Improved main shaft angular contact ball bearing thermal evaluation model

Abstract

The invention discloses an improved main shaft angular contact ball bearing thermal evaluation model, which comprises a thermal node Qb arranged on a rolling ball, and is characterized in that the thermal node Qb is connected with thermal nodes No1 and Ni1 arranged on the inner surface of an outer ring and the outer surface of an inner ring through thermal resistors Rb-o and Rb-i respectively; the hot nodes No1 and Ni1 are respectively connected with a hot node No2 arranged on the outer surface of the outer ring and a hot node Ni2 arranged on the inner surface of the inner ring through equivalent thermal resistors Ro and Ri, and the hot nodes No1 and Ni1 are respectively connected with a hot node Nc arranged in the cavity through thermal resistors Ro-c and Ri-c. The method introduces a bearing structure constraint evaluation function and a structure constraint factor, constructs the equivalent heat transfer resistance of the inner and outer rings of the bearing based on heat transfer equivalence, proposes an improved main shaft angular contact ball bearing thermal resistance network evaluation model considering the structure constraint influence, and improves the evaluation accuracy of the main shaft angular contact ball bearing under the condition of not reducing coupling factors and prediction precision. And the data overhead is effectively reduced.

Description

Technical Field

[0001] This invention relates to a thermal evaluation model for angular contact ball bearings, and more particularly to an improved thermal resistance network model for evaluating the heat transfer of spindle angular contact ball bearings. Background Technology

[0002] High-performance high-speed spindles are crucial for achieving high-speed machining. As the core supporting component of the spindle, bearing heat inevitably leads to degradation of spindle working accuracy and a reduction in service life. Accurately evaluating spindle bearing heat is a key step in controlling spindle thermal error and working accuracy, as well as improving spindle service life. An efficient thermal evaluation model is the core of bearing thermal evaluation. In current thermal evaluation of spindle bearings, the finite element method (FEM) and thermal resistance network (TRN) methods are widely used. While the FEM model can describe the heat transfer of spindle bearings in detail, it incurs significant data overhead. In contrast, the TRN model not only describes the heat transfer between various components of the spindle bearing in detail but also requires far less computation, thus possessing greater practical value in engineering. However, with the increasing demands for the predictive accuracy of TRN evaluation models, more thermally influencing factors are required to be coupled into the thermal evaluation of spindle bearings. Considering the significant impact of structural constraints on the heat transfer of spindle bearings, the structural constraints of the spindle bearing itself and its surroundings are extensively discussed and coupled in the thermal evaluation of spindle bearings. Consequently, the constructed thermal evaluation network for spindle bearings is becoming increasingly complex, and the data overhead is constantly increasing. For a fast and accurate thermal evaluation, it is necessary to evaluate the influence of structural constraints on the heat transfer of spindle bearings and, based on this, provide an efficient thermal evaluation model. Summary of the Invention

[0003] This invention addresses the shortcomings of current spindle bearing thermal evaluation methods by considering the impact of structural constraints on spindle bearing heat transfer. It constructs a structural constraint heat transfer evaluation function and proposes an improved bearing thermal resistance network heat transfer evaluation model based on the structural constraint heat transfer equivalence.

[0004] The technical solution to achieve the above objective is: an improved thermal evaluation model for a spindle angular contact ball bearing, comprising: a ball, a thermal node Qb disposed on the ball, the thermal node Qb being connected to thermal nodes No1 and Ni1 disposed on the inner surface of the outer ring and the outer surface of the inner ring respectively through thermal resistances Rb-o and Rb-i, the thermal node No1 being connected to the thermal node No2 disposed on the outer surface of the outer ring through thermal resistance Ro, and the thermal node Ni1 being connected to the thermal node Ni2 disposed on the inner surface of the inner ring through thermal resistance Ri; The thermal nodes No1 and Ni1 are connected to the thermal node Nc located in the cavity through thermal resistances Ro-c and Ri-c, respectively. The thermal node Nc is connected to the thermal node Ng located in the cage through thermal resistance Rg-c. The thermal node Ng is connected to the thermal node Nb through thermal resistance Rb-g. The thermal node Qb is connected to the thermal node Nc through thermal resistance Rb-c. The thermal node Nc is connected to the thermal node Tin located at the oil and gas inlet of the outer ring of the bearing through thermal resistance Rf. Ro and Ri are the equivalent thermal resistances used to evaluate the total axial and radial heat transfer capacity of the outer and inner rings of the bearing, respectively. The Ro-c and Ri-c mentioned above are the thermal resistances that respectively evaluate the convective heat transfer capacity between the inner surface of the outer ring and the outer surface of the inner ring of the bearing and the oil and gas fluid in the cavity. Rb-o and Rb-i are the thermal resistances that respectively evaluate the contact heat transfer capability between the outer ring and inner ring of the bearing and the rolling balls. Rb-o and Rb-i are the thermal resistances that respectively evaluate the contact heat transfer capability between the outer ring and inner ring of the bearing and the rolling balls. Rg-c and Rb-c are thermal resistances that respectively evaluate the convective heat transfer capacity between the bearing cage and the balls and the oil and gas fluid in the cavity. The Rf is the thermal resistance used to evaluate the heat carried away by the oil-gas fluid injected into the bearing cavity. The thermal node Nc is connected to the thermal node Tout located at the bearing oil and gas outlet, where Tout represents the outlet temperature of the oil and gas discharged from the bearing cavity.

