A method for monitoring the preload of machine tool bearings

Abstract

This invention belongs to the field of machine tools, specifically relating to a method for monitoring the preload of machine tool bearings, comprising: Step 1, selecting a temperature measurement point and arranging a temperature sensor at the measurement point; Step 2, rotating the machine tool spindle under a certain load and speed until the machine tool reaches thermal equilibrium, and measuring the steady-state temperature T of the measurement point on the spindle box using the temperature sensor; Step 3, establishing a relationship between the steady-state temperature of the measurement point on the spindle box and the heat generation power of the monitored bearing, and calculating the heat generation power of the monitored bearing based on this relationship; Step 4, calculating the rotational speed and angular velocity of each part of the bearing; Step 5, calculating the bearing clearance P. d This invention enables quantitative monitoring of preload during spindle operation.

Description

Technical Field

[0001] This invention belongs to the field of machine tools, and specifically relates to a method for monitoring the preload of machine tool bearings. Background Technology

[0002] The preload of machine tool spindle bearings affects factors such as the spindle's motion accuracy, the spindle system's rigidity, bearing heat generation, and lifespan, which in turn impact the machining quality. Insufficient spindle preload compromises motion accuracy and reduces spindle rigidity, ultimately leading to decreased machining quality. Conversely, excessive preload increases bearing heat generation, reduces bearing life, and exacerbates thermal deformation of the spindle system, also resulting in decreased machining quality. Therefore, the preload of machine tool spindle bearings should be maintained at an appropriate level.

[0003] After a machine tool is put into production, its preload can change due to factors such as bearing wear, nut loosening, and temperature variations. When changes in the spindle bearing preload lead to problems with machining quality, it can result in significant losses in various aspects. Furthermore, knowing the spindle bearing preload information during machine tool production and debugging can improve production efficiency and the quality of the produced machine tools. Therefore, a method for monitoring spindle bearing preload is needed to ensure the smooth operation and maintenance of machine tools.

[0004] Currently, there is a lack of effective methods for detecting the preload of machine tool spindle bearings. Most methods rely on experience to determine the preload status, and these experience-based methods are performed when the machine tool spindle is not in operation. However, the preload of spindle bearings differs between operating and non-operating states, making it more meaningful to understand the preload of spindle bearings during operation.

[0005] To address the aforementioned issues, this invention proposes a method for monitoring spindle bearing preload by monitoring the temperature of the machine tool spindle box, thereby achieving quantitative monitoring of preload during spindle operation. Summary of the Invention

[0006] To overcome the shortcomings of existing technologies, this invention provides a technical solution for monitoring the preload of machine tool bearings.

[0007] A method for monitoring the preload of machine tool bearings, comprising:

[0008] Step 1: Select the temperature measurement point and place the temperature sensor at the temperature measurement point;

[0009] Step 2: Rotate the machine tool spindle under a certain load and speed until the machine tool reaches thermal equilibrium. Use a temperature sensor to measure the steady-state temperature T at the temperature measuring point on the spindle box.

[0010] Step 3: Establish the relationship between the steady-state temperature of the temperature measuring point on the spindle box and the heat generation power of the monitored bearing, and calculate the heat generation power of the monitored bearing based on this relationship.

[0011] Step 4: Calculate the rotational speed and angular velocity of each part of the bearing;

[0012] Step 5, calculate the bearing clearance P. d .

[0013] Furthermore, the operation in step 2 needs to meet the following requirements:

[0014] a. When the spindle rotates to bring the machine tool to thermal equilibrium, a constant radial load needs to be applied to the spindle so that the radial force borne by the monitored roller bearing reaches 0.8%-1.2% of its rated static load;

[0015] b. When the spindle rotates to bring the machine tool to thermal equilibrium, the spindle speed needs to be maintained at one-quarter to one-half of the spindle's limit speed;

[0016] c. When monitoring the temperature at a temperature measuring point on the spindle box, the temperature at the measuring point at time t1 is T1, and the temperature measured at time t2 is T2, where t2 > t1. When ξ≤1%, it can be considered that the monitored machine tool has reached thermal equilibrium at time t2, and the steady-state temperature of the temperature measuring point is T2.

[0017] Furthermore, the relationship between the steady-state temperature of the temperature measuring point on the spindle box and the heat generation power of the monitored bearing in step 3 is as follows:

[0018]

[0019] In the formula, a and b are constants.

