Differential Transformer (Microsynchronizer) RVDT

1 Preface

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

RVDT and LVDT both adopt the principle of differential transformer structure, which transfers the rotational/linear displacement of mechanical components to the rotating shaft/moving rod, drives the iron core to rotate/move in a straight line, changes the induced voltage/inductance in the coil through electromagnetic induction, and outputs voltage/current signals proportional to the rotation angle/linear displacement. Due to the adoption of a non-contact structure, it has performance characteristics such as non-contact, noise free, high sensitivity, high repeatability, high reliability, infinite resolution, theoretical infinite lifespan, and good high-frequency response characteristics. Due to its strong environmental applicability, it is widely used in automated measurement and monitoring systems for harsh national defense and industrial environments such as water, oil, steam, dust, high and low temperatures, vibration and impact.

In today's aerospace field, especially in automatic control systems, the application scope and functions of RVDT/LVDT are becoming increasingly widespread, such as the position of the engine inlet valve, nozzle blade position/throat area, main engine guide cylinder piston rod displacement, load rod displacement, etc. Together with the controller, they form a measurement, feedback, and control system.
2 Micro synchronizers

2.1 Structure and working principle of micro synchronous sensor

Micro synchronizers are divided into two types: torque type and signal type. The former is a torque output device, while the latter is suitable for measuring angular displacement. Signal type micro synchronous sensor, abbreviated as micro synchronous sensor, is a high-precision, variable reluctance (or transformer type) rotary transformer (therefore called angle sensor) that applies electromagnetic induction (transformer) principle to change the magnetic resistance of the rotating armature. As its name suggests, its actual working angle is generally very small. For a certain excitation voltage and frequency, at small angles (usually ± 10 ° or ± 12 °), its output voltage is proportional to the rotation angle of the rotor and has high linearity. Compared with other angle sensors, it has some significant characteristics: good linearity, no contact reaction torque, small additional torque, and reliable operation. Therefore, it is widely used in aerospace, aviation, and navigation instruments as precision angle sensors such as accelerometers and rate gyroscopes, converting angular displacement into proportional surge 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, material, and other fields.

Micro synchronizers convert mechanical angles into electrical signals (voltage or current) corresponding to the angle, which can reflect the magnitude and direction of the mechanical angle. The electrical signal equation is:

U_OUT=K·α                                  (1)

Among them: UOUT - output electrical signal of microsynchronizer

α - mechanical angle received by microsynchronizer

K - Scale factor of microsynchronizer (output gradient or output slope)

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

A typical microsynchronizer structure consists of a stator component and a rotor component. The stator component consists of two parts: the stator core and the winding. The stator core is made of laminated soft magnetic material with good magnetic permeability, and has 4n convex poles evenly distributed on its circumference (n is a positive integer). 2n primary winding coils and 2n secondary winding coils are staggered and embedded on the convex poles, and adjacent primary or secondary winding coils have opposite winding directions (or polarities) and are connected in series. The rotor component is made of laminated soft magnetic material, and 2n convex poles are uniformly distributed on the outer surface. The most commonly used are 4-pole, 8-pole, 12 pole, and 16 pole, and as the number of poles increases, their linear angle range decreases. Figure 1a is a schematic diagram of the structure of a 12 pole microsynchronizer. The most commonly used one is a 4-pole (n=1) microsynchronizer, which can theoretically achieve a maximum linear angle range of ± 40 °.

Figure 1 Structure of Microsynchronizer

Figure 1a - Schematic diagram of the structure of a 12 pole microsynchronizer; Figure 1b, Figure 1c - Schematic diagram of the structure of a 4-pole microsynchronizer;

Figure 1d - Physical picture of stator assembly of 4-pole microsynchronizer; Figure 1e - Physical picture of the rotor assembly of the 4-pole microsynchronizer;

2.2 Output characteristics of traditional quadrupole micro synchronous sensor
      Taking the traditional structure quadrupole microsynchronizer (as shown in Figure 2) as an example, this article introduces its working principle. Four primary coils N11, N12, N13, and N14 are respectively embedded on the four convex poles of the stator and connected in series to form a primary side coil (i.e. excitation winding coil). When an AC excitation voltage U is supplied, the magnetic flux generated on each convex pole of the stator is Φ 1, Φ 2, Φ 3, and Φ 4, and its instantaneous direction is shown in Figure 2a. Due to the presence of pulsating magnetic fields in the iron core, induced electromotive force will be generated in the four secondary coils N21, N22, N23, and N24. The connection of the secondary coil should ensure that e21 and e23 are in phase and in phase with e22 and e24. Therefore, the connected primary and secondary coils are shown in Figures 2a and 2b. In this way, its output voltage is
U_O=(e₂₂+e₂₄)- (e₂₁+e₂₃)  

