CN114004121B - Multistep static loading calculation method for tire grounding print - Google Patents
Multistep static loading calculation method for tire grounding print Download PDFInfo
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- 238000004364 calculation method Methods 0.000 title claims abstract description 23
- 230000003068 static effect Effects 0.000 title claims abstract description 21
- 238000011068 loading method Methods 0.000 title claims abstract description 15
- 238000006073 displacement reaction Methods 0.000 claims abstract description 31
- 238000000034 method Methods 0.000 claims abstract description 22
- 238000006243 chemical reaction Methods 0.000 claims description 11
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- 230000008569 process Effects 0.000 description 10
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- 230000009286 beneficial effect Effects 0.000 description 1
- 239000002131 composite material Substances 0.000 description 1
- 238000010276 construction Methods 0.000 description 1
- 239000013013 elastic material Substances 0.000 description 1
- 230000002706 hydrostatic effect Effects 0.000 description 1
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- 229920001778 nylon Polymers 0.000 description 1
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/20—Design optimisation, verification or simulation
- G06F30/23—Design optimisation, verification or simulation using finite element methods [FEM] or finite difference methods [FDM]
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- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
- G06F2119/14—Force analysis or force optimisation, e.g. static or dynamic forces
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Abstract
The invention relates to a multi-step static loading calculation method for a tire grounding print, and belongs to the field of tire structural design. Firstly, carrying out inflation analysis on the tire, then searching contact nodes by giving a pressure depth value, applying forced displacement to the contact points to solve a grounding print, and correcting the forced displacement boundary condition of the contact area by changing the pressure depth value for a plurality of times until the total constraint counter force in the vertical direction of the contact points is balanced with the external load when the tire is actually contacted. The advantages are that: the principle is simple, and the implementation is convenient; compared with the existing ground contact footprint solving method, the method does not need to establish a complex contact pair, does not need to consider a contact nonlinearity problem, and can solve and obtain the shape of the ground contact footprint and the contact pressure cloud pattern of the tire by performing finite element analysis by modifying the forced displacement boundary condition of the contact area by changing the pressure depth value for multiple times.
Description
Technical Field
The invention relates to the field of tire structural design, in particular to a multi-step static loading calculation method for tire grounding imprinting.
Background
Contact of the tire with the ground is a complex mechanical phenomenon and is also an important cause of tire damage up to failure and destruction. The traditional tire ground contact footprint calculation is generally solved through a finite element method, and the nonlinear finite element method is required to be adopted to process the problems of material, geometry and contact nonlinearity, so that the analysis flow is complex.
The tire contact problem belongs to the boundary nonlinear problem, and is one of the most difficult nonlinear problems, because the contact boundary is unknown, and meanwhile, the contact boundary is changed at the moment in the loading process, that is, the displacement and the contact force generated in the tire contact process are unknown, so that the solving difficulty is greatly increased. In the finite element analysis, it is necessary to identify in real time whether a point on the tire boundary is in contact with the ground, and if so, the corresponding contact force must be calculated. Since the contact forces of the boundary points affect the deformation of adjacent points, this process requires repeated calculations until the correct state of all possible points of contact on the tire is found. When general commercial software solves the tire ground footprint, the method of applying a load to the ground by applying a fixed constraint to the rim is equivalent to the actual contact process of the tire, complex contact pairs are required to be established for solving, contact nodes are required to be searched repeatedly in the calculation process, and convergence solutions are not easy to obtain. Because the main component of the tire is a cord rubber composite material, the problems of material nonlinearity and geometric nonlinearity also need to be considered, and the difficulty of solving the tire ground contact footprint is further increased.
Disclosure of Invention
The invention aims to provide a multi-step static loading calculation method for tire grounding imprinting, which solves the problems existing in the prior art. According to the invention, fixed constraint is applied to the rim, and the forced displacement boundary condition of the contact area is corrected by changing the pressure depth value for a plurality of times until the total constraint counter force in the vertical direction of the contact point is balanced with the external load when the tire is actually contacted. The invention does not need to consider complex contact nonlinearity, and is simple and easy to realize.
The above object of the present invention is achieved by the following technical solutions:
the multi-step static loading calculation method of the tire ground contact footprint comprises the following steps:
(1) Building a tire finite element model, performing inflation analysis, and calculating coordinate values of nodes on the outer surface of the tire after inflation;
(2) Searching a contact point by a given pressure depth, defining a forced displacement boundary condition, carrying out static finite element analysis on the basis of inflation analysis, and calculating a contact point constraint counter force;
(3) Deleting the forced displacement constraint of the point with negative constraint reaction force in the vertical direction, and carrying out finite element calculation again until the constraint reaction force in the vertical direction of all contact points is positive;
(4) Changing the pressure depth value by adopting a dichotomy until the sum of constraint counter forces in the vertical direction of the contact point is equal to the external load born by the tire in actual contact;
(5) And calculating the contact pressure according to the constraint counter force in the vertical direction of the constraint node, and obtaining a contact pressure cloud chart.
