Connecting structure of shaft, bushing and bearing inner ring and calculation method of raceway deformation of shaft, bushing and bearing inner ring
By precisely controlling the interference fit and clearance fit of the shaft, bushing and bearing inner ring, the problem of efficient and accurate calculation of bearing inner ring raceway deformation is solved, realizing the precise design of mechanical systems, and is suitable for high-precision transmission equipment and heavy-duty machinery.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-12-03
- Publication Date
- 2026-04-10
AI Technical Summary
Existing technologies cannot efficiently and accurately calculate bearing inner ring raceway deformation under complex installation and usage conditions. In particular, calculations are time-consuming and inefficient in mechanical system design, making it difficult to meet the requirements of short design cycles and fast parameter optimization response.
This paper provides a connection structure of a shaft, bushing, and bearing inner ring and a method for calculating its deformation. By accurately controlling the interference fit and clearance fit of the shaft, bushing, and bearing inner ring, and combining the preload characteristics of the interference fit and the dynamic stress law of the clearance fit, the deformation of the bearing inner ring raceway is calculated.
It enables efficient and accurate calculation of bearing inner ring raceway deformation, avoiding calculation deviations caused by neglecting the details of the fit in traditional methods. It provides an efficient tool for the precise design of mechanical systems, and has practical value, especially in high-precision transmission equipment and heavy-duty machinery.
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Figure CN121828344A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to a method for calculating the deformation of raceways in shafts, bushings, and bearing inner rings, specifically to a connection structure for shafts, bushings, and bearing inner rings, and a method for calculating the deformation of raceways in shafts, bushings, and bearing inner rings. This invention belongs to the field of bearing technology. Background Technology
[0002] In mechanical system design, a bushing structure is usually added between the bearing inner ring and the shaft to accommodate the assembly tolerances of the bearing and the shaft, and to ensure the installation feasibility and assembly accuracy of related components. Although this bushing can solve the assembly compatibility problem, it makes the stress and deformation system of the bearing inner ring more complex.
[0003] Specifically, the deformation of the bearing inner ring raceway is influenced by a combination of factors: First, the fit between the shaft, bushing, and bearing inner ring (such as interference fit or transition fit) generates an initial assembly preload, which acts directly on the bearing inner ring. Second, temperature fluctuations during system operation cause differences in the coefficients of thermal expansion between components, resulting in thermal stress, which, combined with the assembly preload, forms a composite stress field. Third, the rotational speed of the shaft introduces centrifugal loads and dynamic impact loads, further altering the stress state of the bearing inner ring. The superposition of these multiple forces leads to a highly nonlinear deformation of the bearing inner ring raceway, and its precise quantification has become a key technical bottleneck in mechanical system design.
[0004] In existing technologies, the only feasible solution for calculating the deformation of the bearing inner ring raceway under such complex working conditions is the finite element analysis method. However, this method requires the construction of a refined three-dimensional solid model, has stringent requirements on the density and quality of the mesh, and requires convergence through a large number of iterative calculations. This not only places high demands on the computing power of the computing hardware but also suffers from drawbacks such as long computation time and low efficiency. Especially in the rapid iterative verification scenario during the mechanical system design phase, it is difficult to meet the practical engineering requirements of short design cycles and fast parameter optimization response.
[0005] In summary, there is currently no analytical calculation method in the field of bearing inner ring raceway that can comprehensively consider the coupling effect of shaft and bushing and the influence of multiple working conditions (fitting, temperature, speed). It is impossible to achieve efficient and accurate calculation of bearing inner ring raceway deformation under complex installation and use conditions. There is an urgent need to propose new technical solutions to fill this technical gap. Summary of the Invention
[0006] This invention aims to address the problem that traditional calculation methods for bearing inner ring raceway deformation analysis cannot achieve efficient and accurate calculation of bearing inner ring raceway deformation under complex installation and usage conditions. Therefore, it provides a connection structure of shaft, bushing, and bearing inner ring, as well as a calculation method for the deformation of shaft, bushing, and bearing inner ring raceway.
[0007] To address the aforementioned problems, this application provides the following technical solution:
[0008] A shaft, bushing, and bearing inner ring connection structure, comprising a shaft, bushing, and bearing inner ring;
[0009] The shaft is inserted into the bushing, and the bushing is inserted into the inner ring of the bearing. The shaft is hollow.
