Transducers and Transducer Calibration GENERAL MEASUREMENT SYSTEM

Transcription

1 Transducers and Transducer Calibration Abstracted from: Figliola, R.S. and Beasley, D. S., 1991, Theory and Design for Mechanical Measurements GENERAL MEASUREMENT SYSTEM Assigning a specific value to a physical variable is done with the help of a measurement system. Once a value has been assigned to a physical variable it becomes known as a measured value. There are four stages to the process of assigning a value to a physical variable. Generally these stages are: 1. A Sensor-Transducer Stage 2. A Signal Conditioning Stage 3. An Output Stage 4. A Feedback Stage These stages form a bridge between the input to and the output from a measurement system. Each stage leads to the assignment of a quantity to a physical variable, which infers its value. The relationship between the input information and the output information is established by a calibration of the measurement system. Calibration of a system is the act of applying a known input to a system to observe the systems reaction or output. The goal of the sensor-transducer stage is to convert the sensed information into a form that can be easily quantified. The sensor in a measurement system is typically a physical element that employs some natural phenomenon by which it senses the variable being measured. The transducer in a measurement system is a device that converts the sensed information into a detectable signal. This signal can be visual, mechanical, or electrical. The signal conditioning stage is the point that a signal from the transducer stage may be modified. This stage is optional and sometimes includes increasing a signal magnitude though amplification and applying filtering techniques. This stage provides a mechanical or optical linkage between the transducer and the output stage, for example, converting a transitional displacement of a sensor to a rotational a displacement of a pointer. The output stage provides the identification of the value of the variable being measured. For examples, a digital read out or a disk drive. For those measurement systems involved in process control the feed back control stage would contain a controller that would interpret the measured variable and make a decision regarding the control of the process. An example of a simple measurement system with a fee back control stage is a household thermostat.

2 EXPERIMENTAL TEST PLAN Engineering measurements are not as simple as turning on the equipment and reading the numbers. Relevant information can only be extracted from test data obtained from a well though out measurement test plan. A test plan should be drawn from the following three steps: 1. Parameter Design Plan. An identification of process variables and parameters and a means for their control. 2. System and Tolerance Design Plan. The selection of a measurement technique, equipment, and test procedure based on some preconceived tolerance limits for error. 3. Data Reduction Design Plan. A methodology for analyzing, presenting and using the acquired data. Experimental design includes the development of a measurement test plan. Such a plan assists the engineering in achieving an optimization between time, accuracy, and cost. Expenditure regarding acquiring and analyzing test data versus information obtained. The identification of relevant process parameters and variables is the first step in developing a measurement strategy. All known variables should be listed and evaluated for any possible cause and effect relationships. Independent variables are variables that can be changed independently and without affecting any other variables. A dependent variable is a variable that is affected by changes in one or more variables. The control of a variable is important. A variable is controlled if it can be held at a relatively constant value during a measurement. The cause and effect relationship between an independent and dependent variable is found by applying a controlled value of the independent variable while measuring the dependent variable, also known as calibration. Variables can also be described as being discrete and continuous in nature. A discrete variable is a variable whose value can be enumerated. For example, variables that describe test specimens, testing devices, or operators are discrete variables. A continuous variable is a variable that is not discrete, such as displacement, pressure, or strain. In most instances variables that cannot be controlled but have an affect on the value of the variable being measured are present. These variables are known as extraneous variables. Extraneous variables can take form of signals superimposed over the measured signal such as noise or drift. Parameters are functional relationships between variable. A parameter that has an effect on the behavior of the measured variable is called a control parameter. Available methods for establishing control parameters based on known process variables include similarity and dimensional analysis techniques and physical laws. A control parameter is completely controlled if it can be held at a constant value during a set of measurements.

