Method for calculating pre-tightening force of split bearing anti-slip clamping ring

Abstract

This invention provides a method for calculating the preload of the anti-slip clamping ring in a split bearing, comprising the following steps: S1: obtaining the operating parameters and structural parameters of the split bearing; S2: calculating the total frictional torque. M f =Frictional torque caused by moment of inertia M I + Frictional torque caused by external load M r + Frictional torque generated by the viscous friction of the lubricant M v S3: The pressure required to prevent relative slippage between the inner ring and the shaft is calculated using the integral method. F d S4: Calculate the contact stress between the clamping ring and the inner ring caused by the temperature difference. P S5: Calculate the expansion force on a single connecting bolt caused by the temperature difference between the clamping ring and the inner ring. F Z S6: Integration pressure F d With expansion force F Z The axial load that a single connecting bolt needs to withstand is calculated. P Lmax , P Lmax This is the minimum preload required for the retaining ring; when this preload is met, it can be ensured that the inner ring of the split bearing and the retaining ring do not slip during operation; the retaining ring preload that satisfies the condition of no slippage inside the split bearing can be solved.

Description

Technical Field

[0001] This invention belongs to the field of split bearing technology, and in particular to the calculation method of the preload of the anti-slip clamping ring of split bearings. Background Technology

[0002] Split bearings offer advantages such as convenient installation and the ability to replace components without disassembling adjacent parts. They are widely used in large equipment such as heavy machinery and marine drive shafts where overall disassembly is inconvenient. The inner ring, outer ring, and cage of a split bearing all employ a split structure. The inner ring is typically secured to the spindle using a split retaining ring for pre-tightening. Pre-tightening force is applied through the retaining ring's connecting bolts, causing the retaining ring to fit snugly against the inner ring of the split bearing. This creates an interference fit between the spindle and the inner ring, enabling torque transmission and preventing loosening.

[0003] During operation, slippage between the inner ring and shaft of a split bearing can lead to wear and heat generation on the mating surfaces, causing vibration and noise, and in severe cases, serious equipment failure. Currently, the determination of preload in the design and installation of split bearing retaining rings largely relies on experience, usually based on static or steady-state conditions, which has significant limitations: it ignores the dynamic inertial torque generated by the system's rotational inertia during transient processes such as startup and braking; and it does not consider the frictional torque of the split bearing body due to lubrication and load during operation. In summary, the lack of precise theoretical basis for the design of preload for split bearing retaining rings is a key reason for slippage in split bearings. Summary of the Invention

[0004] In view of the above problems, the purpose of this application is to provide a calculation method for the preload of the anti-slipping clamping ring of a split bearing, to calculate the load on the connecting bolts on the clamping ring, to apply calculus to the engineering calculation process, to perform step-by-step calculation according to the different sources of force on the clamping ring, to integrate the friction torque and contact stress to obtain the total load borne by the connecting bolts, and to compare it with the actual preload provided by the split bearing to determine whether the clamping ring will slip.

[0005] To achieve some or all of the above objectives or other objectives, this application provides the following technical solution: a method for calculating the preload of the anti-slip clamping ring in a split bearing, comprising the following steps:

[0006] S1: Obtain the operating parameters and structural parameters of the split bearing, including the rotational speed. n Acceleration time t Moment of inertia I External load, operating temperature, and lubrication type; the structural parameters include the material properties and geometric dimensions of the split bearing inner ring and clamping ring.

[0007] S2: Based on the aforementioned operating parameters and structural parameters, calculate the total frictional torque between the inner ring and the shaft during the operation of the split bearing. M f The total frictional torque M f =Frictional torque caused by moment of inertia M I + Frictional torque caused by external load M r + Frictional torque generated by the viscous friction of the lubricant M v ;

[0008] S3: Based on the total frictional torque M f and the coefficient of friction between the inner ring and the shaft μ The total frictional torque is converted into the pressure required to tighten the connecting bolts on the clamping ring by means of integration. F d ;

[0009] S4: Calculate the contact stress between the clamping ring and the inner ring caused by the temperature difference. P ;

[0010] S5: Calculate the expansion force on a single connecting bolt caused by the temperature difference between the clamping ring and the inner ring. F Z ;

[0011] S6: Integrate the pressure F d With expansion force F Z The axial load that a single connecting bolt needs to withstand is calculated. P Lmax The P Lmax This is the minimum preload required for the retaining ring; when this preload is met, it can be ensured that the inner ring of the split bearing and the retaining ring do not slip during operation.