[0010] A connection structure for a shaft, bushing, and bearing inner ring is provided, wherein the shaft and bushing have a clearance fit or an interference fit, and the bushing and bearing inner ring have a clearance fit or an interference fit. The basic dimension of the shaft's inner bore is d. s The basic outer diameter of the shaft is d. c The basic inner diameter of the bushing is d. c The basic outer diameter of the bushing is e, the basic inner diameter of the bearing inner ring is d, and the raceway diameter of the bearing inner ring is d. i The flange diameter of the bearing inner ring is d. b The equivalent outer diameter of the bearing inner ring is d. e .
[0011] A method for calculating the deformation of the raceway of shafts, bushings, and bearing inner rings, the method being implemented according to the following steps:
[0012] Step 1: Install the shaft, bushing, and bearing inner ring sequentially from the inside out.
[0013] The initial geometric fit between the shaft and the bushing is denoted as f. sc The initial geometric fit between the bearing inner ring and the bushing is denoted as f. ic ,
[0014] The equivalent outer diameter d of the bearing inner ring e The calculation using the average value method is expressed as follows:
[0015] d e =(d i +d b ) / twenty one)
[0016] Step 2: Simplify the shaft, bushing, and bearing inner ring into rings A, B, and C, respectively;
[0017] When there is an interference fit between the shaft and the bushing, the initial geometric fit amount f between the shaft and the bushing sc <0, the initial fitting pressure between their mating surfaces is P a ,
[0018] When there is an interference fit between the bearing inner ring and the bushing, the initial geometric fit amount f between the bearing inner ring and the bushing is... ic When <0, the mating pressure between the mating surfaces is P. b
[0019] When interference fits are used between the shaft and bushing, and between the bushing and the bearing inner ring, the interaction forces between the shaft and bushing, and between the bushing and the bearing inner ring, are superimposed, increasing the pressure on the mating surfaces between the rings. At this point, the mating pressure between ring A and ring B increases from P... a The pressure between ring B and ring C changes to P1, and the fitting pressure between them changes from P to P1. b It becomes P2;
[0020] Step 3: When f sc When <0, the initial geometric fit amount f between ring A and ring B is... sc The fitting pressure P between ring A and ring B a The relationship is:
[0021]
[0022] When f ic When <0, the initial geometric fit amount f between ring B and ring C ic The mating pressure P between ring B and ring C a The relationship is:
[0023]
[0024] In the formula, E s E c E i These are the elastic moduli of the shaft, bushing, and bearing inner ring, respectively. s u C u i These are the Poisson's ratios for the shaft, bushing, and bearing inner ring, respectively.
[0025] Step 4: When f sc <0 and f ic When >0, if the pressure P is applied a Below, the change in the outer diameter of ring B is After the three rings are assembled, the fit between ring B and ring C changes from clearance to interference, i.e., P2>0. P2 = 0,
[0026]
[0027] When f sc >0 and f ic When <0, if the pressure P is applied b Below, the change in the inner diameter of ring B is: After the three rings are assembled, the fit between ring A and ring B changes from clearance to interference, i.e., P1>0. P1 = 0,
[0028]
[0029] When the fitting pressure P1>0 and the fitting pressure P2>0, the change in the outer diameter of ring A under pressure P1 is: The change in the inner diameter of ring C under pressure P2 is: The change in the inner diameter of ring B under pressures P1 and P2 is: The change in outer diameter is Calculate using the following formula:
[0030]
[0031] Change in outer diameter of ring A Change in the inner diameter of ring C Change in the inner diameter of ring B Change in the outer diameter of ring B The fit between the initial geometry of ring A and ring B is f. sc The initial geometric fit between ring B and ring C is f. ic The relationship between them is:
[0032]
[0033] The center diameter d of ring B M for:
[0034] d M =(d c +d) / 2 (11)
[0035] If we ignore ring C and only consider the fitting pressure P between ring A and ring B, a The center diameter d of ring B M Generate diameter change for:
[0036]
[0037] If we ignore ring A and only consider the fitting pressure P between ring C and ring B, b The center diameter d of ring B M Generate diameter change for:
[0038]
[0039] When the three rings are interference-fitted together, the center diameter d of ring B is... M Generate diameter change for:
[0040]
[0041] The relationship between them can be approximated as follows:
[0042]
[0043] Solving equations (10) and (15) simultaneously yields the initial geometric fit between rings A and B as f. sc The initial geometric fit between ring B and ring C is f. ic The fitting pressure P1 between lower ring A and ring B and the fitting pressure P2 between ring B and ring C.
