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Nov 29 2019

Differential Transformer and Its Application

Ⅰ Introduction

A differential transformer is an electromagnetic inductive displacement sensor that converts mechanical displacement into an electrical signal. It mainly relies on the displacement of the movable iron core in the cylindrical coil, and establishes a mutual induction relationship between the input coil and the output coil of the cylindrical coil, and the displacement of the movable core can be obtained by measuring the induced voltage of the output coil proportional to it.


Characteristics of Differential Transformer

(1) There are many types of linear ranges, and it is easy to select according to the use. Usually, there are about 10 types between ±2 mm and ±200 mm.

(2) The structure is simple, so the vibration resistance and impact resistance are strong.

(3) It does not wear, does not deteriorate, and has excellent durability.

(4) The output voltage has a precise ratio to the displacement of the core, that is, the linearity is good. Generally, the full stroke deviation of this sensor is less than 1%, and it can be guaranteed to be ±0.2% to ±0.3% in high-grade products.

(5) Because of the high sensitivity, a large output voltage can be obtained, and a small displacement can be detected without requiring an advanced circuit.

(6) Since the output changes smoothly, high-resolution detection is possible.

(7) The zero point is stable, and its use as a reference point for measurement is good for maintaining accuracy.

(8) A high response speed from 500 Hz to 100 Hz can be obtained.


Ⅱ The Working Principle and Structure of the Differential Transformer

The structure of the differential transformer is divided into two types: variable-gap type and solenoid type. Since the variable-gap type differential transformer has a small stroke and a complicated structure, it is rarely used at present, and the solenoid type is usually adopted.

The basic components of the solenoid type differential transformer include an armature, a primary coil, a secondary coil, and a coil frame. The primary coil acts as an excitation and corresponds to the primary side of the transformer. The secondary coil is formed by inverting two coils of the same structural size and parameters to form the secondary side of the transformer. There are two-section, three-section and multi-section according to the initial and secondary arrangement. The zero potential of three-section is small, the two-section is more sensitive than the three-section, and the linear range is large. The four-section and five-section are all efforts to improve the linearity of the sensor.

The working principle of the differential transformer can be explained by the principle of the transformer. The difference is: the general transformer is the closed magnetic circuit, and the differential transformer is the open magnetic circuit; the mutual inductance of the original transformer and the secondary side is constant, and the mutual inductance between the primary and secondary sides of the differential transformer changes as the armature moves. The operation of the differential transformer is based on the change of mutual inductance.

The construction principle of the differential transformer is as shown in figure 1, and is composed of a cylindrical coil and a core that is completely separated from it. A typical differential transformer has three cylindrical coils, each of which is one-third of the total length, with a primary coil in the middle and a secondary coil on each side. The iron core added to the cylindrical coil is used to link the magnetic lines of force in the coil to form a magnetic circuit.

 Figure 1. The Construction Principle of the Differential Transformer

Figure 1. The Construction Principle of the Differential Transformer

When an alternating voltage is applied to the primary coil in the middle (ie, excitation), an electromotive force is generated due to the mutual inductance with the coils at both ends (this is the same as that of a normal transformer).

Since the secondary coils are connected in series with each other in opposite polarity, the induced electromotive forces in the two secondary coils are opposite in phase, and as a result of the addition, a potential difference between the two is generated at the output end. At the center of the coil length direction, the induced voltages of the two secondary coils are equal in opposite directions, and thus the output is zero. This position is called the mechanical zero point of the differential transformer (or simply zero point). When the iron core changes position from zero point to a certain direction, the voltage of the secondary coil in the displacement direction increases, and the voltage of the other secondary coil decreases.

The product design guarantees that the potential difference is proportional to the displacement of the core. When the iron core moves from zero point to the opposite direction, a proportional voltage is generated, but the phase is 180° different from the previous one. The relationship between the secondary coil voltage and the output voltage difference with respect to the core displacement is shown in figure 2.

The range in which the voltage difference is proportional to the core displacement is called the linear range, and its proportionality is called linearity, which is the most important indicator of the differential transformer.

 Figure 2. The Core Displacement — Output Relationship of Differential Transformer

Figure 2. The Core Displacement — Output Relationship of Differential Transformer


 The Type of Differential Transformer

The standard differential transformer consists of a cylindrical coil and a rod-shaped iron core. In actual use, there is also a structure with a guide and a spring.

