Design method of inner feedback type static pressure rotary table throttle

Abstract

This invention discloses a design method for an internal feedback hydrostatic turntable throttle, calculating the flow rate of a fan-shaped oil pad. The second-order partial differential equation is discretized using the finite difference method, and solved using the Gauss-Seidel iteration method to obtain the dimensionless pressure of the oil cavity and the three-dimensional velocity distribution in different directions; the flow rate of the rectangular slot is calculated. Since the short side dimension of the rectangular slot throttle is very small, it is considered as a rectangular oil pad, with only the long side sealing the oil acting. After the turntable rotates, the oil flowing through the rectangular slot carries centrifugal force. When solving for the flow rate of the rectangular slot throttle, the rectangular oil pad is equivalent to a fan-shaped oil pad, with its center coinciding with the center of the fan-shaped oil pad, and the equivalent front and rear areas remain unchanged. In the initial state, the oil film thickness in the upper and lower oil cavities is the same. According to the characteristics of the internal feedback structure, the flow rate through the lower oil cavity is equal to the flow rate through the throttling edge. The method for calculating the throttle length in this invention is more realistic.

Description

Technical Field

[0001] This invention relates to the field of hydrostatic turntable oil film support technology, and in particular to a method for calculating the bearing capacity of a sector-shaped oil pad that considers the coupling of multiple factors. Background Technology

[0002] The throttle is a crucial component of a constant-pressure hydrostatic turntable. Under constant oil supply pressure, it automatically adjusts the pressure of each oil chamber to adapt to changes in different loads by relying on the pressure drop generated when lubricating oil flows through this compensating element, enabling the turntable to have high load-bearing capacity under fluid friction conditions. Internal feedback hydrostatic bearings typically employ rectangular gap throttling, as described in patents 202010881714.3 and CN202010874469.3. However, most researchers currently use empirical formulas for design, neglecting the influence of rotational speed on the centrifugal force of the oil, resulting in inaccurate results. Therefore, to more comprehensively reflect the relationship between various parameters, this invention proposes a design method for an internal feedback hydrostatic turntable throttle. Summary of the Invention

[0003] The purpose of this invention is to provide a design method for an internal feedback static pressure turntable throttle.

[0004] The technical solution adopted in this invention is:

[0005] A design method for an internal feedback hydrostatic turntable throttle valve includes the following steps: Step 1: Calculate the flow rate of the sector-shaped oil pad. Both the upper and lower oil pads of the internal feedback hydrostatic turntable are sector-shaped and connected by oil circuits. The oil flows through the upper oil chamber throttle valve, causing a pressure drop, and then flows into the lower oil chamber. Therefore, taking the lower oil chamber as an example, according to hydrostatic fluid lubrication theory, the dimensionless two-dimensional Reynolds equation for the sector-shaped oil pad considering rotational speed in cylindrical coordinates is:

[0006]

[0007] In the formula, p0 is the oil chamber pressure, H0 is the initial oil film thickness, η0 is the viscosity, ρ0 is the oil density, ω is the turntable speed, R4 is the maximum radius of the oil pad, and V is the distance between the two bearing surfaces. The relative moving speed in the direction r (m / s), where U is the relative moving speed (m / s) between the two bearing surfaces in the r direction. The radius is dimensionless. The pressure is dimensionless. The thickness is a dimensionless oil film. The dimensionless distance from the z-axis is the distance from the z-axis. Let r be the dimensionless velocity along the two bearing surfaces. For two bearing surfaces Dimensionless velocity in direction Dimensionless viscosity The density of the oil is a dimensionless liquid. Let z be the dimensionless velocity in the z-direction.

[0008] The second-order partial differential equation is discretized using the finite difference method, and the above equation is solved using the Gauss-Seidel iteration method to obtain the dimensionless pressure of the oil cavity. Substituting into the following formula, we can obtain the three-dimensional velocity distribution in different directions.

[0009]

[0010] In the formula, i is the node number in the r direction, and j is... Directional node number, where k is the node number in the direction of oil film thickness.

[0011] Dimensionless flow The integral of the flow velocity over the area:

[0012]

[0013] In the formula, Ω r and For the oil to flow through r and Area of ​​direction

[0014] Transform the flow rate into the following dimensions:

[0015]

[0016] Step Two: Calculation of Flow Rate Through the Rectangular Slot. Since the short side dimension of the rectangular slot throttle is very small, it can be considered as a rectangular oil pad, with only the long side acting as the sealing edge. After the turntable rotates, the oil flowing through the rectangular slot carries centrifugal force. When calculating the flow rate of the rectangular slot throttle, the rectangular oil pad is equivalent to a fan-shaped oil pad, with its center coinciding with the center of the fan-shaped oil pad. The equivalent area remains unchanged, and the lengths are as follows:

[0017]

[0018] In the formula, B is the total width of the rectangular throttle, b is the width of the oil chamber of the rectangular throttle, R1 is the minimum radius of the oil pad, and l is the length of the rectangular throttle.

