A method for calculating the eccentric load performance of an internal feedback type hydrostatic rotary table

Abstract

The application discloses a kind of inner feedback type static pressure rotary table eccentric load performance calculation methods, including step one: calculating the oil film thickness of each oil cavity after tilting.Step two: according to the theory of fluid lubrication, the pressure of upper and lower oil cavity and supporting moment are calculated.Step three: calculate the rotary table angle under eccentric load;Define oil pad structure parameters, select oil property parameters: the application has the advantages and positive effects: the application fully considers the influence of actual load, and solves the deflection angle through multi-level iteration, rather than directly giving the deflection angle, which is more in line with the actual rotary table operating condition.

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 off-center load performance of an internal feedback hydrostatic turntable. Background Technology

[0002] Internal feedback hydrostatic rotary tables typically employ constant pressure oil supply, with internal gap throttling. The throttling resistance varies with the oil film thickness, resulting in high rigidity, stable operation, and low friction, making them a key component of high-precision machine tools. However, in actual machining, the rotary table tilts due to workpiece shape and clamping position, leading to a decrease in workpiece machining quality. Therefore, clarifying the rotary table's support performance under eccentric load is crucial for its design. While literature such as "Research on the Bearing Characteristics of the Tilting Shaft System of a Grinding Machine Hydrostatic Rotary Table" and patent number CN201410328583.0 mention rotary table tilt calculations, they do not involve internal feedback structures and only provide a given rotary table tilt angle. The method described in this patent is based on an internal feedback rotary table structure with interconnected upper and lower oil pads, fundamentally different from the closed-type opposed oil pads and open-type oil pads mentioned in the literature. Furthermore, it considers the load when calculating the tilt angle, making it more consistent with actual working conditions. Summary of the Invention

[0003] The purpose of this invention is to provide a method for calculating the off-center load performance of an internal feedback hydrostatic turntable.

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

[0005] A method for calculating the off-center load performance of an internal feedback hydrostatic turntable includes the following steps: Step 1: Calculate the oil film thickness of each oil chamber after tilting.

[0006] When the turntable is subjected to an eccentric load W, the turntable tilts, and the tilt angle is θ. The oil film thickness at any point on the turntable is:

[0007]

[0008] R is the radius of any point on the turntable, δ is the angle between the eccentric load and the x-axis, θ is the tilt angle of the turntable surface, and h0 is the initial oil film thickness.

[0009] The overturning moment M of the turntable is:

[0010] M = W·d (2)

[0011] In the formula, d is the distance from the point of application of the eccentric load to the center of the circle.

[0012] According to the principle of force balance, the eccentric force is converted into a force at the center of the turntable and an overturning moment acting together. Therefore, the oil film is first compressed by a load of size W, and then tilts.

[0013] Step 2: Calculate the pressure and supporting torque of the upper and lower oil chambers based on fluid lubrication theory.

[0014]

[0015] p is the oil chamber pressure, h is the oil film thickness, η is the viscosity, ρ is the oil density, ω is the turntable speed, and v is the distance between the two bearing surfaces. The relative moving speed in the direction (m / s) is u, which is the relative moving speed (m / s) of the two bearing surfaces in the direction r.

[0016] The oil flow rate q is the pressure at r and Integral q of directional partial derivative over area 1,2 :

[0017]

[0018] In the formula, q1 is the upper oil cavity, q2 is the lower oil cavity, and S1, S2, S3, and S4 represent the sealing edges through which the oil flows.

[0019] The hydraulic resistance of the oil chamber is the ratio of the oil chamber pressure p0 to the flow rate q.

[0020]

[0021] When using a slit throttling device, the liquid resistance R of the throttling device is... i It can be represented as:

[0022]

[0023] In the formula, l c b is the length of the throttle. c h is the width of the throttle. e η0 represents the film thickness under a certain condition, and η0 represents the oil viscosity.

[0024] Bearing capacity F k1,2 for:

[0025]

[0026] In the formula, i is the node number in the r direction, and j is... Direction node number, p i,j To solve for the pressure matrix after equation (3), Δr is the step size in the r direction. for Directional step size.

[0027] Bearing moment M a for:

[0028]

[0029] In the formula, R TThis is the distance from the center of the oil cavity to the center of the circle;

[0030] Step 3: Calculate the turntable angle under eccentric loading; define the oil pad structure parameters and select the oil property parameters:

[0031] S3.1 Set the initial tilt angle change Δθ;

[0032] S3.2 Calculate the oil film thickness at each location point in each oil cavity according to step one;

[0033] S3.3 Initially, the film thickness change Δh is set, the film thickness after compression in the upper oil chamber is h-Δh, and the film thickness in the lower oil chamber is h+Δh.

[0034] S3.4 Set the initial upper and lower oil chamber pressures p 0k k = 1, 2, representing the upper and lower oil chambers respectively. Based on the film thickness of the upper and lower oil chambers, substitute into step two to calculate the oil chamber pressure distribution, oil chamber fluid resistance and throttling fluid resistance.