The basis for classification of differential transformers is as follows:

(1) According to the voltage input to the primary coil(excitation type)

Commercial power supply type is suitable for practical measuring instruments of 50-60Hz, 6.3V power supply excitation;

Oscillation power supply type is an excitation circuit of 1~5KHz, it is suitable for application measuring instruments requiring certain accuracy and response characteristics;

DC power supply type, the semiconductor device is installed in the coil part of the differential transformer to form the excitation oscillation circuit and the secondary output detection circuit inside the coil. It is a differential transformer whose input and output are both DC, called DC-DT.

(2) According to the displacement range of the iron core (displacement type)

◆ Small displacement type considers how to measure the small displacement below 0.5mm from the structure;

◆ General displacement type is designed for measuring the displacement about 100mm or less;

◆ The long stroke type is designed for long stroke measurement of 120 to 400 mm. 

(3) According to the use environment (environment type)

■ Standard type is used in a normal environment with a temperature of -30℃ to +90℃ and a humidity of about 80%;

Environmentally friendly type is the sensor for high temperature, high humidity, waterproof and radioactive environments.


Features and Specifications

When using a differential transformer as a position sensor, the selected specifications are as follows:

◆ Excitation power supply (frequency, voltage, waveform, etc.);

◆ Structure (whether guides and springs are required);

◆ Linear range (it is usually ±1%, and that of high-grade products is ±0.5%~±0.2%);

◆ Sensitivity (corresponding to the output of the core displacement of 1mm);

◆ Impedance (input, output impedance);

◆ Connection conditions (cables, sockets, input circuits, etc.);

◆ Assembly method (connection method with the object to be tested, etc.);

◆Environmental conditions (temperature, humidity, dust, water resistance, rust-proof conditions, etc.).


Ⅳ Linearity and Sensitivity

(1) Linearity. The linear range of the differential transformer is affected by the non-uniform magnetic field of the solenoid coil. A reasonable design guarantees the required linear range and linearity.

(2) Sensitivity. The sensitivity of the differential transformer refers to the change of the output potential generated by the armature unit displacement. It can be expressed by mV/mm. In practice, considering the influence of the excitation voltage, it is also commonly expressed by mV/mm/V, that is, the potential change generated by the armature unit displacement divided by the excitation voltage value.

The sensitivity of the differential transformer is related to the primary voltage, the number of secondary winding turns, and the frequency of the excitation voltage:

① Relationship with secondary turns

The number of secondary turns increases and the sensitivity increases, which is linear. However, the number of secondary turns cannot be increased indefinitely because the residual voltage at the zero point of the differential transformer also increases.

② Primary voltage

The sensitivity is proportional to the primary voltage, but the primary voltage should not be too large. When the voltage is too large, the differential transformer coil will heat up and cause the output signal to drift. Generally, 3~8V is used.

③ Excitation power frequency

When the frequency is very low, the sensitivity increases with increasing frequency; when the frequency increases, the inductance of the coil is much higher than its resistance, the sensitivity is independent of the frequency; when the frequency exceeds a certain value (the value varies depending on the armature material), the effective resistance of the wire increases due to the skin effect of the wire at a high frequency, and the eddy current loss and hysteresis loss of the armature increase, and the output decreases. Figure 3 is the relationship between the input frequency and sensitivity of a certain magnetically permeable material, which can be used as a reference for selecting the excitation frequency.

 Figure 3. Relationship Between Excitation Frequency and Sensitivity of Differential Transformer

Figure 3. Relationship Between Excitation Frequency and Sensitivity of Differential Transformer


Ⅴ The Cause of the Error

The error refers to the deviation between the actual and ideal characteristics of the sensor. Here, the system error inherent in the sensor itself and random error are mainly analyzed, and the error in the measurement method is not involved.

(1) Influence of amplitude and frequency of excitation power supply

Fluctuations in the magnitude of the excitation supply voltage cause changes in the strength of the excitation field of the coil to directly affect the output potential. The frequency fluctuations have little effect.

(2) The effect of temperature changes

Changes in ambient temperature cause changes in the magnetic permeability of the coil and the magnet, causing a change in the magnetic field of the coil to cause temperature drift. This effect is more severe when the coil quality factor is low. The use of constant current source excitation is more advantageous than the constant voltage source. Properly increasing the quality factor of the coil and using a differential bridge can reduce the effects of temperature.