In the step (2), searching a contact point by a given pressure depth and coordinate values of an outer surface node after the tire is inflated, obtaining a coordinate range of the contact point of the tire between the lowest point coordinate of the pneumatic tire and the lowest point coordinate plus a pressure depth value, and defining a forced displacement boundary condition, wherein the size of the forced displacement is the coordinate value of the lowest point coordinate plus the pressure depth value minus the vertical direction coordinate value of the contact node of the tire; and then, carrying out static finite element analysis on the basis of inflation analysis, and calculating the constraint counter force of the contact point.
In the step (4), the forced displacement boundary condition of the contact area is corrected by changing the pressure depth value for a plurality of times by adopting a dichotomy method until the sum of constraint counter forces in the vertical direction of the contact point is equal to the external load born by the tire in actual contact, so that the aim of solving the ground contact footprint is fulfilled.
In the step (4), according to the linear relation between the contact point constraint counter-force sum and the pressure depth, the corresponding constraint counter-force sum is obtained by solving according to two pressure depth values, and a linear relation expression between the contact point constraint counter-force sum and the pressure depth can be obtained by fitting; according to the linear relation expression, the target external load size is substituted, so that the search interval of the dichotomy can be rapidly reduced, and the purpose of accelerating solution is achieved.
The invention has the beneficial effects that: an effective calculation method is provided for solving the ground contact footprint of the tire, and the method is simple in principle and convenient to implement; compared with the existing method for solving the ground print, the method does not need to establish a complex contact pair, does not need to consider a contact nonlinear problem, can solve and obtain the shape of the ground print and a contact pressure cloud image of the tire by performing finite element analysis by changing the pressure depth value for many times to correct the forced displacement boundary condition of the contact area, and can greatly improve and solve the convergence problem of the ground print.
Drawings
The accompanying drawings, which are included to provide a further understanding of the application and are incorporated in and constitute a part of this specification, illustrate and explain the application and together with the description serve to explain the application.
FIG. 1 is a flow chart of a multi-step static load calculation of the present invention;
FIG. 2 is a schematic representation of the tire and ground geometry of the present invention;
FIG. 3 is a schematic view of a tire contact analysis of the present invention;
FIG. 4 is a finite element model diagram of a tire of the present invention;
FIG. 5 is a cross-sectional view of a tire construction of the present invention;
FIG. 6 is a convergence graph of the present invention;
FIG. 7 is a graph showing the variation of the sum of the pressing depth and the constraint counter force of the contact point according to the present invention;
FIG. 8 is a cloud image comparison of the tire contact reaction force of the present invention;
fig. 9 is a cloud image comparison of the contact pressure of the tire of the present invention.
Detailed Description
The details of the present invention and its specific embodiments are further described below with reference to the accompanying drawings.
Referring to fig. 1 to 9, in the multi-step static loading calculation method of the tire grounding trace, inflation analysis is firstly carried out on a tire, then a contact node is searched for by giving pressure depth, forced displacement is applied to the contact node to solve the grounding trace, and the forced displacement boundary condition of a contact area is corrected by changing the pressure depth value for a plurality of times until the total constraint counter force in the vertical direction of the contact point is balanced with the external load when the tire is actually contacted. When the wheel center is subjected to an external load vertically downward, the tire deforms after the tire contacts the ground. In order to solve the ground footprint, the multi-step static loading calculation method comprises the following steps:
(1) And (3) building a tire finite element model, performing inflation analysis, and calculating coordinate values of nodes on the outer surface of the tire after inflation.
Firstly, building a finite element model of the tire, applying fixed constraint to a rim part, applying pressure to the inside of the tire, performing inflation analysis of the tire, and calculating coordinate values of nodes on the outer surface of the inflated tire.
(2) And (3) searching a contact point by a given pressure depth, defining a forced displacement boundary condition, carrying out static finite element analysis on the basis of inflation analysis, and calculating a contact point constraint counter force.