3 The effects of extraneous variables can be delineated into noise and interference. Noise can be described as a random variation of the value of the measured signal resulting from variations in extraneous variables. Some examples would be thermal or Johnson noise due to random temperature-induced excitation of electrons within current carrying conductors and electronic shot noise common in transistors because of random fluctuations in the rate at which carriers diffuse across transistor junctions. Interference, on the other hand, would produce undesirable deterministic trends on the measured values because of extraneous variables. Examples would include well-defined deterministic variations in environmental conditions, local ac power lenience (60 or 50 Hz,) or fluorescent lighting arc noise (120 or 100 Hz). Interference is most undesirable if the period of the interference is longer than the period over which the measurement is made, because the interference will superimpose a false trend in the behavior of the measured variable. The influence of the extraneous variables can be reduced with the use of proper test strategies. A random test is one such strategy. A random test is defined by a measurement plan that sets a random order in the value of the independent variable applied. This can break up any trend caused by the coupling of uncontrolled extraneous variables with sequential application of independent variables. This type of plan is effective for the control of extraneous variables that change in a continuous manner. Discrete extraneous variables present a different sort of problem. The use of different operators and equipment are examples of discrete extraneous variables. Randomizing a test plan to minimize the influence of discrete variables can be done with the use of random test blocks. A block would consist of a data set of the measured variable where the controlled variable is varied but the extraneous variables are fixed. The extraneous variable would be held constant between blocks. This enables some amount of local control over the discrete extraneous variable. There are many strategies for randomizing blocks as well as advanced statistical methods for data analysis. In general, the estimated value of the measured variable improves with the number of measurements. Repeated measurements made during a test run or a batch of tests are called repetitions. Repetition allows for quantifying the variation in a measured variable as it occurs during any one test while the operating conditions are held under nominal control. However, repetition will not permit an assessment of how exact the operating conditions can be set. An independent duplication of a set of measurements is knows as a replication. This allows for quantifying the variation in a measured variable, as it occurs between different tests, each having the same nominal values operating conditions. All measurement plans should incorporate the use of concomitant methods. The goal is to obtain two or more estimates for the result, each based on a different method, which can be compared as a check for agreement. This may affect the experimental design in that additional variable may need to be measured.

4 CALIBRATION The relationship between the input to the measurement system and the system output is established during a calibration for the measurement system. A calibration is the act of applying a known value of input to a measurement system for the purpose of observing the systems output. The known value used for the calibration is called the standard. By the application of ranges of known values for the input and the observation of the system output, a direct calibration curve can be developed. On such a curve the input, x, is plotted on the abscissa against the measured out put, on the ordinate. In a calibration the input value should be a controlled independent variable, while the measured output value becomes the dependent variable of the calibration. A calibration curve forms the logic by which a measurement systems output can be interpreted during an actual measurement. Using the data created from a direct calibration a correlation between the input and the output can be developed. A correlation will have the form y = f ( x) and is determined by applying physical reasoning and curve fitting techniques to the data. The correlation can be used with later measurements to ascertain the unknown input value based on the systems output. The most common type of calibration is known as a static calibration. In this procedure, a known value is input to the system under calibration and the system output in recorded. The term static refers to a calibration procedure in which the values of the variables involved remain constant during a measurement, that is, they do not change with time. IN static calibration, only the magnitudes of the known input and measured output are important. Dynamic variables are time dependent in both their magnitude and frequency content. The input-output magnitude relation between a dynamic input signal and a measurement system will depend on the time dependent content of the input signal. When time dependent variables are to be measured, a dynamic and static calibration must be preformed. A dynamic calibration determines the relationship between an input of known dynamic behavior and the measurement system output. The slope of a static calibration curve yields the static sensitivity, K, of a measurement system. dy K = dx The static sensitivity is a measure relating the change in the indicated output associated with a given change in a static input. Since calibration curves can be linear or none linear depending on the measurement system and on the variable being measured, K may or may not be constant over a range of input values. The proper procedure for calibrating is to apply known inputs ranging form the minimum to the maximum values for which the measurements system is to be used. These limits define the operating range of the system. The input operating range is defined as

