A friction-reducing design method for tapered roller bearings

Abstract

A friction reduction design method for tapered roller bearings. First, a force analysis is performed on the tapered roller bearing under a certain working condition, a mechanical equilibrium equation is established, the bearing deformation parameters are solved, and the sum of the offsets caused by the influence of each deformation parameter and the bearing structural parameters on the three-line intersection point is solved. Then, the absolute value of the product of the contact load between the roller and the outer ring and the offset of the three-line intersection point is used to reflect the friction temperature rise caused by the force deformation. By adjusting the design tolerances of the bearing roller diameter, inner ring raceway diameter, inner ring large rib thickness, outer ring raceway angle, and inner ring raceway angle parameters, the overall Q of the bearing is reduced. e The L value is optimized, and the high tolerance requirements of the assembly are met to complete the design process. The present invention effectively reduces the sliding friction of the raceway caused by the offset of the three-line intersection point, thereby achieving the purpose of reducing the temperature rise of the bearing under actual working conditions.

Description

Technical Field

[0001] The present invention relates to the technical field of bearing design, in particular to a friction reduction design method for a tapered roller bearing. Background Art

[0002] Tapered roller bearings are rolling bearings, but sliding friction is unavoidable. Friction not only consumes energy, but in severe cases, causes significant wear and loss of bearing precision. It can also lead to excessive temperature rise, burning the working surface, or rendering the lubricant ineffective.

[0003] Current tapered roller bearing design methods ensure geometrically pure rolling in an unloaded state. However, in actual operation, due to the load applied to the bearing, the inner and outer rings undergo relative displacement. The greater the load, the greater the displacement. The intersection of the extended lines of the inner and outer ring raceway generatrixes and the rolling element centerline can shift accordingly, deviating from the bearing's rotational centerline. This disrupts the pure rolling of the rolling elements within the raceways, increases sliding effects, causes frictional heating in the bearing, and can even lead to premature bearing failure. Summary of the Invention

[0004] In order to solve the above technical problems, the present invention provides a friction reduction design method for a tapered roller bearing, the purpose of which is to reduce the sliding friction of the raceway caused by the offset of the three-line intersection point and effectively reduce the temperature rise.

[0005] The technical solution adopted by the present invention is: a friction reduction design method for a tapered roller bearing, the steps are as follows:

[0006] S1. Perform stress analysis on the tapered roller bearing under a certain working condition, establish the mechanical equilibrium equation, solve the bearing deformation parameters, and solve the sum of the offsets L caused by the influence of each deformation parameter and the bearing structure parameters on the intersection of the three lines. i , the i-th roller

[0007] L i =Prr i +Pra i +Prθ i +Pr(Dw) i +Pr(di) i +Pr(a0) i +Pr(α) i +Pr(β) i

[0008] Where Prr i 、Pra i 、Prθ i Pr(Dw) is the offset caused by the radial, axial and angular deformation of the bearing under load on the intersection of the three lines. i 、Pr(di) i 、Pr(a0)i 、Pr(α) i 、Pr(β) i The offsets caused by the design tolerances of the bearing roller diameter, inner ring raceway diameter, inner ring large rib thickness, outer ring raceway angle, and inner ring raceway angle on the intersection of the three lines are respectively. The intersection of the three lines is the intersection of the extension line of the bearing inner and outer ring raceway generatrix and the center line of the rolling element.

[0009] S2, using the contact load Q between the roller and the outer ring ei Offset L from the intersection of three lines i The absolute value of the product reflects the friction temperature rise caused by the deformation under stress, and the Q of each roller is ei L i Sum the values ​​to get the Q of the whole set of n rollers e The L value is

[0010] S3, the obtained Q e The L value is used as the reference value of the bearing under this working condition. By adjusting the design tolerances of the bearing roller diameter, inner ring raceway diameter, inner ring large rib thickness, outer ring raceway angle, and inner ring raceway angle parameters, the new set of bearing n rollers (Q e L)' value, so that (Q e L)'<reference value, while meeting the high tolerance requirements of assembly, completed.