The distance that the center of the wheel moves down due to external load is defined as the depth of pressure during actual contact of the tire. Assuming that the direction of the downward movement of the wheel center is the negative direction of the z axis (related to a tire model coordinate system), the multistep static loading method only needs to set a pressure depth value, and can obtain a contact area node set by combining the coordinate value of an outer surface node of the tire after inflation and the geometric relationship of the tire in the grounding process, wherein the coordinate of the contact node z direction of the outer surface of the tire is between-R and +R+d, R is the radius of the tire, d is the pressure depth, and the schematic diagram of the geometric relationship between the tire and the ground is shown in fig. 2. According to the coordinate relationship, the magnitude of the forced displacement to be applied by each contact node is u z = - (R-d) -z, wherein z is the z coordinate of the contact node. And after the forced displacement required to be applied by the contact node is obtained, defining a forced displacement boundary condition for finite element analysis.
The tire footprint analysis is performed on the basis of the inflation analysis, and thus it is necessary to read the results of the inflation analysis, and for super-elastic near-incompressible rubber materials, it is necessary to obtain the hydrostatic pressure and the rate of change of volume of the last incremental step of the inflation analysis step in addition to the displacement results.
(3) And deleting the forced displacement constraint of the point with negative constraint reaction force in the vertical direction, and carrying out finite element calculation again until the constraint reaction force in the vertical direction of all contact points is positive.
After the corresponding forced displacement boundary condition is applied to the tire model, static finite element analysis is carried out on the basis of inflation analysis, and as tiny pits appear in the center part of the tire tread in the actual contact process, the vertical constraint counter force of the forced displacement point is ensured to be positive at first, and then the actual contact process is more met. Therefore, if the vertical constraint counter force of the constraint node applying the forced displacement has a negative value, the point needs to be deleted from the contact area node set, the forced displacement boundary condition is redefined, and finite element analysis is performed until the vertical constraint counter force of all the nodes in the contact area node set is positive.
(4) And repairing the positive pressure depth value by adopting a dichotomy method until the sum of constraint counter forces in the vertical direction of the contact point is equal to the external load born by the tire in actual contact.
When the static tire is subjected to external load in the vertical direction, the tire can be contacted with the ground to generate deformation, the ground is fixed in the actual contact of the tire, and the wheel center moves under the action of the external load. The multi-step static loading calculation applies a fixed constraint to the rim, the inflation analysis is performed first, then the contact node is searched for given pressure depth, and the forced displacement is applied to the contact node to solve the ground footprint, as shown in fig. 3. The forced displacement boundary condition of the contact area is corrected by changing the pressure depth value a plurality of times until the external load is balanced when the tire is in actual contact. According to Newton's third law, as long as the sum of the restraining reaction forces in the vertical direction of the contact point is equal to the external load born by the wheel center when the tire is actually contacted with the ground, the footprint can be determined to be the grounding footprint of the actual tire when the tire is loaded in the vertical direction, the pressing depth at the moment is the downward moving distance of the wheel center in the actual contact process, and the area of the restraining node is the area of the tire actually contacted at the moment. If the sum of constraint reaction force is not equal to the external load born by the wheel center when the tire is in actual contact with the ground, the pressure depth value is required to be changed, and the forced displacement boundary condition is redefined to perform finite element calculation until balance is met.
Because the function of the sum of constraint counter-force in the vertical direction of the contact point and the pressure depth belongs to a monotonically increasing function, the invention adopts a dichotomy to change the pressure depth value until the balance of force is satisfied. In order to quickly obtain accurate pressure depth, a large number of simulation experiments prove that: under the same tire pressure, the sum of constraint counter-force of the contact points and the pressure depth are in a linear relation. And the corresponding constraint counter-force sum is obtained by solving according to the two pressure depth values, and the linear relation expression of the contact point constraint counter-force sum and the pressure depth can be obtained by fitting. According to the linear relation expression, the target external load size is substituted, so that the search interval of the dichotomy can be rapidly reduced, and the purpose of accelerating solution is achieved.
(5) And calculating the contact pressure according to the constraint counter force in the vertical direction of the constraint node, and obtaining a contact pressure cloud chart.
And dividing the constraint counter force in the vertical direction of the constraint node obtained by finite element analysis by the unit area corresponding to each node to obtain the contact pressure of each node. After the tire is deformed by contact, the unit area of the contact node can be calculated by dividing the sum of the areas of all the surface units connected by each contact node by the corresponding number of units. And drawing a contact pressure cloud chart of the tire according to the contact pressure of each point.
