Differential Transformer (Micro Synchronizer) RVDT

1 Preface

The differential transformer type linear displacement sensor LVDT (Linear Variable Differential Transformer) and RVDT (Rotary Variable Differential Transformer), as mechanical linear/angle displacement measurement elements, are widely used in various industries and fields such as aviation, electronics, machinery, textiles, ships, metallurgy, etc., in order to form position feedback systems and positions for various actuators, mechanical arms, load/displacement rods and other equipment.

Both RVDT and LVDT adopt the principle of differential transformer structure, that is, the rotational/linear displacement of mechanical components is transmitted to the rotating shaft/linear rod, which drives the iron core to perform rotational/linear motion. Through electromagnetic induction, the induced voltage/inductance changes in the coil, and outputs a voltage/current signal proportional to the rotational angle/linear displacement. Due to the non-contact structure, they have the characteristics of no contacts, no noise, high sensitivity, high repeatability, high reliability, infinite resolution, theoretical infinite lifespan, good high-frequency response, etc. Moreover, due to their strong environmental adaptability, they are widely used in automated measurement and monitoring systems in harsh defense and industrial usage environments such as water, oil, steam, dust, high and low temperatures, vibration and shock.

In the current aerospace field, especially in automatic control systems, the application scope and functions of RVDT/LVDT are becoming increasingly extensive. For example, in aspects such as engine fuel inlet valve position, nozzle blade position/duct area, main compressor guide cylinder piston rod displacement, load rod displacement, etc., they work together with the controller to form a measurement, feedback and control system.

2. Micro-motion synchronizer

2.1  Structure and Working Principle of Micro-motion Synchronous Sensor

Micro-motion synchronizers are divided into two types: the torque type and the signal type. The former is a torque output device, while the latter is suitable for measuring angular displacement. The signal-type micro-motion synchronous sensor is simply called the micro-motion synchronizer and is a high-precision, electromagnetic induction (transformer) principle-based rotating armature changing magnetic resistance type variable reluctance (or transformer type) rotary transformer (hence called an angle sensor). As its name suggests, its actual working angle is generally very small. For a certain excitation voltage and frequency, at small angles (generally ±10°or ±12°), its output voltage is proportional to the rotor's rotation angle and has a high linearity. Compared with other angle sensors, it has some significant characteristics: good linearity, no contact reaction torque, small additional torque, reliable operation, and is therefore widely used in aerospace, aviation, and marine instruments as precision angle sensors such as accelerometers and rate gyroscopes, converting angle displacement into proportional current voltage signals. It plays an important role in guidance or stabilization systems such as inertial navigation, inertial guidance, and autopilot, involving various technologies in mechanical, electrical, and materials fields.

The micro-motion synchronizer converts the mechanical rotation angle into an electrical signal (voltage or current) corresponding to this rotation angle. This signal can reflect the magnitude and direction of the mechanical rotation angle. The equation for the electrical signal is:

UOUT= K·α

Among them: UOUT- Micro-motion synchronizer output signal

α - The mechanical rotation angle received by the micro-motion synchronizer

K - The scale factor of the micro-motion synchronizer (output gradient or output slope)

We know that for all sensors, the scale factor K is an important indicator for measuring the sensor. The variation and characteristics of K directly affect the output of the sensor and the performance of the entire control feedback.

The typical structure of a micro-motion synchronizer consists of a stator component and a rotor component. The stator component includes the stator core and the winding. The stator core is formed by stacking laminations of soft magnetic materials with good magnetic conductivity. Four n slots (n is a positive integer) are evenly distributed around its circumference. On the slots, 2n primary winding coils and 2n secondary winding coils are misalignedly embedded, and the winding directions (or polarities) of adjacent primary or secondary windings are opposite and are connected in series. The rotor component is formed by laminations of soft magnetic materials. The outer circular surface is evenly distributed with 2n slots. The most commonly used types are 4-pole, 8-pole, 12-pole and 16-pole. As the number of poles increases, the linear angle range decreases. Figure 1a is the structural schematic diagram of a 12-pole micro-motion synchronizer. The one we use most frequently is the 4-pole (n=1) micro-motion synchronizer, and its theoretical maximum linear angle range can reach ±40°.