[0019] Substituting the equivalent dimensions into equations (1), (2), and (3), the dimensionless flow rate through the throttle can be obtained. The pressure of the throttle is equal to the oil supply pressure P. s It satisfies the following relationship:

[0020]

[0021] In the formula, λ is the throttling ratio.

[0022] The dimensionless value of the flow rate through the throttle is:

[0023]

[0024] Step 3: The dimensions of a rectangular slot throttle mainly include the length and width of the throttling edge, typically given as the throttling edge width b. z To calculate the length. Initially, the oil film thickness in the upper and lower oil chambers is the same. Based on the characteristics of the internal feedback structure, the flow rate Q through the lower oil chamber is... F The flow Q of the throttling edge L equal.

[0025] 3.1 Define the oil pad structure parameters, select the oil property parameters, and define the throttling edge width b. z ;

[0026] 3.2 Setting the throttle length range [l] a , l b ], solve for the flow rate Q according to step one. F Define the throttling ratio and take the length of the throttle. Calculate the flow rate Q according to step two. L ;

[0027] 3.3 If |Q F -Q L |>ε, where ε is the convergence difference, when Q F >Q L Let l = l a When Q F <Q L Let l = l b Return to step two to continue the calculation;

[0028] 3.4 When |Q F -Q L When | < ε, the calculation ends and the length l is output.

[0029] The advantages and positive effects of this invention are as follows: This invention fully considers the influence of rotational speed and calculates the flow rate by establishing the Reynolds equation. In the paper "Design of Direct Drive Internal Feedback Closed Static Pressure Turntable for Torque Motor", the length of the throttle is calculated according to an empirical formula, ignoring the influence of centrifugal force caused by rotational speed. Therefore, the throttle length calculation method proposed in this invention is more in line with reality. Attached Figure Description

[0030] Figure 1 Fan-shaped oil pad structure

[0031] Figure 2 Rectangular throttle equivalent

[0032] Figure 3 Throttling device design process Detailed Implementation

[0033] To further understand the invention's content, features, and effects, the following embodiments are provided, and detailed descriptions are given below in conjunction with the accompanying drawings:

[0034] A design method for an internal feedback static pressure rotary table throttle, comprising the following steps: Step 1: Calculate the flow rate of the sector-shaped oil pad. For example... Figure 1 The structure is a fan-shaped oil pad. Both the upper and lower oil pads on the internal feedback hydrostatic turntable are fan-shaped and connected by oil passages. The oil flows through the upper oil chamber throttle, causing a pressure drop, and then flows into the lower oil chamber. Therefore, taking the lower oil chamber as an example, according to hydrostatic fluid lubrication theory, the dimensionless two-dimensional Reynolds equation for the fan-shaped oil pad considering rotational speed in cylindrical coordinates is:

[0035]

[0036] In the formula, dimensionless: p0 is the oil chamber pressure, H0 is the initial oil film thickness, η0 is the viscosity, ρ0 is the oil density, ω is the turntable speed, R4 is the maximum radius of the oil pad, V is the relative moving speed (m / s) of the two bearing surfaces in the r direction, and U is the distance between the two bearing surfaces. Relative speed of movement in direction (m / s) The radius is dimensionless. The pressure is dimensionless. The thickness is a dimensionless oil film. The dimensionless distance from the z-axis is the distance from the z-axis. Let r be the dimensionless velocity along the two bearing surfaces. For two bearing surfaces Dimensionless velocity in direction Dimensionless viscosity The density of the oil is a dimensionless liquid. Let z be the dimensionless velocity in the z-direction.

[0037] The second-order partial differential equation is discretized using the finite difference method, and the above equation is solved using the Gauss-Seidel iteration method to obtain the dimensionless pressure of the oil cavity. Substituting into the following formula, we can obtain the three-dimensional velocity distribution in different directions:

[0038]

[0039] In the formula, i is the node number in the r direction, and j is... Directional node number, where k is the node number in the direction of oil film thickness.

[0040] Dimensionless flow The integral of the flow velocity over the area:

[0041]

[0042] In the formula, Ω r and For the oil to flow through r and Area of ​​direction

[0043] Transform the flow rate into the following dimensions:

[0044]

[0045] Step Two: Calculation of Rectangular Gap Flow Rate. Since the short side dimension of the rectangular gap throttle is very small, it can be considered as a rectangular oil pad, where only the long side sealing the oil is effective. Figure 2 As shown. After the turntable rotates, the oil flowing through the rectangular slit carries centrifugal force. When solving for the flow rate of the rectangular slit throttle, the rectangular oil pad is equivalent to a fan-shaped oil pad, with its center coinciding with the center of the fan-shaped oil pad. The equivalent area remains unchanged before and after, and the lengths are as follows:

[0046]

[0047] In the formula, B is the total width of the rectangular throttle, b is the width of the oil chamber of the rectangular throttle, R1 is the minimum radius of the oil pad, and l is the length of the rectangular throttle.

[0048] Substituting the equivalent dimensions into equations (1), (2), and (3), the dimensionless flow rate through the throttle can be obtained. The pressure of the throttle is equal to the oil supply pressure P. s It satisfies the following relationship:

[0049]

[0050] In the formula, λ is the throttling ratio.