[0011] As a preferred solution, in step S2, for the bearing under a single load condition, the Q of each roller is ei L i Sum the values ​​to get the Q of the whole set of n rollers e The L value is

[0012] Where j=1.

[0013] As a preferred solution, in step S2, for a tapered roller bearing with varying working loads, the deformation parameters of the bearing under m working conditions are calculated according to the load spectrum, and the deformation parameters are summed with the influence of the structural parameters to obtain the Q of the bearing under m working conditions. e The L value is Where j = 1, 2, 3...m.

[0014] As a preferred solution, in step S3, meeting the high tolerance requirement of the assembly means that when adjusting the tolerance, the variation of the assembly height needs to be reviewed. To meet the high tolerance requirement of the assembly, the variation of the bearing assembly height is:

[0015] ΔT=Kn×Δdi+Ka×Δa0+Kg×ΔDw-Kw×ΔE

[0016] Where Kn, Ka, Kg, and Kw are the influence coefficients of each parameter. According to the standard or the user's high assembly requirements, the constraints of the bearing parameter tolerance are:

[0017] ΔT min <ΔT(ΔDw,Δdi,Δa0,ΔE)<ΔT max .

[0018] The beneficial effects of the present invention are:

[0019] This solution provides a friction reduction design method for tapered roller bearings. By analyzing the deformation parameters of the tapered roller bearings under actual working stress conditions and the influence of the bearing structural parameters on the extension lines of the inner and outer ring raceway generatrixes and the intersection of the rolling element centerline, the design tolerances of the bearing roller diameter, inner ring raceway diameter, inner ring large rib thickness, outer ring raceway angle, inner ring raceway angle and other parameters are adjusted to reduce the overall Q of the bearing. e The L value is used to reduce the sliding friction of the raceway and effectively reduce the temperature rise. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are only some embodiments of the invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0021] Figure 1 Schematic diagram of roller deformation of bearing under load;

[0022] Figure 2 Schematic diagram of the intersection of the three bearing lines after the roller diameter changes;

[0023] Figure 3 This is a schematic diagram of the increase in the inner ring raceway diameter;

[0024] Figure 4 This is a schematic diagram of the inner ring rib enlargement;

[0025] Figure 5 is a process flow chart of the present invention;

[0026] Figure 6 Schematic diagram of the influence of bearing deformation parameters on the intersection of three lines;

[0027] Figure 7 Schematic diagram of the influence of bearing size parameters on the intersection of three lines;

[0028] Figure 8 This is a schematic diagram of the calculation results of the front load-bearing area rollers optimized in Example 1;

[0029] Figure 9 Schematic diagram of the calculation results of the load-bearing area roller after optimization of Example 1. DETAILED DESCRIPTION

[0030] The present invention is described in detail below by way of exemplary embodiments, but it should be understood that elements and features of one embodiment may also be beneficially combined in other embodiments without further description.

[0031] This proposal is a friction-reducing design method for tapered roller bearings. By analyzing the deformation parameters of the tapered roller bearing under actual working stress conditions and the influence of the bearing structural parameters on the intersection of the extension lines of the bearing inner and outer ring raceway generatrixes and the rolling element centerline, the bearing structural parameter tolerances are adjusted to achieve the purpose of reducing raceway sliding friction.

[0032] It should be noted that the three-line intersection mentioned in this article is the intersection of the extension line of the bearing inner and outer ring raceway generatrix and the center line of the rolling element;

[0033] In this scheme, radial displacement, axial displacement, and deflection angle cause the offset of the intersection point of the three lines; Figure 6 and Figure 7 The table lists the offset of the intersection of the three lines when each deformation parameter increases or decreases; radial displacement and axial displacement cause the rolling element to be compressed, Figure 1 The figure shows the offset of the "three-line intersection point" after the rolling element is compressed and deformed; the table lists the offset of the three-line intersection point when each size parameter increases or decreases. Figure 6 and Figure 7 In the table, "↑" and "↓" respectively indicate that the parameter increases and decreases, and "-" indicates that the change of the parameter has no effect on the intersection of the three lines; Figure 2 The change of the intersection point of the three bearing lines after the roller diameter increases; Figure 3 and Figure 4 The middle ones are the increase of inner ring raceway diameter and inner ring rib.

