Bearing thermal evaluation network considering influence of oil film on contact heat transfer between ball and channel

Abstract

The invention discloses a bearing thermal evaluation network considering the influence of an oil film on ball-channel contact heat transfer, which comprises a thermal node Qb arranged on a rolling ball, the Qb is respectively connected with a thermal node No1 and a thermal node Ni1 through thermal resistors Reb-o and Reb-i, the No1 is connected with a thermal node No2 through a thermal resistor Ro1, the No2 is respectively connected with thermal nodes No3, No4 and No5 arranged on an outer ring through thermal resistors Ro2, Ro3 and Ro4, and the thermal nodes No3, No4 and No5 are respectively connected with the thermal nodes No1, No2, No3, No4 and No5 through thermal resistors Reb-o and Reb-i. Ni1 is connected with a hot node Ni2 through a thermal resistor Ri1, the hot node Ni2 is respectively connected with hot nodes Ni3, Ni4 and Ni5 arranged on an inner ring through thermal resistors Ri2, Ri3 and Ri4, and Qb is connected with a hot node Nc through a thermal resistor Rb-c. According to the method, relative movement between the bearing lubricating oil film and the rolling ball and between the rolling ball and the inner ring and the outer ring rolling path is considered, an equivalent contact heat transfer model between the bearing rolling ball and the channel is constructed, a bearing heat network model coupled with the influence of the lubricating oil film is established, and the contact heat transfer between the bearing rolling ball and the channel and bearing heating are further accurately and comprehensively evaluated.

Description

Technical Field

[0001] This invention relates to a contact heat transfer model between a bearing ball and its raceway, and more particularly to a heat transfer model of an angular contact ball bearing thermal resistance network that considers the influence of the lubricating oil film. Background Technology

[0002] Angular contact ball bearings, as typical support components, are widely used in various applications, and their service accuracy and lifespan are closely related to their thermal characteristics. The introduction of Hertzian elastic contact theory has laid a solid foundation for the quasi-static and dynamic analysis of ball bearings. Based on this, scholars have successively conducted research on bearing load / torque, ball-raceway rolling / sliding friction, dynamic characteristics of rolling elements and cage, and bearing-raceway contact heat transfer under different operating conditions. Simultaneously, a large number of studies on heat dissipation mechanisms and evaluation have also been carried out. Among the many studies related to bearing temperature, given its significant impact on heat dissipation performance, the contact heat transfer problem between components has also attracted widespread attention from researchers. Based on Gaussian equations and fractal theory, researchers have proposed several empirical models for calculating the thermal contact resistance between solid-solid contact surfaces. To accurately describe the actual contact state between components, the surface morphology of the workpiece is often simulated using functions such as the WM formula. Meanwhile, the influence of fractal dimension and amplitude coefficient on contact heat transfer has also been explored. Lubrication is widely used as an effective means of reducing bearing friction, wear, and vibration. Numerous studies have explored the morphology, load, and stiffness variations of oil films under different operating conditions, and have experimentally measured and modeled oil film thickness. Meanwhile, many scholars have dedicated themselves to studying the influence of oil films on bearing thermal properties. The impact of lubrication on the thermodynamic properties of ball bearings (friction, wear, temperature rise, stiffness, damping, etc.) has been extensively discussed, and oil film thickness, as a key parameter for accurate thermodynamic characterization of bearings, has been evaluated through theoretical and experimental methods. Furthermore, existing research has incorporated bearing-racene contact and shaft-bearing contact into the analysis of bearing heat dissipation, and established mathematical models of the influence of ball-raceway Hertzian contact on heat transfer. However, current research remains incomplete. To date, a systematic description of heat transfer between ball and raceway contacts is lacking, particularly neglecting the role of the oil film in the contact area during bearing thermal conduction. To accurately characterize the thermal changes of bearings, it is necessary to evaluate the influence of the oil film in the ball-groove contact area on the heat transfer of the bearing and provide an equivalent thermal evaluation model accordingly. Summary of the Invention

[0003] This invention addresses the shortcomings of current bearing thermal evaluation by constructing an equivalent thermal resistance network model between the bearing ball and raceway, considering the relative motion between the oil film, rolling elements, and raceway. It also proposes a heat transfer model for angular contact ball bearings that takes into account the influence of the lubricating oil film.