Figure 1 Structure of Micro-motion Synchronizer

Figure 1a - Schematic diagram of 12-pole micro-motion synchronizer structure;

Figure 1b, Figure 1c - Schematic diagram of the 4-pole micro-motion synchronizer structure;

Figure 1d - Physical diagram of the stator component of the 4-pole micro-motion synchronizer；

Figure 1e - Physical diagram of the rotor component of 4-pole micro-motion synchronizer;

2.2 Output characteristics of the traditional four-pole micro-motion synchronous sensor

Taking the traditional structure four-pole micro-motion synchronizer (as shown in Figure 2) as an example, we will introduce its working principle. On the four poles of the stator， four primary coils N11， N12， N13， and N14 are wound respectively and connected in series to form the primary side coil (i.e.， the excitation winding coil). When an alternating excitation voltage U is supplied， the magnetic flux generated on each of the four poles is Φ1， Φ2， Φ3， and Φ4， and their instantaneous directions are as shown in Figure 2a. Due to the pulsating magnetic field in the iron core， an induced electromotive force will be generated in the four secondary coils N21， N22， N23， and N24. The connection method of the secondary coils should ensure that e₂₁ and e₂₃ are in phase and are out of phase with e₂₂ and e₂₄. Therefore， the connected primary and secondary coils are as shown in Figure 2a and Figure 2b. Thus， the output voltage is    

U_O=(e₂₂+e₂₄)- (e₂₁+e₂₃)  

Figure 2 Connection method of the four-pole micro-motion synchronizer's windings and induced electromotive force

Figure 3 Equivalent magnetic circuit of the four-pole micro-motion synchronizer and geometric parameters of stator and rotor.

To study the output characteristics of the four-pole micro-motion synchronizer, the equivalent magnetic circuit should be analyzed, as shown in Figure 3a. Some geometric parameters of the stator and rotor, such as those shown in Figure 3b, are set. δ represents the gap thickness between the stator pole face and the rotor extreme surface; Sa and Sb represent the covered surface areas of the stator pole face and the rotor extreme surface; r represents the rotor radius; α represents the rotor angle, with units of rad (radian); h represents the effective width of the stator-rotor core; 2 represents the angle of the stator magnetic poles, with units of rad (radian). Let μ0 be the air magnetic permeability coefficient.

Assumption conditions:

(1)The structural geometry is symmetrical, and the number of windings is also symmetrical.

(2) The operating points of the magnetic poles in the stator and rotor cores do not include the linear segment of the coercivity curve of the core material, and the initial permeability of the material is extremely high.

(3) The magnetic reluctance of the core, the magnitude and nature of the load, as well as the leakage reactance and iron loss, are neglected.

Then the magnetic resistance of the magnetic circuit is completely the air-gap magnetic resistance, which is

Since the number of turns of the four upper primary windings is equal, N11=N12=N13=N14=N1, the currents flowing through them are also equal, all being /1, and the magnetic potential is also equal, that is, FM1=FM2=FM3=FM4=N1 /1. According to the equivalent magnetic circuit diagram, the magnetic flux can be calculated as

When the system is unloaded, the induced electromotive forces of each secondary coil can be calculated as

In the formula,  f — the frequency of the excitation power supply.

Since the number of turns of the secondary coils on the four poles is equal, N₂₁=N₂₂=N₂₃=N₂₄=N₂, substituting Equations (5), (6), and (7) into Equation (2) yields

U
_O=8πf N₁ N₂ I₁μ₀ r h α/δ=K·α

In the formula, K - the sensitivity of the micro-motion synchronizer, K = 8πf N1 N2 I1μ0 r h/δ, with the unit being V/rad (volts per radian).