[0034] Combine Figure 5 The process flow chart describes the design steps of this scheme in detail:

[0035] The force analysis of the tapered roller bearing under a certain working condition is carried out, the mechanical equilibrium equation is established, and the bearing deformation parameters are solved. The whole set of bearings contains n rollers. The influence of the deformation parameters of the i-th roller in the bearing and the influence of the bearing parameters are superimposed to obtain the theoretical offset of the three-line intersection point, that is, L i =Pr r i +Pr a i +Prθ i +Pr(Dw) i +Pr(di) i +Pr(a0) i +Pr(α)i +Pr(β) i

[0036] In the formula, the rollers at different positions are subjected to different forces, and the offset of the three-line intersection is also different; the contact load Q between the roller and the outer ring is used ei Offset L from the intersection of three lines i The absolute value of the product reflects the friction temperature rise caused by the deformation under stress; the Q of each roller ei L i Sum the values ​​to get the Q of the whole set of n rollers e The L value is

[0037]

[0038] For tapered roller bearings with varying working loads, the deformation parameters of the bearings under m working conditions are calculated according to the load spectrum, and the deformation parameters are summed with the influence of the structural parameters to obtain the Q of the bearing under m working conditions. e The L value is

[0039]

[0040] It should be noted that the tolerance value of bearing parameters is relatively small, and the influence on the contact load between the raceway and the roller can be ignored; L i The value is the superposition of the effects of various parameters. By adjusting the tolerance of parameters such as roller diameter, the offset of the intersection point of the three bearing lines caused by the load can be offset or reduced, that is, L can be reduced. i The force on each roller is different, and the offset changes accordingly. Parameter adjustment may reduce the offset of some rollers or increase the offset of some rollers. The overall Q of the bearing should be guaranteed. e The L value decreases.

[0041] The tolerances of the roller diameter, the inner ring raceway large end diameter, and the inner ring rib thickness are parameters that affect the intersection of the three lines and are also key dimensions that affect the bearing assembly height. When adjusting the tolerances, the variation in assembly height must be reviewed to ensure that the assembly height tolerance requirements are met.

[0042] The bearing assembly height variation is

[0043] ΔT=Kn×Δdi+Ka×Δa0+Kg×ΔDw-Kw×ΔE

[0044] Where, Kn, Ka, Kg, and Kw are the influence coefficients of each parameter;

[0045] According to the standard or the user's high assembly requirements, the constraints of the bearing parameter tolerance are

[0046] ΔT min <ΔT(ΔDw,Δdi,Δa0,ΔE)<ΔTmax .

[0047] Example 1

[0048] The present invention will be described below by taking a specific single-row tapered roller bearing as an example:

[0049] The bearing parameters are as follows: inner diameter 60mm, outer diameter 110mm, width 23.75, outer ring raceway angle 15.11°, inner ring raceway angle 11.11°, rib angle 78.35°, roller small end diameter 12.425, roller large end diameter 13.507, roller effective length 14.59, number of rollers 19;

[0050] Bearing structural parameter tolerances: outer ring raceway diameter tolerance (0-0.046), inner ring raceway diameter tolerance (+0.0250), inner ring rib width tolerance (+0.02 0), roller diameter tolerance (+0.01 0);

[0051] The load conditions are as follows: radial load 11000N, axial load 4500N, moment load 100Nm.