5 extending from xmin to xmax. This range defines its input scan expressed as the difference between the range limits. r i = x max x min Similarly, the output operating range is specified from ymin to ymax. The output span or full-scale-operating range (FSO) is expressed as r o = y max y min It is important to avoid extrapolation beyond the range of known calibration during measurement since the behavior of the measurement system is uncharted in these regions. The accuracy of a system can be estimated during calibration. The accuracy of a measurement system refers to its ability to indicate a true value exactly. Accuracy is related to absolute error. Absolute error,, is defined as the difference between the true value applied to a measurement system and the indicated valued of the system: = truevalue indicated value from which the percent relative accuracy is found by 1 A = *100% true value By definition, accuracy can be determined only when the true value is known, such as during a calibration. The repeatability or precision of a measurement system refers to the ability of the system to indicate a particular value upon repeated but independent applications of a specific value of input. Precision error is a measure of the random variation to be expected during such repeatability trials. An estimate of a system that repeatedly indicates the same wrong value upon repeated application of a particular input would be considered precise regardless of its known accuracy. The average error in a series of repeated calibration measurements defines the error measure known as bias. Bias error is the difference between the average and the true values. Both precision and bias error affects the measure of a system s accuracy. In any measurement other than a calibration the error cannot be known exactly since the true value is not known. However, based on the results of a calibration, the operator might feel confident that the error is within certain bounds, i.e. a plus or minus range of the indicated reading. Since the magnitude of the error in any measurement as the uncertainty present in the measurement as the uncertainty present in the measured value. Uncertainty is caused by errors present in the measurement system, its calibration, and the measurement technique and is manifested by measurement system s bias and precision error.

6 A sequence calibration applies a sequential variation in the input value over the desired input range. This may be accomplished by increasing the input value (upscale direction) or by decreasing the input value (downscale direction) over the full input range. A sequence calibration is an effective diagnostic technique for identifying and quantifying hysteresis error in a measurement system. Hysteresis error refers to differences between an upscale sequence calibration and a downscale sequence e = y y. calibration. The hysteresis error of a system is given by h ( ) upscale ( ) down scale Hysteresis is usually specified for a measurement system in terms of the maximum hysteresis error as a percentage of the full-scale output range (FSO): ( ) e = ( eh( x) ) % h max ro max*100 Hysteresis occurs when the output of a measurement system is dependent on the previous value indicated by the system. Such dependencies can be brought about through some realistic system limitations such as friction or viscous damping in moving parts or residual change in electrical components. Some hysteresis is normal for any system and affects fe precision of the system. A random calibration applies a randomly selected sequence of values of a known input over the intended calibration range. The random application of input tends to minimize the impact of interference. It breaks up hysteresis effects and observation errors. It ensures that each application of input value is independent of the previous. This reduces calibration bias error. Generally, such random variations in input value will more closely simulate the actual measurement situation. A random calibration provides an important diagnostic test for the delineation of several of the measurement system performance characteristics based on a set of random calibration test data. In particular, linearity error sensitivity error, zero error, and instrument repeatability error can be quantified from a static random calibration. Many instruments are designed to give a linear relationship between the static input and the output. The static calibration curve from these instruments should have the form: where the curve fit y L ( x) y ( x) = a + a x L o 1 provides a predicted output value based on a linear relation between x and y. Due to the fact that linear behavior is only approximately achieved measurement device specifications usually provide a statement as to the expected linearity of the static calibration curve for the device. The relation between y L ( x) and the measured value y(x is a measure of the nonlinear behavior of the system: )

7 ( ) e ( x) = y( x) y ( x) L where el x is the linearity error that arises in describing the actual system behavior? For a measurement system that is essentially linear in behavior, the extent of possible nonlinearity in a measurement device is often specified in terms of the maximum expected linearity error as a percentage of full-scale output range: ( ) ( e ( x) ) L % e L max = ro L max*100

