ࡱ> XZWqnM $Cbjbj== WW9l@@@@hhh$,,,,4-$O2....6/22 3*N,N,N,N,N,N,N$O QPNh 3/22 3 3PN7@@.6/N777 3l@.Lh6/*N7 3*N7V7 =IhThJ6/&. g ZB,w4@JJtN0OPJXR/5RJ7@@@@Displacement sensor axis misalignment error Vladimir Tudi Polytechnic in Karlovac, Ivana Meatrovia 10, 47000 Karlovac, Croatia vladimir.tudic@vuka.hr Abstract  Because of valve displacement great importance in valve systems in many marine power aggregates and other servomechanisms and equipment, controlling measurement of this parameter would be taken. Hysteresis measurement must also be taken after every mounting and periodically revision activities. Controlling measurement complies of displacement sensor and computer system applied with adequate hardware and software solutions. Displacement sensor axis misalignment error cannot be avoided in any situation where sensor axis line of symmetry is not parallel with axis line of valve movement. Therefore, elevation error must be considered. Other errors and imperfections in measuring process because of clearly thesis description in this paper are negligible (measuring method, sensor class, nonlinearity, software signal transition). Paper goal is pointing error values regarding sensor axis elevation and its presentation in meaningful ways, with comprehensive further influences. Key words valve, LVDT sensor, axis elevation, system error 1. INTRODUCTION Valve displacement determination has great contribution to quality and working characteristics of any system in power aggregates and servomechanisms, also in machine tools. Measurement of displacements is not easily carried out by direct comparison with a reference such as is done when using a micrometer. Instead, displacement measurements are generally made using recalibrated systems involving sensor-detectors, transducers, signal conditioners, and a recording device. The linear variable differential transformer (LVDT) is a type of electromechanical transformer used for measuring linear displacement, overwrite in [1], [5] and [6]. LVDT are commonly used for position feedback in servomechanisms, pneumatic valves, power aggregates governing valve systems, and many other industrial and scientific applications (e.g. for measurement force, weight and pressure). Many sensors with great precisions are used for determinations of hysteresis of the mechanical and servo mechanical power aggregate valve systems. Nevertheless regarding purpose, displacement sensors must be mounted in a way that position ensures free line movement. On the other hand some sensors are mounted inside of machine or aggregate housing. In that case control checking and displacement of instrument is more difficult to achieve. Sensor tube body placing must apply parallel position regarding to line of valve displacement. If not so, axis misalignment error occurs in absolute displacement measuring. The purpose of this paper is to familiarize users in many LVDT measurements how to apply axis misalignment error to analyze the resulting data and to present this information in meaningful ways. 2. LVDT APPLICATIONS The LVDT transformer has three solenoid coils placed end-to-end around a tube body. The centre coil is the primary, and the two outer coils are the secondary. A cylindrical ferromagnetic core, attached to the object whose position is to be measured, slides along the axis of the tube, throw open bore on both ends of tube body. As the core moves, these mutual inductances change, causing the voltages induced in the secondary to change. Output of sensor is a direct and linear function of the input, standardized in voltages or mili amperes. The external housing of the LVDT is fabricated of material having a high-magnetic permeability (nickel-iron alloy) therefore desensitizing the device from the effects of external magnetic fields. The core extension rod must be fabricated from material with low magnetic permeability, such as aluminium, brass, or some stainless steels (Figure 1). Sensor robust construction provides high reliability, it has extremely fine resolution, excellent zero repeatability over time and temperature, medium cost, high ruggedness and therefore long life time. The thermal response characteristics of the LVDT are excellent for static and quasi-static thermal environments. LVDT can operate in vertical, horizontal, or other axes misalignment. Sensor rod surface is smoothly, as expected of measuring unit surface.  