[0052] The calculated radial displacement of the bearing inner ring relative to the outer ring is 0.0072mm, the axial displacement is 0.0148mm, and the angular displacement is 0°. The roller load Q at different angular positions is e and Q e L value see Figure 8 Table content;

[0053] Adjust the bearing parameter tolerances: outer ring raceway diameter tolerance (0-0.044), inner ring raceway diameter tolerance (+0.0200), inner ring rib width tolerance (+0.02 0), roller diameter tolerance (+0.013+0.005). After adjustment, the bearing assembly height tolerance range is 0.02~0.173, which is still within the original tolerance range. The calculation results of each roller in the load-bearing area are shown in Figure 9 Table contents in the table.

[0054] Compared with before adjustment, it can be seen that the entire bearing Q e The L value was reduced by 44%, and the sliding friction caused by the bearing deformation due to stress was greatly reduced.

[0055] It should be noted that although the present invention has been described with reference to the above embodiments, the present invention may also have other various embodiments. Without departing from the spirit and scope of the present invention, it is obvious that those skilled in the art may make various corresponding changes and modifications to the present invention, and such changes and modifications shall fall within the scope of protection of the appended claims and their equivalents.

Claims

1. A friction reduction design method for a tapered roller bearing, characterized by: Here are the steps: S1. Perform stress analysis on the tapered roller bearing under a certain working condition, establish the mechanical equilibrium equation, solve the bearing deformation parameters, and solve the sum of the offsets L caused by the influence of each deformation parameter and the bearing structure parameters on the intersection of the three lines. i , the i-th roller L i =Prr i +Pra i +Prθ i +Pr(Dw) i +Pr(di) i +Pr(a0) i +Pr(α) i +Pr(β) i Where Prr i 、Pra i 、Prθ i Pr(Dw) is the offset caused by the radial, axial and angular deformation of the bearing under load on the intersection of the three lines. i 、Pr(di) i 、Pr(a0) i 、Pr(α) i 、Pr(β) i The offsets caused by the design tolerances of the bearing roller diameter, inner ring raceway diameter, inner ring large rib thickness, outer ring raceway angle, and inner ring raceway angle on the intersection of the three lines are respectively. The intersection of the three lines is the intersection of the extension line of the bearing inner and outer ring raceway generatrix and the center line of the rolling element. S2, using the contact load Q between the roller and the outer ring ei Offset L from the intersection of three lines i The absolute value of the product reflects the friction temperature rise caused by the deformation under stress, and the Q of each roller is ei L i Sum the values ​​to get the Q of the whole set of n rollers e The L value is S3, the obtained Q e The L value is used as the reference value of the bearing under this working condition. By adjusting the design tolerances of the bearing roller diameter, inner ring raceway diameter, inner ring large rib thickness, outer ring raceway angle, and inner ring raceway angle parameters, the new set of bearing n rollers (Q e L)' value, so that (Q e L)'<reference value, while meeting the high tolerance requirements of assembly, completed.

2. The friction reduction design method for a tapered roller bearing according to claim 1, characterized in that: In the step S2, for the bearing under a single load condition, the Q of each roller is ei L i Sum the values ​​to get the Q of the whole set of n rollers e The L value is Where j=1.

3. The friction reduction design method for a tapered roller bearing according to claim 1, characterized in that: In step S2, for a tapered roller bearing with varying working loads, the deformation parameters of the bearing under m working conditions are calculated according to the load spectrum, and the deformation parameters are summed with the influence of the structural parameters to obtain the Q of the bearing under m working conditions. e The L value is Where j = 1, 2, 3...m.

4. The friction reduction design method for a tapered roller bearing according to claim 1, characterized in that: In step S3, meeting the assembly height tolerance requirement means that when adjusting the tolerance, the assembly height variation needs to be reviewed. To meet the assembly height tolerance requirement, the bearing assembly height variation is: ΔT=Kn×Δdi+Ka×Δa0+Kg×ΔDw-Kw×ΔE Where Kn, Ka, Kg, and Kw are the influence coefficients of each parameter. The high assembly requirements are determined according to the standard or the user. The constraint condition of the bearing parameter tolerance is ΔT min <ΔT(ΔDw,Δdi,Δa0,ΔE)<ΔT max .

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