[0020] Furthermore, step 4 specifically includes: calculating the rotational speed and angular velocity of each part of the bearing according to the following set of equations:

[0021]

[0022]

[0023]

[0024]

[0025] In the formula, n i n o These are the rotational speeds of the inner and outer rings of the bearing, n. m n is the rotational speed of the roller. R ω is the rotational speed of the roller. iω o ω represents the angular velocities of the inner and outer rings of the bearing, respectively. m Let ω be the angular velocity of the roller's revolution. R The angular velocity of the roller's rotation is γ = D / d m D is the roller diameter, d m V is the pitch circle diameter of the bearing. i V is the sliding speed of the roller relative to the inner ring. o This represents the sliding speed of the roller relative to the outer ring.

[0026] Furthermore, step 5 specifically includes: calculating the bearing clearance P according to the following set of equations. d :

[0027]

[0028]

[0029]

[0030]

[0031] F r =ZQ max J r (ε) (13)

[0032]

[0033]

[0034] In the formula, ε and J r (ε) is a dimensionless intermediate variable introduced for ease of calculation, δ r ψ is the amount of movement of the bearing shaft. l Q is the maximum angle of the loaded area of ​​the rolling element. max Radial load F r The roller directly opposite the bearing will bear the largest load, which is important for ball bearings. For roller bearings K n Let be the stiffness coefficient, and let be the load distributed to the j-th roller. With F r The included angle is ψ j Q ij This refers to the contact force between the inner and outer raceways and the rollers, and Z represents the number of rolling elements; μ i μ o These are the coefficients of friction between the roller and the inner and outer raceways, respectively.

[0035] The principle of this invention is as follows: When the spindle operates under a certain load and speed, the preload of the spindle bearing affects its heat generation power. When the heat generation power of the spindle bearing is different, the temperature at the same location on the spindle housing will also be different. Therefore, the heat generation power of the spindle bearing can be calculated by measuring the temperature on the spindle housing, and then the preload of the bearing can be calculated based on the heat generation power of the spindle bearing.

[0036] Compared with existing technologies, the beneficial effects of this invention are: this invention achieves quantitative monitoring of preload during spindle operation. This invention can be applied by machine tool manufacturers during production debugging to guide production, and can also help users better understand the preload status of machine tool spindle bearings when using machine tools. Attached Figure Description

[0037] Figure 1 This is a flowchart of the present invention;

[0038] Figure 2 This is a schematic diagram of the forces acting on a single roller.

[0039] Figure 3 This is a schematic diagram of the front support structure of a lathe spindle;

[0040] Figure 4 This is a graph showing the relationship between the heating power of a double-row short cylindrical roller bearing and the temperature at the measuring point. Detailed Implementation

[0041] The invention will now be further described with reference to the accompanying drawings.

[0042] Please see Figure 1 A method for monitoring the preload of machine tool bearings includes the following steps:

[0043] Step 1: Select the temperature measurement point and place the temperature sensor at the temperature measurement point.

[0044] In terms of selecting the temperature measurement point, theoretically, this point can be any point on the spindle box. However, considering that the temperature change may not be significant at locations far from the spindle bearing in actual conditions, and in order to reduce the influence of other bearings' heating on the temperature of the measurement point, the selected temperature measurement point should be as close as possible to the bearing to be monitored, while facilitating the placement of the sensor.

[0045] Step 2: Rotate the machine tool spindle under a certain load and speed until the machine tool reaches thermal equilibrium. Use a temperature sensor to measure the steady-state temperature T at the temperature measuring point on the spindle box.

[0046] This step needs to meet the following requirements:

[0047] a. When the spindle rotates to bring the machine tool to thermal equilibrium, a constant radial load needs to be applied to the spindle so that the radial force borne by the monitored double-row short cylindrical roller bearing reaches about 1% of its rated static load.

[0048] b. When the spindle rotates to bring the machine tool to thermal equilibrium, the spindle speed needs to be maintained at about one-third of the spindle's limit speed.

[0049] c. When monitoring the temperature at a temperature measuring point on the spindle box, if the temperature at the measuring point at time t1 is T1, and the temperature measured at time t2 some time later is T2, when... When the temperature reaches t2, it can be considered that the monitored machine tool has reached thermal equilibrium at time t2, and the steady-state temperature of the temperature measuring point is T2.