[0012] Further, in step S2, the formula for calculating the frictional torque caused by the moment of inertia is: In the formula: I It is the moment of inertia, measured in kg·m. 2 ; β It is angular acceleration, with units of s. -2 .

[0013] Further, in step S2, the formula for calculating the frictional torque caused by the external load is: In the formula: f 1 It is a coefficient related to the split bearing structure and load;F β This is the calculated load for determining the frictional torque of the split bearing, i.e., the equivalent static load of the split bearing, in N. F β The calculation formula is determined based on the type of split bearing. When the split bearing is a cylindrical roller split bearing with a cage, F β Calculation formula ,in F r It is the radial load of the split bearing; d m This refers to the pitch circle diameter of the split bearing, in mm.

[0014] Further, in step S2, the formula for calculating the frictional torque generated by the viscous friction of the lubricant is: If v 0 n ≥2000, ;like v 0 n <2000, In the formula: v 0 This is kinematic viscosity, which is related to the lubrication method and temperature, and is measured in mm. 2 / s; f 0 This is a coefficient related to the type of split bearing and the lubrication method; d m This refers to the pitch circle diameter of the split bearing, in mm.

[0015] Furthermore, in step S3, the pressure F d The integral method formula is as follows: In the formula: N 0 It is pressure per unit radius. In the formula: , D 2 It is the inner diameter of the inner ring; the inner ring and the shaft press against each other, providing the inner ring with pressure in the radial direction away from the center, and the angle between it and the vertical line is... .

[0016] Furthermore, in step S4, the contact stress between the clamping ring and the inner ring caused by the temperature difference... P The calculation formula is: In the formula: D It is the inner diameter of the clamping ring. D 1 It is the outer diameter of the clamping ring. D 2 It is the inner diameter of the inner ring, in mm; ξ 1 It is the Poisson's ratio of the clamping ring. ξ 2 It is the inner circle Poisson's ratio. E 1 It is the elastic modulus of the clamping ring. E 2 It is the elastic modulus of the inner ring, in MPa; interference fit. In the formula: U 0 It is the initial interference fit between the inner ring and the retaining ring of the split bearing, in mm; afas It is the coefficient of linear expansion of the inner ring. afai It is the linear expansion coefficient of the clamping ring; Δ T 1 It is the difference between the operating temperature of the clamping ring and the reference temperature, Δ. T 2 It is the difference between the inner ring operating temperature and the reference temperature, in °C.

[0017] Furthermore, in step S5, the expansion force on the individual connecting bolt caused by the temperature difference between the clamping ring and the inner ring... F Z The calculation formula is: F Z = PS In the formula: S It is the contact area between the clamping ring and the inner ring, in mm. 2 .

[0018] Furthermore, in step S6, the axial load that a single connecting bolt needs to withstand... P Lmax The calculation formula is: , m This refers to the number of bolts used to connect the retaining ring.

[0019] Compared with the prior art, the beneficial effects of the present invention are as follows: the function of the split bearing retaining ring is to ensure that the split bearing remains stable during high-speed rotation, without displacement or slippage, thereby ensuring the normal operation of the machine. It can also withstand the radial and axial forces on the split bearing and transmit them to the shaft to ensure that the shaft can withstand all loads.

[0020] Furthermore, the retaining ring of a split bearing can improve the durability and lifespan of the split bearing by increasing friction and contact area. When loosening occurs between the split bearing and the shaft, the retaining ring can maintain a tight grip, preventing the split bearing from being damaged by vibration.