[0005] Existing bearing multi-node models (see) Figure 2 In this model, the influence of axial structural constraints on bearing heat dissipation is coupled into the bearing's thermal evaluation, thus providing a more comprehensive assessment compared to existing seven-node models (see...). Figure 1 The number of nodes more than doubles, leading to a surge in data overhead. This invention introduces a bearing structural constraint evaluation function and a structural constraint factor, and constructs an equivalent thermal resistance network evaluation model for the inner and outer rings of the bearing based on heat transfer equivalence. It proposes an improved model that considers the influence of structural constraints on the thermal resistance network of the spindle angular contact ball bearing. Compared with existing multi-node bearing models, the number of thermal nodes in the bearing thermal resistance network is greatly reduced without reducing the bearing thermal influence factors, effectively reducing data overhead. Compared with the existing seven-node model, the axial structural constraints are coupled, resulting in higher accuracy in thermal evaluation.

[0006] The advantages of this invention are that when the improved spindle angular contact ball bearing thermal evaluation model proposed in this invention is used to create a spindle thermal evaluation network model, the spindle thermal evaluation network can be greatly simplified due to the introduction of structural constraint factors and equivalent thermal resistance, thereby greatly improving the efficiency of thermal evaluation and making it more suitable for engineering applications. Attached Figure Description

[0007] Figures 1 to 3 The following are, in order, the thermal resistance network planning diagrams of the seven-node heat transfer model of the bearing, the multi-node heat transfer model of the bearing, and the improved thermal resistance network evaluation model of the spindle angular contact ball bearing.

[0008] In the diagram: ball (1), outer ring (2), inner ring (3), cage (4); Qb(5), No1(6), No2(7), Nc(8), Ni1(9), Ni2(10), Ng(11), Tin(12), Tout(13); Ri(20), Rb-o(21), Ro(22), Ro-c(23), Rf(24), Rb-c(25), Rb-g(26), Rg-c(27), Ri-c(28), Rb-i(29). Detailed Implementation

[0009] The invention will now be further described with reference to the accompanying drawings.

[0010] like Figure 3 As shown, an improved thermal evaluation model for a spindle angular contact ball bearing includes: a ball (1), a thermal node Qb (5) disposed on the ball (1), the thermal node Qb (5) being connected to thermal nodes No1 (6) and Nil (9) disposed on the inner surface of the outer ring (2) and the outer surface of the inner ring (3) respectively through thermal resistances Rb-o (21) and Rb-i (29), the thermal node No1 (6) being connected to the thermal node No2 (7) disposed on the outer surface of the outer ring (2) through thermal resistance Ro (22), and the thermal node Nil (9) being connected to the thermal node Ni2 (10) disposed on the inner surface of the inner ring (3) through thermal resistance Ri (20); The hot nodes No1 (6) and Ni1 (9) are connected to the hot node Nc (8) in the cavity through thermal resistances Ro-c (23) and Ri-c (28), respectively. The hot node Nc (8) is connected to the hot node Ng (11) in the cage (4) through thermal resistance Rg-c (27). The hot node Ng (11) is connected to the hot node Qb (5) through thermal resistance Rb-g (26). The hot node Nb (5) is connected to the hot node Nc (8) through thermal resistance Rb-c (25). The hot node Nc (8) is connected to the hot node Tin (12) in the oil and gas inlet of the bearing outer ring through thermal resistance Rf (24). The meanings of the hot nodes marked in the attached figure are shown in Table 1.

[0011] Table 1 Hot Node Settings

[0012]

[0013] The thermal resistance settings shown in the attached figure are illustrated in Table 2.