Examples:
the ground footprint analysis was performed with reference to a model aircraft tire as shown in fig. 4. Fig. 5 shows the distribution of each component of tread, sidewall, carcass, apex, nylon scrim, inner liner, bead ring, wherein bead ring and carcass cord are wire elastic materials, and the material parameters are shown in table 1. The other components are all isotropic superelastic rubber materials. The rubber material adopts a Mooney-Rivlin constitutive model, and the material parameters are shown in Table 2, wherein A 10 and A 01 are material constants, and K is bulk modulus. In tire finite element simulation, it is necessary to determine not only the cord material properties, but also parameters such as the diameter of individual cords, the distance between adjacent cords, the angle of laying the cords, etc., which are all detailed in table 3. The tire pressure is 2.6MPa during inflation analysis, the vertical load applied to the tire center is 60000N, the total model is 44.3 ten thousand units, 46.7 ten thousand nodes and 140.1 ten thousand degrees of freedom. When the multi-step loading calculation method is adopted, the difference of the constraint counter force sum of the contact nodes minus the vertical load applied to the wheel center is defined as a residual error, and the calculation is terminated when the absolute value of the residual error divided by the vertical load applied to the wheel center is less than 10 -3. As the number of iterations (number of corrected depths) increases, the value of the absolute value of the residual divided by the vertical direction load to which the wheel center is subjected becomes closer to 0, and the convergence curve of the absolute value of the residual divided by the load outside the wheel center is shown in fig. 6. The curve of the sum of the pressing depth and the constraint counter force of the contact node is shown in fig. 7. The contact reaction force cloud chart and the contact pressure cloud chart calculated by the commercial software ABAQUS and by the multi-step static loading calculation method are shown in fig. 8 and 9, respectively, and the result pairs of the contact reaction force maximum value and the contact pressure maximum value are shown in table 4. Through result comparison, the contact counter force cloud patterns obtained through the multi-step static loading calculation method and the ABAQUS software calculation are similar in shape, meanwhile, the shapes of the obtained contact pressure cloud patterns are basically consistent, and the numerical errors are all within 1%.
TABLE 1 cord and bead Material parameters
Table 2 parameters of tire rubber materials
TABLE 3 reinforcing cord parameters for carcass layers
Table 4 comparison of the results of the ground print
The above description is only a preferred example of the present invention and is not intended to limit the present invention, but various modifications and variations can be made to the present invention by those skilled in the art. Any modification, equivalent replacement, improvement, etc. of the present invention should be included in the protection scope of the present invention.
Claims (1)
1. A multi-step static loading calculation method for a tire ground contact patch is characterized by comprising the following steps of: the method comprises the following steps:
(1) Building a tire finite element model, performing inflation analysis, and calculating coordinate values of nodes on the outer surface of the tire after inflation;
(2) Searching a contact point by a given pressure depth, defining a forced displacement boundary condition, carrying out static finite element analysis on the basis of inflation analysis, and calculating a contact point constraint counter force;
Searching a contact point by setting the pressure depth and the coordinate value of an external surface node after the tire is inflated, obtaining the coordinate range of the contact point of the tire between the lowest point coordinate of the inflated tire and the lowest point coordinate plus the pressure depth value, and defining a forced displacement boundary condition, wherein the size of the forced displacement is the coordinate value of the lowest point coordinate plus the pressure depth value of the tire minus the vertical coordinate value of the contact node; then carrying out static finite element analysis on the basis of inflation analysis, and calculating the constraint counter force of the contact point;
(3) Deleting the forced displacement constraint of the point with negative constraint reaction force in the vertical direction, and carrying out finite element calculation again until the constraint reaction force in the vertical direction of all contact points is positive;
(4) Changing the pressure depth value by adopting a dichotomy until the sum of constraint counter forces in the vertical direction of the contact point is equal to the external load born by the tire in actual contact;
The forced displacement boundary condition of the contact area is corrected by changing the pressure depth value for a plurality of times by adopting a dichotomy method until the sum of constraint counter forces in the vertical direction of the contact point is equal to the external load born by the tire in actual contact, so that the aim of solving the ground print is fulfilled;
According to the linear relation between the contact point constraint counter-force sum and the pressure depth, solving according to two pressure depth values to obtain a corresponding constraint counter-force sum, and fitting to obtain a linear relation expression of the contact point constraint counter-force sum and the pressure depth; according to the linear relation expression, substituting the target external load size can quickly reduce the search interval of the dichotomy, so as to achieve the aim of acceleration;
(5) And calculating the contact pressure according to the constraint counter force in the vertical direction of the constraint node, and obtaining a contact pressure cloud chart.
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- 2021-11-03 CN CN202111292608.2A patent/CN114004121B/en active Active
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| JP2018079789A (en) * | 2016-11-16 | 2018-05-24 | 東洋ゴム工業株式会社 | Tire ground contact simulation method, device, and program |
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| CN109325268A (en) * | 2018-08-31 | 2019-02-12 | 江苏大学 | A kind of Vehicular turn resistance considering tire and pavement friction away from calculation method |
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