[0004] The technical solution to achieve the above objective is: a bearing thermal evaluation network considering the influence of oil film on the contact heat transfer between the ball and the raceway, comprising: rolling balls, and thermal nodes Q disposed on the rolling balls. b Hot node Q b Through thermal resistance R respectively cb-o and R cb-i With thermal nodes N respectively located on the inner surface of the outer ring and the outer surface of the inner ring. o1 and N i1 Connected, hot node N o1 Through thermal resistance R o1 With the thermal node N located inside the outer ring o2 Connected, hot node N o2 Through thermal resistance R o2 With the thermal node N set on the outer surface of the outer ring o3 Connected, hot node N o2 Through thermal resistance R respectively o3 and R o4 Respectively connected to the thermal nodes N located at both ends of the outer ring. o4 and N os Connected; The hot node N i1 Through thermal resistance R i1 With the thermal node N located in the inner ring (3) i2 Connected, hot node N i2 Through thermal resistance R i2 With the thermal node N located on the inner surface of the inner ring i3 Hot node N i2 Through thermal resistance R respectively i3 and R i4 Respectively connected to the thermal nodes N located at both ends of the inner ring. i4 and N i5 Connected; The hot node Q b Through thermal resistance R b-c The thermal node N, located within the bearing cavity, represents the cavity temperature. c Connected, hot node N c By passing through the thermal resistance R respectively oil and R air With hot node T in Connected, hot node N c Through thermal resistance R g-c With the thermal node N located on the cage g Connected, hot node N g Through thermal resistance R b-g With hot node Q b Connected; The hot node N o1 and N i1 Through thermal resistance R respectively o-c and Ri-c With hot node N c Connected; The R cb-o The equivalent thermal resistance for heat transfer between the bearing balls and the outer raceway is given by the thermal resistance R. ωbo R ωRo R oildo and R cbo The R ωbo R ωRo and R oildo After parallel connection with R cbo Series; The R cb-i The equivalent thermal resistance for heat transfer between the bearing balls and the inner raceway is given by the thermal resistance R. ωbi R ωRi R oildi and R cbi The R ωbi R ωRi and R oildi After parallel connection with R cbi Series; The hot node N c With the thermal node T located at the bearing oil and gas outlet out Connected, the T out This represents the outlet temperature of the oil and gas flow discharged from the bearing cavity.

[0005] In existing bearing heat transfer models, the contact heat transfer between the rolling balls and the inner and outer ring raceways widely adopts the Hertz contact heat transfer model under unlubricated conditions, without considering the influence of the lubricating oil film on the contact heat transfer between the rolling balls and the inner and outer ring raceways. This invention considers the lubricating oil film and the relative motion between the rolling balls and the inner and outer ring raceways, and establishes a thermal resistance model R. ωRi and R ωRo To evaluate the heat exchange between the ball and the oil film during pure rolling along the inner and outer raceways, a thermal resistance model R was established. ωbi and R ωbo To evaluate the convective heat exchange between the ball and the inner and outer oil films during the ball's spin motion, the thermal resistance R... oildi and R oildo This indicates the radial thermal conductivity of the inner and outer ring oil films, further accurately evaluating the influence of the oil film on the contact thermal resistance between the bearing balls and the raceway.

[0006] This invention considers the heat exchange caused by the relative motion between the bearing lubricating oil film and the inner and outer raceways, and further integrates Hertz contact heat transfer between the balls and raceways, thereby increasing R... ωRi R ωbi and R oildi After parallel connection with thermal resistance R cbiTo calculate the equivalent contact thermal resistance between the rolling ball and the inner groove in series, R ωRo R ωbo and R oildo After parallel connection with thermal resistance R cbo The equivalent contact thermal resistance between the rolling balls and the outer ring raceway was calculated by cascading the series connection, which accurately and comprehensively evaluated the contact heat transfer between the bearing rolling balls and the raceway.

[0007] This invention utilizes the equivalent thermal resistance R cb-o and R cb-i The influence of the lubricating oil film on the contact heat transfer between the bearing balls and raceways was coupled into the bearing heat generation evaluation. A bearing heat generation evaluation network model coupled with the influence of the lubricating oil film was constructed, which further accurately evaluated the bearing heat generation. Attached Figure Description

[0008] Figures 1 to 3 The following are, in order: bearing heat transfer model considering the influence of lubricating oil film, equivalent thermal resistance network between bearing ball and outer groove, and equivalent thermal resistance network between bearing ball and inner groove.

[0009] In the diagram: ball (1), outer ring (2), inner ring (3), cage (4); Q b (5), N o1 (6), N o2 (7), N o3 (8), N o4 (9), N o5 (10), N i1 (11), N i2 (11), N i3 (13), N i4 (14), N i5 (15), N g (16), T in (17), T out (18), N c (19); R eb-o (21), R o1 (22), R o2 (23), R o1 (22), R o3 (24), R o4 (25); R o-c (26), R b-g (27), R g-c (28), R oil (29), R air (30); R eb-i (31), R i1(32), R i3 (34), R i4 (35), R i-c (36), R b-c (37); N o21 (41), N o22 (42), N o23 (43), N o24 (44); R ωbo (51), R ωRo (52), R oildo (53), R cbo (54); R ωb i(55), R ωRi (56), R oildi (57), R cbi (58); Detailed Implementation

[0010] The invention will now be further described with reference to the accompanying drawings.

