Crown design method for cylindrical rollers used in backing bearings of multi-roll mills

Abstract

The present invention discloses a crown design method for cylindrical rollers used in multi-roller mill backing bearings. The method is characterized by comprising the following design steps: S1. Establishing a roller crown design formula based on a conventional formula; S2. Calculating the edge crown value; and S3. Determining the crown profile curve. By improving the shape of the roller crown curve, the present invention achieves a balance between suppressing stress concentration under heavy loads and improving rotational accuracy under light loads. This addresses the existing problem of using logarithmic crown designs for cylindrical rollers used in multi-roller mill backing bearings, which results in large crowns under high load conditions, difficulty improving rotational accuracy, and an inability to balance suppressing edge stress concentration under heavy loads with improving bearing life under light loads.

Description

Technical Field

[0001] The present invention relates to the field of bearing processing technology, in particular to a convexity design method for a cylindrical roller used in a multi-roller mill backing bearing, which is used to optimize the roller surface profile to improve the bearing's load-bearing capacity and rotation accuracy. Background Art

[0002] Multi-roll cold rolling mills play a vital role in the production of metal strip materials such as stainless steel and silicon steel. Their backing bearings, as key components of the support rollers, must meet the dual requirements of high precision and high load capacity. Traditional roller bearings often use a logarithmic crown design to avoid edge stress concentration, but this design has significant drawbacks under high-load conditions: 1. The logarithmic crown curve is complex and difficult to machine, making it difficult to ensure the straightness of the roller's center section, resulting in increased runout error during bearing rotation; 2. While edge stress concentration is alleviated under heavy loads, the bearing life is not significantly improved under light loads. Therefore, traditional designs cannot meet the performance requirements of backing bearings under the combined conditions of high-precision machining and heavy-load rolling, and optimized crown curve design is urgently needed. Summary of the Invention

[0003] In view of the shortcomings of the existing technology, the present invention provides a convexity design method for cylindrical rollers for multi-roller mill backing bearings, in order to solve the problems in the existing technology that when cylindrical rollers for multi-roller mill backing bearings adopt logarithmic convexity design, the convexity design is large under high-load conditions, it is difficult to improve the rotation accuracy, and it is impossible to take into account both the suppression of edge stress concentration under heavy load and the improvement of bearing life under light load.

[0004] To achieve the above object, the present invention provides a crown design method for a cylindrical roller used in a multi-roll mill backing bearing, which is characterized by comprising the following design process:

[0005] S1. The roller crown design formula is established based on the traditional formula: Ph=1.0115*a*f(x), where a is the crown value of the roller profile edge, f(x) is the dimensionless crown profile curve, and Ph is the roller crown value;

[0006] S2. Calculate the edge convexity: Calculate the roller profile edge convexity using the formula a=4*Phl, where Phl=k0*Q / lwe*(1.1935+ln(lwe / 2b)), where k0 is the material correlation coefficient, Q is the maximum roller load, and Lwe is the roller length. b=(2*k0 Q / R / Lwe)^0.5, where R=2*Dwp / (Dwp-Dwe) / Dwe, where Dwp is the bearing center diameter and Dwe is the roller diameter.

[0007] S3. Calculate the convexity profile curve: Calculate the f(x) convexity profile curve according to the formula f(x)=e^(-(x-lwe / 1.94595 / 0.112593 / lwe)^2), where x is the ratio of the distance from a point on the roller contour line to the roller midpoint to the effective length of the roller.

[0008] The benefits of adopting the above technical solution are: the edge convexity value a derived through the formula chain in the above technology forms a composite shape of "near straight line in the middle section + exponential decline on both sides", so that the edge stress of the roller decays rapidly when overloaded, avoiding the edge stress concentration problem of traditional logarithmic convexity. At the same time, the convexity in the middle section is close to a straight line, which is easy to process and ensures running accuracy, and the convexity on both sides declines faster, ensuring that edge stress concentration does not occur under heavy load conditions, the entire curve is smoothly connected, and the service life is longer when running smoothly under light load.

[0009] The present invention further provides: based on step S2, Q is the maximum roller load calculated under 0.3Cr~0.5Cr, wherein Cr is the rated dynamic load of the backing bearing.

[0010] The benefits of adopting the above technical solution are: the load range in the above technology covers the typical working range of the backing bearing, and the convexity value a calculated by the formula can accurately match the actual load, avoiding the loss of rotation accuracy due to excessive convexity or excessive edge stress due to too small convexity. At the same time, the exponential decay characteristics on both sides of the convexity curve can effectively reduce the edge micro-slip damage under light load. Combined with the low friction characteristics of the straight profile of the middle section, the light-load life of the bearing is improved compared with the traditional logarithmic convexity design.

[0011] The present invention further provides that: based on step S3, the x needs to meet the following condition: 0≤x≤0.5lwe.