[0021] This calculation method is mainly applicable to devices that are locked by bolts. The preload of the clamping ring is calculated based on the working conditions and the specifications and dimensions of the parts. By comparing the calculated force with the actual preload, if the actual preload is greater than the calculated force, slippage will not occur between the clamping ring and the inner ring. Attached Figure Description

[0022] Figure 1 This is a flowchart of the method of the present invention;

[0023] Figure 2 This is a sectional view of the split bearing;

[0024] Figure 3 for Figure 2 AA view;

[0025] Figure 4 A schematic diagram of the cage structure and rollers;

[0026] Figure 5 This is a schematic diagram of the forces acting on the inner ring.

[0027] Figure 6 This is a schematic diagram of the structure of the inner ring and the shaft;

[0028] In the diagram: 1. Fastening washer, 2. Outer half ring, 3. Cage screw, 4. Half cage seat, 5. Inner half ring, 6. Roller, 7. Cage connecting plate, 8. Cage cover screw, 9. Cage cover, 10. Clamping screw, 11. Clamping spring washer, 12. Clamping ring, 13. Spindle. Detailed Implementation

[0029] To make the structure and function of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings.

[0030] See appendix Figure 1-6A single split bearing includes two symmetrically arranged inner rings 5 ​​and two symmetrically arranged outer rings 2. The two inner rings 5 ​​are joined together to form a complete inner ring, and the two outer rings 2 are joined together and fitted over the two inner rings 5, forming an annular raceway between them. A plurality of rollers 6 are arranged circumferentially within the annular raceway. A cage assembly includes two cage seats 4, a cage cover 9, and a cage connecting plate 7 connecting the two cage seats 4. The cage connecting plate 7 connects the two cage seats 4 by cage screws 3. The cage seats 4, cage connecting plate 7, and cage cover 9 together constitute a structure for accommodating and... The cage structure of the separator roller 6 includes a semi-cage seat 4 and a cage cover 9 connected by a cage cover screw 8; an axial fastening assembly including a clamping ring 12, a clamping screw 10, and a clamping spring washer 11, wherein the clamping ring 12 is fixed to the outer end face of the semi-inner ring 5 by the clamping screw 10 and the clamping spring washer 11 to limit the axial displacement of the semi-inner ring 5; and a connecting fastener including a cage cover screw 8 penetrating the cage cover 9 and the semi-cage seat 4 and a fastening washer 1 sleeved on the cage cover screw 8, for connecting and fixing the cage cover 9 and the semi-cage seat 4 to ensure their stability and integrity.

[0031] The split bearing is sleeved on the main shaft 13. The inner ring and the main shaft 13 are pre-tightened by the clamping ring 12. The pre-tightening force is applied by the connecting bolt of the clamping ring to make the clamping ring fit with the inner ring of the split bearing, thereby forming an interference fit between the main shaft 13 and the inner ring, realizing torque transmission and preventing loosening.

[0032] The calculation method for the preload of the anti-slip clamping ring of a split bearing includes the following steps:

[0033] S1: Obtain the operating parameters and structural parameters of the split bearing, including the rotational speed. n Acceleration time t Moment of inertia I External load, operating temperature, and lubrication type; the structural parameters include the material properties and geometric dimensions of the split bearing inner ring and clamping ring.

[0034] S2: Based on the aforementioned operating parameters and structural parameters, calculate the total frictional torque between the inner ring and the shaft during the operation of the split bearing. M f The total frictional torque M f =Frictional torque caused by moment of inertia M I + Frictional torque caused by external load M r + Frictional torque generated by the viscous friction of the lubricant M v ;

[0035] S3: Based on the total frictional torque M f and the coefficient of friction between the inner ring and the shaft μ The total frictional torque is converted into the pressure required to tighten the connecting bolts on the clamping ring by means of integration. F d ;

[0036] S4: Calculate the contact stress between the clamping ring and the inner ring caused by the temperature difference. P ;

[0037] S5: Calculate the expansion force on a single connecting bolt caused by the temperature difference between the clamping ring and the inner ring. F Z ;

[0038] S6: Integrate the pressure F d With expansion force F Z The axial load that a single connecting bolt needs to withstand is calculated. P Lmax The P Lmax This is the minimum preload required for the retaining ring; when this preload is met, it can be ensured that the inner ring of the split bearing and the retaining ring do not slip during operation.

