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AMAZON multi-meters discounts AMAZON oscilloscope discounts AMAZON multi-meters discounts AMAZON oscilloscope discounts An integrated manufacturing environment typically consists of:
The integrated system monitors the environment to understand the progress of the product in the production scheme. The sensors interact with the controllers and provide a detailed account of status of the process as well as environmental conditions. The controller sends signals to the actuators, which respond according to the functions. Sensor-based manufacturing systems consist of data measurement by a plurality of sensors, sensor integration, signal processing, and pattern recognition. Motion measurement (especially the measure of displacement, position, and velocity of physical objects) is essential for many feedback control applications (especially those used in robotics, process, and automotive industries). Motion transducers are a class of transducers used for the measurement of mechanical quantities that include:
• Temperature Primary and Secondary Transducers Sometimes the transducer measures one phenomenon in order to measure another variable. The primary transducer senses the preliminary data and converts it into another form, which is again converted into some usable form by a secondary transducer. As an example, measurement of force is performed using a spring element, and the resulting displacement of the spring is measured using another electrical transducer. The force causes the spring to extend and the mechanical displacement is proportional to the force. The spring is considered to be the primary transducer, which converts force into displacement. The end of the spring is connected to another electrical transducer, which senses its displacement and transmits it as an electrical signal. This electrical transducer is called a secondary transducer. In most measurement systems, it's common to have such combinations of transducer elements in which a primary transducer is the mechanical element, and an electrical transducer (acting in the secondary stage) is the secondary unit. AMAZON multi-meters discounts AMAZON oscilloscope discounts Selection Criteria for a Transducer
Transducers of the electrical, electromechanical, optical, pneumatic, and piezoelectric types are commonly used in motion measurement. Transducer Classification Based on the Principle of Transduction
Whenever certain piezoelectric crystals are subjected to mechanical motion, an electric voltage is induced. This effect can be reversed by applying an electric voltage and deforming the crystal. 1 Resistance Transducers Potentiometric Principle A displacement transducer using variable resistance transduction principle can be manufactured with a rotary or linear potentiometer. A potentiometer is a transducer in which a rotation or displacement is converted into a potential difference. As shown in Ill. 10, the displacement of the wiper of a potentiometer causes the output potential difference obtained between one end of the resistance and the slider. This device converts linear or angular motion into changing resistance, which may be converted directly to a voltage or current signal. The position of the slider along the resistance element determines the magnitude of the electrical potential. The voltage across the wiper of linear potentiometer is measured in terms of the displacement, d, and given by the relationship. ILL. 10 POTENTIOMETER TRANSDUCER PRINCIPAL Here E is the voltage across the potentiometer, and L is the full-scale displacement of the potentiometer. If the movement of the slider is in a circular path along a resistance element, then rotational information is converted into information in the form of a potential difference. The output of the rotary transducer is proportional to the angular movement. If there is any loading effect from the output terminal, the linear relationship between the wiper position and the output voltage will change. The error, which is called the loading error, is caused by the input impedance of the output devices. To reduce the loading error, a voltage source, which is not seriously affected by load variations (e.g., stabilized power source) and signal-conditioning circuitry with high-input impedance should be used. it's also advisable to isolate the wiper of the potentiometer from the sensing shaft. The disadvantage of the potentiometric transducer is its slow dynamic performance, low resolution, and susceptibility to vibration and noise. However, displacement transducers with a relatively small traverse length have been designed using strain-gauge-type resistance transducers. SUMMARY Potentiometric Principle A transducer in which a rotation or displacement is converted into a potential difference. This type of transducer (Ill. 11) converts linear or angular motion into changing resistance, which is converted directly to a voltage or current signal. The position of the slider along the resistance element deter mines the magnitude of the electrical potential. The voltage across the wiper of linear potentiometer is measured in terms of the displacement, d, and given by the relationship where E is the voltage across the potentiometer and L is the full-scale displacement of the potentiometer. Rotary Potentiometer If the movement of the slider is in a circular path along a resistance element, rotational information is converted into information in the form of a potential difference. The output of the rotary transducer is proportional to the angular movement. Features
Applications