[0012] The benefits of adopting the above technical solution are: in the above technology, the profile calculation range is limited to the single-sided half length of the effective length of the roller, ensuring that the convexity curve is symmetrical about the center of the roller, avoiding the risk of overloading caused by asymmetric design, and at the same time, through the dimensionless processing of x, the curve shape is decoupled from the actual length of the roller, which is suitable for the design of backing bearing rollers of different specifications and sizes. BRIEF DESCRIPTION OF THE DRAWINGS

[0013] Figure 1 Schematic diagram of the roller profile designed by the Lundberg formula and the method of the present invention;

[0014] Figure 2 Schematic diagram of contact stress of the roller designed by Lundberg formula and the method of the present invention under 0.05Cr load. DETAILED DESCRIPTION

[0015] The present invention provides a method for designing the crown of a cylindrical roller for a backing bearing of a multi-roll mill, which is characterized by comprising the following design process:

[0016] S1. The roller crown design formula is established based on the traditional formula: Ph=1.0115*a*f(x), where a is the crown value of the roller profile edge, f(x) is the dimensionless crown profile curve, and Ph is the roller crown value;

[0017] S2. Calculate the edge convexity: Calculate the roller profile edge convexity using the formula a=4*Phl, where Phl=k0*Q / lwe*(1.1935+ln(lwe / 2b)), where k0 is the material-related coefficient, k0=2.81*10^-6mm2 / N, Q is the maximum roller load, Lwe is the roller length, and b=(2*k0 Q / R / Lwe)^0.5. In this formula, R=2*Dwp / (Dwp-Dwe) / Dwe, where Dwp is the bearing center diameter and Dwe is the roller diameter.

[0018] S3. Calculate the convexity profile curve: Calculate the f(x) convexity profile curve according to the formula f(x)=e^(-(x-lwe / 1.94595 / 0.112593 / lwe)^2), where x is the ratio of the distance from a point on the roller contour line to the roller midpoint to the effective length of the roller.

[0019] Further: Based on step S2, Q is the maximum roller load calculated under 0.3Cr~0.5Cr, where Cr is the rated dynamic load of the backing bearing.

[0020] Furthermore: based on step S3, the x needs to satisfy the following condition: 0≤x≤0.5lwe.

[0021] Specific embodiment: A backing bearing is selected, and the backing bearing parameters are: rated dynamic load Cr is 1740 kN, roller diameter Dwe is 29.5 mm, roller length Lwe is 52 mm, and roller chamfer is 0.8 mm.

[0022] Using the above data, the roller profile shape calculated by substituting 0.05Cr into the above formula is as follows: Figure 1 As shown, the contact stress of the roller profile is simulated and calculated in commercial software as follows: Figure 2 shown.

[0023] Comparison revealed that the roller profile provided by the design method of the present invention differs from the profile curve obtained using the Lundberg formula in both the straight segments and the curved segments on both sides. Under a load of 0.05Cr, the contact stress distribution in the middle segment calculated using the present formula is more even, and the length is longer, resulting in lower peak stress, which in turn extends the bearing life. Furthermore, trial production has shown that because the middle segment of the cylindrical roller profile obtained using the present formula is nearly straight, it is easier to machine with high precision. Backing bearings using these rollers can achieve rotational accuracy above P4, with cross-sectional runout below 2μm.

[0024] The above shows and describes the basic principles and main features of the present invention and the advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The above embodiments and descriptions are only for explaining the principles of the present invention. Without departing from the spirit and scope of the present invention, the present invention may have various changes and improvements, which shall fall within the scope of the present invention to be protected. The scope of protection of the present invention is defined by the attached claims and their equivalents.

Claims

1. A method for designing the crown of a cylindrical roller for a backing bearing of a multi-roll mill, characterized by: The design process includes the following: S1. The roller crown design formula is established based on the traditional formula: Ph=1.0115*a*f(x), where a is the crown value of the roller profile edge, f(x) is the dimensionless crown profile curve, and Ph is the roller crown value; S2. Calculate the edge convexity: Calculate the roller profile edge convexity using the formula a=4*Phl, where Phl=k0*Q*(1.1935+ln(lwe / 2b)) / lwe, where k0 is the material correlation coefficient, Q is the maximum roller load, and Lwe is the roller length. b=(2*k0*(Q / R / Lwe))^0.5, where R=2*Dwp / ((Dwp-Dwe)*Dwe), where Dwp is the bearing center diameter and Dwe is the roller diameter. S3. Calculate the convexity profile curve: Calculate the f(x) convexity profile curve according to the formula f(x)=e^(-(((|x|-lwe / 1.94595) / 0.112593 / lwe)^2)), where x is the ratio of the distance from a point on the roller contour line to the roller midpoint to the effective length of the roller.

2. A method according to claim 1, characterized in that: Based on step S2, Q is the maximum roller load calculated under 0.3Cr~0.5Cr, where Cr is the rated dynamic load of the backing bearing.

3. The method according to claim 1, characterized in that: Based on step S3, the x must satisfy the following condition: 0≤x≤0.5lwe.

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