(3) Zero residual voltage

When the armature of the differential transformer is in the neutral position, the ideal output voltage should be zero. But in fact, when using a bridge circuit, there is always a small voltage value (from a few millivolts to tens of millivolts) at zero point, which is called the zero residual voltage. Figure 4 is an enlarged output characteristic of the zero residual voltage. The dotted line is the ideal characteristic and the solid line indicates the actual characteristics. The presence of a zero residual voltage causes an insensitive zone near the zero point.

 Figure 4. Zero Residual Voltage of the Differential Transformer

Figure 4. Zero Residual Voltage of the Differential Transformer

The waveform of the zero residual voltage is very complicated and irregular. It is analyzed to include the fundamental wave in-phase component, the fundamental wave orthogonal component, and the second and third harmonics as well as the electromagnetic interference waves with small amplitude.

The reasons why the zero residual voltage is generated are as follows:

① Fundamental wave component: Since the winding of the two secondary windings of the differential transformer can not be completely identical in process, its equivalent circuit parameters (mutual inductance, self-inductance and loss resistance, etc.) cannot be completely equal, thus two induced potential values are not equal. The copper loss resistance of the primary coil, the iron loss and material non-uniformity of the magnetically permeable material and the presence of the inter-turn coil capacitance cause the excitation current to be out of phase with the generated magnetic flux.

The above factors cause the induced potentials in the two secondary coils to be not only unequal in value but also in phase. The zero residual voltage generated by the difference in phase cannot be eliminated by adjusting the armature displacement.

② High-order harmonics: The high-order harmonics are mainly caused by the nonlinearity of the magnetization curve of the magnetically permeable material. Due to the effects of hysteresis loss and magnetic saturation, the excitation current is inconsistent with the magnetic flux waveform, resulting in a non-sinusoidal wave (mainly the third harmonic flux), thereby inducing a non-sinusoidal potential in the secondary winding.

General method for eliminating zero residual voltage:

— From the design and process, try to ensure the symmetry of the coil and the magnetic circuit. The structure can adopt the magnetic circuit adjustment mechanism; when selecting the working point of the magnetic circuit, it should be ensured that the magnetic field does not work in the saturation region of the magnetization curve.

— Use the appropriate measurement line. The phase sensitive detection circuit can not only identify the moving direction of the armature, but also eliminate the high-order harmonic zero residual voltage of the armature in the middle position. As shown in figure 5, after using the phase sensitive detection, the characteristic curve of the armature reverse stroke changes from 1 to 2, thereby eliminating the zero residual voltage.

 Figure 5. Output Characteristics After Phase-sensitive Detection

Figure 5. Output Characteristics After Phase-sensitive Detection

— Use compensation lines. In applications of differential transformer, there are many circuit types used to eliminate the zero residual voltage, which can be summarized as follows:

▲Add series resistors to eliminate the in-phase component of the fundamental wave; generally the resistance of the series resistor is very small such as 0.5~5Ω, and is wound with constantan wire.

▲Add parallel resistors to eliminate the fundamental wave orthogonal component, but it has an effect on the in-phase component of the fundamental wave; the resistance of the shunt resistor is from tens to hundreds of kiloohms.

▲Shunt capacitor, change phase shift, and compensate for high-order harmonics; parallel capacitor value is in the range of 100 ~ 500pf.

▲Add feedback winding and feedback capacitor to compensate for fundamental wave and high-order harmonics.

In fact, these values are determined experimentally; based on the working principle of the differential transformer and the cause of the zero residual voltage, the above methods can be modified and combined, and it is also possible to design a new compensation circuit. Figure 6 shows some line schematics for compensating for zero residual voltage for reference.

 Figure 6. Zero Residual Voltage Compensation Circuit of Differential Transformer

Figure 6. Zero Residual Voltage Compensation Circuit of Differential Transformer


Ⅵ The Measurement Circuit

(1) Differential DC output circuit

The output voltage of the differential transformer is an AC signal whose amplitude is proportional to the armature displacement. If the output value is measured with an AC voltmeter, it can only reflect the magnitude of the armature displacement and cannot reflect the direction of the displacement. Secondly, there is a certain zero residual voltage in the AC voltage output. Even with various compensation methods, it can only be reduced and cannot be completely eliminated. Therefore, the DC output circuit is commonly used in engineering practice, which can reflect the displacement direction of the armature and compensate the zero residual voltage.