[0044] The fitting pressure P2 between the bearing inner ring and the bushing, relative to the bearing inner ring raceway diameter d, can be calculated using the following formula. i diameter change δ Pdi for:
[0045]
[0046] The above process describes the calculation method for the deformation of the shaft, bushing, and bearing inner ring raceway.
[0047] The technical advantages of this application compared to existing technologies are as follows:
[0048] 1. This solution addresses the problems of complex and inefficient calculation of bearing inner ring raceway deformation in existing technologies. Its core breakthrough lies in achieving a technological breakthrough through precise control of the interference fit and clearance fit between the shaft, bushing, and bearing inner ring. Compared to traditional finite element methods, this solution offers significant advantages. In terms of fit optimization, this solution avoids calculation errors caused by neglecting the details of fit conditions in existing technologies.
[0049] 2. Based on the preload characteristics of interference fit and the dynamic force law of clearance fit, this application solves the problem of insufficient accuracy caused by the lack of consideration of fit relationship in traditional analytical methods through the fit of shaft-bulb-bearing inner ring, and provides a reliable basis for deformation calculation.
[0050] 3. The calculation method for the deformation of shafts, bushings and bearing inner ring raceways provided in this application provides an efficient tool for the precise design of bearing assembly in mechanical systems. It has strong practical value and broad prospects for promotion, especially in fields such as high-precision transmission equipment and heavy-duty machinery where the requirements for fitting accuracy are stringent. Attached Figure Description
[0051] Figure 1 This is a schematic diagram of the structure of the shaft, bushing, and bearing inner ring of the present invention;
[0052] Figure 2This is a simplified schematic diagram of the shaft 1, bushing 2, and bearing inner ring 3 of the present invention, which are respectively represented as ring A4, ring B5, and ring C6. Detailed Implementation
[0053] Combination Figure 1 This embodiment describes a connection structure for a shaft, bushing, and bearing inner ring, which includes a shaft 1, a bushing 2, and a bearing inner ring 3.
[0054] Shaft 1 is inserted into bushing 2, and bushing 2 is inserted into bearing inner ring 3. Shaft 1 is a hollow shaft.
[0055] Combination Figure 1 As shown, shaft 1 and bushing 2 have a clearance fit or an interference fit, and bushing 2 and bearing inner ring 3 have a clearance fit or an interference fit. The basic dimension of the inner hole of shaft 1 is d. s The basic outer diameter of shaft 1 is d. c The basic inner diameter of bushing 2 is d. c The basic outer diameter of bushing 2 is d, the basic inner diameter of bearing inner ring 3 is d, and the raceway diameter of bearing inner ring 3 is d. i The flange diameter of the inner ring 3 of the bearing is d. b The equivalent outer diameter of the bearing inner ring 3 is d. e .
[0056] Combination Figure 1 and Figure 2 This embodiment describes a method for calculating the deformation of the raceway of the shaft, bushing, and bearing inner ring. The method is implemented according to the following steps:
[0057] Step 1: Install the shaft 1, bushing 2, and bearing inner ring 3 sequentially from the inside out.
[0058] The initial geometric fit between shaft 1 and bushing 2 is denoted as f. sc The initial geometric fit between the bearing inner ring 3 and the bushing 2 is denoted as f. ic ,
[0059] The equivalent outer diameter d of the bearing inner ring 3 e The calculation using the average value method is expressed as follows:
[0060] d e =(d i +d b ) / twenty one)
[0061] Step 2: Simplify shaft 1, bushing 2 and bearing inner ring 3 into rings A4, B5 and C6 respectively;
[0062] When there is an interference fit between shaft 1 and bushing 2, the initial geometric fit amount f between shaft 1 and bushing 2 is... sc<0, the initial fitting pressure between their mating surfaces is P a ,
[0063] When there is an interference fit between the inner ring 3 of the bearing and the bushing 2, the initial geometric fit amount f between the inner ring 3 of the bearing and the bushing 2 is... ic When <0, the mating pressure between the mating surfaces is P. b
[0064] When the shaft 1 and bushing 2, as well as the bushing 2 and bearing inner ring 3, are all fitted with an interference fit, the interaction forces between the shaft 1 and bushing 2, and between the bushing 2 and bearing inner ring 3, are superimposed, and the pressure on the mating surfaces between the rings will increase. At this time, the fitting pressure between ring A4 and ring B5 is increased by P. a The pressure between rings B5 and C6 changes to P1, and the fitting pressure between them changes from P to P1. b It becomes P2;
[0065] Step 3: When f sc When <0, the initial geometric fit amount f between ring A4 and ring B5 is... sc The fitting pressure P between ring A4 and ring B5 a The relationship is:
[0066]
[0067] When f ic When <0, the initial geometric fit amount f between ring B5 and ring C6 ic The mating pressure P between ring B5 and ring C6 a The relationship is:
[0068]
[0069] In the formula, E s E C E i The elastic moduli of shaft 1, bushing 2, and bearing inner ring 3 are respectively, u s u C u i These are the Poisson's ratios of shaft 1, bushing 2, and bearing inner ring 3, respectively.