[0039] In step S2, the formula for calculating the frictional torque caused by the moment of inertia is: In the formula: I It is the moment of inertia, measured in kg·m. 2 ; β It is angular acceleration, with units of s. -2 .

[0040] In step S2, the formula for calculating the frictional torque caused by the external load is: In the formula: f 1 It is a coefficient related to the split bearing structure and load; F β This is the calculated load for determining the frictional torque of the split bearing, i.e., the equivalent static load of the split bearing, in N. F β The calculation formula is determined based on the type of split bearing. When the split bearing is a cylindrical roller split bearing with a cage, F β Calculation formula ,in F r It is the radial load of the split bearing; d m This refers to the pitch circle diameter of the split bearing, in mm.

[0041] In step S2, the formula for calculating the frictional torque generated by the viscous friction of the lubricant is: If v 0 n ≥2000, ;like v 0 n <2000, In the formula: v 0 This is kinematic viscosity, which is related to the lubrication method and temperature, and is measured in mm. 2 / s; f 0 This is a coefficient related to the type of split bearing and the lubrication method; d m This refers to the pitch circle diameter of the split bearing, in mm.

[0042] In step S3, the pressure F d The integral method formula is as follows: In the formula: N 0 It is pressure per unit radius. In the formula: , D 2 It is the inner diameter of the inner ring; the inner ring and the shaft press against each other, providing the inner ring with pressure in the radial direction away from the center, and the angle between it and the vertical line is... .

[0043] In step S4, the contact stress between the clamping ring and the inner ring caused by the temperature difference... P The calculation formula is: In the formula: D It is the inner diameter of the clamping ring. D 1 It is the outer diameter of the clamping ring. D 2 It is the inner diameter of the inner ring, in mm; ξ 1 It is the Poisson's ratio of the clamping ring. ξ 2 It is the inner circle Poisson's ratio. E 1 It is the elastic modulus of the clamping ring. E 2 It is the elastic modulus of the inner ring, in MPa; interference fit. In the formula: U 0 It is the initial interference fit between the inner ring and the retaining ring of the split bearing, in mm; afas It is the coefficient of linear expansion of the inner ring. afai It is the linear expansion coefficient of the clamping ring; ΔT 1 It is the difference between the operating temperature of the clamping ring and the reference temperature, Δ. T 2 It is the difference between the inner ring operating temperature and the reference temperature, in °C.

[0044] In step S5, the expansion force on the individual connecting bolt caused by the temperature difference between the clamping ring and the inner ring... F Z The calculation formula is: F Z = PS In the formula: S It is the contact area between the clamping ring and the inner ring, in mm. 2 .

[0045] In step S6, the axial load that a single connecting bolt needs to withstand. P Lmax The calculation formula is: , m This refers to the number of bolts used to connect the retaining ring.

[0046] Calculation process:

[0047] Split bearing radial load F r =700kN, SKFLGWA2 grease is selected, kinematic viscosity at 40℃ v 0 185mm 2 kinematic viscosity at 100℃ / s v 0 15mm 2 / s.

[0048] Typical operating conditions: The motor starts and accelerates at rated torque (acceleration time not exceeding 100s) to 220rpm, runs for about 10 minutes (maximum 2 hours), and then decelerates (deceleration time not exceeding 100s) to 0; the above cycle is repeated no less than 15 times a day, about 2000 times a year.

[0049] Moment of inertia I =128.22 kg·m 2 Accelerate to within 100 seconds n =220r / min, the coefficient of friction between the inner ring and the shaft is taken as... Inner diameter D 2 =700mm, pitch circle diameter d m =884mm, and two M24 bolts with a strength of 12.9 are used on the clamping ring.

[0050] 1.1 Frictional torque caused by moment of inertia

[0051] angular acceleration β (1.1)

[0052] Torque provided by rotational inertia M I (1.2)

[0053] 1.2 Frictional torque caused by external load

[0054] Frictional torque M r Calculation formula (1.3)

[0055] In the formula: f 1 This is a coefficient related to the split bearing structure and load, which can be found in Table 1.1, and is taken as 0.0003; F β This is the calculated load for the frictional torque of a cylindrical roller split bearing with a cage, in N.