[0035] S3.5 Constant Pressure Hydrostatic Turntable Oil Chamber Pressure p r and oil supply pressure p s The following relationship must be satisfied:

[0036]

[0037] In the formula, λ is the liquid resistance ratio, and R i For the fluid resistance of the throttle, R o For oil flow resistance.

[0038] Use the above formula to check the pressure in the upper and lower oil chambers, and set the convergence accuracy ε1. If |p r -p 0k If |>ε1, then change the oil chamber pressure and resubmit it to step 3.4 until the difference in oil chamber pressure reaches the set convergence accuracy.

[0039] S3.6 Calculate the bearing capacity of the upper and lower oil cavities according to formula (7), and set the convergence accuracy ε2. If |F k1 -F k2 If -W|>ε2, then change the oil film thickness and resubmit it to step 3.2 until the difference in bearing capacity between the upper and lower oil chambers reaches the set convergence accuracy.

[0040] S3.7 Calculate the total supporting moment M after the superposition of each oil cavity according to formula (8). a Set the convergence precision ε3, if |M a If -M|>ε3, then change the tilt angle and return to step one to recalculate until the difference in tilt angles reaches the set convergence accuracy.

[0041] The advantages and positive effects of this invention are: it fully considers the influence of actual load and solves the deflection angle through multi-level iteration, rather than directly giving the deflection angle, which is more in line with the actual operating conditions of the turntable. Attached Figure Description

[0042] Figure 1 Turntable skew model.

[0043] Figure 2 Fan-shaped oil pad structure.

[0044] Figure 3 Calculation process for off-center load performance. Detailed Implementation

[0045] To further understand the invention's content, features, and effects, the following embodiments are provided, along with detailed descriptions in conjunction with the accompanying drawings:

[0046] A method for calculating the off-center load performance of an internal feedback hydrostatic turntable includes the following steps: Step 1: Calculate the oil film thickness of each oil chamber after tilting.

[0047] like Figure 1 As shown, when the turntable is subjected to an eccentric load W, the turntable tilts, and the tilt angle is θ. The oil film thickness at any point on the turntable is:

[0048]

[0049] R is the radius of any point on the turntable, δ is the angle between the eccentric load and the x-axis, θ is the tilt angle of the turntable surface, and h0 is the initial oil film thickness.

[0050] The overturning moment M of the turntable is:

[0051] M = W·d (2)

[0052] In the formula, d is the distance from the point of application of the eccentric load to the center of the circle.

[0053] According to the principle of force balance, the eccentric force is converted into a force at the center of the turntable and an overturning moment acting together. Therefore, the oil film is first compressed by a load of size W, and then tilts.

[0054] Step Two: As Figure 2 As shown, and R1, R2, R3, and R4 are the inner and outer half angles of the oil cavity, respectively, and the radii of the sector-shaped oil pad are the radii. Based on fluid lubrication theory, calculate the pressure and supporting torque of the upper and lower oil cavities.

[0055]

[0056] p is the oil chamber pressure, h is the oil film thickness, η is the viscosity, ρ is the oil density, ω is the turntable speed, and v is the distance between the two bearing surfaces. The relative moving speed in the direction (m / s) is u, which is the relative moving speed (m / s) of the two bearing surfaces in the direction r.

[0057] The oil flow rate q is the pressure at r and Integral q of directional partial derivative over area 1,2 :

[0058]

[0059] In the formula, q1 is the upper oil cavity, q2 is the lower oil cavity, and S1, S2, S3, and S4 represent the sealing edges through which the oil flows.

[0060] The hydraulic resistance of the oil chamber is the ratio of the oil chamber pressure p0 to the flow rate q.

[0061]

[0062] When using a slit throttling device, the liquid resistance R of the throttling device is... i It can be represented as:

[0063]

[0064] In the formula, l c b is the length of the throttle. c h is the width of the throttle. e η0 represents the film thickness under a certain condition, and η0 represents the oil viscosity.

[0065] Bearing capacity F k1,2 for:

[0066]

[0067] In the formula, i is the node number in the r direction, and j is... Direction node number, p i,j To solve for the pressure matrix after equation (3), Δr is the step size in the r direction. for Directional step size.

[0068] Bearing moment M a for:

[0069]

[0070] In the formula, R T This is the distance from the center of the oil cavity to the center of the circle;

[0071] Step 3: Calculate the turntable angle under off-center loading. The calculation process is as follows: Figure 3 As shown; define the oil pad structure parameters and select the oil property parameters:

[0072] S3.1 Set the initial tilt angle change Δθ;

[0073] S3.2 Calculate the oil film thickness at each location point in each oil cavity according to step one;

[0074] S3.3 Initially, the film thickness change Δh is set, the film thickness after compression in the upper oil chamber is h-Δh, and the film thickness in the lower oil chamber is h+Δh.

[0075] S3.4 Set the initial upper and lower oil chamber pressures p 0k k = 1, 2, representing the upper and lower oil chambers respectively. Based on the film thickness of the upper and lower oil chambers, substitute into step two to calculate the oil chamber pressure distribution, oil chamber fluid resistance and throttling fluid resistance.

