Tire tread multi-section arc profile parameterization design method based on segmentation constraint

Abstract

The invention relates to a tire tread multi-section arc profile parameterization design method based on segmentation constraint, and belongs to the field of tire design. Basic parameters of the tire tread are determined, wherein the basic parameters comprise the outer diameter, the tread width and the shoulder sinkage; transversely dividing the width of the driving surface into n sections of arcs according to a preset proportion; establishing a longitudinal coordinate double-boundary constraint system of the right end point of the crown arc, wherein the minimum value and the maximum value are determined by the whole section of arc passing through the left end point of the crown arc and the tire shoulder end point and the y value of the tangent line passing through the left end point of the crown arc at the right end point of the crown arc; selecting a y value in the extreme value interval, and calculating the coordinates of the center of circle of the crown arc on the Y axis; the minimum value and the maximum value of the vertical coordinate of the right end point of the arc close to one side of the tire shoulder are determined by the whole section of arc passing through the left end point of the arc and the end point of the tire shoulder and the y value of the tangent line passing through the left end point at the right end point of the arc; sequentially generating endpoint coordinates of each section of arc and corresponding circle centers; a tire shoulder arc Sn is generated through the tire shoulder endpoint, and a tread contour is formed.

Description

Technical Field

[0001] The present invention relates to the field of tire design, and in particular to a segmented constraint-based parametric design method for multi-segment arc profiles of tire treads, which is particularly suitable for rapid design and optimization of crown profiles of commercial vehicle tires. Background Art

[0002] As we all know, the traditional tire tread multi-segment arc design has the following defects:

[0003] (1) The coordinates of each arc segment endpoint rely on manual trial and error adjustment, which results in low design efficiency (a single adjustment takes >2 hours);

[0004] (2) The lack of systematic parameter control logic leads to discontinuous curvature of adjacent arc segments;

[0005] (3) The mathematical correlation model between the endpoint coordinates and the center position has not been established.

[0006] In view of the above defects, it is necessary to develop a faster and more intelligent method for generating multi-segment arc profiles of tire treads.

[0007] Korean patent KR 10-2006-0042618 discloses a tire tread profile design method based on a quadratic function model, focusing on solving the problem of uniform distribution of tread ground contact pressure. However, its three-zone static division is difficult to adapt to the multi-order variation characteristics of the tread curvature. Summary of the Invention

[0008] In order to overcome the shortcomings of the existing technology, the present invention provides a parametric design method for multi-segment arc profile of tire tread based on segmented constraints, which overcomes the following technical defects: (1) the traditional function model is incompatible with manufacturing process constraints; (2) the edge stress concentration caused by fixed partition ratio; and (3) the superposition of wear peak areas caused by single curvature transition.

[0009] The technical solution adopted by the present invention to solve the technical problem is: a tire tread multi-segment arc profile parametric design method based on segmented constraints, characterized in that the method includes the following steps:

[0010] (1) Determine the basic parameters of the tire tread, including the outer diameter D, the running surface width W, and the shoulder drop h;

[0011] (2) According to the width of the driving surface W, according to the preset ratio L1:L2:...:L n Divide horizontally into n arcs S1, S2, ..., S n , generate node sequence P0,P1,...,P n , whose horizontal coordinates are x0,x1,...,x n Satisfy x0=0 and

[0012] (3) Establish a double boundary constraint system of the ordinate y1 of the right endpoint P1 of the crown arc S1, where:

[0013] The minimum value y_min is the value between the left end point P0 of the crown arc and the end point P of the shoulder arc. n The y value of the entire arc at x1 is determined, and the center of the arc is on the Y axis;

[0014] The maximum value y_max is determined by the y value of the tangent line passing through point P0 at x1.

[0015] (4) According to the user-selected y1∈[y_min,y_max], combined with the coordinates of the left endpoint P0, the coordinates of the crown arc center O1 are automatically calculated so that the center of the circle is located on the Y axis;

[0016] (5) Establish the tangency constraint mechanism between adjacent arcs S1 and S2:

[0017] When the minimum value of y2 is determined, the left end point P1 of arc S2 and the shoulder end point P n The center of the entire arc should be on the straight line O1P1;

[0018] When determining the maximum value of y2, the tangent line through point P1 should be perpendicular to the straight line O1P1 and point toward the shoulder of the tire;

[0019] (6) Iterate steps (4) and (5) to generate S2, S3, ..., S n-1 The coordinates of each arc endpoint and the corresponding center;

[0020] (7) Take Generate shoulder arc S n , and finally form a complete tread profile.