2 Inductance Transducers Inductive transducers are used for proximity sensing and also for motion position detection, motion control, and process control applications. Inductive transducers are based on the Faraday's law of induction in a coil. Faraday's law of induction specifies that the induced voltage, or electromotive force (EMF), is equal to the rate at which the magnetic flux through the circuit changes. If varying magnetic flux is applied to a coil, then electromotive force appears at every turn of the coil. If the coil is wound in such a manner that each turn has the same area of cross section, the flux through each turn will be the same. The induced voltage equation is shown in Equation 9. Here, N is the number of turns, and , where B is the magnetic field and A is the area of the coil. It follows that the voltage output can be changed by changing the flux enclosed by the circuit. This can be done by changing the amplitude of the magnetic field B or area of the coil A. The equation can also be expressed as […] where ... Here, N is the number of turns in the circuit, and is the total flux linkages of the circuit. it's concluded that the voltage generated is equal to the rate of change of flux linkages. it's also known that the magnetic field B, produced by a current i in any circuit, is proportional to the current and geometry of the coil. The total flux linkages of the circuit can be expressed in terms of a constant L, which is the inductance of the circuit. Inductance of the circuit is defined as the flux linkage per unit current, as given in Equation 3-12. The inductance change can be caused by variations in any of the following:
The change in self-inductance caused by the geometric configuration is the result of the coil arrangement. There are two parts of the coil mounted on iron cores. One part is stationary, and the other movable. The displacement changes the position of the movable part of the coil, which produces a change in the self-inductance of the coil. Transducers also can be designed which utilize variations in the number of turns. The output relationship becomes L r N2 r (displacement) Change in Mutual Inductance Inductive transducers based on the principle of variation of mutual inductance use multiple coils. The presence of an induced emf in a circuit due entirely to a change of current in another circuit is called mutual induction. To illustrate, consider two coils, 1 and 2, with turns N1 and N2, respectively. The current i, flowing in coil 1, produces a flux [...] If R is the reluctance of the magnetic path, the induced emf in coil 2 due to current in coil 1 is In Equation 22, K is known as the coefficient of coupling between the two coils. Thus, mutual inductance between the coils can be changed by variations in either of the self-inductances or the coefficient of coupling. Inductance transducers for measuring displacement use the principle of change in mutual inductance of a coil at varying core positions. When the core is centrally located, the voltage induced in each secondary is the same. When the core is displaced, the change in flux linkage causes one secondary voltage to increase and the other to decrease. The secondary windings are generally connected in series opposition, so the voltage induced in each are out of phase with the other. The output voltage is zero when a core is centrally located and increases as the core is moved either in or out. The voltage amplitude is linear with core displacement over some range of core travel. The signal-conditioning circuit produces a voltage output, which is proportional to the dis placement. The polarity of the output voltage derivative is relative to the direction of core motion. 3 Linear Variable Differential Transformer (LVDT) LVDTs are the most widely used transducers. They are used to measure displacement directly as a sensing element in a number of situations involving motion. LVDTs can resolve very small displacements. Their high resolution, high accuracy, and good stability make them an ideal device for applications involving short displacement measurements. LVDTs consist of one primary winding, P1, and two secondary windings, S1 and S2. Each is wound on a cylindrical former with rod-shaped magnetic cores positioned centrally inside the coil assemblies. This provides a dedicated path for the magnetic flux linking the coils. An oscillating excitation voltage is applied to the primary coil. The current through the primary creates voltages in secondary windings. The ferromagnetic core concentrates the magnetic field. If the core is closer to one of the secondary coils, the voltage in that coil will be higher. ILL. 12 SCHEMATIC OF LINEAR VARIABLE DIFFERENTIAL TRANSFORMER (LVDT) Let the output of the secondary winding S1 be Es1 and that of S2 be Es2. When the core is at its normal null position, equal voltages are induced in each coil. When these two outputs are connected in phase opposition, as shown in Ill. 12, the magnitude of the resultant voltage will be zero. This is known as the null position, and the output Es1 will be equal to Es2. As the moving core is displaced, the mutual inductance between the fixed coils changes. The LVDT outputs a bipolar volt age proportional to displacement. The output voltage is positive and gives no indication of the direction in which the core has been moved. Proper signal conditioners can be designed to give indication of the direction. LVDTs have limitations when used for dynamic measurements. They are not well suited for frequencies greater than 1/10 of the excitation frequency. In addition, the mass of the core introduces some amount of mechanical loading error. Proper selection of a LVDT depends on the range of displacement measurement. The voltage versus displacement is linear up to a certain point, but nonlinear beyond that region. The sensitivity of the transducer is also dependent on the excitation signal frequency, f, and the primary current, I_p. For good results, the linearity range of travel should be limited to the width of the primary coil. Typical LVDT range is from _2 to _400 mm with non linearity errors of about _0.25%. The signal output E0, in relation to the other characteristics of the coil, is given by Equation 2 where f = excitation signal frequency Ip = primary current np = number of turns in primary ns = number of secondary turns b = width of primary coil w = width of secondary coil x = core displacement r0 and r1 = the outer and inner radius of the coil 4 Rotary Variable Differential Transformer (RVDT) The RVDT can be used wherever precision angular rotations are measured. The RVDT uses the same principle as LVDT, except it has a rotating magnetic core. Some RVDTs have a typical range of _40° with a linearity error around _0.5% of the range. Although LVDTs and RVDTs are used as primary transducers, they also can be used as a secondary transducer in areas of measurement of force, weight, pressure, and flow. Typical applications of inductance transducers include the following.
