Design method for multi-section tangent arc convexity of roller bearing

Abstract

The invention provides a roller bearing multi-section tangent arc convexity design method which comprises the following steps: S1, establishing a formula Y = Aln [1 / (1-0.975 (2X / L) 2)] based on a logarithmic curve convexity design principle, where A value is a convexity axial compression coefficient, L value is the total length of a horizontal axis corresponding to a logarithmic curve, X value is the coordinate value of the horizontal axis of the logarithmic curve, and Z value is the coordinate value of the horizontal axis of the logarithmic curve; the Y value is a longitudinal axis coordinate value of the logarithmic curve; s2, taking 1 / 2 of the total length L of the abscissa of the logarithmic curve as a unit, taking the total length Y of the ordinate as a unit, and performing nondimensionalization respectively; a dimensionless coordinate point (Xn, Yn) of the arc tangent point is defined, and Xn = 2Xi / L; yn = Yi / Ymax = ln [1 / (1-0.975 (2Xi / L) 2)] / 3.689; and S3, comprehensively considering the calculation precision in engineering and the machining convenience of the product, and selecting five sections, seven sections or any higher section of tangent arc convexity to machine the bearing surface profile of the roller bearing. By means of the method, the multiple sections of tangent arc type convexity can be efficiently machined in a high-precision mode, the convexity of the logarithmic curve contour can be approximated through the multiple sections of tangent arcs, and the purposes of accuracy and convenience are achieved.

Description

Technical Field

[0001] The invention relates to the field of bearing processing, in particular to a design method for multi-segment tangent arc convexity of a roller bearing. Background Art

[0002] Roller bearings, including cylindrical roller bearings, tapered roller bearings, and spherical roller bearings, are widely used. These bearings use raceways and rollers as load-bearing surfaces to transfer load between inner and outer rings. The design profile of the load-bearing surface is complex and variable depending on the load and tilt conditions of the bearing. When using logarithmic curves to design their crown, existing technologies generally use parametric equations or small line segment approximation methods to obtain the machine tool processing path for grinding wheel dressing and grinding. The grinding wheel correction width needs to be greater than the width of the workpiece to ensure edge processing quality. However, the design length of the crown is based on the width of the workpiece, and the extension of the grinding wheel width at both ends must be additionally considered during processing. This leads to the following problems in existing technologies: Improper discretization step size setting of the parametric equation can lead to uneven curves, requiring multiple step size adjustments to balance processing accuracy and efficiency. When the machine tool does not support direct input of parametric equations, CAM software must be used to generate dense code (including the extension of the grinding wheel width) and then import it into the machine tool for processing. This process is cumbersome and prone to errors, requiring production personnel to have high skills. Summary of the Invention

[0003] In response to the shortcomings of the existing technology, the present invention provides a design method for the convexity of multiple tangent arcs of roller bearings. The method can obtain several simple arc coordinate points for machine tool processing through optimization and calculation in the design stage. A smooth and accurate logarithmic curve can be obtained without complex G-code conversion, and the method is highly practical and convenient.

[0004] To achieve the above object, the present invention provides a method for designing a multi-segment tangent arc convexity of a roller bearing, which is characterized by comprising the following steps: S1, establishing a formula based on the design principle of logarithmic curve convexity: Y=Aln[1 / (1-0.975(2X / L) 2 )], where A is the axial compression coefficient of the convexity, L is the total length of the horizontal axis corresponding to the logarithmic curve, X is the horizontal axis coordinate value of the logarithmic curve, and Y is the vertical axis coordinate value of the logarithmic curve; S2, take 1 / 2 of the total length of the horizontal coordinate L of the logarithmic curve and the total length of the vertical coordinate Y as units, and make them dimensionless respectively; define the dimensionless coordinate point (X) of the tangent point of the arc n , Y n ), where X n = 2X i / L;Y n = Y i / Ymax = ln[1 / (1-0.975(2X i / L) 2 )] / 3.689; S3. Taking into account the engineering calculation accuracy and product processing convenience, five-segment, seven-segment or any higher-segment tangent arc convexity can be selected to process the load-bearing surface profile of roller bearings.

[0005] As a further configuration of the present invention, the convexity axial compression coefficient A value can be any constant.

[0006] As a further configuration of the present invention, the lengths of the horizontal coordinates corresponding to the arc lengths of the tangent arcs decrease in a geometric progression.

[0007] As a further configuration of the present invention, the horizontal coordinate of the tangent point of any arc segment is: n = 2X i / L=(1-r i ) / (1-r).