[0021] In the step (1), according to the basic parameters of the tire tread, it can be known that the center coordinates of the tire tread are The coordinates of the shoulder endpoint are

[0022] In the step (2), the preset ratio is an equal proportion division or a user-defined non-uniform ratio, and the length of each arc segment satisfies

[0023] In step (2), the node P i The horizontal coordinate is calculated as follows:

[0024]

[0025] In step (3), the minimum value y_min of the ordinate y1 of the right endpoint P1 of the crown arc S1 is calculated as follows:

[0026] 1) Establish a pass point and The arc equation with the center on the Y axis is:

[0027]

[0028] 2) Solve equation (2) and get

[0029] 3) Substitute x = x1 into the arc equation (1) and find the two y1 values. Since the arc is above the center, the larger value is taken as y_min.

[0030] In the step (3), the maximum value y_max of the ordinate y1 of the right endpoint P1 of the crown arc S1 is determined by the y value of the tangent through point P0 at x1. At this time, the tangent through point P0 is Therefore

[0031] In step (4), y1 can take values ​​continuously within the interval [y_min, y_max], usually as a percentage of the interval length, as shown in the following formula:

[0032] y1=y_min+(y_max-y_min)*d, where d∈[0,0.2,0.4,0.6,0.8].

[0033] In the step (4), the coordinates of the crown arc center O1 are satisfy:

[0034] The solution is

[0035] In step (5), the tangency constraint mechanism is applicable to all adjacent arcs. For any adjacent arc S k and S k+1 , determine y k+1 The minimum value is calculated as follows:

[0036] 1) Calculate line segment P k P n The midpoint coordinates are and line segment P k P n The slope Thus, the line segment P is determined k P n The perpendicular bisector P′ k P′ n Point-slope form of the equation

[0037] 2) Determine the straight line O k P k Two-point equation of a line Where (x k,0 ,y k,0 ) is O k coordinate;

[0038] 3) Calculate the intersection of the two straight lines to obtain the arc S k+1 The center of the circle O k+1 ;

[0039] 4) Establish a point O k+1 is the center of the circle, passing through point P k and P k+1 The arc equation, substituting x k+1 Get y k+1 The two values ​​of , the larger value is taken as y k+1 The minimum value of .

[0040] In step (5), the tangency constraint mechanism is applicable to all adjacent arcs. For any adjacent arc S k and S k+1 , determine y k+1 The maximum value is calculated as follows:

[0041] 1) Calculate the straight line O k P k The slope

[0042] 2) Determine the passing point P k And with the straight line O k P k Perpendicular tangent line equation

[0043] 2) x k+1 Substitute the tangent equation to get y k+1 , which is y k+1 The maximum value of .

[0044] The present invention offers the advantage of a multi-degree-of-freedom design process. First, the horizontal coordinates of each arc segment are determined based on the travel width and a custom ratio. Second, dual-constraint boundary conditions are applied to the intersections of adjacent arcs to define the range of the vertical coordinate, which varies continuously within the maximum range. Finally, by adjusting the shoulder drop as another adjustment dimension, the resulting set of diverse solutions can fully meet design and simulation requirements. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] The present invention will be further described below with reference to the accompanying drawings and examples.

[0046] Figure 1 It is a schematic diagram of the overall structure of the tread profile;

[0047] Figure 2 It is a schematic diagram of the horizontal division of each arc segment of the tread profile;

[0048] Figure 3 It is a schematic diagram of the upper and lower limits of the vertical coordinate value of the right end point of the crown arc;

[0049] Figure 4 This is a schematic diagram of crown arc center calculation;

[0050] Figure 5 It is a schematic diagram of the tangency constraint of adjacent arcs;

[0051] Figure 6 It is a schematic diagram of a four-segment arc design example;

[0052] Figure 7 This is a comparison chart of parameterized multi-solution effects;

[0053] Figure 8 This is a partial enlarged schematic diagram of the parameterized multi-solution of the third and fourth arc segments. DETAILED DESCRIPTION

[0054] The present invention takes a commercial vehicle tire 29560R22.5 with a four-segment arc tread design (n=4) as an example to further specifically illustrate the implementation of the present invention. Figure 1 The overall structure of the tread profile is shown, including the markings of the tire's outer diameter D, running surface width W, and shoulder drop h, the distribution of multiple arcs S1 to S4, and the positions of nodes P0 to p4.

