A method for calculating the critical oil film thickness of a sliding bearing

Abstract

This invention relates to the field of sliding bearing design technology, specifically disclosing a method for calculating the critical oil film thickness of a sliding bearing. The method considers the machining roughness of the bearing bush and journal, the journal deformation under average pressure, the deformation due to shaft bending, and the tolerance deviation of the journal and bearing bush along the circumferential cross-section to calculate the critical oil film thickness of the sliding bearing. This calculation method can be used as a basis for calculating the critical oil film thickness in bearing design; the method is accurate and reasonable.

Description

Technical Field

[0001] This invention belongs to the field of sliding bearing design technology, and specifically relates to a method for calculating the critical oil film thickness of a sliding bearing. Background Technology

[0002] In the design of sliding bearings, it is usually required that the minimum oil film thickness must be greater than the critical oil film thickness. There is usually a unified formula for calculating the minimum oil film thickness, but the requirements for calculating the critical oil film thickness vary significantly among different bearing design manuals. Some bearing manuals select the critical oil film thickness based on the shaft diameter (Guo Hong and Ling Shaoqi, *Design of Cylindrical and Conical Hydrostatic Sliding Bearings*), without considering the effects of machining accuracy, load, and shaft bending, which is clearly unreasonable. Some bearing design manuals require the critical oil film thickness to be determined based on the machining roughness of the bearing shell and shaft diameter (Yang Guoan, *Practical Technology for Fault Diagnosis of Sliding Bearings*), which considers machining accuracy but does not consider the effects of shaft bending. If the shaft system is subjected to a large concentrated load, this calculation method is not accurate enough. Some bearing design manuals require consideration not only of machining roughness but also of shaft diameter deformation, rotor bending deformation, and tolerances (Chen Jinbao, *Calculation and Design of Sliding Bearings*), which considers the bending of the shaft elastic line in the bearing shell caused by bending and also calculates the circumferential cross-sectional tolerances of the journal and bearing shell, resulting in an overestimation of the critical oil film thickness, which is also not accurate enough.

[0003] Therefore, there is an urgent need to develop a reasonable and scientific method for calculating the critical oil film thickness of sliding bearings in order to accurately calculate the critical oil film thickness of sliding bearings. Summary of the Invention

[0004] The purpose of this invention is to provide a method for calculating the critical oil film thickness of a sliding bearing, which can reasonably and accurately calculate the critical oil film thickness of a sliding bearing.

[0005] The technical solution of the present invention is as follows:

[0006] A method for calculating the critical oil film thickness of a sliding bearing is proposed, which takes into account the machining roughness of the bearing bush and journal, the deformation of the journal under average pressure, the deformation of the shaft system due to bending, and the tolerance deviation of the journal and bearing bush along the circumferential cross section, and calculates the critical oil film thickness of the sliding bearing.

[0007] Based on the calculated minimum oil film thickness, the machining roughness of the bearing bush and shaft diameter is selected according to the standard as the calculation item for the critical oil film thickness;

[0008] The bending deformation of the shaft system and the tolerance of the journal and bearing along the circumferential cross section are compared, and the larger of the two is taken as the calculation item for the critical oil film thickness.

[0009] Considering the journal deformation under average pressure, the journal deformation value is calculated and used as a calculation item for critical oil film thickness;

[0010] Finally, by summing up all the above calculations, the critical oil film thickness of the sliding bearing is obtained.

[0011] Specifically, the following steps are included:

[0012] Step 1: Calculate the minimum oil film thickness based on the bearing parameters.

[0013] h min =0.5dψ(1-χ) (1)

[0014] In equation (1), h min Where d is the minimum oil film thickness, ψ is the shaft diameter, ψ is the relative clearance between the bearing and the shaft diameter, and x is the eccentricity.

[0015] Step 2: Select the machining roughness of the bearing bush and journal according to the standard.

[0016] Based on the calculated minimum oil film thickness h min Refer to GB / T39741.2-202 standard to determine the micro-roughness height h of the journal surface. m and the circumferential cross-sectional tolerance h of the journal and bearing bush i ;

[0017] Based on the measured bearing outer diameter, refer to GB / T7308.1-2021 standard to determine the micro-roughness height h of the bearing bush surface. b ;

[0018] Step 3: Calculate the effect of journal deformation on critical oil film thickness

[0019] Considering the journal deformation under average pressure, the minimum clearance reduction h caused by the journal deformation is calculated using the Cortner formula. k :

[0020] h k =1.595d{(l / d) 2 +1.8l}(l / d) 2 p m 10 -6 (2)

[0021]

[0022] In equations (2) and (3), h k p represents the minimum reduction in clearance caused by journal deformation, in μm. m d is the average pressure of the bearing bush, in Pa; d is the bearing diameter, in mm; l is the bearing bush length, in mm; W is the bearing bush load, in N.