8 TRANSDUCER AND TRANSDUCER CALIBRATION Liner Veritable Displacement Transducer (LVDT) Calibration Significance of Uses This procedure is used to determine a calibration constant for a liner veritable displacement transducer. The calibration constant is used in converting a transducer output to useable engineering units. The calibration constant is developed by applying known displacements to the LVDT and measuring its output. Apparatus 1. Liner Veritable Displacement Transducer (LVDT) An LVDT is a transducer used to measure displacement. 2. Micrometer Head A micrometer head is a device that can be used to measure displacement to in. 3. Calibration Stand The calibration stand is a frame used to hold an LVDT and micrometer head so that the micrometer head can be used to displace the LVDT sensor a known distance. 4. Multimeter The multimeter will be used to monitor, remotely, the output of the transducer. 5. DC Power Supply The power supply will be used to supply an excitation voltage to the LVDT 6. Transducer Junction Box the junction boxes provide a link between the testing area and the data acquisition system 7. Data Acquisition System A computer controlled system with capability of measuring voltages and passing information on to a storage system. 8. Control and Storage System The control and storage system is computer-running software designed for data acquisition. Procedure 1. Obtain an LVDT, micrometer head, calibration stand, multimeter, and power supply. The lab group is responsible for the safe return of each piece of equipment. 2. Record the serial number of the transducer on your data sheet. 3. Place the micrometer head into the frame so that the base of the head is against the stand. Secure the micrometer into the frame by turning the hex bolt clockwise. Set the micrometer so that it is some where between and in. 4. Insert the LVDT so that the sensor is completely displaced. Secure the LVDT into the frame by turning the hex bolts clockwise. 5. Connect the power supply to the junction boxes. The input voltage should supplied to the terminals marked Input #1. 6. Connect the multimeter to the junction box. The multimeter should be connected to the terminal marked monitor. 7. Connect the LVDT to the junction box. The LVDT should be connected to a transducer port. 8. Turn on the power supply and set the outputs to 10 volts. 9. Turn on the multimeter and set the selector switch to Input #1. The multimeter should read a voltage identical to the output of the power supply. 10. Retract the micrometer so that the LVDT is at or close to zero displacement and the micrometer is on an increment of in. 11. Read and record the initial reading from the micrometer. This can referred to as X o. 12. Read and record the initial transducer output. This can be referred to as V o. 13. Create a table containing micrometer readings beginning at X o to maximum transducer displacement and returning to X o. Do not repeat displacements. 14. Begin the data acquisition system to read and return to the test station to perform the calibration. 15. Allow the data acquisition system to read and record at least four voltages at the X o position. 16. Displace the LVDT to the X 1 position and allow the data acquisition system to read and record at least four voltages at the X 1 position. Read and record voltage at the X 1 position on your table for reference.

9 17. Repeat steps sixteen for X 2, X 3, X 4 X 15, X o. Each time allowing the data acquisition system to record at least four voltages and record the voltage (V 2, V 3, V 4 V 15, V o ) from the multimeter on your table to refer to later. 18. After returning to X o stop the data acquisition task. Pressure Transducer Significance of Uses This procedure is used to determine the calibration constant for a pressure transducer. The calibration constant is used in converting a transducer output to useable engineering units. Applying known pressures to the transducer and measuring its output develops the calibration constant. Apparatus 1. Pressure Transducer A transducer used to measure pressures. 2. Amerek Pressure Pump A device used to apply known pressures to a transducer. 3. Multimeter The multimeter will be used to monitor, remotely, the output of the transducers. 4. DC Power Supply The power supply will be used to supply an excitation voltage to the pressure transducer. 5. Transducer Junction Box The junction boxes provide a link between the testing area and the data acquisition system. 6. Data Acquisition System A computer controlled system, which is capable of measuring voltages and passing information on to a storage system. 7. Control and Storage System The control and storage system is computer-running software designed for data acquisition. Procedure 1. Obtain a pressure transducer, multimeter, and power supply. The lab group is responsible for the safe return of each piece of equipment. 2. Record the serial number of the transducer. 3. Place the transducer into the pressure pump. 4. Connect the power supply to the junction boxes. The input voltage should be applied to the terminals marked Input #1. 5. Connect the multimeter to the junction box. The multimeter should be connected to the terminal marked monitor. 6. Connect the transducer to the junction box. The transducer should be connected to a transducer port. 7. Turn on the power supply and set the output to 10 volts. 8. Turn on the multimeter and set the selector switch to Input #1. The multimeter should read a voltage identical to the output of the power supply. 9. Apply a pressure of 5 psi as instructed by the T.A. This pressure can be referred to as P o. 10. Read and record the initial transducer output. This can be referred to as V o. 11. Create a table containing pressures beginning at P o =5 psi to P max = maximum transducer pressure and returning to P o. Do not repeat pressures. 12. Begin the data acquisition task and return to the test station to perform the calibration. 13. Allow the data acquisition system to read and record at least four voltages at the P o position. 14. Increase the pressure to the P 1 position and allow the data acquisition system to read and record at least four voltages at the P 1 position. Read and record the voltage at the P 1 position on your table for reference. 15. Repeat step fourteen for P 2, P 3, P 4 P 15, P o. Each time allowing the data acquisition system to record at least four voltages and record the voltage (V 2, V 3, V 4 V 15, V o ) from the multimeter on your table to refer to later. 16. After returning to X o stop the data acquisition task. Force Transducer (Load Cell)

