Method for calculating bearing capacity of static pressure fan-shaped oil pad by considering surface roughness and centrifugal force

Abstract

The invention discloses a static pressure fan-shaped oil pad bearing capacity calculation method considering surface roughness and centrifugal force. The method comprises the steps that 1, the average oil film thickness formed between the surface of a rotary table and the surface of an oil pad is calculated; and 2, calculating the bearing capacity of the fan-shaped oil pad when the surface roughness is considered. And 3, establishing a quantitative fan-shaped oil pad bearing capacity mathematical model considering the centrifugal force. 4, the mathematical model of the oil film thickness and the bearing capacity of a single fan-shaped oil pad is obtained through derivation when the surface roughness is considered, and h is replaced to obtain the mathematical model of the bearing capacity of the fan-shaped oil pad when the surface roughness and the centrifugal force are considered. According to the method, the relationship among the oil pad, the surface roughness of the rotary table, the centrifugal force and the bearing capacity of the fan-shaped oil pad is fully considered, the bearing capacity of the oil pad under any film thickness he can be calculated according to the method, and actual working conditions are better met.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of hydrostatic bearing, in particular to a hydrostatic fan-shaped oil pad load capacity calculation method considering surface roughness and centrifugal force. BACKGROUND

[0002] Liquid hydrostatic rotary table has the advantages of high precision, low energy consumption, stable operation, etc., and has become the core functional component of equipment machining in various fields. In recent years, with the development of science and technology, the requirements for machine tool machining precision, machining efficiency, bearing performance, etc. are increasing. In the existing research, the invention patent with publication number CN106503391A discloses a quick calculation method of rectangular hydrostatic oil pad considering fluid-structure coupling, which solves the oil film bearing capacity by mutual iterative integration of Reynolds equation and deformation equation. However, the current level of mechanical processing will cause the oil pad and the rotary table surface to have "uneven" micro-topography characteristics, and the existence of rough peaks will cause the actual value of the oil film thickness to deviate from the preset value, changing the oil pad bearing capacity. At the same time, the centrifugal force in the rotation process of the rotary table will cause the imbalance of the oil cavity pressure inside the supporting oil pad, further affecting the change of the oil pad bearing capacity. Therefore, the influence of surface roughness and centrifugal force on the oil pad bearing capacity cannot be ignored when calculating the oil pad bearing capacity. In view of this situation, a hydrostatic fan-shaped oil pad is taken as the research object, and a hydrostatic fan-shaped oil pad bearing capacity calculation method considering surface roughness and centrifugal force is established. SUMMARY

[0003] The present application aims to provide a hydrostatic fan-shaped oil pad bearing capacity calculation method considering surface roughness and centrifugal force. The main feature of this method is to fully consider the influence of surface roughness and centrifugal force on the oil pad and rotary table when calculating the hydrostatic fan-shaped oil pad bearing capacity.

[0004] The technical scheme adopted by the present application is as follows:

[0005] A hydrostatic fan-shaped oil pad bearing capacity calculation method considering surface roughness and centrifugal force, which comprises the following steps: step one: calculating the average oil film thickness formed between the rotary table surface and the oil pad surface. Since the existing processing conditions cannot achieve absolute smoothness of the component surface, the oil film thickness in actual processing is not only the gap between the two surfaces, but also considers the rough peaks of the uneven surface. At present, scientists generally believe that the rough peaks of the surface follow a normal distribution, so the equivalent oil film thickness can be calculated by referring to the form of Greenwood-Tripp model.

[0006] Assume that the composite rough peak z of the rotary table and the fan-shaped oil pad surface obeys a normal distribution with a mean of 0 and a standard deviation of σ, and the gap between the oil pad and the rotary table is h. As shown in Figure 1 The density function of the rough peak z conforming to the normal distribution is:

[0007]

[0008] In ideal conditions: oil film thickness is h, when there is a rough peak height of z in some place of the surface, the local residual oil film thickness is:

[0009]

[0010] In the formula, h l is the residual oil film thickness.

[0011] Since the oil film is distributed on the effective bearing surface of the oil pad, the average oil film thickness between the rotary table and the oil pad can be solved by integral method, the definition of integral method for solving the average oil film thickness is: the effective average oil film thickness is the local oil film thickness of all possible rough peak positions weighted by probability, that is:

[0012]

[0013] In the formula, the lower limit of integral is-∞, because the rough surface is uneven, so the lower limit range is indefinite.

[0014] Further simplifying and calculating the integral of formula (3) obtains:

[0015]

[0016] In the formula, the integral result of the first term is:

[0017]

[0018] In the formula, the integral result of the second term is:

[0019]

[0020] Therefore, the integral result of the equivalent oil film thickness is:

[0021]

[0022] In the formula, is the error function about the oil film thickness. When calculating the normal distribution by using the error function, the numerical approximation and library function can be used, so as to avoid numerical integration.

[0023] Step two: calculate the bearing capacity of the sector oil pad considering the surface roughness. The assumed conditions are: 1. the flow state of lubricating oil is laminar flow; 2. the lubricating oil has no slip with the contact wall surface; 3. the lubricating oil viscosity is constant; 4. the lubricating oil only flows along the circumferential and radial directions.

