Design of magnetic coupling of continuous wave of measurement while drilling

2.2.1. Calculation of distance sleeve wall thickness

The characteristics of high pressure and low radial dimension determine that the magnetic coupling wall is thick, and the wall thickness ${\delta }_t$ is calculated according to the following formula [2-3]:

In the formula, $P$ – pressure difference of interior and exterior cavities, MPa; $R$ – inner diameter of distance sleeve, mm; $\left[{\delta }_b\right]$ – permissible stress, MPa, $\left[{\delta }_b\right]={\delta }_b/n_b$; ${\delta }_b$ – ultimate strength, MPa; $n_b$ – safety coefficient, 3.5-5.

2.2.2. Calculation of distance sleeve radial deformation

Downhole tools have narrow radial space. The radial clearance between the distance sleeve and the internal and external magnetic rotor is very small. the distance sleeve radial deformation calculation formula is shown as follows [3]:

In the formula, $\mathrm{\Delta }S$ – distance sleeve radial displacement, mm; $E$ – elasticity modulus, MPa; $\mu$– Poisson's ratio.

3.1.1. Influence of corner on torque

The torque generated by magnetic coupling coupling magnetic filled is related to permanent magnet performance, physical dimension and many other factors. In addition, it is also related to internal and external magnetic rotor corner $\theta$ (right of Fig. 2). When the $\theta =$ 30°, the torque is the maximum aiming at magnetic couplings with $m=$ 6 poles, the maximum torque represents the upper limit of actually transmitted torque during operation of the magnetic coupling. Table 1 shows the torque value of several groups of corners for calculation.

The figure shows that magnetic force line is gradually ‘skewed’ with corner increase, skew is more severe, magnetic filled distribution is more uneven and the transmitted torque is larger. When $\theta =$ 30°, magnetic force line is skewed most severely. The radial component of the internal and external magnetic pole acting force is the maximum; therefore, the torque acted on the external magnetic rotor is the maximum.

3.1.2. Influence of magnetic steel on torque

The influence is explained according to magnetic circuit theory. Magnetic steel is equivalent to the conductor in the magnetic circuit, permanent magnet is the power supply, working air gap is the resistance [2], and it can improve the utilization rate of the magnetic materials. Internal and external magnetic steel not only can prevent interference and influence of external magnetic filled, but also can lead the distribution of magnetic force s in the magnetic filled, and adjust leakage flux. Table 2 shows the torque of several different magnetic steel thicknesses.

Fig. 3Distribution drawing of magnetic force lines at different corners

a)$\theta =$ 0°

b)$\theta =$ 15°

c)$\theta =$ 30°

Magnetic steel thickness has low influence on torque. However, when the magnetic steel is too thin, and no magnetic saturation appears in the magnetic steel, the magnetic resistance is increased, air gap flux density is reduced, and the torque increment is decreased as a result. When the magnetic steel is too thick, the rotational inertia of rotating parts is larger, thereby increasing the starting torque of the whole system and the instability of the moving parts is increased.

3.1.3. Influence of magnet thickness on torque

Permanent magnet provides magnetic potential in the magnetic circuit. It is clear that the magnetism of the magnetic materials is higher, the magnetic density in the air gap is larger, and the generated torque is larger. When the materials are the same, magnet thickness also affects torque, Table 3 and Table 4 show the torque of several groups of different magnet thicknesses.

Table 3 shows that when the internal and external magnets have the same thickness, torque is increased with the increase of magnet thickness. When the permanent magnet is increased to certain value, the torque increase is decelerated because after the magnet thickness reaches certain value, magnetic saturation appeared in the magnetic steel, the magnetic resistance is increased, air gap flux density is reduced, and the torque increment is decreased as a result.

Table 4 shows that when the internal and external magnet thicknesses are different, though the torque is also increased with the magnet thickness increase; the torque value is smaller compared with that with the same magnet thickness because magnetic potentials of internal and external magnets are not matched, and the leakage flux is increased.

3.1.4. Influence of magnetic pole quantity no torque

In the design of the magnetic circuit, magnetic pole quantity is an important design parameter. According to the magnetostatic energy expression, it is known that when the N and S poles are changed once, magnetostatic energy storage is increased once, therefore more magnetic poles are beneficial for magnetostatic energy storage, magnetostatic energy is finally converted into kinetic energy, which is released.