[0070] Step 4: When f sc <0 and f ic When >0, if the pressure P is applied a Below, the change in the outer diameter of ring B5 is After the three rings are assembled, the fit between ring B5 and ring C6 changes from clearance to interference, i.e., P2>0. P2 = 0,
[0071]
[0072] When f sc >0 and f ic When <0, if the pressure P is applied b Below, the change in the inner diameter of ring B5 is... After the three rings are assembled, the fit between ring A4 and ring B5 changes from clearance to interference, i.e., P1>0. P1 = 0,
[0073]
[0074] When the fitting pressure P1>0 and the fitting pressure P2>0, the change in the outer diameter of the ring A4 under pressure P1 is: The change in the inner diameter of ring C6 under pressure P2 is: The change in the inner diameter of ring B5 under pressures P1 and P2 is: The change in outer diameter is Calculate using the following formula:
[0075]
[0076]
[0077] Change in outer diameter of ring A4 Change in inner diameter of ring C6 Change in inner diameter of ring B5 The change in the outer diameter of the ring B(5) The initial geometric fit between ring A4 and ring B5 is f. sc The initial geometric fit between ring B5 and ring C6 is f. ic The relationship between them is:
[0078]
[0079] The center diameter d of ring B5 M for:
[0080] d M =(d c +d) / 2 (11)
[0081] If we ignore ring C6 and only consider the fitting pressure P between ring A4 and ring B5, a The center diameter d of ring B5 M Generate diameter change for:
[0082]
[0083] If we ignore ring A4 and only consider the fitting pressure P between ring C6 and ring B5, b The center diameter d of ring B5 M Generate diameter change for:
[0084]
[0085] When the three rings are interference-fitted together, the center diameter d of ring B5 is... M Generate diameter change for:
[0086]
[0087] The relationship between them can be approximated as follows:
[0088]
[0089] Solving equations (10) and (15) simultaneously yields the initial geometric fit between rings A4 and B5 as f. sc The initial geometric fit between ring B5 and ring C6 is f. ic The fitting pressure P1 between lower ring A4 and ring B5 and the fitting pressure P2 between ring B5 and ring C6.
[0090] The fitting pressure P2 between the bearing inner ring 3 and the bushing 2 relative to the raceway diameter d of the bearing inner ring 3 can be calculated using the following formula. i diameter change δ Pdi for:
[0091]
[0092] The above process is the calculation method for the deformation of the raceway of shaft 1, bushing 2, and bearing inner ring 3.
[0093] This implementation method achieves a technological breakthrough by precisely controlling the mixed fits of interference fits and clearance fits between the shaft, bushing, and bearing inner ring. Compared to traditional finite element methods, it effectively avoids calculation deviations caused by neglecting the details of the fit conditions in existing technologies. The method of fitting the shaft, bushing, and bearing inner ring solves the problem of insufficient accuracy in traditional analytical methods due to the lack of consideration for fit relationships, providing a reliable basis for deformation calculations.
Claims
1. A connection structure for a shaft, bushing, and bearing inner ring, characterized in that: It includes a shaft (1), a bushing (2), and a bearing inner ring (3); The shaft (1) is inserted into the bushing (2), the bushing (2) is inserted into the inner ring (3) of the bearing, and the shaft (1) is a hollow shaft.
2. The connection structure of a shaft, bushing, and bearing inner ring according to claim 1, characterized in that: The shaft (1) and bushing (2) are fitted with a clearance fit or an interference fit, the bushing (2) and bearing inner ring (3) are fitted with a clearance fit or an interference fit, and the basic dimension of the inner hole of the shaft (1) is d. s The basic outer diameter of shaft (1) is d. c The basic inner diameter of bushing (2) is d. c The basic outer diameter of the bushing (2) is d, the basic inner diameter of the bearing inner ring (3) is d, and the raceway diameter of the bearing inner ring (3) is d. i The flange diameter of the bearing inner ring (3) is d. b The equivalent outer diameter of the bearing inner ring (3) is d. e .