SUMMARY Linear Variable Differential Transformer Principle: Based on the Faraday's law of induction in a coil, which specifies that the induced voltage, or electromotive force (EMF), is equal to the rate at which the magnetic flux through the circuit changes V = N d phi /dt Here, N is the number of turns, and phi = BA, where B is the magnetic field and A is the area of the coil. Description: Ill. 13 consists of one primary winding P1 and two secondary windings S1 and S2, where each is wound on a cylindrical former with rod-shaped magnetic cores positioned centrally inside the coil assemblies. This provides a dedicated path for the magnetic flux linking the coils. An oscillating excitation voltage is applied to the primary coil. The current through the primary creates voltages in secondary windings. The ferromagnetic core concentrates the magnetic field. If the core is closer to one of the secondary coils, the voltage in that coil will be higher. Rotary Variable Differential Transformer The RVDT uses the same principle as LVDT, except it has a rotating magnetic core. Features
Applications
5 Capacitance Transducers The variation in capacitance between two separated members (electrodes) is used for the measurement of many physical phenomenon. Capacitance is a function of the effective area of the conductors, the separation between the conductors, and the dielectric strength of the material. A change in capacitance can be brought about by varying any one of the three parameters. These variations are summarized here.
Ill. 14 illustrates the variable capacitance principle for displacement measurement utilizing the parallel-plate capacitor. In Figures 3-14(a) and 3-14(b), the gap is varied, and Ill. 14(c) presents the situation where a dielectric material is inserted between the parallel plates. ILL. 14 PRINCIPLE OF VARIABLE CAPACITANCE The ratio of the amount of charge stored on one of the plates to the amount of voltage across the capacitor is the capacitance. The capacitance is directly proportional to the area of plates and inversely proportional to the distance between them. The governing equation is given in Equation 2 The constant of proportionality E, known as the permittivity, is a function of the type of material separating the plates. For a capacitance transducer with insulating material, the capacitance between the plates is defined as [ … ] where constant of the insulating medium (for air ) permittivity of air or free space (in a vacuum), which is , 8.85 pF/m, or A = overlapping area in plates, m^2 d = distance between electrodes or plates, m. This equation establishes a relationship between the plate area and the distance between the plates. Varying either of them linearly changes the capacitance, which can be measured by a circuit. The equation is valid for parallel-plate capacitors. However, if the geometry of the electrodes changes, the equation must be modified. Variable capacitance transducers have applications in the area of liquid level measurement, chemical plants, and in situations where non-conductors are required. Let, , and represent the changes in area, position, and capacitance, respectively, can be represented as delta C Capacitance Transducers Using Change in Distance Between Plates Ill. 15 illustrates a typical arrangement of a capacitance transducer that employs plate distance variations causing a change in capacitance. The right plate is fixed, and the left plate is movable by the displacement which is to be measured. The capacitance is computed as ILL. 15 CAPACITANCE CHANGE DUE TO PLATE SEPARATION If air is the dielectric medium, E r = 1. The capacitance is inversely proportional to the distance between the plates. The overall response of the transducer is not linear, as shown by the distance versus capacitance plot of Ill. 16; however, transducers of this type are used for the measurement of extremely small displacements where the relationship is approximately linear. The sensitivity factor is expressed as [...] Capacitance Transducers Using Change in Area of Plates For parallel-plate capacitors, the capacitance is […] where L = the length of overlapping part of plates w = the width of overlapping part of plates The sensitivity of the capacitance transducer becomes There is a linear relationship between displacement and the capacitance. The preceding equations show that the capacitance is directly proportional to the area of the plates and varies linearly with changes in the displacement between the plates. Transducers of this type are used for the measurement of relatively large displacements (Ill. 17). ILL. 17 CAPACITANCE VARIATION BY CHANGE IN AREA Capacitance Transducers Using Change in Area (Cylindrical Shapes) A cylindrical-shaped capacitor consists of two coaxial cylinders with the outer diameter of the inner cylinder defined as D1, the inner diameter of outside cylinder as D2, and the length as L. Consider an example involving overlapping conductors, in which the inner cylinder can be moved with respect to the outer cylinder, causing a change in capacitance (Ill. 18). ILL. 18 CHANGE IN AREA BASED ON CYLINDRICAL SHAPES The capacitance is computed as [...] Capacitance Transducers for Angular Rotation The basic principle