[0050] Step 3: Based on the method described above, establish the relationship between the steady-state temperature of the temperature measuring point on the spindle box and the heat generation power of the monitored bearing, and determine a and b in equation (35). Substitute the steady-state temperature T of the temperature measuring point into equation (35) to calculate the heat generation power of the monitored bearing.

[0051] Step 4: Substitute the spindle speed and the dimensional parameters of each part into equations (2) to (5) to calculate the speed and angular velocity of each part of the bearing.

[0052] Step 5, adjust the heating power The rotational speeds and angular velocities of each part calculated in step ④, along with other relevant parameters, are substituted into the system of equations (9) to (13), (15), and (24) to solve simultaneously, thereby obtaining the bearing clearance P. d .

[0053] The above formulas are detailed below.

[0054] The reasons for the requirements proposed in step 2 are as follows:

[0055] The relationship between the clearance of double-row short cylindrical roller bearings and their heat generation power shows that the greater the radial load they bear, the more significant the impact of clearance on heat generation power. Furthermore, since most machine tools primarily rely on double-row short cylindrical roller bearings to bear radial loads, an increase in the radial load on the spindle leads to a significant increase in the heat generation power of the double-row short cylindrical roller bearings, while the increase in the heat generation power of the roller bearings is less pronounced. Considering these two reasons, when using the proposed method to monitor the preload of a machine tool spindle, a certain radial load needs to be applied to the spindle to improve the accuracy of the measurement. Generally, when the spindle rotates and the machine tool reaches thermal equilibrium, a constant radial load is applied to the spindle, ensuring that the radial force borne by the monitored double-row short cylindrical roller bearing reaches approximately 1% of its rated static load.

[0056] The reason why the proposed solution has certain requirements on the spindle speed is that too low a speed will result in insignificant bearing heating, while too high a speed will not be applicable to the formula given by Palmgren. Both excessively high and low speeds will lead to reduced calculation accuracy. In summary, when the spindle rotation brings the machine tool to thermal equilibrium, the spindle speed needs to be maintained at about one-third of the spindle's limit speed.

[0057] The technical principle of this invention is as follows: When the spindle operates under a certain load and speed, the preload of the spindle bearing affects its heat generation power. When the heat generation power of the spindle bearing is different, the temperature at the same location on the spindle housing will also be different. Therefore, the heat generation power of the spindle bearing can be calculated by measuring the temperature on the spindle housing, and then the preload of the bearing can be calculated based on the heat generation power of the spindle bearing.

[0058] To achieve this process, it is necessary to clarify the relationship between the temperature of the temperature measuring point on the spindle box and the heat generation power of the monitored bearing, as well as the relationship between the preload of the double-row short cylindrical roller bearing and the heat generation power. Once these two relationships are established, the preload of the spindle bearing can be monitored by measuring the temperature of the temperature measuring point on the spindle box.

[0059] Short cylindrical roller bearings are commonly used spindle bearings in CNC lathes and machining centers to bear radial loads. The preload of these bearings is of utmost concern to us. The derivation of the relationship between preload and heat generation is as follows:

[0060] (1) Determine the bearing structural parameters

[0061] D i D is the inner diameter of the bearing. o D is the outer diameter of the bearing, and d is the diameter of the roller. i d o d represents the diameter of the inner and outer raceway bottoms of the bearing. m This is the pitch circle diameter of the bearing.

[0062]

[0063] (2) Calculate the speed of each part of the bearing

[0064] n i n o These represent the inner and outer ring speeds, respectively, n m n is the rotational speed of the roller. R Let ω be the rotational speed of the roller, and ω be the angular velocity corresponding to each rotational speed. i ω o ω m ω R Let γ = D / d m but:

[0065] The revolution speed of the roller is the same as that of the cage, which is:

[0066]

[0067] The rotational speed of the roller is:

[0068]

[0069] The sliding speed of the roller relative to the inner ring is:

[0070]

[0071] The sliding speed of the roller relative to the outer ring is:

[0072]

[0073] (3) Force Analysis

[0074] When the radial load on the bearing is 2F r At that time, the radial load borne by a single-row bearing is F r Radial load F r The load will be distributed among several rollers, and the load distributed to the j-th roller is... With F r The included angle is ψ j radial load F r The roller directly opposite will receive the maximum load Q. max .

