Improved design of Tc bearing structure used for measurement while drilling

2.1. Dynamic pressure equation of Tc bearing at steady state

Fig. 2 shows the coordinate system of Tc bearing dynamic pressure equation, $z$ axis is along the width direction of the bearing, its origin o is located on the midpoint of bearing outer ring width $l$; coordinate $xoy$ can be established through the cross section of bearing outer ring center $o$; the eccentric distance between bearing outer ring center o and axle journal (bearing inner ring and axle matched section are known collectively as axle journal) center $o_1$ is expressed with $e$; $\theta$ is the angle with $o{o}_1$ ligature during maximum liquid film thickness as starting edge for rotating along the direction of axle rotation. $\phi$ is the included angle between $o{o}_1$ ligature and external load $G$. It is set that the axle journal is rotated counterclockwise at angular velocity $\omega$. Tc bearing static property refers to the performance of the bearing liquid film when the bearing is operated at static balance position.

Fig. 2Coordinate system of Tc bearing dynamic pressure equation

Reynolds equation about liquid film dynamic pressure is the foundation of fluid dynamic pressure sliding bearing. The general form is shown as follows [3-6]:

In the Eq. (1), $\mathbf{U}$ is velocity of moving surface along $x$ direction, m/s; $p$ refers to liquid film pressure intensity, N/m²; $\mu$ refers to lubricant viscosity, pa.s; $h$ refers to liquid film thickness, wherein$h=c\left(1+\epsilon \mathrm{c}\mathrm{o}\mathrm{s}\theta \right)$, m; $c$ refers to bearing gap,$c=(D-d)/2$, $d$ and $D$ are axle and bearing diameters, m; $\epsilon$ refers to eccentricity ratio,$\epsilon =e/c$.

2.2. Tc bearing of sand transmission groove type and steady state dynamic pressure equation thereof

The liquid film pressure in the Tc bearing convergent wedge is larger than the pressure of bearing external environment. Therefore, a part of drilling fluid is squeezed from two ends of the bearing. While the liquid film in the divergent wedge is lower than the pressure of the external environment, a part of external drilling fluid can be pressed into the divergent wedge. After the solid particle enters into the bearing through the divergent wedge negative pressure zone, since the viscidity can rotate and enter into the convergent wedge with the inner ring rotary, it can be moved from the part with the maximum liquid film thickness to the part with the minimum thickness. If it is not flushed by the fluid squeezed from two ends of the bearing due to the high pressure in the convergent wedge, when solid particle passes through the part with the minimum liquid film thickness, and the load is higher than the designed limit, solid particle cannot pass through the gap between the inner ring and the outer ring, bearing inner ring is pushed out of the outer ring by solid particles as a result, the eccentricity ratio is reduced, the bearing carrying capacity is reduced, thereby resulting in bit bouncing accident. The surface structure of existing Tc bearing outer ring is improved in order to increase the change of discharging solid particles from bearings, a sand transmission groove is designed, Fig. 3 shows the end map of the Tc bearing outer ring after improvement designed. The originally flat hard alloy blocks in Fig. 1 are slightly protruded from the base body, which are neatly arranged along the axial direction. When particles fall into the liquid film, it can be pushed into the nearest groove along the fluid flow rotation direction, thereby increasing the possibility of being flushed by high pressure liquid and reducing bit bouncing accidents caused by particles.

Fig. 3Tc bearing with sand transmission groove on the outer ring

Reynolds dynamic pressure equation of Tc bearing primary structure is also applicable to the sand transmission groove structure, the liquid film thickness of the part with a groove expression is shown as follows (In the formula, $h_g$ is groove depth):

3.1. Dimensionless liquid film pressure of liquid film

The distribution of liquid film dynamic pressure in two bearing convergent wedges is obtained through calculation. The pressure distribution of primary structure Tc bearing convergent wedge liquid film is shown in the left part of Fig. 4. The dynamic pressure of the sand transmission groove bearing convergent wedge liquid film is shown in the right part of Fig. 4.

Fig. 4Three-dimensional diagram of liquid film dynamic pressure

a)

b)

The pressure distribution shapes thereof are different. The dynamic pressure of the sand transmission groove Tc bearing liquid film is smaller than that of primary structure because the liquid film is not continuous due to the sand transmission groove of the sand transmission groove Tc bearing outer ring, and the pressure value is reduced. Fig. 5 shows the distribution comparison diagram of dynamic pressure in liquid film circumference of Tc bearings in two structures. The two figures are compared (left $\epsilon =$ 0.4 and right $\epsilon =$ 0.6), and the follows can be obtained: the maximum pressure value difference thereof is also increased with the increase of the eccentricity ratio. The originally integral convergent wedge is divided into several wedges by grooving. Meanwhile, the circumferential pressure distribution scope is also increased. It has the characteristics of multi-lobe bearing and multi-wedge bearing liquid films, and the dynamic property of the liquid film is improved.

Fig. 5Peripheral direction pressure profile of liquid film dynamic pressure

a)

b)

3.2. Dimensionless carrying capacity of liquid film

The calculation of unit width dimensionless carrying capacity under Reynolds condition [5] is shown as follows:

The carrying capacity change conditions of Tc bearings in two structures with eccentricity ratio and width diameter ratio in Fig. 6 are compared, and the follows are obtained: 1) The carrying capacity of the two structures are increased with the increase of eccentricity ratio and width diameter ratio; 2) When the width diameter ratio is not changed, and the eccentricity ratio is changed, sand transmission groove carrying capacity is only one fifth of the primary structure carrying capacity; 3) When the eccentricity ratio is not changed, and the width diameter ratio is changed, the sand transmission groove carrying capacity is only one third of the primary structure carrying capacity.

Fig. 6Comparison diagram of liquid film bearing capacity

a)

b)

3.3. Dimensionless discharging capacity discharged from bearing end

Tc bearing structure belongs to a radial bearing without an oil duct. The rectangular integral formula adopted in the both-end discharge flow is dimensionless flow rate computational formula [5] as follows:

The follows are obtained through analyzing Fig. 7: 1) The end discharging capacity of two structures is prominently increased with the increase of eccentricity ratio and width diameter ratio; 2) The sand transmission groove discharging capacity is three to four times of primary structure end discharging capacity.

Fig. 7Discharging capacity comparison diagram

a)

b)