3. A method for calculating the deformation of the raceway of the shaft, bushing, and bearing inner ring as described in claim 1 or 2, characterized in that: The method is implemented according to the following steps: Step 1: Insert and install the shaft (1), bushing (2), and bearing inner ring (3) sequentially from the inside out. The initial geometric fit between shaft (1) and bushing (2) is denoted as f. sc The initial geometric fit between the bearing inner ring (3) and the bushing (2) is denoted as f. ic , The equivalent outer diameter d of the bearing inner ring (3) e The calculation using the average value method is expressed as follows: d e =(d i +d b ) / 2 (1) Step 2: Simplify the shaft (1), bushing (2) and bearing inner ring (3) into ring A (4), ring B (5) and ring C (6) respectively; When there is an interference fit between the shaft (1) and the bushing (2), the initial geometric fit amount f between the shaft (1) and the bushing (2) is... sc <0, the initial fitting pressure between their mating surfaces is P a , When there is an interference fit between the bearing inner ring (3) and the bushing (2), the initial geometric fit amount f between the bearing inner ring (3) and the bushing (2) is... ic When <0, the mating pressure between the mating surfaces is P. b When the shaft (1) and bushing (2) and the bushing (2) and the bearing inner ring (3) are both interference fit, the interaction forces between the shaft (1) and bushing (2) and the bushing (2) and the bearing inner ring (3) are superimposed, and the pressure on the mating surfaces between the rings will increase. At this time, the fitting pressure between ring A (4) and ring B (5) is P a The pressure between ring B(5) and ring C(6) changes to P1, and the fitting pressure between them changes from P to P1. b It becomes P2; Step 3: When f sc When <0, the initial geometric fit between ring A(4) and ring B(5) is f sc The fitting pressure P between ring A(4) and ring B(5) a The relationship is: When f ic When <0, the initial geometric fit of ring B(5) and ring C(6) is f ic The pressure P of the mating rings B(5) and C(6) a The relationship is: In the formula, E s E C E i The elastic moduli of the shaft (1), bushing (2), and bearing inner ring (3) are respectively, u s u C u i The Poisson's ratios are those of the shaft (1), bushing (2), and bearing inner ring (3), respectively. Step 4: When f sc <0 and f ic When >0, if the pressure P is applied a Below, the change in the outer diameter of ring B(5) is After the three rings are assembled, the fit between ring B(5) and ring C(6) changes from clearance to interference, i.e., P2>
0. P2 = 0, When f sc >0 and f ic When <0, if the pressure P is applied b Below, the change in the inner diameter of ring B(5) is After the three rings are assembled, the fit between ring A(4) and ring B(5) changes from clearance to interference, i.e., P1>
0. P1 = 0, When the fitting pressure P1>0 and the fitting pressure P2>0, the change in the outer diameter of the ring A(4) under pressure P1 is: The change in the inner diameter of the ring C(6) under pressure P2 is: The change in the inner diameter of ring B(5) under pressures P1 and P2 is: The change in outer diameter is Calculate using the following formula: Change in the outer diameter of ring A(4) Change in the inner diameter of ring C(6) Change in the inner diameter of ring B(5) The change in the outer diameter of the ring B(5) The initial geometric fit between ring A(4) and ring B(5) is f. sc The initial geometric fit between ring B(5) and ring C(6) is f. ic The relationship between them is: The middle diameter d of ring B(5) M for: d M =(d c +d) / 2 (11) If we ignore ring C(6) and only consider the fitting pressure P between ring A(4) and ring B(5), a The intermediate diameter d of the ring B(5) M Generate diameter change for: If we ignore ring A(4) and only consider the fitting pressure P between ring C(6) and ring B(5), b The intermediate diameter d of the ring B(5) M Generate diameter change for: When the three rings are interference-fitted together, the center diameter d of ring B(5) M Generate diameter change for: The relationship between them can be approximated as follows: Solving equations (10) and (15) simultaneously, we can obtain the initial geometric fit between ring A (4) and ring B (5) as f. sc The initial geometric fit between ring B(5) and ring C(6) is f. ic The fitting pressure P1 between the lower ring A(4) and ring B(5) and the fitting pressure P2 between ring B(5) and ring C(6) The fitting pressure P2 between the bearing inner ring (3) and the bushing (2) for the raceway diameter d of the bearing inner ring (3) can be calculated using the following formula. i diameter change δ Pdi for: The above process is a calculation method for the deformation of the raceway of the shaft (1), bushing (2), and bearing inner ring (3).