Then the output characteristic curve (voltage/angle curve) of the traditional four-pole micro-motion synchronizer is a proportional function curve:

Figure 4 Output characteristic curve of the four-pole micro-motion synchronizer

This theory has often been subjected to engineering processing in practical applications. On the four magnetic poles of the stator, not every magnetic pole has a coil wound around it, but two poles share one coil. That is, the excitation winding consists of 2 coils and the output winding also consists of 2 coils, as shown in Figure 2c.

3 Micro-motion Synchronizer Type RVDT Structure and Working Principle

3.1 Typical Output Characteristics of RVDT

The output characteristics of RVDT must be adapted to the working mode of the subsequent processing chip and circuit. Currently, the processing circuits used in the digital control field are the AD598 and AD698 modules. The form of the processing module determines whether the output characteristics of RVDT must include two output windings for voltage signals VA and VB, and more importantly, (VA + VB) must be a constant independent of the mechanical rotation angle. Otherwise, the output signal cannot be recognized and processed by the AD598 module.

Both AD598 and AD698 are single-chip LVDT/RVDT signal conditioning systems produced by Analog Devices of the United States. AD698 is an improved version of AD598. AD598/AD698, when combined with LVDT/RVDT, can accurately and reproducibly convert the mechanical displacement of LVDT/RVDT into single-polarity or bipolar DC voltages. Their functional block diagrams are shown in Figures 5 and 6.

By comparing the functional block diagrams of AD598 and AD698, we can easily find the following differences:

(1) AD598 requires that the output of the RVDT must be three-wire type and must be able to output the VA and VB signals, which are used for calculating (VA + VB); while AD698 only requires the differential output (VA - VB) signal. It does not require that the LVDT/RVDT be able to output the VA and VB signals, and no longer requires that (VA + VB) is a constant that remains fixed in response to the mechanical input quantity.

Figure 5 Functional Block Diagram of AD598

Figure 6 Functional Block Diagram of AD698

(2) The main difference between AD698 and AD598 lies in the fact that AD698 employs a different circuit transfer function from AD598. The transfer function of AD698 is UOUT ∝ A/B, while that of AD598 is UOUT ∝ (VA - VB) / (VA + VB).

(3) AD698 drives the LVDT/RVDT using a sine wave oscillator and power amplifier, and uses two synchronous demodulation stages to decode the primary and secondary voltages. The decoder determines the ratio of the output voltage to the input driving voltage (VA - VB) / VP. The filter stage and amplifier can be compared to determine the output result. AD698 eliminates all offset effects by calculating the ratio of the LVDT/RVDT output to the input excitation, thereby avoiding the influence of drift on the output gain.

After analyzing the requirements for the output characteristics of LVDT/RVDT by AD598 and AD698, as well as the typical output characteristics of LVDT, we can conclude that the typical output characteristics of RVDT should meet the following requirements:

(1) It has two independent output windings, and the output characteristics of the windings are in the form of a linear function curve.

(2) The two output windings are connected in differential mode to form a differential output voltage. Its output characteristic is a proportional function curve.

(3) When the two windings are connected in series, the value is constant (the amplitude does not change with the rotation of the rotor)

Based on the above basic requirements, we can obtain the typical output characteristic curve of RVDT, as shown in Figure 7.

Figure 7 Typical Output Characteristics of RVDT

Therefore, from the perspective that the RVDT output signal can be processed by either AD598 or AD698, the output characteristics of the traditional structure four-pole micro-motion synchronizer do not meet the requirements of having two output windings and a non-zero constant value. Strictly speaking, its output characteristics do not comply with the requirements of the typical output characteristics of the RVDT specified in Figure 7. That is to say: the traditional structure four-pole micro-motion synchronizer is not a true RVDT in the strict sense.