[0024] Firstly, the effective included angle α of the oil film formed by the oil liquid is calculated e .

[0025]

[0026] Secondly, the shadow part is the effective load area A of the oil film formed by the oil e To calculate the area, the inner and outer radii R of the effective load area should be calculated first e1 R e2 .

[0027]

[0028] The effective radial width b of the oil pad, i.e. the difference between the effective inner and outer radii, is calculated.

[0029] b=R e2 -R e1 (10)

[0030] The equivalent radius R e .

[0031]

[0032] The length L of the straight sealing oil edge in the circumferential direction.

[0033]

[0034] Step three: Based on the above formula, a quantitative mathematical model of the load capacity of the sector-shaped oil pad considering centrifugal force is established.

[0035] Given the rotation speed of the turntable as ω, the flow rates Q1 and Q2 of the straight sealing oil edges on the left and right sides of the oil pad are calculated according to the flow rate formula of the flat plate gap.

[0036]

[0037] The flow rates Q3 and Q4 of the circumferential inner and outer arc sealing oil edges under the action of centrifugal force.

[0038]

[0039] Therefore, the oil supply quantity Q0 of a single oil pad can be calculated.

[0040]

[0041] In the formula,

[0042]

[0043] C3=0.05ρ.

[0044] For a quantitative oil-supply static pressure turntable, Q0 is always a constant value. When the oil film thickness remains stable, the pressure in the sector-shaped oil cavity is Δp.

[0045]

[0046] Effective load-carrying area A of oil film in sector oil pad e .

[0047]

[0048] Therefore, the load-carrying capacity W of a single sector oil pad.

[0049]

[0050] Step four: the above derivation has obtained the mathematical model of the oil film thickness and the load-carrying capacity of a single sector oil pad considering the surface roughness, and now only needs to replace h in formula (18) with formula (7) to obtain the mathematical model of the load-carrying capacity of the sector oil pad considering the surface roughness and the centrifugal force, as follows.

[0051]

[0052] The present application has the advantages and positive effects that the present application fully considers the relationship between the oil pad, the surface roughness of the rotary table, the centrifugal force and the load-carrying capacity of the sector oil pad, and according to the above method, the load-carrying capacity of the oil pad under any film thickness h e can be calculated. Therefore, the static pressure sector oil pad load-carrying capacity calculation method considering the surface roughness and the centrifugal force proposed by the present application is more in line with the actual working condition. BRIEF DESCRIPTION OF DRAWINGS

[0053] Figure 1 Schematic diagram of surface roughness peaks of rotary table and oil pad.

[0054] Figure 2 Schematic diagram of sector oil pad.

[0055] Figure 3 Oil pad load-carrying capacity calculation process. DETAILED DESCRIPTION

[0056] In order to further understand the inventive content, characteristics and effects of the present application, the following examples are given, and are described in detail as follows in conjunction with the drawings:

[0057] A static pressure sector oil pad load-carrying capacity calculation method considering the surface roughness and the centrifugal force, which comprises the following steps: step one: since the existing machining conditions cannot achieve absolute smoothness of the surface of the part, therefore in actual machining, the oil film thickness is not only the gap between the two surfaces, but also needs to consider the roughness peaks of the uneven surface. At present, scientists generally believe that the surface roughness peaks follow normal distribution, therefore the oil film thickness can be calculated by referring to the form of Greenwood-Tripp model. For example Figure 1h is the oil film gap between the sector oil pad and the turntable, z is the composite roughness peak height of the turntable and the surface of the sector oil pad, which obeys the density function of the normal distribution with a mean of 0 and a standard deviation of θ, and the local residual oil film thickness is:

[0058]

[0059] where h l is the residual oil film thickness.

[0060] The effective average oil film thickness is:

[0061]

[0062] The integral of formula (3) is further simplified and calculated as:

[0063]

[0064] The integral result of the first term is:

[0065]

[0066] The integral result of the second term is:

[0067]

[0068] where, is the error function about the oil film thickness. When calculating the normal distribution using the error function, its numerical approximation and library function can be used to avoid numerical integration.

[0069] Therefore, the integral result of the equivalent oil film thickness is:

[0070]

[0071] Step two: Calculate the bearing capacity of the sector oil pad considering surface roughness and centrifugal force. The assumptions are: 1. The flow state of the lubricating oil is laminar flow; 2. The lubricating oil has no slip with the contact wall surface; 3. The lubricating oil viscosity is constant; 4. The lubricating oil only flows along the circumferential and radial directions.

[0072] First, calculate the effective angle α e of the oil film formed by the oil, as shown in Figure 2 .

[0073]

[0074] Second, Figure 2 The shaded part in is the effective bearing area A e of the oil film formed by the oil, to calculate this area, the inner and outer radii R e1 and R e2.

[0075]

[0076] The effective radial width b of the oil pad, i.e. the difference between the effective inner and outer radii, is calculated.