[0014] Table 2 Thermal Resistance Settings

[0015]

[0016] Ro(22) and Ri(20) are equivalent thermal resistances. Based on the equivalent total axial and radial heat transfer of the bearing, the calculation models for the thermal resistances Ro(22) and Ri(20), which represent the total axial and radial heat transfer capacity of the bearing, are as follows: In the formula, d ext and d int These are the outer diameter and inner diameter of the bearing's inner / outer rings, respectively, k D Where P is the thermal conductivity of the inner / outer ring material of the bearing, L is the thermal conductivity width of the inner / outer ring of the bearing, and P is the thermal conductivity of the inner / outer ring material. D R is the structural constraint factor. rth The radial thermal resistance of the bearing inner / outer ring; The R rth Calculate using the following formula: R = ln(d ext / d int ) / 2πk Dr L (2) The structural constraint factor P D The influence of axial and radial structural constraints on the bearing's heat dissipation capacity was considered, and the calculation was performed using the structural constraint evaluation function shown in the following formula: In the formula, A r A a These are the radial outer surface area and end area of ​​the inner / outer rings of the bearing, respectively.

[0017] The thermal resistances Rb-o(21) and Rb-i(29) are calculated with reference to the following contact heat transfer model: 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.

[0018] The thermal resistances Ri-c(28), Ro-c(23), and Rb-c(25) are solved by the following formula for thermal convection resistance: In the formula, A w k is the convective heat transfer area. Df L is the thermal conductivity of air. f Where is the natural length of thermal convection, and Nu is the Nusselt number; The Nusselt numbers corresponding to the thermal resistances Ri-c(28), Ro-c(23), and Rb-c(25) are calculated with reference to Table 3 below.

[0019] Table 3 Nusselt Number Calculation

[0020]

[0021] The thermal resistance Rf(24) is calculated using the following formula: In the formula, ρ eff Let q be the density of the oil and gas fluid. oilair C represents the flow rate of oil and gas fluids. p Specific heat of oil and gas fluids.

[0022] The thermal resistance Rg-c(27) is calculated using the following formula: In the formula, L c-s and L c-r These are the thickness and width of the cage, respectively; A c-s A c-o and A c-i These are the cage end area, radial outer surface area, and radial inner surface area, respectively; K Doil-air It is the thermal conductivity of the oil-gas fluid inside the bearing cavity.

[0023] The bearing heat generated by Qb(5) is calculated using the following formula: In the formula, ω r It is the spindle rotational angular velocity; f1 is the load coefficient; P1 is the calculated load; d m This corresponds to the bearing pitch circle diameter; M v The frictional torque caused by the viscosity of the lubricant is calculated as follows: In the formula, f0 is a coefficient that depends on the bearing type and lubrication method, v is the dynamic viscosity of the lubricant, and n is the spindle speed.

Claims

1. An improved thermal evaluation model for spindle angular contact ball bearings, characterized in that, It includes: A rolling ball (1) is provided with a hot node Qb (5). The hot node Qb (5) is connected to the hot nodes No1 (6) and Ni1 (9) provided on the inner surface of the outer ring (2) and the outer surface of the inner ring (3) respectively through thermal resistances Rb-o (21) and Rb-i (29). The hot nodes No1 (6) and Ni1 (9) are connected to the hot node No2 (7) provided on the outer surface of the outer ring (2) and the hot node Ni2 (10) provided on the inner surface of the inner ring (3) respectively through thermal resistances Ro (22) and Ri (20). The hot node Nc(8) placed in the cavity is connected to the hot nodes No1(6), Ni1(9), Qb(5) and the hot node Ng(11) set on the cage (4) through thermal resistances Ro-c(23), Ri-c(28), Rb-c(25) and Rg-c(27), respectively. The hot node Tin(12) set on the oil and gas inlet of the outer ring of the bearing is connected to Nc(8) through thermal resistance Rf(24) and the hot node Tout(13) set on the oil and gas outlet of the bearing, representing the outlet temperature of the oil and gas fluid discharged from the bearing cavity. Ro(22) and Ri(20) are equivalent thermal resistances. Based on the equivalent total axial and radial heat transfer of the bearing, the calculation models for the thermal resistances Ro(22) and Ri(20), which represent the total axial and radial heat transfer capacity of the bearing, are as follows: In the formula, d ext and d int These are the outer diameter and inner diameter of the bearing's inner / outer rings, respectively, k D Where P is the thermal conductivity of the inner / outer ring material of the bearing, L is the thermal conductivity width of the inner / outer ring of the bearing, and P is the thermal conductivity of the inner / outer ring material. D R is the structural constraint factor. rth The radial thermal resistance of the bearing inner / outer ring; The structural constraint factor P D The influence of axial and radial structural constraints on the bearing's heat dissipation capacity was considered, and the calculation was performed using the structural constraint evaluation function shown in the following formula: In the formula, A r A a These are the radial outer surface area and end area of ​​the inner / outer rings of the bearing, respectively.

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