[0011] like Figure 3 As shown, a bearing thermal evaluation network considering the influence of oil film on contact heat transfer between the ball and the raceway includes: a rolling ball (1), and a thermal node Q disposed on the rolling ball (1). b (5), hot node Q b (5) Pass through the thermal resistance R respectively cb-o (21) and R cb-i (31) and thermal nodes N respectively located on the inner surface of the outer ring (2) and the outer surface of the inner ring (3). o1 (6) and N i1 (11) Connected, hot node N o1 (6) Through thermal resistance R o1 (22) and the thermal node N located in the outer ring (2) o2 (7) Connected, hot node N o2 (7) Through thermal resistance R o2 (23) and the thermal node N set on the outer surface of the outer ring (2) o3 (8) Connected, hot node N o2 (7) Pass through the thermal resistance R respectively o3 (24) and R o4 (25) respectively connected to the hot nodes N set at both ends of the outer ring (2) o4 (9) and N o5 (10) Connected; The hot node Ni1(11) is connected to the thermal resistance R. i1 (32) and the thermal node N located in the inner ring (3) i2(12) Connected, hot node N i2 (12) Through thermal resistance R i2 (33) and the thermal node N located on the inner surface of the inner ring (3) i3 (13), hot node N i2 (12) Pass through thermal resistance R respectively i3 (34) and R i4 (35) respectively connected to the hot nodes N set at both ends of the inner ring (3) i4 (14) and N is (15) Connected; The hot node Q b (5) Through thermal resistance R b-c (37) and the thermal node N, which represents the cavity temperature, located in the bearing cavity. c (19) Connected, hot node N c (19) By passing through the thermal resistance R respectively oil (29) and R air (30) and hot node T in (17) Connected, hot node N c (19) Through thermal resistance R g-c (28) and the thermal node N set on the cage (4) g (16) Connected, hot node N g (16) Through thermal resistance R b-g (27) Connected to hot node Qb(5); The hot node N o1 (6) and N i1 (11) Pass through thermal resistance R respectively o-c (26) and R i-c (36) and hot node N c (19) Connected, hot node N c (19); The R eb-o (21) is the equivalent thermal resistance for heat transfer between the bearing balls and the outer raceway, which includes the thermal resistance R. ωbo (51), R ωRo (52), R oildo (53) and R cbo (54); The R ωbo (51), R ωRo (52) and R oildo (53) After parallel connection with R cbo (54) Series connection; The R cb-i (31) is the equivalent thermal resistance for heat transfer between the bearing balls and the inner raceway, which includes the thermal resistance R. ωbi (55), R ωRi (56), R oildi(57) and R cbi (58); The R ωbi (55), R ωRi (56) and R oildi (57) After parallel connection with R cbi (58) Series connection; The hot node N c (19) and the thermal node T located at the bearing oil and gas outlet out (18) Connected, the T ou t(18) represents the outlet temperature of the oil and gas flow discharged from the bearing cavity.

[0012] The thermal resistance settings shown in the attached figure are as shown in Table 1.

[0013] Table 1 Thermal Resistance Settings

[0014]

[0015] The R ωRi (56) and R ωR0 (52) is the convective heat transfer resistance between the rolling ball (1) and the inner and outer oil films due to pure rolling. It is calculated according to the following model: In the formula, h v It is the convective heat transfer coefficient. It is the thermal conductivity of the oil film, L is the characteristic length, and A is the characteristic length. e Let A be the elliptical contact area between the rolling ball and the groove. e The calculation formula is as follows: A e =a·b (2) In the formula, a is the major semi-axis of the contact ellipse, b is the minor semi-axis of the contact ellipse, and Nu... oil It is the Nusselt number of the lubricating oil film, Nu oil The calculation formula is as follows: In the formula, R e It is the Reynolds number of the oil film, P r It is the Prandtl number of the oil film.

[0016] The R ωbo (51) and R ωbi (55) is used to represent the heat exchange caused by the spin of the bearing balls, and its corresponding Nusselt number Nu is calculated with reference to the following model: In the formula, R e is the Reynolds number of the oil film, and Pe is the Pelet number of the oil film.

[0017] The thermal resistance Roildi (57) and R oildo (53) represents the radial thermal resistance of the inner and outer ring oil films, which is calculated according to the following model: In the formula, h0 is the thickness of the contact oil film between the ball and the groove, and A e Let be the elliptical contact area between the ball and the groove. It refers to the thermal conductivity of lubricating oil.