[0075] According to Hertz's contact theory, the relationship between the load Q on the roller and the deformation δ of the roller is as follows:

[0076] Q = Kδ n (6)

[0077] In the formula, for ball bearings For roller bearings K is a coefficient related to material and dimensional parameters such as the elastic modulus, Poisson's ratio, and curvature of the rollers and raceways.

[0078] The sum of the contact deformations between the roller and the inner and outer raceways is the total deformation of the roller. Therefore:

[0079] Q = K n δ n (7)

[0080] in:

[0081]

[0082] Based on this, the relationship between the various parameters of the bearing can be derived as follows:

[0083]

[0084]

[0085]

[0086]

[0087] F r =ZQ max J r (ε) (13)

[0088]

[0089] In the formula: P d For bearing clearance; δ r ψ represents the amount of movement of the bearing shaft. l ε is the maximum angle of the loaded area of ​​the rolling element; J r (ε) is a dimensionless intermediate variable introduced for ease of calculation. Here, the bearing clearance is what we call preload.

[0090] The j-th roller is subjected to the following force: Figure 2 As shown, Q ij Q oj These represent the contact forces between the inner and outer raceways and the rollers, μ. i μ o μ m These are the coefficients of friction between the rollers and the inner and outer raceways and the cage, respectively, F. mj To maintain the normal force between the frame and the rollers, F d F represents the turbulence resistance experienced by the rollers due to the lubricant. c It is centrifugal force.

[0091] Based on the load and torque balance of the roller, it can be concluded that:

[0092]

[0093] Q oj =Q ij +F c (16)

[0094] μ m F mj =μ i Q ij +μ O Q Oj (17)

[0095] (4) Obtain the heating power

[0096] The frictional power consumption between the roller and the inner and outer rings is:

[0097]

[0098]

[0099] The heat generation rate of the oil stirring friction of the roller is:

[0100]

[0101] The resistance between the cage and the inner ring guide surface in the bearing is the viscous frictional force F of the lubricant. CL The rate of heat generated by sliding friction between the cage and the inner ring guide surface is:

[0102]

[0103] There is also sliding friction between the roller and the cage pocket. When the spindle rotates at a constant speed, the frictional heat generation rate between the roller and the cage pocket can be obtained from equation (17):

[0104]

[0105] Therefore, the total heat generation power of the double-row short cylindrical roller bearing is:

[0106]

[0107] Substituting equations (18), (19), and (22) into equation (23) and rearranging, we get:

[0108]

[0109] Among them, centrifugal force, turbulence resistance, and the resistance between the cage and the inner ring guide surface are calculated as the viscous friction force of the lubricant using the following formulas:

[0110]

[0111]

[0112]

[0113] In the formula, m is the mass of the roller, and C d Let ρ be the turbulence resistance coefficient, ρ be the density of the lubricant in the bearing cavity, and l be the length of the roller. η0 is the dynamic viscosity of the lubricant, and w is the viscosity of the bearing cavity. cR To maintain the total width of the guide surface of the frame, d cR To maintain the diameter of the cage guide surface, d iR The diameter is the inner guide surface diameter.

[0114] Equations (9) to (13) and (15) and (24) describe the relationship between the preload and the heat generation power of a double-row short cylindrical roller bearing.

[0115] For a bearing in operation, ε, P d δ r Q max , ψ l J r (ε), Q ij The bearing heating power is an unknown quantity. Substituting these equations into the system of equations (9) to (13), (15), and (24), the bearing clearance can be solved.

[0116] The relationship between the temperature on the spindle box and the heat generation power of the bearings:

[0117] The steady-state temperature at various points on the spindle box is related to the heat generation power of the spindle bearing. After selecting the temperature measurement point, finite element software is used to establish the relationship between the steady-state temperature of the temperature measurement point on the spindle box and the heat generation power of the spindle bearing, thereby realizing the calculation of the heat generation power of the spindle bearing by monitoring the temperature of the temperature measurement point on the spindle box.

[0118] First, a model of the monitored machine tool is established using finite element method software. The heat generation power of each bearing in the spindle is input into the model as boundary conditions. The heat generation power of the ball bearings can be calculated using the formula given by Palmgren.