[0076] S3.5 Constant Pressure Hydrostatic Turntable Oil Chamber Pressure p r and oil supply pressure p s The following relationship must be satisfied:

[0077]

[0078] In the formula, λ is the liquid resistance ratio, and R i For the fluid resistance of the throttle, R o For oil flow resistance.

[0079] Use the above formula to check the pressure in the upper and lower oil chambers, and set the convergence accuracy ε1. If |p r -p 0k If |>ε1, then change the oil chamber pressure and resubmit it to step 3.4 until the difference in oil chamber pressure reaches the set convergence accuracy.

[0080] S3.6 Calculate the bearing capacity of the upper and lower oil cavities according to formula (7), and set the convergence accuracy ε2. If |F k1 -F k2 If -W|>ε2, then change the oil film thickness and resubmit it to step 3.2 until the difference in bearing capacity between the upper and lower oil chambers reaches the set convergence accuracy.

[0081] S3.7 Calculate the total supporting moment M after the superposition of each oil cavity according to formula (8). a Set the convergence precision ε3, if |M a If -M|>ε3, then change the tilt angle and return to step one to recalculate until the difference in tilt angles reaches the set convergence accuracy.

[0082] The advantages and positive effects of this invention are: it fully considers the influence of actual load and solves the deflection angle through multi-level iteration, rather than directly giving the deflection angle, which is more in line with the actual operating conditions of the turntable.

Claims

1. A method for calculating the off-center load performance of an internal feedback hydrostatic turntable, characterized in that, The method includes the following steps: Step 1: Calculate the oil film thickness in each oil cavity after tilting; When the turntable is subjected to an eccentric load W, the turntable tilts, and the oil film thickness at any point on the turntable is: R is the radius of any point on the turntable, δ is the angle between the eccentric load and the x-axis, and θ is the tilt angle of the turntable surface. This represents the initial oil film thickness. The overturning moment M of the turntable is: In the formula, d is the distance from the point of application of the eccentric load to the center of the circle; According to the principle of force balance, the eccentric force is converted into the combined action of the force at the center of the turntable and the overturning moment; the oil film is first compressed by a load of size W, and then tilts; Step 2: Calculate the pressure and supporting torque of the upper and lower oil chambers based on fluid lubrication theory; Where h is the oil chamber pressure and h is the oil film thickness. Viscosity, For the density of the oil, The rotational speed of the turntable. For two bearing surfaces Direction relative to speed of movement The relative moving speed of the two bearing surfaces in the r direction; The oil flow rate q is the integral of the partial derivatives of the pressure in the r and φ directions over the area q. 1,2 : In the formula, S1, S2, S3, and S4 represent the sealing edges through which the oil flows into the oil cavity, respectively; The hydraulic resistance of the oil chamber is the ratio of the oil chamber pressure p0 to the flow rate q. When using a slit throttling device, the liquid resistance R of the throttling device is... i Represented as: In the formula, l c b is the length of the throttle. c h is the width of the throttle. e The film thickness under a certain condition. This refers to the viscosity of the oil. Bearing capacity for: In the formula, i is the node number in the r direction, and j is... Direction node number, p i,j To solve for the pressure matrix after equation (3), ∆r is the step size in the r direction and ∆φ is the step size in the φ direction; Bearing moment M a for: In the formula, R T This is the distance from the center of the oil cavity to the center of the circle; Step 3: Calculate the turntable angle under eccentric loading; define the oil pad structure parameters and select the oil property parameters: Step 3.1 Set the initial tilt angle change ∆θ; Step 3.2 Calculate the oil film thickness at each location point in each oil cavity according to Step 1; Step 3.3 Initially set the film thickness change ∆h, the film thickness after compression in the upper oil chamber is h-∆h, and the film thickness in the lower oil chamber is h+∆h; Step 3.4 Set the initial upper and lower oil chamber pressures p 0k k=1, 2, representing the upper and lower oil chambers respectively. Based on the film thickness of the upper and lower oil chambers, substitute into step two to calculate the oil chamber pressure distribution, oil chamber fluid resistance and throttling fluid resistance. Step 3.5 Oil chamber pressure of constant pressure hydrostatic rotary table and oil supply pressure The following relationship must be satisfied: In the formula, λ is the liquid resistance ratio. For the fluid resistance of the throttle, For oil outlet resistance; By checking the pressure in the upper and lower oil chambers, and setting the convergence accuracy ε1, if |p r -p 0k If |>ε1, then change the oil chamber pressure and resubmit it to step 3.4 until the difference in oil chamber pressure reaches the set convergence accuracy; Step 3.6 Calculate the bearing capacity of the upper and lower oil cavities according to equation (7), set the convergence accuracy ε2, if |F k1 - F k2 If -W|> ε2, then change the oil film thickness and resubmit it to step 3.2 until the difference in bearing capacity between the upper and lower oil chambers reaches the set convergence accuracy; Step 3.7 Calculate the total supporting moment M after the superposition of each oil cavity according to equation (8). a Set the convergence precision ε3, if |M a If -M|>ε3, then change the tilt angle and return to step one to recalculate until the difference in tilt angles reaches the set convergence accuracy.

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