Optimizing Compensation Loop for Quartz Accelerometer

The quartz flexure accelerometer mainly consists of torque generator, pendulum assembly, differential capacitance sensor, and rebalancing loop, widely used in the aerospace field as a critical component of inertial navigation systems. Among these, the torque generator is a device that generates a feedback torque to balance the inertial torque when there is acceleration acting on the input shaft, consisting of magnetic yoke, magnetic steel, magnetic cap, compensation ring, and coil assembly.

Fig.1 Internal structure of quartz flexible accelerometer

1.Introduction

The scale factor K₁ is the feedback current required when the accelerometer input unit acceleration is proportional to the pendulum effect and inversely proportional to the torque generator coefficient, i.e.,

K_b is the pendulum effect; K_t is the torque generator coefficient; m is the mass of the pendulum assembly; L is the length from the pivot to the center of mass of the pendulum assembly; r is the coil radius; n is the number of turns of the coil; R is the distance from the coil center to the flexure point of the pendulum piece; B is the working air gap magnetic flux density. The torque generator coefficient and pendulum effect together determine the magnitude of the accelerometer scale factor, ultimately affecting the accuracy of the entire system.

Temperature is one of the important factors affecting the torque generator coefficient. Firstly, temperature changes cause deformation of the torque generator, leading to thermal error due to thermal expansion and contraction effects; secondly, temperature alters the magnetic properties of various components, thereby affecting the magnitude and stability of the working air gap magnetic flux density.

In general, the measurement accuracy of high-precision quartz flexure accelerometers is better than 10^-4, and the scale factor requirement is 1.1mA/g~1.5mA/g, with a temperature coefficient of the scale factor less than 60×10^-6/℃. The magnetic flux density B is the parameter in equation (1) that has the greatest impact on the scale factor. Even if the change is small, it will have a significant impact on the entire system and should be analyzed in detail.

2.Methods

The schematic diagram of the torque generator of the quartz flexure accelerometer is shown in Figure 2.

The upper part of Figure 2 shows a schematic diagram of a single torque generator, and the lower part shows a schematic diagram of the upper and lower magnetic circuits. Among them, the magnetic steel, magnetic cap, and compensation ring form a magnetic steel assembly through interference fit, fixed in the upper and lower magnetic yokes, forming opposing axial magnetized magnetic circuits, with each other as the opposite magnetic poles, and most of the magnetic lines are squeezed into the air gap, basically eliminating axial magnetic leakage.

In addition, the two torque coils are also connected in push-pull mode, which can not only eliminate the nonlinearity error caused by the demagnetization effect formed by the torque current but also compensate for errors caused by uneven material properties and processing asymmetry. The quartz flexure accelerometer has high upper and lower symmetry in structure, and each magnetic circuit is independent of each other, allowing for experimental research on one of the torque generators.

The working air gap is the region where the torque coils are located, and the stability of its magnetic field directly affects the stability of the scale factor. It can be seen from Figure 2 that the range of the air gap occupied by the torque coils is very small. Even at the maximum swing amplitude of the pendulum piece, it only fluctuates up and down by ±0.02mm, so only the change in the magnetic field at the working air gap needs to be analyzed with temperature.

The calculation of the magnetic circuit of the permanent magnet is an important part of designing the torque generator. The working point of the magnet should be selected above the maximum energy product point. When the temperature rises, the values of the residual magnetization intensity B_r and coercive force H_c of the permanent magnet decrease, resulting in a change in the magnetic flux density in the area where the coil is located. At present, there are mainly two solutions:

Seek new types of magnetic steel materials. The second-generation rare earth permanent magnet material Sm₂Co₁₇ has been widely used in high-precision accelerometers, and its lower residual magnetization temperature coefficient and coercive force temperature coefficient have reduced the magnetic field temperature drift to a certain extent.

Optimize the structural dimensions of the torque generator. Wang C et al. found that when the cylindrical magnetic pole pieces are changed to cap-shaped magnetic caps, the magnetic field in the air gap becomes more uniform, and the dimensions are optimized, improving the linearity of the accelerometer. To improve the temperature stability of the working air gap magnetic flux density, it is mainly achieved by paralleling compensation rings on the magnetic steel.

The material of the compensation ring is a magnetic temperature compensation alloy, and its relative magnetic permeability increases with decreasing environmental temperature. The calculation formula for the temperature coefficient δ_u of the magnetic permeability is:

Formula. 2

u_r1 is the relative magnetic permeability of the compensation ring at temperature T₁, u_r2 is the relative magnetic permeability of the compensation ring at temperature T₂, neglecting the influence of the magnetic cap and magnetic yoke, it can be seen that the magnetic flux of the permanent magnet is equal to the sum of the air gap and the magnetic flux of the magnetic temperature compensation alloy, i.e.,

If the cross-sectional area and vertical magnetic flux density passing through the compensation ring can be adjusted correctly so that ∂·B_mag·S_mag/ΔT=∂·B_com·S_com/ΔT, ∂B_gap·S_gap·ΔT=0, thus ensuring the temperature stability of the air gap magnetic flux density. Finite element simulation by ANSYS shows that the magnetic field formed around the magnetic steel assembly in its surrounding air gap is not a uniform magnetic field, and the compensation ring is in contact with the bottom of the magnetic yoke, so the vertical magnetic flux density passing through the compensation ring is related to its height, height and cross-sectional area are the key factors affecting the temperature stability of the working air gap magnetic flux density.

3.Conclusion

In summary, this paper proposes methods to improve the stability and measurement accuracy of quartz flexure accelerometers: using advanced materials and optimizing the dimensions of compensation rings. It is worth noting that the performance of the quartz flexure accelerometer ER-QA-03C1 is very high, with a scale factor temperature coefficient of ≤±15 ppm/℃, zero offset repeatability of ≤15μg, and scale factor repeatability of ≤15 ppm. In addition to aerospace applications, it can also be used for static and dynamic acceleration measurements.