[0055] The basic implementation steps of a segment-constrained parametric design method for tire tread multi-segment arc profile are as follows:

[0056] (1) Determine the basic parameters of the tire tread.

[0057] Enter tire specifications:

[0058] The outer diameter D = 926.6 mm, the running surface width W = 258 mm, and the shoulder sinking amount h = 12 mm.

[0059] Calculate the initial coordinates:

[0060] Center point P0 (0, D / 2) = (0, 463.3), shoulder endpoint p4 (W / 2, D / 2-h) = (129, 451.3)

[0061] (2) Division ratio and node generation.

[0062] like Figure 2 As shown, the non-uniform ratio L1:L2:L3:L4=3:2:2:3 is selected, the total number of proportional units L=3+2+2+3=10, and the horizontal coordinates of each segment are:

[0063] x0=0 (1)

[0064] x1=(3 / 10)×W / 2=38.7 (2)

[0065] x2=(3+2) / 10×W / 2=64.5 (3)

[0066] x3= (3+2+2) / 10×W / 2 = 90.3 (4)

[0067] x4= W / 2=129 (5) Generate a node sequence:

[0068] P0(0,463.3), P1(38.7,y1), P2(64.5,y2), P3(90.3,y3), P4(129,451.3). (6)

[0069] (3) Calculation of double boundary constraints of crown arc (taking point P1 as an example).

[0070] like Figure 3 As shown, the minimum value y_min of y1 is determined by the value of the entire arc of P0 and P4 at x1, and the maximum value y_max of y1 is determined by the value of the tangent of P0 at x1. Specifically,

[0071] 1) y_min calculation:

[0072] Establish the equation of the entire arc passing through P0 and P4:

[0073]

[0074] The coordinates of the circle center are O(0,D / 2-R)=(0,-236.075). Substitute x=x1 to solve for y:

[0075] (38.7-0) 2 + (y1+236.075) 2 =699.375 2 (8)

[0076] Take the upper intersection point y_min=462.2284

[0077] 2) y_max calculation:

[0078] The horizontal tangent line y passing through P0 is 463.3. Substituting x into x1, we get y_max = 463.3.

[0079] (4) Determine the vertical coordinate of the right endpoint of the crown arc and calculate the center of the crown arc.

[0080] Take d = 0.4 (40% position of the y1 value interval), we have

[0081] y1=y_min+(y_max-y_min)*d=462.657 (9) The geometric relationship between the crown arc center and the left and right endpoints is as follows Figure 4 As shown, substitute into the circle center formula

[0082]

[0083] The center of the circle is O1(0,D / 2-R)=(0,-701.3327).

[0084] (5) Iteration of adjacent arc tangency constraints (taking S1→S2 as an example, calculating the maximum value of y2).

[0085] like Figure 5 As shown, by constraining the center of the entire arc of P1 and P4 to be on the straight line O1P1, the value of the entire arc at x2 is calculated to determine the minimum value y_min of y2, and the maximum value y_max of y2 is determined by the value of the tangent of P1 at x2. Specifically,

[0086] 1) Minimum value constraint:

[0087] i) Construct the perpendicular bisector of P1P4:

[0088] Calculate the midpoint coordinates of line segment P1P4 as and the slope of line segment P1P4,

[0089]

[0090] Thus, the point-slope equation of the perpendicular bisector P′1P′4 of the line segment P1P4 is determined.

[0091]

[0092] ii) Determine the two-point linear equation of line O1P1

[0093] Points O1 (0, -701.3327) and P1 (38.7, 462.657), the equation is:

[0094]

[0095] iii) Calculate the intersection of the two lines, which is the center of arc S2, o2 (22.2245, -33.0086);

[0096] iv) Construct the equation of the arc with point o2 as the center and passing through points P1 and P4:

[0097] (x-22.2245) 2 +(y+33.0086) 2 =(38.7-22.2245) 2 +(462.657+33.0086) 2 (14)

[0098] Substitute x2=64.5 to obtain two values ​​of y2, and take 461.1256 as the minimum value of y2.