The DC output circuit has two forms: one is a differential phase sensitive detector circuit, and the other is a differential rectifier circuit.

The differential rectifier circuit is shown in Figure 7. This circuit is relatively simple. It does not need to compare the voltage windings. It does not need to consider the influences if the phase adjustment and the zero residual voltage. The influence on the sensing and distributed capacitance can also be ignored. In addition, since the rectifying portion is on the differential output side, the two DC conveying lines are convenient to connect, and can be transported at a long distance, and are widely used.

 Figure 7. Differential Rectifier Circuit

Figure 7. Differential Rectifier Circuit

a) full wave current output         b) half wave current output

c) full wave voltage output         d) half wave voltage output

Differential phase sensitive detector circuits come in many forms. Figure 8 shows two examples, one is a full wave circuit and the other is a half wave circuit. The phase sensitive detector circuit requires that the comparison voltage and the secondary transformer output voltage of the differential transformer have the same frequency and the same phase or opposite phase. To ensure this, a phase shifting circuit is usually connected to the circuit. In addition, it is required that the comparison voltage amplitude should be as large as possible (because the comparison voltage acts as a switch in the detector circuit, and if it is less than the signal voltage, the switch cannot be turned on), generally it should be 3 to 5 times the signal voltage. In the figure, Rw is the bridge zero potentiometer. For the case of measuring small displacements, since the output signal is small, the input amplifier is also connected to the circuit.

 Figure 8. Differential Phase-sensitive Detection Circuit

Figure 8. Differential Phase-sensitive Detection Circuit

a) full-wave detection         b) half-wave detection

(2) DC differential transformer circuit

The working principle of the DC differential transformer is exactly the same as that of the ordinary differential transformer described above. The only difference is that the power supply used in the instrument is a DC power supply (dry battery, battery, etc.). The schematic diagram of the DC differential transformer is shown in figure 9. It consists of a DC power supply, a multivibrator, a differential rectifier circuit, a filter and so on.

 Figure 9. Schematic Diagram of DC Differential Transformer Circuit

Figure 9. Schematic Diagram of DC Differential Transformer Circuit

The multivibrator provides a high frequency excitation power supply for the differential transformer, which can be a square wave, a triangular wave or a sine wave. DC differential transformers are commonly used in the following applications:

◆ The measuring point is far from the control room (more than 100m);

◆ Simultaneous use of multiple differential transformers and it requires no interference with each other and with other equipment;

◆ Where explosion protection is required;

◆ Requires easy to carry, such as working in the field.


Ⅶ The Application of Differential Transformer

Displacement measurement is the most important use of differential transformers. Any physical quantity that can be transformed into a displacement can be measured with a differential transformer. It is noted that the differential transformer measurement is generally contact type. In some cases, it will affect the state of the measured object (such as vibration), which is so-called “load effect”. In this case, other types of sensors must be used such as eddy current sensors, etc.

◆ It can be used as the main component of many precision measuring instruments, such as making high-precision inductance comparator with corresponding measuring devices, which can perform various precise measurements on parts: length, inner diameter, outer diameter, non-parallelism, non-flatness, non-perpendicularity, vibration, eccentricity, and ellipticity.

◆ As the main measuring part of the bearing rolling element automatic sorting machine, it can sort large and small steel balls, large and small cylinders, large and small round vertebrae, needle roller and so on.

◆ It is used to measure the expansion, elongation, strain, movement, etc. of various parts. With a variety of sensors, its displacement measurement range can be from ±3μm to over 1000mm.

◆ Vibration and acceleration measurements. An accelerometer for measuring vibration can be constructed by using a differential transformer and a cantilever beam elastic support.

◆ Pressure measurement. The differential transformer and the elastic sensitive component (diaphragm, bellows, spring tube, etc.) can be combined to form a pressure sensor of the open-loop system and a force-balanced pressure gauge of the closed-loop system.

Due to the excellent characteristic of differential transformer as the displacement sensor, it has been applied in almost all industrial fields and several specific examples are described below.