[0023] Step 4: Calculate the bending deformation of the shaft and compare it with the circumferential cross-sectional tolerances of the journal and bearing shell. The inflection of the shaft's elastic line in the bearing shell is calculated according to formula (4):

[0024] h n =0.5lθ (4)

[0025] In equation (4), h n θ represents the inflection point of the axial elastic line within the bearing bush, in μm; l represents the bearing bush length, in mm; θ represents the deformation angle caused by the bending deformation of the shaft system, in radians.

[0026] Compare h n with h i The larger of the two values ​​is used for calculation;

[0027] Step 5: Calculate the critical oil film thickness

[0028] h kp =h m +h b +h k +max{h n h i} (7)

[0029] In equation (7), h kp h is the critical oil film thickness. m h is the micro-roughness height of the journal surface. b h represents the surface roughness height of the bearing bush; k h is the minimum clearance reduction caused by journal deformation. n h represents the inflection point of the axial elastic line within the bearing bush. i This refers to the tolerance deviation of the journal and bearing cross-section along the circumferential direction.

[0030] In step 4, for a double-supported bearing with a concentrated load acting between the two bearings, the deformation angle θ caused by the bending deformation of the shaft system is determined according to equations (5) and (6):

[0031]

[0032]

[0033] In equations (5) and (6), E is the elastic modulus of the shaft in GPa, and I is the moment of inertia in mm. 4 All values ​​were obtained by consulting the "Mechanics of Materials" handbook; F is the external load borne by the bearing, which is a known condition in the bearing design, and the unit is N; L is the bearing spacing, L1 is the distance between bearing B and the load application point, and L2 is the distance between bearing A and the load application point, which were obtained by measurement, and the unit is μm.

[0034] In step 2, hm Take the corresponding Ra value from the standard.

[0035] In step 2, h i Take the standard roundness tolerance t1 value.

[0036] In step 2, h b Take the corresponding Ra value of the bearing sliding surface from the standard.

[0037] It can be applied to the design of sliding bearings.

[0038] The significant advantages of this invention are:

[0039] (1) The method of the present invention takes into account the roughness of the bearing shell and journal, the deformation of the journal under the action of average pressure, calculates the deformation of the shaft system bending and compares it with the tolerance of the journal and bearing shell along the circumferential cross section, takes the larger value of the two as the basis for calculation, and finally calculates the critical oil film thickness that best fits the actual situation, which is more accurate and reasonable than other methods.

[0040] (2) The calculation method of the present invention can be used as the basis for calculating the critical oil film thickness in bearing design.

[0041] (3) The calculation method of the present invention is simple, feasible and has good executability.

[0042] (4) The calculation method of the present invention can be applied to the design of sliding bearings, making the design of sliding bearings more reliable. Attached Figure Description

[0043] Figure 1 This is a schematic diagram showing the shaft tilting within the bearing.

[0044] Figure 2 This is a schematic diagram of rotor bending deformation. Detailed Implementation

[0045] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0046] Minimum oil film thickness is a fundamental parameter characterizing the fluid lubrication state of a bearing. When the minimum oil film thickness equals the critical oil film thickness, the bearing lubrication will transition from fluid lubrication to mixed lubrication, leading to bearing wear. Therefore, the minimum oil film thickness must be greater than the critical oil film thickness, with a certain safety margin. Bearing design generally requires:

[0047] h min >h kp +2um

[0048] In the formula, h min For the minimum oil film thickness, h kp The critical oil film thickness;

[0049] Critical oil film thickness is the limit thickness of the oil film; it is the boundary between a bearing transitioning from mixed operating conditions to liquid lubrication conditions or vice versa. Critical oil film thickness is related to factors such as the machining roughness of the bearing bush and journal, journal deformation, and shaft misalignment within the bearing due to shaft deflection.

[0050] A method for calculating the critical oil film thickness of a sliding bearing includes the following steps: Based on the calculated minimum oil film thickness, the machining roughness of the bearing shell and shaft diameter is selected according to standards as one of the calculation items for the critical oil film thickness; the bending deformation of the shaft system is applied to the calculation of the critical oil film thickness and compared with the circumferential cross-sectional tolerances of the journal and bearing shell, and the larger of the two is taken as one of the calculation items for the critical oil film thickness; considering the journal deformation under average pressure, the journal deformation value is calculated according to the Cortner formula and is also taken as one of the calculation items for the critical oil film thickness; finally, by summing up the above calculation items for the critical oil film thickness, the critical oil film thickness of the sliding bearing can be calculated relatively accurately. The method specifically includes the following steps:

[0051] Step 1: Calculate the minimum oil film thickness based on the bearing parameters.