[0051] The dimensionless value of the flow rate through the throttle is:

[0052]

[0053] Step 3: The dimensions of a rectangular slot throttle mainly include the length and width of the throttling edge, typically given as the throttling edge width b. z To calculate the length. Initially, the oil film thickness in the upper and lower oil chambers is the same. Based on the characteristics of the internal feedback structure, the flow rate Q through the lower oil chamber is... F The flow Q of the throttling edge L equal.

[0054] 3.1 Define the oil pad structure parameters, select the oil property parameters, and define the throttling edge width b. z ;

[0055] 3.2 Setting the throttle length range [l] a , lb ], solve for the flow rate Q according to step one. F Define the throttling ratio and take the length of the throttle. Calculate the flow rate Q according to step two. L ;

[0056] 3.3 If |Q F -Q L |>ε, where ε is the convergence difference, when Q F >Q L Let l = l a When Q F <Q L Let l = l b Return to step two to continue the calculation;

[0057] 3.4 When |Q F -Q L When | < ε, the calculation ends and the length l is output.

[0058] The advantages and positive effects of this invention are as follows: This invention fully considers the influence of rotational speed and calculates the flow rate by establishing the Reynolds equation. In the paper "Design of Direct Drive Internal Feedback Closed Static Pressure Turntable for Torque Motor", the length of the throttle is calculated according to an empirical formula, ignoring the influence of centrifugal force caused by rotational speed. Therefore, the throttle length calculation method proposed in this invention is more in line with reality.

Claims

1. A design method for an internal feedback static pressure turntable throttle, characterized in that, The method includes the following steps: Step 1: Calculate the flow rate of the sector-shaped oil pad; the upper and lower oil pads of the internal feedback hydrostatic turntable are both sector-shaped and connected by oil circuits. The oil flows through the upper oil chamber throttle, causing a pressure drop, and then flows into the lower oil chamber; according to the hydrostatic fluid lubrication theory, the dimensionless two-dimensional Reynolds equation for the sector-shaped oil pad considering rotational speed in cylindrical coordinates is: （1） In the formula, , , , , , , , , , , The pressure in the oil chamber. The initial oil film thickness. The pressure in the oil chamber. Viscosity, For the density of the oil, The rotational speed of the turntable. The maximum radius of the oil pad. For two bearing surfaces Relative speed of movement in direction (m / s) The relative moving speed (m / s) of the two bearing surfaces in the r direction. The radius is dimensionless. The pressure is dimensionless. The thickness is a dimensionless oil film. Let z be the dimensionless distance from the walk. Let r be the dimensionless velocity along the two bearing surfaces. For two bearing surfaces Dimensionless velocity in direction Dimensionless viscosity The density of the oil is a dimensionless liquid. The z-axis velocity is dimensionless. The second-order partial differential equation is discretized using the finite difference method, and the above equation is solved using the Gauss-Seidel iteration method to obtain the dimensionless pressure of the oil cavity. Substituting into the following formula, we obtain the three-dimensional velocity distribution in different directions. （2） In the formula, i is the node number in the r direction, and j is... Directional node number, where k is the node number in the direction of oil film thickness. Dimensionless flow The integral of the flow velocity over the area: （3） In the formula, and For the oil to flow through r and Area of ​​direction Transform the flow rate into the following dimensions: （4） Step 2: Calculation of flow rate through the rectangular slot; After the turntable rotates, the oil flowing through the rectangular slot carries centrifugal force; When solving for the flow rate of the rectangular slot throttle, the rectangular oil pad is equivalent to a fan-shaped oil pad, with its center coinciding with the center of the fan-shaped oil pad, and the equivalent area remains unchanged. The lengths are as follows: （5） In the formula, B is the total width of the rectangular throttle, and b is the width of the oil chamber of the rectangular throttle. The minimum radius of the oil pad, The length of the rectangular throttle; Substituting the equivalent dimensions into equations (1), (2), and (3), the dimensionless flow rate through the throttle is obtained. The pressure of the throttle is equal to the oil supply pressure. It satisfies the following relationship: （6） In the formula, The throttling ratio is given; the flow rate through the throttling device is dimensionlessly converted to: (7); Step 3: The dimensions of the rectangular slot throttle include the length and width of the throttling edge. Given the width of the throttling edge... To calculate the length; in the initial state, the oil film thickness in the upper and lower oil chambers is the same. Based on the characteristics of the internal feedback structure, the flow rate through the lower oil chamber is... and flow rate of the throttling edge equal.

2. The design method of an internal feedback static pressure turntable throttle according to claim 1, characterized in that, Step 3 includes the following steps: S3.1 Define the oil pad structure parameters, select the oil property parameters, and define the throttling edge width. ; S3.2 Set the throttle length range [ , ], calculate the flow rate according to step one. Define the throttling ratio and take the length of the throttle. Calculate the flow rate according to step two. ; S3.3 If , To converge the difference, when ,make ,when Then let Return to step two to continue the calculation; S3.4 When satisfied When the calculation ends, the length is output. .

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