[0008] The beneficial effect of this setting is that the coordinates of the tangent point, radius, angle of each tangent arc and the center position coordinates of the arc can be calculated, and these parameters can be directly input into the machine tool to produce a curve with higher precision. BRIEF DESCRIPTION OF THE DRAWINGS

[0009] Figure 1 This is a convexity diagram designed using the logarithmic curve equation of ISO16281; Figure 2 A schematic diagram of the convexity designed according to seven tangent arc segments in an embodiment of the present invention; Figure 3 The relevant parameters of the convexity designed according to the seven tangent arcs in the embodiment of the present invention and the extension line thereof for the grinding wheel; Figure 4 Schematic diagram of dressing the convexity of a grinding wheel and its convexity extension section when grinding a workpiece in an embodiment of the present invention; DETAILED DESCRIPTION

[0010] An embodiment of a method for designing the convexity of a multi-segment tangent arc of the present invention is shown in the figure: The method is based on the design principle of the logarithmic curve convexity to establish the formula: Y=Aln[1 / (1-0.975(2X / L) 2 )], where A is the axial compression coefficient of convexity, ln is the natural logarithm, L is the total length of the horizontal axis corresponding to the logarithmic curve, X is the horizontal axis coordinate value of the logarithmic curve, and Y is the vertical axis coordinate value of the logarithmic curve; According to the principle that the settlement slope at both ends of the logarithmic curve gradually increases, the present invention defines the horizontal coordinate value corresponding to the arc length of the first segment of each tangent arc, and the remaining arc lengths are a decreasing geometric progression with a common ratio r.

[0011] The present invention assumes that the horizontal coordinate corresponding to the endpoint (tangent point) of the middle segment of the multi-segment tangent arc profile is X1=±0.5L*k, and the horizontal coordinate length values of the arcs tangent to the left and right sides of the middle segment are set in the form of a decreasing geometric progression, where the common ratio is r. Then, the horizontal coordinate point X of the i-th segment tangent arc is known to be i = X1*(1- r i ) / (1-r), the corresponding vertical coordinate value Y i = ln[1 / (1-0.975(2X i / L) 2 )]; On this basis, the unit is 1 / 2 of the total length L of the horizontal coordinate of the logarithmic curve and the unit is the total length Y of the vertical coordinate, respectively, and the dimensionless coordinate point (X n , Y n ), where X n = 2X i / L=(1-r i ) / (1-r);Y n = Y i / Y = ln[1 / (1-0.975(2X i / L) 2 )] / 3.689; where i is the number of tangent points corresponding to a length of 0.5L. The first arc length coefficient k, the common ratio r, and the number of arc tangent points i are interrelated, as described below: When i=3, the logarithmic curve can be transformed into five tangent arc lines, k=(1-r) / (1- r i ) By optimizing the values of k and r, we can obtain a five-segment tangent arc curve that best fits the logarithmic curve. Similarly, when i=4, the logarithmic curve can be converted into a seven-segment tangent arc. The larger the i value, the more segments of the tangent arc, and the higher the fit with the logarithmic curve. By adopting the above method, the first arc length coefficient k=0.2868 and the common ratio coefficient r value are optimized to be 0.45. When i=4, the tangent point coordinates, radius and center position coordinates of the seven tangent arc convexities obtained by the present invention are as shown in the accompanying drawings. Figure 3 As shown in the figure, the mean square error of the difference between the drop of the seven-segment tangent arc convexity and the drop of the corresponding logarithmic curve convexity is 0.25% of the maximum drop Y at both ends of the curve. The overlap of the two curves is more than 99.994%. This accuracy makes no difference in engineering applications.

[0012] Among them, the coordinates of the tangent points of the seven tangent arcs can be solidified as shown in the following table: The radius and center coordinates of each tangent arc can be calculated using the coordinates of the tangent points of the tangent arcs mentioned above. In addition, the two ends of the seven tangent arcs are easy to extend during machine tool processing, which can effectively ensure that the dressing surface of the dressing wheel is larger than the width of the workpiece, thereby ensuring the grinding quality of the grinding wheel edge and achieving good use results. And through this setting, the coordinates of the tangent point, radius and center position of each tangent arc can be calculated, and these parameters can be directly input into the machine tool to process high-precision convex curves.

[0013] The above example is only one preferred specific example of the present invention. Common changes and substitutions made by those skilled in the art within the scope of the technical solution of the present invention are all included in the protection scope of the present invention.

Claims

1. A design method for multi-segment tangential arc convexity of a roller bearing, characterized in that: The following steps are included: S1. Based on the design principle of logarithmic curve convexity, the formula is established: Y=Aln[1 / (1-0.975(2X / L) 2 )], where A is the axial compression coefficient of convexity, L is the total length of the horizontal axis corresponding to the logarithmic curve, X is the horizontal axis coordinate value of the logarithmic curve, and Y is the vertical axis coordinate value of the logarithmic curve; S2. Make the unit of the total length of the horizontal coordinate of the logarithmic curve L and the total length of the vertical coordinate Y dimensionless; Define the dimensionless coordinates of the arc tangent point (X n , Y n ), where X n = 2X i / L;Y n = Y i / Ymax = ln[1 / (1-0.975(2X i / L) 2 )] / 3.689; S3. Taking into account the engineering calculation accuracy and product processing convenience, five-segment, seven-segment or any higher-segment tangent arc convexity can be selected to process the load-bearing surface profile of roller bearings.

2. The design method for multi-segment tangential arc convexity of a roller bearing according to claim 1, characterized in that: The convex axial compression coefficient A value can be any constant.

3. The design method for multi-segment tangential arc convexity of a roller bearing according to claim 1, characterized in that: The lengths of the horizontal coordinates corresponding to the arc lengths of each tangent arc decrease in the form of a geometric progression.

4. The design method for multi-segment tangential arc convexity of a roller bearing according to claim 1, characterized in that: The horizontal coordinate of the tangent point of any arc segment is: X n = 2X i / L=(1-r i ) / (1-r).

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