[0119]

[0120] In the formula: M is the frictional torque of the bearing, which can be calculated using the following formula:

[0121] M = M1 + M V (29)

[0122] M1 is the torque caused by the applied load:

[0123]

[0124]

[0125] In the formula: F s It is the equivalent static load, C s This is the basic static load rating, and α is the bearing contact angle. It is the pitch circle diameter. Table 1 lists the values ​​of z and y.

[0126] Table 1. Values ​​of z and y

[0127]

[0128] ① The smaller value applies to light-duty bearings, and the larger value applies to heavy-duty bearings.

[0129] F β Take the larger value between equations (32) and (33):

[0130]

[0131]

[0132] in, It is the axial load on the bearing. The radial load on the bearing

[0133] M V It is the torque generated by the viscous friction of the lubricant:

[0134]

[0135] In equation (34) v o The unit is centistokee (cSt), f o These are coefficients related to bearing type and lubrication method, listed in Table 2:

[0136] Table 2 f o The value of

[0137]

[0138] ① For paired or double-row bearings, use 2f o

[0139] ② The smaller value applies to light-duty bearings, and the larger value applies to heavy-duty bearings.

[0140] ③ Only applicable to double row bearings

[0141] These formulas are conclusions drawn by Palmgren based on experiments with various types and sizes of bearings. Extensive practical experience has proven that these formulas are quite accurate when bearings are operating at medium and low speeds.

[0142] After inputting the heat generation power of each bearing in the spindle into the model, the steady-state temperature of the measuring point can be calculated using finite element software. Subsequently, without changing the heat generation power of other bearings in the model, multiple sets of data are obtained by inputting different heat generation powers of the monitored bearings. Finally, these data are fitted into a function to obtain the relationship between the steady-state temperature of the measuring point in the spindle box and the heat generation power of the spindle bearings. Since the thermal conductivity of metallic materials is minimally affected by temperature, the steady-state temperature of the measuring point and the heat generation power of the monitored bearings should have a linear relationship, i.e.:

[0143]

[0144] Theoretically, the temperature measurement point can be any point on the spindle box. However, considering that the temperature change may not be significant at locations far from the spindle bearing in actual conditions, and in order to reduce the influence of other bearing heating on the temperature of the measurement point, the selected temperature measurement point should be as close as possible to the bearing to be monitored, while facilitating the placement of the sensor.

[0145] Example

[0146] The front support structure of a certain lathe is as follows Figure 3 As shown, a temperature sensor is embedded in the support hole wall of the double-row short cylindrical roller bearing in the lathe spindle box. A radial load is applied to the lathe spindle until the double-row short cylindrical roller bearing is subjected to a radial load of 5000N. This load is kept constant, and then the spindle is rotated at a speed of 1000 rpm until the lathe reaches thermal equilibrium.

[0147] When the lathe spindle ran continuously for 40 minutes, the temperature at the measuring point was 40.875℃. After running for 50 minutes, the temperature at the measuring point was 41.243℃. This indicates that the machine tool has reached thermal equilibrium, and the steady-state temperature of the temperature measuring point is T = 41.243℃.

[0148] A model of the machine tool was built using finite element method (FEM) software. Using the formula given by Palmgren, the heat output of the double-row angular contact ball bearing in the front support was calculated to be 60.22 W. This heat output was then input as a boundary condition into the FEM software. Next, different heat outputs of the double-row short cylindrical roller bearing were input to obtain multiple sets of data, such as... Figure 4 As shown.

[0149] Therefore, the relationship between the steady-state temperature of the measuring point and the heat generation power of the monitored bearing can be obtained as follows:

[0150]

[0151] Using equation (36), the heat generation power of the bearing at this time can be obtained as follows:

[0152]

[0153] The dimensional parameters of the double-row short cylindrical roller bearing in the front support of this lathe are shown in Table 3:

[0154] Table 3 Dimensional parameters of double-row short cylindrical roller bearings

[0155]

[0156]

[0157] Other relevant parameters at this temperature are shown in Table 4:

[0158] Table 4 Other relevant parameters

[0159]

[0160] The lathe spindle speed is 1000 rpm, that is:

[0161] n i =1000rpmn (38)

[0162] n o =0 (39)

[0163] According to equations (2) to (5), we can obtain:

[0164] V i =1.23×10 -4 m / s (40)

[0165] V0 = 1.68 × 10 -4 m / s (41)

[0166] ω R =770.997rod / s (42)

[0167] ω m =48.797rod / s (43)

[0168] ω i =104.67 rod / s (44)

[0169] Heat generation power The rotational speeds and angular velocities of each part calculated in equations (40) to (44), as well as other relevant parameters, are substituted into the system of equations (9) to (13), (15), and (24) to solve simultaneously. The results are shown in Table 5.