10 Significance of Uses This procedure is used to determine the calibration constant for a load cell. The calibration constant is used in converting a transducer output to useable engineering units. The calibration constant is developed by applying known loads to the transducer and measuring its output. Apparatus 1. Force Transducer or Load Cell A transducer used to measure loads. 2. Loading Frame A device used to ably known force to a transducer. 3. multimeter The multimeter will be used to monitor, remotely the output of the transducer. 4. DC Power Supply The power supply will be used to supply an excitation voltage to the force transducer. 5. Transducer Junction Box The junction boxes provide a link between the testing area and the data acquisition system. 6. Data Acquisition System A computer controlled system with capabilities of measuring voltages and passing information on to a storage system. 7. Control and Storage System The control and storage system is computer-running software designed for data acquisition. Procedure 1. Obtain a force transducer (load cell), multimeter, and power supply. The lab group is responsible for the safe return of each piece of equipment. 2. Record the serial number of the transducer. 3. Place the transducer into the loading frame as directed by your T.A. 4. Connect the power supply to the junction boxes. The input voltage should be applied to the terminals marked Input #1. 5. Connect the multimeter to the junction box. The multimeter should be connected to the terminal marked monitor 6. Connect the transducer to the junction box. The transducer should be connected to the transducer port. 7. Turn on the power supply and set the output to 10 volts. 8. Turn on the multimeter and set the selector switch to Input #1. The multimeter should read a voltage identical the output of the power supply. 9. Apply a known force as instructed by the T. A. This load can be referred to as F o. 10. Read and record the initial transducer output. This can be referred to as V o. 11. Create a table containing loads beginning at F 0` 5 lbs. to F max = maximum transducer load and returning to F 0. Do not repeat loads. 12. Begin the data acquisition task and return to the test station to perform the calibration. 13. Allow the data acquisition system to read and record at least four voltages at the F o position. 14. Increase the load to the F 1 position and allow the data acquisition system to read and record at least four voltages at the F 1 position. Read and record the voltage at the F 1 position on your table for reference. 15. Repeat steps fourteen for F 2, F 3, F 4,.. F 15, F o. Each time allowing the data acquisition system to record at least four voltages and record the voltage ( V 2, V 3,V 4, V 15, V o ) from the multimeter on your table to refer to later. 16. After returning to the F o stop the data acquisition task.

11 DATA SHEET Date: Group Number: Input Channel: Transducer Type: Transducer Serial #: Output Channel File Name: Transducer Input Voltage (V o 1) Micrometer Readings(in) Applied Force (lbf) Applied Pressure (psi) Displacement (in) Change in force (lbf) Change in Pressure (psi) Transducer Output (mvol) Change in Transducer output (Vol)