[0052] h min =0.5dψ(1-χ) (1)

[0053] In equation (1), h min Minimum oil film thickness, in μm; d is shaft diameter, in mm; ψ is the relative clearance between the bearing and the shaft diameter; x is eccentricity.

[0054] Step 2: Select the machining roughness of the bearing bush and journal according to the standard.

[0055] Based on the calculated minimum oil film thickness h min Refer to GB / T39741.2-2021 Sliding Bearings Tolerances Part 2: Geometric Tolerances and Surface Roughness Standards for Shafts and Thrust Shoulders to determine the micro-roughness height h of the journal surface. m and the circumferential cross-sectional tolerance h of the journal and bearing bush i Based on the measured bearing outer diameter, refer to GB / T7308.1-2021 Sliding bearings with or without flanges, thin-walled bearing shells, Part 1: Tolerances, structural elements and inspection methods, to determine the surface roughness height h of the bearing shell. b ;

[0056] Among them, h m The micro-roughness height of the journal surface is taken as the corresponding Ra value in the standard.

[0057] h i The tolerance deviation of the journal and bearing along the circumferential cross section is taken as the standard roundness tolerance t1 value;

[0058] h b The bearing surface micro-roughness height is taken as the corresponding Ra value of the bearing sliding surface in the standard.

[0059] Step 3: Calculate the effect of journal deformation on critical oil film thickness

[0060] Considering the journal deformation under average pressure, the minimum clearance reduction h caused by the journal deformation is calculated using the Cortner formula. k As a calculation item for critical oil film thickness:

[0061] h k =1.595d{(l / d) 2 +1.8l}(l / d) 2 p m 10 -6 (2)

[0062]

[0063] In equations (2) and (3), h k p represents the minimum reduction in clearance caused by journal deformation, in μm. m d is the average pressure of the bearing bush, in Pa; d is the bearing diameter, in mm; l is the bearing bush length, in mm; W is the bearing bush load, in N.

[0064] Step 4: Calculate the bending deformation of the shaft and compare it with the circumferential cross-sectional tolerances of the journal and bearing shell.

[0065] The inflection of the axial elastic line within the bearing bush is related to the deflection of the entire span of the shaft outside the bearing bush; such as Figure 1 As shown, the inflection point of the axial elastic line in the bearing bush can be calculated according to equation (4):

[0066] h n =0.5lθ (4)

[0067] In equation (4), h n θ represents the inflection point of the axial elastic line within the bearing bush, in μm; l represents the bearing bush length, in mm; θ represents the deformation angle caused by the bending deformation of the shaft system, in radians.

[0068] The deformation angle θ caused by the bending deformation of the shaft system can be calculated based on the bending deformation in material mechanics, such as... Figure 2 As shown, for a commonly used double-supported bearing with concentrated loads acting between two bearings, the deformation angle θ caused by shaft bending deformation can be determined according to equations (5) and (6):

[0069]

[0070]

[0071] In equations (5) and (6), E is the elastic modulus of the shaft in GPa, and I is the moment of inertia in mm. 4 All values ​​were obtained by consulting the "Mechanics of Materials" handbook; F is the external load borne by the bearing, which is a known condition in the bearing design, and the unit is N; L is the bearing spacing, L1 is the distance between bearing B and the load application point, and L2 is the distance between bearing A and the load application point, which were obtained by measurement, and the unit is μm;

[0072] Compare h n with h i The larger of the two values ​​is used for calculation to make the critical oil film thickness calculation result relatively accurate.

[0073] Step 5: Calculate the critical oil film thickness

[0074] Calculate the critical oil film thickness according to formula (7);

[0075] h kp =h m +h b +h k +max{h n h i} (7)

[0076] In equation (7), h kp The critical oil film thickness is expressed in μm; h m h represents the micro-roughness height of the journal surface, in μm. b h represents the surface roughness height of the bearing bush, in μm. k h represents the minimum reduction in clearance caused by journal deformation, in μm. n h represents the bend of the axial elastic line within the bearing bush, measured in μm. i The tolerance deviation of the journal and bearing cross-section along the circumferential direction is expressed in μm.

[0077] The method of this invention comprehensively considers the machining roughness of the bearing bush and journal, the deformation of the journal under average pressure, calculates the deformation of the shaft system bending and compares it with the tolerance of the journal and bearing bush along the circumferential cross-section, taking the larger value as the calculation basis. Finally, the critical oil film thickness calculated according to formula (7) best fits the actual situation and is more accurate and reasonable than other methods. The calculation method of this invention can be used as the basis for calculating the critical oil film thickness in bearing design.

[0078] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. It will be apparent to those skilled in the art that the present invention is not limited to the details of the exemplary embodiments described above, and that the invention can be implemented in other specific forms without departing from its spirit or basic characteristics. Therefore, the embodiments should be considered exemplary and non-limiting in all respects, and the scope of the invention is defined by the appended claims rather than the foregoing description. Thus, it is intended that all variations falling within the meaning and scope of equivalents of the claims be included within the present invention.