(1) Steel industry: blast furnace top level detection, continuous casting roll gap, sand type vibration, convexity detection, position detection of sliding water nozzles such as ladle and tundish.

(2) Heavy motor industry: the main valve of the steam turbine, the valve lift detection of the bypass valve, and the posture monitoring of the elevator.

(3) Construction machinery industry: Measuring head for numerical control machine tool simulation test.

(4) Ceramic industry: thermal expansion testing of refractory materials, shape detection of templating glass.

(5) Ship and vehicle industry: fuel classification position detection of diesel engine, dynamic characteristic detection of fuel injection valve of automobile engine, and eccentricity detection of tire and wheel.

(6) Weighing machine industry: a device that automatically measures the weight of the bag, and a weighting machine for the asphalt carrying device.

(7) Measuring instrument, testing machine industry: used for traction test, creep test of metal materials and plastics, signal conversion part of flow meter and liquid level meter, mechanical test of civil building components.

(8) General industry: spacer separators for assembling bearings, motion deviation detection during stamping, and measurement of workpiece size and shape deviation.


Ⅷ Application Circuit Examples of Differential Transformer

8.1 MZK-4R Grinding Machine Automatic Control Device

This device is used on automatic or semi-automatic grinding machines. During the grinding process of the workpiece, the control device can accurately output 4 signals according to the amount of the pre-regulation to control the introduction of the grinding head, rough grinding, fine grinding, light grinding and exit, etc., thus to realize the automatic measurement and control of the grinding process.

(1) Working process of the grinding machine

When the workpiece is loaded, the measuring device first enters the workpiece for measurement. If the workpiece size meets the pre-adjusted result, the control device sends a “starting” signal, the grinding head enters the workpiece and moves forward quickly to the machining direction, and coarse grinding starts. Taking the internal grinding as an example, as the workpiece size of the grinding wheel becomes smaller, the output signal of the measuring head also becomes smaller. When the preset position is reached, the trigger sequentially sends three signals, that is, the “rough grinding end” signal, indicating that the rough grinding is finished, so that the moving speed of the grinding wheel is reduced, and the fine grinding starts; when the fine grinding is finished, the “finishing end” signal is issued, so that the grinding wheel stops moving and the light grinding starts; when the preset size is reached, the “light grinding end” signal is issued to make the grinding wheel and the detection device exit quickly.

(2) Working principle of measuring head (sensor)

The measuring head adopts a differential transformer type displacement sensor, and its structure is as shown in figure 10(a). The iron core moves to the right, so that the induced potential of the winding A decreases, and the induced potential of the winding B increases (and vice versa). The two windings and the resistors R1 and R2 in the measuring device form a bridge to realize differential output, as shown in figure 10(b).

 Figure 10. Schematic Diagram of the Differential Transformer

Figure 10. Schematic Diagram of the Differential Transformer

The primary coil is excited by a square wave generator with a square wave frequency of 3 kHz and a effective voltage value of 3.5V. Along with the change of the displacement of the core, a corresponding voltage variable is generated between the boom of the potentiometer Rw and the secondary common tap (ground) of the measuring head. The displacement-voltage characteristic curve in figure 11 is obtained after the voltage variable is amplified and phase-sensitive rectified.

 Figure 11. Output Characteristic Curve of Differential Transformer

Figure 11. Output Characteristic Curve of Differential Transformer

In the figure, the S-T segment is the full linear range, wherein the H-E segment (high precision) is the ×1 gear indication range, and the K-C segment (low precision) is the ×10 gear indication range. The“start”signal 0 is sent in the D-A segment, the“rough grinding end”signal 1 is sent in the G-B segment, and the“fine grinding end”signal is 2 sent in the 0-F segment. The“light grinding end”signal 3 is sent at point 0.

(3) Principle of the circuit

①The circuit block diagram shown in figure 12.

 Figure 12. Circuit Block Diagram of Control Device

Figure 12. Circuit Block Diagram of Control Device

②Explanation of the circuit principle

The device consists of six parts:

Input bridge, the two arms are composed of two secondary windings of the measuring head, the other two arms are composed of R84 and R85, the potentiometer VR1 is used for the electrical zero point coarse adjustment, the VR2 is used for the zero point fine adjustment, and the R86 is used to limit the zero point adjustment range.