[0056] F β The calculation formula is determined based on the type of split bearing. In this embodiment, F β Calculation formula (1.4)

[0057] The calculation results of (1.4) and f 1 Substituting 0.0003 into (1.3) gives M r

[0058] (1.5)

[0059] Table 1.1 Split cylindrical roller bearings f 1 and F β value

[0060]

[0061] Note: Smaller values ​​are used for light-duty split bearings, and larger values ​​are used for heavy-duty split bearings.

[0062] 1.3 Frictional torque generated by viscous friction of lubricant

[0063] Calculate the frictional torque generated by the viscous friction of the lubricant M v empirical formula

[0064] likev 0 n ≥2000, (1.6)

[0065] like v 0 n <2000, (1.7)

[0066] In the formula: f 0 This is a coefficient related to the type of split bearing and the lubrication method, which can be found in Table 1.2, and is taken as 1.5.

[0067] Known v 0 n =185×220=40700>2000,

[0068] (1.8)

[0069] Table 1.2 Cylindrical roller bearings under different lubrication conditions f 0 value

[0070]

[0071] Note: Smaller values ​​are used for light-duty bearings, and larger values ​​are used for heavy-duty bearings.

[0072] 1.4 Expansion force caused by temperature difference

[0073] Contact stress P

[0074] (1.9)

[0075] In the formula: D It is the inner diameter of the clamping ring. D 1 It is the outer diameter of the clamping ring. D 2 It is the inner diameter of the inner ring, in mm; ξ 1 It is the Poisson's ratio of the clamping ring. ξ 2 It is the inner circle Poisson's ratio. E 1 It is the elastic modulus of the clamping ring. E 2 It is the elastic modulus of the inner ring, in MPa.

[0076] Interference U

[0077] (1.10)

[0078] In the formula: U 0 It is the initial interference fit between the inner ring and the retaining ring of the split bearing, in mm; afas It is the coefficient of linear expansion of the inner ring. afai It is the linear expansion coefficient of the clamping ring; Δ T 1 It is the difference between the operating temperature of the clamping ring and the reference temperature, Δ. T 2 It is the difference between the inner ring operating temperature and the reference temperature, in °C.

[0079] The contact stress caused by temperature difference between the clamping ring and the inner ring was calculated. P =15.14MPa, contact area between clamping ring and inner ring S =104571mm 2 The expansion force on a single connecting bolt caused by the temperature difference between the clamping ring and the inner ring. F Z = P × S / 2=791602N.

[0080] Calculation results

[0081] because M r and M v Based on empirical formulas, it also includes the effect of the rolling elements sliding in the cage pockets. Therefore, the frictional torque on a split bearing can be considered as the sum of the frictional torque caused by the load and the viscous frictional torque. M = M r + M v =185640+122605=308245 (N·mm).

[0082] The inner ring and the shaft press against each other, providing the inner ring with pressure in the radial direction away from the center, and the angle between the inner ring and the vertical line is... .

[0083] Total frictional torque on the inner ring M f (1.11)

[0084] (1.12)

[0085] In the formula: N 0 Tension force is expressed in units of radians.

[0086] The pressure per unit radius can be obtained N 0 (1.13)

[0087] Pressure F d (1.14)

[0088] Axial load borne by a single connecting bolt P Lmax (1.15)

[0089] In the description of this invention, it should be noted that the terms "upper", "lower", "inner", "outer", "front end", "rear end", "both ends", "one end", "the other end", etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limiting this invention.

[0090] The above-disclosed embodiments are merely preferred embodiments of this application and should not be construed as limiting the scope of this application. Therefore, any equivalent variations made in accordance with the claims of this application shall still fall within the scope of this application.