[0099] 2) Maximum value constraint:

[0100] i) Calculate the slope of the line o1P1:

[0101]

[0102] ii) Determine the equation of the tangent line passing through point P1 and perpendicular to line O1P1:

[0103]

[0104] iii) Substituting x² = 64.5 into the tangent line equation yields y² = 461.7994, which is the maximum value of y².

[0105] (6) Parametric generation

[0106] Repeat steps (4) and (5) to calculate the coordinates of the center of each arc and subsequent nodes, where the vertical coordinates of each arc intersection are constrained to be d1 = 0.4, d2 = 0.6, d3 = 0.8, d4 = 0, and finally the parameters of the four arc segments are obtained, as shown in the figure. Figure 6 As shown:

[0107] Arc Center coordinates (mm) Radius (mm) End point coordinates (mm) <![CDATA[S1]]> (0,-701.6327) 1164.9327 (0,463.3),(38.7,462.657) <![CDATA[S2]]> (-2.4227,-774.5193) 1237.8596 (38.7,462.657),(64.5,461.5299) <![CDATA[S3]]> (-20.7785,-1113.5483) 1577.3851 (64.5,461.5299),(90.3,459.9209) <![CDATA[S4]]> (80.8775,326.4483) 133.8048 (90.3,459.9209),(129,451.3)

[0108] Finally, the vertical coordinates of the intersection points of adjacent arcs are traversed by a computer program d∈

[0109] [0,0.2,0.4,0.6,0.8], we get 5 3 A design scheme with the following effect: Figure 7 As shown. The third and fourth arcs are partially enlarged and shown as Figure 8 shown.

[0110] In summary, the segmented constraint-based parametric design method for tire tread multi-segment arc profiles proposed in this paper achieves efficient optimization design of tread profiles through geometric constraints and dynamic boundary control. Its core innovations can be summarized as follows:

[0111] 1) Innovative application of the double-boundary constraint system

[0112] For the vertical coordinates of each arc endpoint, a dual-boundary constraint model was constructed based on the geometric continuity of the entire arc (lower limit) and the tangent curvature constraint (upper limit). This model ensures a smooth transition in the tread profile while avoiding the stress concentration caused by sudden changes in curvature in traditional designs.

[0113] 2) Multi-solution space parametric design mechanism

[0114] By introducing a preset proportional division and an interval interpolation coefficient (d value), a multi-dimensional design solution space is generated for the same driving surface width. Taking a four-arc design as an example, each intermediate node provides five levels of adjustable parameters (d∈[0, 0.2, 0.4, 0.6, 0.8]), theoretically generating 5^(n-1) design options (n≥2), significantly increasing the diversity of design solutions. Practical applications have shown that this method can shorten the traditional design cycle from 5-7 days to less than 2 hours.

[0115] 3) Dynamic iterative tangency constraint algorithm

[0116] The proposed adjacent arc tangency constraint mechanism ensures the continuous differentiability of multiple arcs through the collinearity constraint of the circle centers (minimum condition) and the orthogonality constraint of the tangents (maximum condition).

[0117] 4) Engineering applicability verification

[0118] This method has been successfully applied to the development of a series of passenger car tire products. Its parametric design framework can also be extended to complex contour design scenarios such as truck tires and aircraft tires, providing an innovative solution for digital design in the tire industry.

[0119] The advantages of the present invention are: (1) establishing a double-boundary constraint system, in which the lower limit ensures the geometric continuity of the tread profile by constraining the left endpoint to be in the same arc as the shoulder endpoint; the upper limit prevents sudden changes in curvature by constraining the tangent constraint, ensuring manufacturing feasibility; (2) realizing multi-solution space design: different curvature design schemes can be generated by dividing the tread at the same ratio.

