably accurate signal conditioning system could be developed for a constructed LVDT.

The MET students enjoyed constructing the LVDT sensor and were gratified to see that the integrated system functioned as intended. They indicated that this exercise gave them a sense of closure and purpose not usually obtained from a more theoretical study of sensors and their operating principles. The EET students appreciated that they could apply their knowledge of LabVIEW signal conditioning to a real physical system and were able to develop a fully functional signal conditioning system within a few hours despite having little prior knowledge of LVDTs. One EET group indicated that this project was among the best in their educational experience.

Alternate Exercises

MET students have also constructed LVDTs in a separate exercise that does not include a signal conditioning circuit. Excitation is supplied by a signal generator and LVDT output is measured with an oscilloscope. This exercise is especially beneficial for mechanical students because it allows them to investigate various excitation frequencies and voltages. EET students could also perform this same exercise to investigate system performance without any errors introduced by sine waves produced from signal-conditioned square waves. Students find that there is one frequency where maximum output voltage can be measured from the secondary coils, and that the electrical properties of the system change when the core is added. The exercise has also been used to investigate the effects of the number of turns on the windings, the turn ratio between primary and secondary windings, and the sensitivity and range of the LVDT for different lengths of primary and secondary coils. Although various coils lengths have been successfully used, this exercise employed 1-inch-long coils to simplify mathematical calculations.

When using commercial AC-to-AC LVDT sensors, EET students can analyze signal conditioning effects without building their own LVDT. Note, however, that separation of the two student disciplines eliminates the teamwork aspects of the project and reduces the shared sense of accomplishment for the students.

While the MET students were quite interested in the completed LVDT sensor and integrated LabVIEW program, it is likely that they would be more fully engaged by using the electromechanical system for a typical dimensional measurement task. An extension of this work is to have student teams collaborate to measure some object with the completed position measurement system, such as measuring the lift of engine camshaft lobes as a function of angular camshaft position. This application would require a fixture to support the camshaft on its bearings, a clamp to support the LVDT sensor above the selected cam lobe, a rotational position sensor such as a one-turn potentiometer, and suitable readout and data collection equipment. Another example might be a closed-loop control system for position of a damper in a ventilation system. The MET students would be responsible for the linkage, damper actuator, LVDT mounting and construction, and temperature sensor placement in the ductwork, while EET students would be responsible for the LVDT signal conditioning, temperature detection, system or programmable logic controller, and amplifier for the damper actuator.

Finally, students could be assigned to compare the performance of their LVDTs to the performance of commercial devices. The students would be required to search existing literature to find manufacturers and models of LVDTs with similar measurement capacities as their units. Students could also compare prices and power requirements of the commercial devices with their constructed sensors. This type of search should reveal that commercial LVDT manufacturers offer linearity to 0.25%, measurement ranges from a fraction of an inch to over ten inches, and prices typically in the range of a few hundred dollars.6

Conclusion

This paper has described the development of a complete LVDT position measurement system by students in different program disciplines. MET students constructed the LVDT core and windings and EET students developed the accompanying signal conditioner in LabVIEW software. The completed system was shown to have satisfactory linearity, and student feedback about this exercise was generally positive. EET students experienced a practical application of LabVIEW and MET students applied their knowledge of manufacturing and gained an understanding of the basic sensor principles. Student groups in each discipline worked in separate teams to design, construct, and analyze the integrated system.

References

1. Novacek, G. “Accurate Linear Measurement Using LVDTs.” Circuit Cellar Ink 106 (May 1999): 20-27.

2. Beckwith, T., R. Marangoni, and J. Lienhard. Mechanical Measurements. 5th ed. Reading, Mass.: Addison Wesley, 1993.

3. Bishop, R. H. Learning with LabVlEW. Menlo Park, Calif.: Addison Wesley, 1999.

4. Analog Devices. Analog Devices Specification Sheet: AD2S99, Programmable Oscillator. Norwood, Mass.: Analog Devices, 1995.

5. National Semiconductor. National Semiconductor Specification Shed: LM759/LM77000, Power Operational Amplifiers. Arlington, Tex.: National Semiconductor, 1995.

6. Sensotec Inc., Columbus, Ohio. Available: http://www.sensotec.com /Ivdt.htm.

Richard B. Englund received his bachelor’s degree in Mechanical Engineering from Washington State University and his master’s degree in Mechanical Engineering from SUNY at Buffalo. Prior to his current position as an assistant professor of Engineering at Penn State Eric, he worked for Bettis Atomic Power Lab and CE-Air Preheater. His research interests include threaded fasteners and biomechanics.

Robert S. Weissbach received his bachelor’s degree in Electrical Engineering from the University of Florida, his master’s degree in Electrical Engineering from Rensselaer Polytechnic Institute, and his doctoral degree from Arizona State University. Previously employed at General Dynamics Electric Boat Division in Groton, Connnecticut, he is currently an assistant professor of Engineering at Penn State Eric and a co-director of the Electrical Design Center, an applied research center located at the campus. His research interests include power electronics and flywheel energy storage systems.

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