of change in area also can be used for rotational measurement. As shown in Ill. 19, one plate is fixed and the other is movable. The angular displacement to be measured is applied to the movable plate. This angular displacement changes the effective area between plates and , thus, changes the capacitance. The capacitance is maximum when the plates completely overlap each other. ILL. 19 ANGULAR ROTATION OF PLATES The maximum value of the capacitance is computed as The capacitance at angle (Ill. 20) is computed as ILL. 20 CAPACITANCE VARIATION ON ROTATION …where angular displacement […] is in radians. The relationship is linear and the maximum angular displacement is 180°. The sensitivity is calculated as … Capacitance Transducers Using Variation of Dielectric Constant The change in capacitance caused by a change in the dielectric constant of the separating material is another principle which can be used in capacitance transducers. Ill. 21 shows an arrangement of two plates separated by a material of different dielectric constant. As this material is moved, it causes a variation of dielectric constant in the region separating the two electrodes, resulting in a change in capacitance. ILL. 21 TWO PLATES SEPARATED BY A MATERIAL OF DIFFERENT DIELECTRIC CONSTANT: Displacement, Bottom plate, Top plate As shown in Ill. 22, the top plate and bottom plate are partially separated by the dielectric material. As the material moves a distance x as shown, the distance l1 decreases and l2 increases. ILL. 22 VARIATION OF CAPACITANCE BY DIELECTRIC CONSTANT The initial value of the capacitance, assuming a dielectric material of thickness d and width w, can be described as Equation 3-35 has two terms. One represents the capacitance of the two electrodes separated by air, and the other represents the capacitance of the dielectric material between the electrodes. If the dielectric material is moved through a distance x, as shown in Ill. 22, the capacitance increases from C to C _C, and the change in capacitance is shown as The change in capacitance is proportional to the displacement x. This principle is also used in devices for measuring levels in nonconducting liquids. As shown in Ill. 22, the electrodes are two concentric cylinders and the nonconducting liquid provides a dielectric medium between them. At the lower end of the outer cylinder, there are holes which allow passage of liquid. As the fluid level changes, the dielectric constant between the electrodes changes, which subsequently results in a change in capacitance. Capacitance Transducers Based on Differential Arrangement Differential capacitance transducers are also used for precision displacement measurement. Ill. 23 shows two fixed plates and a movable plate to which the displacement is applied. ILL. 23 DIFFERENTIAL ARRANGEMENT OF PLATES A capacitive transducer is a displacement-sensitive transducer. A suitable processing circuit is necessary to generate a voltage corresponding to the capacitance change. General losses in the capacitance are attributed to:
Capacitance transducers have several advantages. They require extremely small forces to operate, are very sensitive, and require low power to operate. Their frequency response is good up to 50 kHz, making them good candidates for applications involving dynamics. Disadvantages include the need to insulate metallic parts from each other and loss of sensitivity due to error sources associated with the cable connecting the transducer to the measuring point. Other Arrangements 1. Three material configuration: Indices 1, 2, and 3 indicate layers of different permittivity and thickness, d, for a configuration with three materials. 2. Alternately connected multiplate configuration: This is the expression of capacitance for a transducer of n alternately connected plates. This transducer has n = 1 times the capacitance of one pair of plates. SUMMARY Capacitance Transducer Principle: Capacitance is a function of effective area of the conductors, the separation between the conductors, and the dielectric strength of the material. The governing equation is The constant of proportionality, p known as the permittivity, is a function of the type of material separating the plates. The variation in capacitance between two separated electrodes is used for the measurement of many physical phenomenon. A change in capacitance can be brought about by varying the following parameters. • Changing the distance between the two parallel electrodes. • Changing the dielectric constant, permittivity, of dielectric medium • Changing the area of the electrodes, A. Description Ill. 24 shows the variable capacitance principle for displacement measurement. Features Capacitance transducers can be used in high humidity, high temperature, or nuclear radiated zones. They are very sensitive and have high resolution. They can be expensive and need significant signal conditioners. Applications Capacitance transducers are generally only suitable for measuring small displacements. Examples of these are surface profile sensing, wear measurement, or crack growth. [omitted math content] NEXT: Digital Sensors |
Updated:
Monday, March 19, 2012 7:13
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