In order to obtain the reference voltage for amplifier calibration, a voltage is obtained by the square wave generator, and another bridge is formed by transformers TR4, R88, and R89, and VR4 is used to adjust the reference voltage.

The amplifier amplifies the weak signal obtained in the input circuit to have sufficient amplitude to complete the measurement and control. T15, T17, and T18 form a voltage amplifier with gains of about 10, 20, and 20 dB, respectively. T16 is a buffer stage. T19 and T20 form a push-pull power amplifier stage, and the voltage gain of the amplifier is about 60 to 70 dB. In order to achieve higher stability and linearity, deeper negative feedback is added to each stage. The negative feedback of first stage is adjustable, and the total gain of the amplifier is adjusted by VR3.

Phase-sensitive rectification and indicating circuit is used to complete the rectification and identify the phase of the input signal. The half-wave rectification circuit is composed of D15 and D16, and the blocking voltage is 13V, which is provided by the square wave generator.

The rectified DC ramp signal is used as an input to the trigger on the one hand and as a panel indicator on the other. The μ meter is a microampere meter with a full-scale of 150μA, and full-scale indications of 50μ and 500μ are obtained with shunt resistors R90 and R91. D33 is used as a voltage clamp to protect the meter head.

Square wave generator, which is used to generate the excitation voltage required by the measuring head and the blocking voltage required for phase sensitive rectification. The high rectangular coefficient multivibrator circuit is composed of T21 and T22, which is easy to start, high in frequency and amplitude stability, and its oscillation frequency is 3 to 3.5 KHz.

Trigger, according to the comparison of the output voltage of the phase sensitive rectification and the pre-adjustment voltage, four different control signal outputs are sequentially generated. The circuit adopts a trigger with an emitter coupled by a zener tube, which has small temperature drift and convenient backlash adjustment. Among them, VR5, VR6, VR7, and VR8 are used as the adjustment potentiometers for the four signals of “0”, “1”, “2”, and “3” on the panel.


-24V, used for power relay after rectification and filtering;

-15V, generated by the series regulator circuit and is used as the collector voltage of each transistor and the trigger pre-call;

+6V, generated by the shunt regulator circuit and is supplied for the bias and pre-call of the trigger.

(4) Main technical indicators

✿ Instrument indexing and error:

High precision (G) 1μ/division; full scale -10~+50μ; error ≤1.5μ

Low precision (D) 20μ/division; full scale -100~+500μ; error ≤30μ

✿ Adjustable range of control signal :

Signal "0", 350~500μ;

Signal "1", 30~100μ;

Signal "2", 0 ~ 30μ;

Signal "3", -10 ~ +10μ

✿ Electrical zero adjustable range:

Not less than 100μ, and ±5μ fine adjustment

✿ Repeat error:

No more than 1μ

✿ (Grid) voltage adjustment error:

No more than 3μ

✿ Instability:

Time drift is no more than 10μ/4 hours; temperature drift is no more than 10μ/ 10℃

8.2 ZD41B Short Cylindrical Roller Sorting Machine

This machine is composed of high-precision micrometer (differential transformer), combined with transistor circuit to form measurement and logic control device to complete the task of automatically sorting short cylindrical bearing rollers.

(1) Main technical indicators

◆ Measurement range:

length is no more than 15mm

5 to 15 mm in diameter

◆ Accuracy:

1μ, 2μ, 3μ

If the magnification and radial grouping potentiometer are re-tuned, any grouping in the range of 0.5 to 5μ can be obtained.

◆ Number of groups:

10 groups.

◆ Speed:

28/min to 65/min,can be adjusted arbitrarily

(2) Working principle

The measurement and classification of the radial dimensions of the roller is automated. The roller to be tested is manually placed in a disc-shaped hopper, passed through the vibrating roller to the feeding position along the pipe, and then pushed into the measuring portion by the reciprocating push rod for radial measurement.

When different sizes of rollers enter the measurement site for measurement, the differential transformer guide core is displaced in the coil, so that the differential transformer outputs an alternating current signal proportional to the change in the size of the roller, and tiny electrical signal is amplified, rectified, and then amplified by the DC amplifier, so that the corresponding trigger drives the relay and the electromagnet to open the storage valve of the sorting group, so that the measured rollers of different diameters are placed in different sorting bins for automated measurement and sorting.