[0079] Furthermore, it should be understood that although this specification describes embodiments, not every embodiment contains only one independent technical solution. This narrative style is merely for clarity. Those skilled in the art should consider the specification as a whole, and the technical solutions in each embodiment can also be appropriately combined to form other embodiments that can be understood by those skilled in the art.

Claims

1. A method of calculating a critical oil film thickness of a sliding bearing, characterized by: The critical oil film thickness of the sliding bearing is calculated by considering the machining roughness of the bearing bush and the shaft journal, the shaft journal deformation under the average pressure, the shaft system bending deformation, and the tolerance deviation of the shaft journal and the bearing bush along the circumferential cross section; According to the calculated minimum oil film thickness, the machining roughness of the bearing bush and the shaft journal is selected according to the standard as the calculation item of the critical oil film thickness; The shaft system bending deformation and the tolerance deviation of the shaft journal and the bearing bush along the circumferential cross section are compared, and the larger one is taken as the calculation item of the critical oil film thickness; The shaft journal deformation under the average pressure is considered, and the shaft journal deformation value is calculated as the calculation item of the critical oil film thickness; Finally, the calculation items are added up to obtain the critical oil film thickness of the sliding bearing; Specifically, the method comprises the following steps: Step 1: calculating the minimum oil film thickness according to the bearing parameters; h min = 0.5dψ(1 - x) (1) In formula (1), h min is the minimum oil film thickness, d is the shaft diameter, ψ is the bearing shell-to-shaft diameter relative clearance, and x is the eccentricity. Step 2: selecting the machining roughness of the bearing bush and the shaft journal according to the standard; According to the calculated minimum oil film thickness h min According to GB / T 39741.2-202 standard, determine the micro-roughness height h of the journal surface m And the tolerance deviation h of the circumferential cross section of the journal and the bearing bush i ; According to the measured bearing outer diameter, the bearing outer diameter is determined according to the GB / T7308.1-2021 standard, and the micro-roughness height h of the bearing bush surface is determined b ; Step 3: calculating the influence of the shaft journal deformation on the critical oil film thickness; Considering the deformation of the shaft neck under the average pressure, the minimum gap reduction value h caused by the deformation of the shaft neck is calculated according to the Cotterell formula k : h k = 1.595d{(l / d) 2 + 1.81}(l / d) 2 p m 10 -6 (2) In formula (2), (3), h k is the minimum gap reduction value caused by journal deformation, in units of μm; p m is the average bearing shell pressure, in units of Pa; d is the shaft diameter, in units of mm; l is the bearing shell length, in units of mm; and W is the bearing shell load, in units of N. Step 4: calculating the shaft bending deformation and comparing it with the tolerance deviation of the shaft journal and the bearing bush along the circumferential cross section; The turning of the shaft elastic line in the bearing bush is calculated according to formula (4): h n = 0.5 lθ (4) In formula (4), h n is the turning of the shaft elastic line in the bearing bush, in units of pm; l is the bearing bush length, in units of mm; and Q is the deformation angle caused by the shafting bending deformation, in units of radian. Compare h n With h i Take the larger of the two values for calculation; Step 5: calculating the critical oil film thickness; h kp = h m + h b + h k + max{h n , h i} (7) In formula (7), h kp is the critical oil film thickness; h m is the surface micro roughness height of the journal; h b is the surface micro roughness height of the bearing; h k is the minimum clearance reduction due to journal deformation; h n is the turning of the shaft elastic line in the bearing; h i is the circumferential cross section tolerance deviation of the journal and the bearing.

2. A method of calculating a critical oil film thickness of a sliding bearing according to claim 1, characterized in that: In step 4, for the double support bearing with concentrated load acting between two bearings, the deformation angle θ value caused by the shaft system bending deformation is determined according to formula (5) and (6): In formula (5), (6), E is the elastic modulus of the shaft, in GPa, I is the moment of inertia, in mm 4 F is the external load borne by the bearing, which is a known condition in bearing design, in N; L is the bearing spacing, L1 is the distance between bearing B and the load action point, and L2 is the distance between bearing A and the load action point, each obtained by measurement, in μm.

3. A method of calculating a critical oil film thickness of a sliding bearing according to claim 1, characterized in that: In step 2, h m Take the corresponding Ra value from the standard.

4. A method of calculating a critical oil film thickness of a sliding bearing according to claim 1, characterized in that: In step 2, h i Take the standard roundness tolerance t1 value.

5. A method of calculating a critical oil film thickness of a sliding bearing according to claim 1, characterized in that: In step 2, h b Take the corresponding bearing sliding surface Ra value in the standard.

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