Deep hole connector design and oil film pressure study

2.1. Deep hole connector structure design

The deep hole connector designed in this paper is shown in Fig. 1, with the front end machined with internal threads for fixed connection with the existing deep hole drill bit and the rear end machined with external threads for fixed connection with the existing deep hole drill rod. The connector is installed with four double-bridge strain gauges and four tiltable tiles. The four double-bridge strain gauges are connected as two Wheatstone bridges. The dynamic data collector provides the input voltage and collects the output voltage signal. The four tiltable tiles can be tilted around the central axis, and the piezoelectric ceramic stack controls the tilt angle (referred to as tilt angle). This connector is suitable for machining with a rotating tool feed of the workpiece [6].

Table 1 shows the relevant structural parameters of the deep hole connector.

2.2. Principle of increasing Tool system rigidity

In the process of deep hole machining, four tiltable tiles are tilted to form a wedge gap with the workpiece wall at the same time, and the workpiece rotates at high speed to drive the viscous cutting fluid to flow from the large end to the small end, which meets the condition of forming dynamic oil film. The dynamic oil film produces equal oil film pressure on the surface of the four tiltable tiles, and the pressure distribution is obtained according to the one-dimensional Reynold equation, as shown in Fig. 2. Similar to a four-jaw chuck, it has the effect of increasing the rigidity of the tool system. The greater the oil film pressure generated, the greater the oil film support stiffness and rigidity.

Fig. 1Model of the connector with double-bridge strain gauges and tiltable tiles

Fig. 2Tiltable tile and cutting fluid circumferential pressure distribution

2.3. Principle of counteracting the unbalanced radial force on the tool system

Fig. 3 shows the principle of the tool system to counteract the unbalanced radial force. Two Wheatstone Bridges composed of four double-bridge strain gauges measure the dynamic radial force generated by the front end of the tool system in two perpendicular directions, respectively. First, the radial force information is input to the control system, and then the control system controls the angle of the corresponding tilting block to change and form a wedge oil film with the hole wall. The wedge oil film generates an oil film pressure of equal magnitude and opposite direction to the radial force, which counteracts the unbalanced radial force of the tool system.

Fig. 3Schematic diagram of dynamic radial force adjustment system

After the derivation of the formula, the relationship between the radial force $\mathrm{\Delta }F$ of the tool in the $x$ or $y$ direction and the output voltage $U_A$ of the Wheatstone Bridge is derived as:

where $E$ is the modulus of elasticity, $U_E$ is the input voltage, $L\mathrm{\text{'}}$ is the distance of the double-bridged strain gauge from the top of the tool, and $d$ is the internal diameter of the drill pipe. $k$ is the strain coefficient, the exact value specified on each strain gauge package. Typically, metal strain gauges have a strain coefficient of approximately 2.

$E$, $U_E$, $L\mathrm{\text{'}}$, $D_1$, $d$ and $k$ are known quantities, and the radial force $\mathrm{\Delta }F$ of the tool can be obtained by collecting the output voltage signal $U_A$ through the data collector.

The forces on the tool system are shown in Fig. 4, which gives:

where $\mathrm{\Delta }{F}_x$, $\mathrm{\Delta }{F}_y$ are the unbalanced radial forces in the $x$ and $y$ directions, respectively $F_x$, and $F_y$ are $x$, and $y$ direction and its offset oil film pressure.

In summary, the deep hole connector designed in this paper is used in deep hole machining to increase the system’s rigidity and counteract the unbalanced radial force. The study of the oil film pressure is the focus.

Fig. 4Schematic diagram of the force on the tool system

3.1. Oil film thickness formula

As shown in Fig. 5, the oil film gap function is $h$, ignoring the deformation, the tiltable tile rotates around its midpoint $N$, the rotation tilt angle is $\alpha$, the eccentricity of the tiltable tile center $O\mathrm{\text{'}}$ for the deep hole center $O$ is $e$, the deep hole radius is $R$, the tiltable tile radius is $R\mathrm{\text{'}}$, and $\theta$ is the circumferential coordinate.

Fig. 5Oil film thickness diagram

In $\mathrm{\Delta }OO\mathrm{\text{'}}N$, $\mathrm{\angle }ONO\mathrm{\text{'}}=\alpha$, then $e=2R\mathrm{\text{'}}\sin \frac{\alpha }{2}$.

In $\mathrm{\Delta }OO\mathrm{\text{'}}M$, $\mathrm{\angle }OO\mathrm{\text{'}}M=\theta$, then$(R\mathrm{\text{'}}+h{)}^2-2e(R\mathrm{\text{'}}+h)\cos \theta +e^2=R^2$, $R\mathrm{\text{'}}+h=e\cos \theta \pm R\sqrt{1-{\left(\frac{e}{R}\right)}^2{\sin }^2\theta }$ can be obtained.

If the trace ${\left(\frac{e}{R}\right)}^2{\sin }^2\theta$ is omitted, and the positive sign of the root equation is taken, the oil film gap function at any position is obtained as:

3.2. Oil film pressure function

The classical Reynolds equation for one-dimensional flow is the basic equation for calculating fluid dynamic pressure lubrication and can be expressed as:

where $p$ is the oil film pressure; $\eta$ is the dynamic viscosity of the lubricant (N·s/m²); $v$ is the sliding speed (m/s); $h$ is the oil film thickness; $h_0$ is the oil film thickness at the maximum pressure.

From Reynold Eq. (4), we can see that the oil film pressure is related to influencing factors such as the viscosity of the lubricant, the sliding speed, and the thickness of the oil film.

According to the literature [7], we know:

where $h_1$ is the wedge-shaped oil film inlet clearance formed by the fluid; $h_2$ is the wedge-shaped oil film outlet clearance formed by the fluid.

Rewriting the Eq. (4) into polar form, i.e., substituting $v=R\omega$, $dx=Rd\theta$ into the above equation, the Reynolds equation in polar form is obtained as:

where $\omega$ is the relative rotational speed of the tool and the deep hole wall.

Integrating the pressure from the start angle ${\theta }_1$ to the end angle ${\theta }_2$ of the oil film, the total oil film pressure is obtained:

The final oil film pressure in the $y$-axis direction is obtained as:

From the above formula derivation, it can be seen that the magnitude of the oil film pressure on the tiltable tile is related to the workpiece speed, cutting fluid viscosity, tile tilt angle, and tile wrap angle, and is proportional to the workpiece speed and cutting fluid viscosity. Therefore, by changing these parameters, the oil film pressure can be adjusted on the individual tiltable tiles and, thus, on the connectors.