[0170] Table 5 shows the results of the solution.

[0171]

[0172] In summary, since monitoring the temperature of the spindle box is not difficult and this monitoring system can be added without major modifications to the existing lathe structure, this invention has the advantages of being simple, effective, and low-cost. Furthermore, the method proposed in this invention is applicable to various machine tools; only material and dimensional parameters need to be modified during use. Finally, this invention can be used by machine tool manufacturers to guide production during commissioning, and it can also help users better understand the preload status of the machine tool spindle bearings when using the machine tool.

[0173] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the above embodiments, or replace some or all of the technical features therein with equivalents. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for monitoring the preload of machine tool bearings, characterized in that, include: Step 1: Select the temperature measurement point and place the temperature sensor at the temperature measurement point; Step 2: Rotate the machine tool spindle under a certain load and speed until the machine tool reaches thermal equilibrium. Measure the steady-state temperature T at the temperature measuring point on the spindle box using a temperature sensor. Step 2 must meet the following requirements: a. When the spindle rotates to bring the machine tool to thermal equilibrium, a constant radial load needs to be applied to the spindle so that the radial force borne by the monitored roller bearing reaches 0.8%-1.2% of its rated static load; b. When the spindle rotates to bring the machine tool to thermal equilibrium, the spindle speed needs to be maintained at one-quarter to one-half of the spindle's limit speed; c. When monitoring the temperature at a temperature measuring point on the spindle box, the temperature at the measuring point at time t1 is T1, and the temperature measured at time t2 is T2, where t2 > t1. When ξ≤1%, it can be considered that the monitored machine tool has reached thermal equilibrium at time t2, and the steady-state temperature of the temperature measuring point is T2; Step 3: Establish the relationship between the steady-state temperature of the temperature measuring point on the spindle box and the heat generation power of the monitored bearing, and calculate the heat generation power of the monitored bearing based on this relationship. The relationship between the steady-state temperature at the temperature measuring point on the spindle box and the heat generation power of the monitored bearing is as follows: In the formula, a and b are constants; Step 4, calculate the rotational speed and angular velocity of each part of the bearing, including: calculating the rotational speed and angular velocity of each part of the bearing according to the following set of equations: In the formula, n i n o These are the rotational speeds of the inner and outer rings of the bearing, n. m n is the rotational speed of the roller. R ω is the rotational speed of the roller. i ω o ω represents the angular velocities of the inner and outer rings of the bearing, respectively. m Let ω be the angular velocity of the roller's revolution. R The angular velocity of the roller's rotation is γ = D / d m D is the roller diameter, d m V is the pitch circle diameter of the bearing. i V is the sliding speed of the roller relative to the inner ring. o This represents the sliding speed of the roller relative to the outer ring. Step 5, calculate the bearing clearance P. d This includes: calculating the bearing clearance P based on the following system of equations. d : In the formula, ε and J r (ε) is a dimensionless intermediate variable introduced for ease of calculation, δ r ψ is the amount of movement of the bearing shaft. l Q is the maximum angle of the loaded area of ​​the rolling element. max Radial load F r The roller directly opposite the bearing will bear the largest load, which is important for ball bearings. For roller bearings K n Let be the stiffness coefficient, and let be the load distributed to the j-th roller. With F r The included angle is ψ j Q ij This refers to the contact force between the inner and outer raceways and the rollers, and Z represents the number of rolling elements, μ i μ o These are the coefficients of friction between the roller and the inner and outer raceways, respectively, F. c For centrifugal force, The rate of heat generation from friction during oil churning by the rollers, To maintain the sliding friction heat generation rate between the frame and the inner ring guide surface, F d F represents the turbulence resistance experienced by the rollers due to the lubricant. CL Let m be the viscous friction force of the lubricant, and C be the mass of the roller. d ρ is the turbulence resistance coefficient, ρ is the density of the lubricant in the bearing cavity, l is the length of the roller, η0 is the dynamic viscosity of the lubricant, and w cR To maintain the total width of the guide surface of the frame, d cR To maintain the diameter of the cage guide surface, d iR The diameter is the inner guide surface diameter.

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