Figure 2: Four pole microsynchronizer winding connection method and induced potential

Figure 3 Equivalent magnetic circuit and stator rotor geometric parameters of quadrupole microsynchronizer
       In order to study the output characteristics of the quadrupole microsynchronizer, its equivalent magnetic circuit should be analyzed, as shown in Figure 3a. Let some geometric parameters of the stator rotor be shown in Figure 3b, where δ is the thickness of the air gap between the stator pole palm and the rotor pole end face; Sa and Sb are the surface areas covered by the stator pole palm and rotor pole end face; R is the radius of the rotor; α is the rotor angle, measured in radians; H is the effective width of the stator rotor iron core; 2 is the angle of the stator magnetic pole, measured in radians. Let μ 0 be the air permeability coefficient.

Assumption conditions:

(1) Symmetrical structural geometry and winding turns;

(2) The working point of the magnetic pole of the stator/rotor iron core does not have a linear segment of the magnetization curve of the iron core material, and the initial magnetic permeability of the material is very high;

(3) Ignore the magnetic resistance of the iron core, ignore the size and properties of the load, ignore the leakage reactance and iron loss.

The magnetic resistance of the magnetic circuit is completely the air gap magnetic resistance

Due to the equal number of turns of the primary coil on all four poles, N11=N12=N13=N14=N1， The current flowing through is equal, all are I1, and the magnetic potential is also equal, that is, FM1=FM2=FM3=FM4=N1 I1. According to the equivalent magnetic circuit diagram, the magnetic flux can be calculated as

In the unloaded state, the induced electromotive force of each secondary coil can be calculated as

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

Because 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

UO=8πf N1 N2 I1μ0 r h α/δ=K·α                                

In the formula, K represents the sensitivity of the microsynchronizer, K=8 π f N1 N2 I1 μ 0 r h/δ, measured in V/rad (volts per radian).

The output characteristic curve (voltage/angle curve) of the traditional quadrupole microsynchronizer is a proportional function curve:

Figure 4 Output characteristic curve of quadrupole microsynchronizer
      This theory is often subjected to engineering treatment in engineering applications. Instead of winding a coil around each of the four magnetic poles of the stator, the two poles share a common coil, with two excitation windings and two output windings, as shown in Figure 2c.

3 Structure and working principle of micro synchronizer type RVDT

3.1 Typical RVDT output characteristics
       The output characteristics of RVDT must be adapted to the working mode of subsequent processing chips and circuits. Currently, the processing circuits used in the field of digital control are AD598 and AD698 modules. The form of processing module used determines whether RVDT's output characteristics must have two output windings to output voltage VA and VB signals. More importantly, VA+VB must be a constant independent of mechanical rotation angle. Otherwise, its output signal cannot be recognized and processed by the AD598 module.

AD598 and AD698 are both single-chip LVDT/RVDT signal conditioning systems produced by Analog Devices in the United States. AD698 is an improved version of AD598. AD598/AD698, when combined with LVDT/RVDT, can accurately and reproductively convert the mechanical displacement of LVDT/RVDT into unipolar or bipolar DC voltage. The functional block diagram is shown in Figure 5 and Figure 6.

By comparing the functional diagrams of AD598 and AD698, we can easily see the following differences between the two:

(1) AD598 requires that the RVDT output must be a three wire system and must be able to output VA and VB signals for solving (VA+VB); AD698 only requires differential output (VA-VB) signals, without requiring LVDT/RVDT to output VA and VB signals, and no longer requiring (VA+VB) to be a constant that varies with mechanical input.

(2)The main feature of AD698 different from AD598 is that it adopts a different circuit transfer function. The transfer function of AD698 is UOUT ∝ A/B, while the transfer function of AD598 is UOUT ∝ (VA-VB)/(VA+VB).

(3)AD698 uses a sine wave function oscillator and power amplifier to drive LVDT/RVDT, and two synchronous demodulation stages to decode the primary and secondary voltages. The decoder determines the ratio of output voltage to input driving voltage (VA-VB)/VP. The filtering stage and amplifier can compare the overall output results. AD698 eliminates all offset effects by calculating the ratio of LVDT/RVDT output to input excitation, thereby avoiding the impact of drift on output gain.

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

(1) Equipped with two independent output windings, the output characteristics of the windings are linear function curves;

(2) The differential output voltage is formed by the differential connection of two output windings, and its output characteristic is a proportional function curve;

(3) After connecting two windings in series, the value remains constant (the amplitude does not change with 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 output signal of RVDT can be processed simultaneously by AD598 or AD698, the output characteristics of traditional four pole micro synchronizers do not meet the requirements of two output windings and a non-zero constant value. Strictly speaking, their output characteristics do not meet the typical output characteristics of RVDT specified in Figure 7, that is, traditional four pole micro synchronizers are not true RVDTs.