[0077] b = R e2 -R e1 (10)

[0078] The equivalent radius R e .

[0079]

[0080] The length L of the straight oil seal in the circumferential direction.

[0081]

[0082] Step three: on the basis of the above formula, a quantitative static pressure fan-shaped oil pad carrying capacity mathematical model is established considering the centrifugal force.

[0083] According to the flow formula of the flat plate gap, the flow rates Q1 and Q2 of the straight oil seals on the left and right sides of the oil pad are calculated.

[0084]

[0085] Under the action of the centrifugal force, the flow rates Q3 and Q4 of the circumferential inner and outer arc oil seals.

[0086]

[0087] Therefore, the oil supply amount Q0 of a single oil pad can be calculated.

[0088]

[0089] In the formula,

[0090]

[0091] C3 = 0.05p.

[0092] For a quantitative oil supply static pressure turntable, Q0 is always a constant value. When the oil film thickness remains stable, the pressure in the fan-shaped oil cavity is Δp.

[0093]

[0094] The effective carrying area A of the oil film in the fan-shaped oil pad e .

[0095]

[0096] Therefore, the load capacity of the single sector oil pad is W.

[0097]

[0098] Step four: the above derivation has obtained the oil film thickness and the load capacity mathematical model of the single sector oil pad considering the surface roughness, now only need to replace h in formula (18) with formula (7) to obtain the load capacity mathematical model of the sector oil pad considering the surface roughness and centrifugal force, as follows.

[0099]

[0100] The application has the advantages and positive effects that the application fully considers the relationship between the oil pad, the surface roughness of the rotary table, the centrifugal force and the load capacity of the sector oil pad, and according to the above method, the load capacity of the oil pad under any film thickness h e Therefore, the static pressure sector oil pad load capacity calculation method considering the surface roughness and the centrifugal force proposed by the application is more in line with the actual working condition.

Claims

1. A method for calculating the load capacity of a hydrostatic sector-shaped oil pad taking into account surface roughness and centrifugal force, characterized in that, The method comprises the following steps: step one, calculating the average oil film thickness formed between the turntable surface and the oil pad surface; Supposing that the composite rough peak z of the turntable and the sector oil pad surface obeys the normal distribution with the mean value of 0 and the standard deviation of sigma, the gap between the oil pad and the turntable is h; the density function of the rough peak z conforming to the normal distribution is: Under ideal conditions: the oil film thickness is h, when there is a rough peak height z at a certain position of the surface, the local residual oil film thickness is: In the formula, h l is the residual oil film thickness; The oil film is distributed on the effective bearing surface of the whole oil pad, the average oil film thickness between the turntable and the oil pad is solved by the integral method, the definition of the integral method for solving the average oil film thickness is that the effective average oil film thickness is the probability weighted average of the local oil film thickness of all possible rough peak positions, namely: In the formula, the lower limit of the integral is -∞ because the rough surface is uneven, so the lower limit range is indefinite; The integral result of the first term in formula (3) is: The integral result of the second term in formula (3) is: Therefore, the integral result of the equivalent oil film thickness is: Step two, calculating the bearing capacity of the sector oil pad considering the surface roughness; conditions are: 1) the flow state of the lubricating oil is laminar flow; 2) the lubricating oil and the contact wall have no slip; 3) the lubricating oil viscosity is constant; wherein is an error function with respect to the oil film thickness; the error function is used to calculate the normal distribution, and its numerical approximation and library function can be used to avoid numerical integration; 4) the lubricating oil only flows along the circumferential and radial directions; The effective radial width b of the oil pad is calculated, that is, the difference between the effective inner and outer radii; First, the effective included angle α of the oil film formed by the oil is calculated e ; Secondly, the shadow part is the effective bearing area A of the oil film formed by the oil e To calculate the area, the inner and outer circle radii R of the effective bearing area need to be calculated first e1 R e2 ; The length L of the straight oil sealing edge in the circumferential direction; b = R e2 - R e1 (10) Equivalent radius R e ; Step three, on the basis of the above formula, a quantitative formula sector oil pad bearing capacity mathematical model considering the centrifugal force is established; Given that the turntable speed is omega, according to the flow formula of the flat plate gap, the flow rates Q1 and Q2 of the straight oil sealing edges on the left and right sides of the oil pad are calculated; Under the action of the centrifugal force, the flow rates Q3 and Q4 of the circumferential inner and outer arc oil sealing edges; Therefore, the oil supply amount Q0 of a single oil pad can be calculated; C3=0.05ρ; In the formulae, For the static pressure turntable with quantitative oil supply, Q0 is always a constant value; when the oil film thickness remains stable, the pressure in the sector oil cavity is Δp; Therefore, the bearing capacity W of a single sector oil pad is: Effective load bearing area A of oil film in sector oil pad e ; Step four: the above derivation has obtained the oil film thickness and the bearing capacity mathematical model of a single sector oil pad considering the surface roughness, now only need to replace h in formula (18) with formula (7) to obtain the mathematical model of the sector oil pad bearing capacity considering the surface roughness and the centrifugal force, as follows: ​

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