Claims

1. A parametric design method for multi-segment arc profile of tire tread based on segmented constraints, characterized in that: The method comprises the following steps: (1) Determine the basic parameters of the tire tread, including the outer diameter D, the running surface width W, and the shoulder drop h; (2) According to the width of the driving surface W, according to the preset ratio L1:L2:...:L n Divide horizontally into n arcs S1, S2, ..., S n , generate node sequence P0,P1,...,P n , whose horizontal coordinates are x0,x1,...,x n Satisfy x0=0 and (3) Establish a double boundary constraint system of the ordinate y1 of the right endpoint P1 of the crown arc S1, where: The minimum value y_min is the value between the left end point P0 of the crown arc and the end point P of the shoulder arc. n The y value of the entire arc at x1 is determined, and the center of the arc is on the Y axis; The maximum value y_max is determined by the y value of the tangent line passing through point P0 at x1. (4) According to the user-selected y1∈[y_min,y_max], combined with the coordinates of the left endpoint P0, the coordinates of the crown arc center O1 are automatically calculated so that the center of the circle is located on the Y axis; (5) Establish the tangency constraint mechanism between adjacent arcs S1 and S2: When the minimum value of y2 is determined, the left end point P1 of arc S2 and the shoulder end point P n The center of the entire arc should be on the straight line O1P1; When determining the maximum value of y2, the tangent line through point P1 should be perpendicular to the straight line O1P1 and point toward the shoulder of the tire; (6) Iterate steps (4) and (5) to generate S2, S3, ..., S n-1 The coordinates of each arc endpoint and the corresponding center; (7) Take Generate shoulder arc S n , and finally form a complete tread profile.

2. The tire tread multi-segment arc profile parametric design method based on segmented constraints according to claim 1, characterized in that In the step (1), according to the basic parameters of the tire tread, it can be known that the center coordinates of the tire tread are The coordinates of the tire shoulder endpoint are 3. The tire tread multi-segment arc profile parameterization design method based on segmented constraints according to claim 1, characterized in that In the step (2), the preset ratio is an equal proportion division or a user-defined non-uniform ratio, and the length of each arc segment satisfies 4. The tire tread multi-segment arc profile parameterization design method based on segmented constraints according to claim 1, characterized in that In step (2), node P i The horizontal coordinate is calculated as follows:

5. The tire tread multi-segment arc profile parametric design method based on segmented constraints according to claim 1, characterized in that In step (3), the minimum value y_min of the ordinate y1 of the right endpoint P1 of the crown arc S1 is calculated as follows: 1) Establish a pass point and The arc equation with the center on the Y axis is: 2) Solve equation (2) and get 3) Substitute x = x1 into the arc equation (1) and find the two y1 values. Since the arc is above the center, the larger value is taken as y_min.

6. The tire tread multi-segment arc profile parametric design method based on segmented constraints according to claim 1, characterized in that In the step (3), the maximum value y_max of the ordinate y1 of the right endpoint P1 of the crown arc S1 is determined by the y value of the tangent through point P0 at x1. At this time, the tangent through point P0 is Therefore 7. The tire tread multi-segment arc profile parameterization design method based on segmented constraints according to claim 1, characterized in that In step (4), y1 can take values ​​continuously within the interval [y_min, y_max], usually as a percentage of the interval length, as shown in the following formula: y1=y_min+(y_max-y_min)*d, where d∈[0,0.2,0.4,0.6,0.8].

8. The tire tread multi-segment arc profile parametric design method based on segmented constraints according to claim 1, characterized in that In the step (4), the coordinates of the crown arc center O1 are satisfy: The solution is 9. The tire tread multi-segment arc profile parameterization design method based on segmented constraints according to claim 1, characterized in that In step (5), the tangency constraint mechanism is applicable to all adjacent arcs. For any adjacent arc S k and S k+1 , determine y k+1 The minimum value is calculated as follows: 1) Calculate line segment P k P n The midpoint coordinates are and line segment P k P n The slope Thus, the line segment P is determined k P n The perpendicular bisector P′ k P′ n Point-slope form of the equation 2) Determine the straight line O k P k Two-point equation of a line Where (x k,0 ,y k,0 ) is O k coordinate; 3) Calculate the intersection of the two straight lines to get the arc S k+1 The center of the circle O k+1 ; 4) Establish a point O k+1 is the center of the circle, passing through point P k and P k+1 The arc equation, substituting x k+1 Get y k+1 The two values ​​of , the larger value is taken as y k+1 The minimum value of .

10. The tire tread multi-segment arc profile parametric design method based on segmented constraints according to claim 1, characterized in that In step (5), the tangency constraint mechanism is applicable to all adjacent arcs. For any adjacent arc S k and S k+1 , determine y k+1 The maximum value is calculated as follows: 1) Calculate the straight line O k P k The slope 2) Determine the passing point P k And with the straight line O k P k Perpendicular tangent line equation 2) x k+1 Substitute the tangent equation to get y k+1 , which is y k+1 The maximum value of .

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