[0018] The thermal resistance R ebi (58) and R cbo (54) Calculate using the following formula: In the formula: a is the major semi-axis of the contact ellipse, b is the minor semi-axis of the contact ellipse, and P e This represents the Peckle number of the oil film. It is the thermal conductivity of the oil film.

Claims

1. A bearing thermal evaluation network considering the influence of oil film on ball-groove contact heat transfer, characterized in that, It includes: Rolling ball (1), located at the hot node Q of rolling ball (1) b (5), hot node Q b (5) Pass through the thermal resistance R respectively eb-o (21) and R eb-i (31) and thermal nodes N respectively located on the inner surface of the outer ring (2) and the outer surface of the inner ring (3). o1 (6) and N i1 (11) Connected, hot node N o1 (6) Through thermal resistance R o1 (22) and the thermal node N located in the outer ring (2) o2 (7) Connected, hot node N o2 (7) Through thermal resistance R o2 (23) and the thermal node N set on the outer surface of the outer ring (2) o3 (8) Connected, hot node N o2 (7) Pass through the thermal resistance R respectively o3 (24) and R o4 (25) respectively connected to the hot nodes N set at both ends of the outer ring (2) o4 (9) and N o5 (10) Connected; the hot node N i1 (11) Through thermal resistance R i1 (32) and the thermal node N located in the inner ring (3) i2 (12) Connected, hot node N i2 (12) Through thermal resistance R i2 (33) and the thermal node N located on the inner surface of the inner ring (3) i3 (13), hot node N i2 (12) Pass through thermal resistance R respectively i3 (34) and R i4 (35) respectively connected to the hot nodes N set at both ends of the inner ring (3) i4 (14) and N i5 (15) Connected; The hot node Q b (5) Through thermal resistance R b-c (37) and the thermal node N, which represents the cavity temperature, is located in the bearing cavity. c (19) Connected, hot node N c (19) By passing through the thermal resistance R respectively oil (29) and R air (30) and hot node T in (17) Connected, hot node N c (19) Through thermal resistance R g-c (28) and the thermal node N set on the cage (4) g (16) Connected, hot node N g (16) Through thermal resistance R b-g (27) with hot node Q b (5) Connected; the hot node N o1 (6) and N i1 (11) Pass through thermal resistance R respectively o-c (26) and R i-c (36) and hot node N c (19) Connected, hot node N c (19); The R eb-o (21) is the equivalent thermal resistance for heat transfer between the bearing balls and the outer raceway, which includes the thermal resistance R. ωbo (51), R ωRo (52), R oildo (53) and R cbo (54); The R ωbo (51), R ωRo (52) and R oildo (53) After parallel connection with R cbo (54) Series connection; The R eb-i (31) is the equivalent thermal resistance for heat transfer between the bearing balls and the inner raceway, which includes the thermal resistance R. ωbi (55), R ωRi (56), R oildi (57) and R cb i(58); the R ωbi (55), R ωRi (56) and R oildi (57) After parallel connection with R cbi (58) Series connection; The thermal resistance R ωRi (56) and R ωRo (52) is the convective heat transfer resistance between the rolling ball (1) and the inner and outer oil films due to pure rolling. It is calculated according to the following model: In the formula, h V It is the convective heat transfer coefficient. Where A is the thermal conductivity of the oil film, L is the characteristic length, and A is the thermal conductivity of the oil film. e Let A be the elliptical contact area between the rolling ball and the groove. e The calculation formula is as follows: A e =a·b In the formula, a is the major semi-axis of the contact ellipse, b is the minor semi-axis of the contact ellipse, and Nu... oil It is the Nusselt number of the lubricating oil film, Nu oil The calculation formula is as follows: In the formula, R e It is the Reynolds number of the oil film, P r It is the Prandtl number of the oil film; The R ωbo (51) and R ωbi (55) is used to represent the heat exchange caused by the spin of the bearing balls, and its corresponding Nusselt number Nu is calculated with reference to the following model: In the formula, R e is the Reynolds number of the oil film, and Pe is the Pelet number of the oil film. The thermal resistance R oildi (57) and R oildo (53) represents the radial thermal resistance of the inner and outer ring oil films, which is calculated according to the following model: In the formula, h0 is the thickness of the contact oil film between the ball and the groove, and A e Let be the elliptical contact area between the ball and the groove. It refers to the thermal conductivity of lubricating oil. The thermal resistance R cbi (58) and R cbo (54) Calculate using the following formula: In the formula: a is the major semi-axis of the contact ellipse, b is the minor semi-axis of the contact ellipse, and Pe is the Pelet number of the oil film. It is the thermal conductivity of the oil film.

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