Here we mainly introduce the radial dimension measurement part, namely the differential transformer and its secondary circuit. The measuring part of the roller consists of a differential transformer, a 4KHz oscillator, an attenuator, a low frequency AC amplifier, a phase sensitive rectification, a DC amplifier, a regulated power supply, etc.

① Micrometer (differential transformer): The differential transformer is used to convert the diameter of the roller into a change in the amount of electricity. The transformation relationship is:

Formula 1.

E2 is the secondary coil voltage; A is the proportionality constant; Formula is the roller diameter.

The primary coil is excited by a rectangular wave with a frequency of 4 kHz and an amplitude of 2 to 3 volts. Thus, the voltages of u2 and u3 are induced in the secondary coil. The different names of the secondary coils are connected as a common point ground, and the other ends serve as a differential output, and form a bridge balance loop with the resistors R1, R2 and the potentiometer VR. When the iron core is at the center position of the two secondary coils, since the magnetic resistance of the two coils is equal, the bridge is in a balanced state, and the differential transformer output E2=0 (u2=u3). In static state, due to the self-weight of the iron core and the guide rod, the iron core is located at the lowermost end of the secondary coil, thus outputting a negative polarity voltage; when the roller is measured, the guide rod is displaced upward, and the iron core is also displaced upward in the differential coil. The output voltage varies with the displacement. When the displacement exceeds the center position, the differential transformer outputs a positive voltage.

② Oscillator: A high frequency triode is used as a capacitive voltage divider oscillator with an oscillation frequency of 4KHz. This circuit feature avoids the difficulty of inductive oscillator winding. The intermediate transformer is used to couple the output, and then through the first-stage voltage amplification, the two pairs of zener diodes are used to limit the clipping to form a rectangular wave with a constant amplitude (2~3V), one way is for the primary excitation of the differential transformer and the other is for the phase-sensitive rectification comparison voltage.

③ AC amplifier: three-stage amplification circuit and transformer coupled output. In order to keep the amplifier gain stable, 20dB negative feedback is introduced between the first and second stage, and the total gain is 75~80dB.

④ Phase-sensitive rectifier circuit: diode half-wave phase-sensitive rectification is used, the comparison voltage amplitude is high, and both diodes are turned on in the positive half cycle. The signal voltage is small, the positive voltage is output in the same  phase with the comparison voltage, and the negative voltage is output in the opposite phase with the comparison voltage.

⑤ DC differential amplifier: The DC voltage output from the phase-sensitive rectifier circuit is further amplified and the polarity is converted. When inputting ±50mV, the differential output is 4~12V.

8.3 Discussion of Differential Transformer Application

(1) The above example uses the two directions of the differential transformer and is determined for the special purpose of the roller sorting. When measuring with a roller of nominal size, the differential transformer core is just adjusted to the center position, the positive tolerance roller produces a positive displacement, and the positive voltage is output; the negative tolerance roller produces a negative displacement and outputs a negative voltage. This makes full use of the linear range of the differential transformer.

For different applications, especially for small-range, high-precision measurements, there is no need to distinguish the direction of the displacement. It is also possible to use only the displacement of the differential transformer in one direction, and the corresponding circuit can be simplified.

(2) This product was a product of the 1970s, so a transistor discrete component circuit was used. Today's electronic technology and the component levels are no longer the same. AC amplifiers and DC amplifiers can be used with operational amplifiers, and performance is much better than discrete component circuits. The basic principles of the circuit and the various functional parts are still applicable and can be designed accordingly.

(3) Nowadays, the application of single-chip microcomputers can completely replace the various logic circuits in the past. In the case of a single-chip microcomputer, the entire circuit design may vary greatly. For example, the oscillation source can be digitized (crystal oscillator frequency division may be directly generated by a single-chip microcomputer), and the measurement result is digitized (via A/D conversion), and a large number of analog comparators, triggers can be replaced by program judgment methods. Furthermore, with the precise timing and synchronization function of the single-chip microcomputer, A/D conversion can be directly performed on the AC signal sampling, and the phase-sensitive rectifier circuit can be omitted. After the measurement results are digitized, data transmission can be used instead of analog transmission, thus precision will not be lost, interference will not be existed and transmission distance will be long.

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