Claims

1. A method for calculating the preload of the anti-slip clamping ring in a split bearing, characterized in that: Including the following step: S1: Obtain the operating parameters and structural parameters of the split bearing, including the rotational speed. n Acceleration time t Moment of inertia I External load, operating temperature, and lubrication type; the structural parameters include the material properties and geometric dimensions of the split bearing inner ring and clamping ring. S2: Based on the aforementioned operating parameters and structural parameters, calculate the total frictional torque between the inner ring and the shaft during the operation of the split bearing. M f The total frictional torque M f =Frictional torque caused by moment of inertia M I + Frictional torque caused by external load M r + Frictional torque generated by the viscous friction of the lubricant M v ; S3: Based on the total frictional torque M f and the coefficient of friction between the inner ring and the shaft μ The total frictional torque is converted into the pressure required to tighten the connecting bolts on the clamping ring by means of integration. F d ; S4: Calculate the contact stress between the clamping ring and the inner ring caused by the temperature difference. P The calculation formula is: In the formula: D It is the inner diameter of the clamping ring. D 1 It is the outer diameter of the clamping ring. D 2 It is the inner diameter of the inner ring, in mm; ξ 1 It is the Poisson's ratio of the clamping ring. ξ 2 It is the inner circle Poisson's ratio. E 1 It is the elastic modulus of the clamping ring. E 2 It is the elastic modulus of the inner ring, in MPa; interference fit. In the formula: U 0 It is the initial interference fit between the inner ring and the retaining ring of the split bearing, in mm; afas It is the coefficient of linear expansion of the inner ring. afai It is the linear expansion coefficient of the clamping ring; Δ T 1 It is the difference between the operating temperature of the clamping ring and the reference temperature, Δ. T 2 It is the difference between the inner ring's working temperature and the reference temperature, in °C; S5: Calculate the expansion force on a single connecting bolt caused by the temperature difference between the clamping ring and the inner ring. F Z ; S6: Integrate the pressure F d With expansion force F Z The axial load that a single connecting bolt needs to withstand is calculated. P Lmax The P Lmax This is the minimum preload required for the retaining ring; when this preload is met, it can be ensured that the inner ring of the split bearing and the retaining ring do not slip during operation.

2. The method for calculating the preload of the anti-slip clamping ring in a split bearing according to claim 1, characterized in that: In step S2, the formula for calculating the frictional torque caused by the moment of inertia is: In the formula: I It is the moment of inertia, measured in kg·m. 2 ; β It is angular acceleration, with units of s. -2 .

3. The method for calculating the preload of the anti-slip clamping ring in a split bearing according to claim 1, characterized in that: In step S2, the formula for calculating the frictional torque caused by the external load is: In the formula: f 1 It is a coefficient related to the split bearing structure and load; F β This is the calculated load for determining the frictional torque of the split bearing, i.e., the equivalent static load of the split bearing, in N. F β The calculation formula is determined based on the type of split bearing. When the split bearing is a cylindrical roller split bearing with a cage, F β Calculation formula ,in F r It is the radial load of the split bearing; d m This refers to the pitch circle diameter of the split bearing, in mm.

4. The method for calculating the preload of the anti-slip clamping ring in a split bearing according to claim 1, characterized in that: In step S2, the formula for calculating the frictional torque generated by the viscous friction of the lubricant is: If v 0 n ≥2000, ; like v 0 n <2000, In the formula: v 0 This is kinematic viscosity, which is related to the lubrication method and temperature, and is measured in mm. 2 / s; f 0 This is a coefficient related to the type of split bearing and the lubrication method; d m This refers to the pitch circle diameter of the split bearing, in mm.

5. The method for calculating the preload of the anti-slip clamping ring in a split bearing according to claim 1, characterized in that: In step S3, the pressure F d The integral method formula is as follows: In the formula: N 0 It is pressure per unit radius. In the formula: , D 2 It is the inner diameter of the inner ring; the inner ring and the shaft press against each other, providing the inner ring with pressure in the radial direction away from the center, and the angle between it and the vertical line is... .

6. The method for calculating the preload of the anti-slip clamping ring of a split bearing according to claim 1, characterized in that: In step S5, the expansion force on the individual connecting bolt caused by the temperature difference between the clamping ring and the inner ring... F Z The calculation formula is: F Z = PS In the formula: S It is the contact area between the clamping ring and the inner ring, in mm. 2 .

7. The method for calculating the preload of the anti-slip clamping ring of a split bearing according to claim 1, characterized in that: In step S6, the axial load that a single connecting bolt needs to withstand. P Lmax The calculation formula is: , m This refers to the number of bolts used to connect the retaining ring.

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