Figure 1. LVDT displacement sensor 2.1. Displacement value meanings Displacement measuring values have a great importance in valve systems on many power aggregates and servomechanisms worldwide. Absolute displacement and hysteresis values detected by LVDT sensors must be imported to measuring protocols e.g. [4]. Those parameters are surely considered with great notice and should be compared with producing and valid standards. Permitable value of hysteresis can be 0.1 %, due to 100 mm measuring range of sensor the limit value regards to value of 0.1 mm. Another point of view is based to sensor class, whose values are usually between 0.5 and optionally 0.1, mentioned in [3]. Therefore, LVDT range of 100 mm gives error vales from 0.1 mm up to 0.5 mm. Reasonable considerations suggest that the Data acquisition software signal transmission error can be maximum 0.1 %. The result is again value of 0.1 mm. So, if measurable value of displacement 0.1 mm is the same as exact value of real errors or imperfections, reasonable calculations of axis misalignment error must be taken also. 2.2. Modelling measurements Figure 2 shows typical LVDT connection to governing valve (option pneumatics valve). Mechanical assembly is used for alignment of the extended iron core (armature). LVDT moving extended rod is assembly to valve ring or extended plate, with free line movement ability. Sensor position is horizontal, vertical or any other axes misalignment depending of valve system situation. Axe of sensor tube and extended rod must correspond to trajectory of valve displacement, or those must be parallel. Because of easier explanation of axis misalignment error in paper sensor and valve position would be regarded in horizontal position.  Figure 2. LVDT connection to valve system 3. ERROR SOURCES Specific sources of error relevant to the measurement of the displacement by [1] and [2] are as follows: Computer unit equipped with hardware and software solutions and applications convert the voltage output of the LVDT to displacement units. If this factor is incorrect the change in the output of sensor will not correlate with the physical displacement moved be extended rod core. Sensor no linearity of the sensor greater then valve system hysteresis value, instead of no linearity guaranteed in calibration certificate. After a sensor housing mechanical assembly and alignment of the iron core, null point calibration must be preceded. If not, offset error will affect the measuring process. Sensor housing line of symmetry in relation or parallel with line of symmetry of valve. Other sources as power aggregate vibrations, measuring methods imperfectly, temperature coefficient of all elements in measuring environment, extended rod and valve plate surfaces are considered insignificant. 3.1. Error considerations Errors in measuring process by [2] can be divided: Accidental errors, System errors. 3.2. Accidental errors Such errors cannot be totally predicted and therefore cannot be fully eliminated. They occur because of human and environmental influences. Human error is generated in instrument assembly and mistakes in entering coefficients in system. Environmental influences may be axis misalignment because of great clearness, rotation and axis misalignment of sensor housing because of source inside or outside of ship (sea wave disturbance), power aggregate vibrations, insufficient assembly strength sensor housing. 3.3. System errors System errors are measurable, predictable, and controllable and can be calculated in known environment. Example is known value of elements temperature coefficient. If measuring process is fast enough (few seconds) influence in that case is unessential. Error can be insufficient accuracy determination of transit coefficients entered in software application. The significant error can be axis misalignment between axis line of sensor housing and axe line of valve. Error of this type is always possible, and must bee considered in all cases. An example of systematic error can be insufficient accuracy determination of transit coefficients entered in software application, as mentioned in [3]. The biggest potentional error of all mentioned is axis misalignment difference between houses axis and axe of valve. Error of this type is always possible, and all further influences must bee considered. 4. TRACABILITY The sensors used in the calibration are themselves periodically calibrated against a range of plane parallel gauges of known displacement in National Calibration Centre. Computer units (DAQ and Data Logger) and software application (Lab Windows) used to make measurement are traceable to recognized national standards and to the units of measurement realized at the National Physical Laboratory or to other recognized national standards laboratories, as mentioned in [4]. 5. ERROR CALCULATIONS Axe of sensor tube and extended rod must correspond to trajectory of valve displacement, or those must be parallel. Otherwise in the measuring process axis misalignment error will occur. In figure 3 sensor axes line is rotated counterclockvise under some angle from horizontal line, and the displacement value measured with LVDT sensor is named x.  Figure 3. LVDT sensor tube (rod) axe line Valve displacement h is actually displacement of valve spindle face (Figure 4). Axe of valve elements is placed horizontally, and the valve spindle displacement is marked h.  Figure 4. Valve spindle axe line Further on, axis misalignment angle value is named a, and two axes offset on the valve face plate is marked with a. Value is a distance between symmetry lines and therefore carry offset value. Error value in this situation is difference between two values h and x and in paper is marked y.  Figure 5. Values relationship in triangle Therefore, situation can be considered throw right square triangle equations. Difference between those two values can be described as  EMBED Equation.3 . From triangle equation x value can be shown  EMBED Equation.3  (1) Further entering gives relation  EMBED Equation.3  (2) Obviously, equation above describes axis misalignment error functional relationship depending of angle value. Now it is easy to calculate error value if valve displacement is for example 100 mm in angle steps of 0.2 degrees. Table 1. Axis misalignment error calculation ha1 / cos axymmDegree-mmmm1000.01.000000100.0000.0001000.21.000006100.001-0.0011000.41.000024100.002-0.0021000.61.000055100.005-0.0051000.81.000097100.010-0.0101001.01.000152100.015-0.0151001.21.000219100.022-0.0221001.41.000299100.030-0.0301001.61.000390100.039-0.0391001.81.000494100.049-0.0491002.01.000610100.061-0.0611002.21.000738100.074-0.0741002.41.000878100.088-0.0881002.61.001030100.103-0.1031002.81.001195100.120-0.1201003.01.001372100.137-0.137Data from Table 1 unmistakably shows angle and axis misalignment error relation. Angle value of 2.6-degree defines axis misalignment error of 0.1mm. In this situation offset value a (two axes line distance) gives calculation of 4.5 mm. Also, when angle value takes 3.6-degree axis misalignment error rises up to 0.2 mm (a =6.3 mm). Relationship between those two values is not so convenient. Usually, correspondence can be taken between axis misalignment error and offset value. In this case function dependence is shown between two linear values with all implications. 6. GRAPHICAL PRESENTATION Graphical presentation of axis misalignment error is shown in Figure 6. Polynomial equation of second order (3) describes risen trend of error value and equation that approximate relation of two parameters is also given in the chart. Equation is  EMBED Equation.3  (3) Figure 6. Axis misalignment error chart Entry  EMBED Equation.3  in this case means EMBED Equation.3 . Second point of view gives relations between axes misalignment error and offset value (a). In this case function dependence is little bit different, but trend of data is almost the same. Offset value a as dependence of values in right square triangle is given in equation 4 which follows  EMBED Equation.3  (4) Equation of polynom of second order (5) also describes trend of error witch follows increasing risen offset value a. The results of axis misalignment error depending of offset value is also shown throw equation  EMBED Equation.3  (5) Where  EMBED Equation.3  means  EMBED Equation.3 . In most cases offset value can be measurable instead of angle value, which can be only predicted in real practical measurement in field conditions. 7. CONCLUSION Valve displacement value of 0.1 mm can be limit hysteresis value or value of precise sensor class, but also reasonable error of software signal-data transmission. Axis misalignment error calculations presented in this paper suggest that axis misalignment angle greater then 2 degree can also means trouble in displacement measurement. Special attention must be taken when displacement measurement are realizing with very precise LVDT sensor (range of few millimetres with 0.5 1.0 mm step). Small or short housing of some precise LVDT sensor can very often increase axis misalignment error in mounting phase. The paper goal is to familiarize users in many LVDT measurements how to apply or prevent axis misalignment error to analyse the resulting data and to present this information in meaningful ways. REFERENCES [1] ISO 5725, Accuracy (trueness and precision) of Measurement Methods and Results - Part 1: General Principles and Definitions, No. 1, January 1994 [2] DZNM - State office for standardization and metrology, ISO Guide for determination of measurement uncertainty, Zagreb, May 1995 [3] V. Bego, Measurements in electrotechnic , Technical Book, Zagreb, October 1997 [4] M. Brezinaak,  Measurements and calculation in technique and science , Technical Book, Zagreb, June 1967 (5( Herceg, Edward E., Handbook of Measurement and Control, 1976, Schaevitz Engineering, Pennsauken, NJ, pp. 3-4. (6( Nyce, David S., Linear Position Sensors, Theory and Application, 2004, John Wiley and Sons, Hoboken, NJ, p. 96.    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