CN106446336A - Calculation method for tire carcass safety factor of all-steel radial tire - Google Patents

Abstract

The invention relates to the calculation field of a tire carcass safety factor of an all-steel radial tire, especially relates to a calculation method of the tire carcass safety factor of the all-steel radial tire through tire material models and a finite element analysis technique. The calculation method of the tire carcass safety factor of the all-steel radial tire uses self-developed simulation model software to build material model diagrams of the all-steel radial tire with different specifications and calculates a tire carcass structural safety factor of the all-steel radial tire through the finite element analysis.

Description

A kind of carcass safety multiple computational methods of all-steel radial tyre

Technical field

The carcass safety multiple that the present invention relates to all-steel radial tyre calculates field, particularly relates to one and utilizes tire material Material model and finite element analysis technology carry out the computational methods of the carcass safety multiple of all-steel radial tyre.

Background technology

With the fast development of Domestic Automotive Industry, automobile industry is more and more higher to the performance of tire and the requirement of quality. High-quality tyre should have superior security performance, endurance quality and high speed performance.All-steel radial tyre and traditional oblique glue Tire is compared, and owing to its rolling resistance is low, saves fuel and thorn wear-resisting, resistance to, and security performance is high, it has also become the main flow of tire industry Product.According to public security department's statistics, within 2013, whole nation large and medium bus quantity reaches 2,490,000, and lorry quantity reaches 20,160,000, lorry Increase by 1,160,000.Owing to big-and-middle-sized passenger-cargo carriage draws, manned member is many, car loading big, once occurs traffic accident to often result in great Casualties and property loss, be road traffic accident prevention emphasis and difficult point.Current automotive tire burst, fatigue driving with super Speed travels the three big killers having become traffic safety side by side, and tire is as the important component part of vehicle structure, and it is pacified Full position in commerial vehicle traffic safety for the property is especially prominent.Thus the safety multiple calculating formula tire construction at each position of tire The necessary component of design.

Radial has had over half a century since coming out, and it brings excellent property with unique structure Can, in tire development course, its structure is broadly divided into two kinds：Cross-ply structure and radial structure.With this phase Adapting to, the mechanics of tire as Design of Tire Structure theoretical foundation also can be divided into cross-ply structural mechanics and radial Structural mechanics.Owing to the performance of radial becomes more dependent on the design of rational structure, arriving of the model of structural mechanics of tire Developing further, the structure design that these theoretical models are applied to tire has sufficiently shown mechanical analysis at improvement wheel Important function in tire product quality, makes people recognize that structure design has status of equal importance with design of material.To 20 Century the mid-80, application in tire section profile design for the finite element analysis technology make tire section profile design dash forward Broken the constraint of natural equilibrium profile, people be sought for nature profile outside optimum profiles.So that finite element technique Being widely used in Design of Tire Structure, this not only accelerates tire new product development speed, also promotes simultaneously The variation of tire product.

The safety multiple numerical value of all-steel radial tyre is as the index describing tire safety, his institute's focus of attention It is the weakest link of Design of Tire Structure intensity, the shadow to tire working reliability under the conditions of i.e. minimum strength carries with maximum Ring.The mean value of current China's tyre industry custom employing stress and intensity calculates, but the actual numerical value with hydraulic pressure demolition Compare, have very large deviation, be primarily due to the not in place or ignorance calculating vulnerability analysis.

The development of the tyre industry of China has over half a century at present, and present tire yield is already at advanced in the world Status, tire enterprise is also accumulated from more rich knowhow and technical experience, but domestic tire production disperses force, skill Art research and development and design level still have gap with foreign outstanding enterprise.With the development of computer technology, increasingly mature many body system System dynamics simulation software is increasingly widely applied in the exploitation of automobile industry and tyre industry designs.Finite element fraction One very big purposes of analysis can effectively simulate tire test exactly.Can study difference by Finite Element Method makes simultaneously The universal law of mechanical characteristic under the conditions of with.

During current Design of Tire Structure, the commonly used conventional security multiple computing formula based on boundary-layer theory is

Wherein B_LSingle cord Fracture Force (kg/ root) R_drumFor assembly drum radius (cm), u_endsBody cord density (root/ Cm), P is inflation pressure of tire (kg/cm²), R_a、R_b、R_cBe respectively body cord crown center radius, at maximum section width half Footpath and wire loop radius, as it is shown in fig. 7, unit takes cm.

The calculating of all-steel radial tire carcass safety multiple is chosen extremely important for the design of its structure, steel wire, tire Security and several quality problems thereof are relevant with carcass security, problem as quick-fried in the slide fastener on market, steel wire together break problem and Tyre cavity Rose and real drum problem are all chosen with the security of carcass, steel wire etc. close relationship, therefore tire accurately Body safety multiple calculates has important directive function to actual product design, product quality.

Content of the invention

The calculating of all-steel radial tyre safety multiple is one of important parameter of tire design, directly affects tire used peace Quan Xing, the defect simultaneously affecting product is paid compensation for waiting other quality problems.Traditional safety multiple calculates and actual hydraulic pressure explosion examination Test and differ greatly, therefore study a kind of new safety multiple computational methods extremely important.

The safety multiple computational methods of a kind of carcass unit, the method uses below equation to calculate：

Wherein：B is belt single cord Fracture Force, and unit is N/ root；

L_elemFor element length, unit is cm；

a₀For cord density coefficient；

u_endsCord rolls density, and unit is root/cm；

E_elemUnit cord-thread direction is the tensile stress of circumference, and unit is N/cm²；

S_elemUnit cord-thread direction cross-sectional area, unit is cm²；

Described

I.e. assembly drum radius R_dumWith unit radius of gravity center R_elemRatio.

The carcass safety multiple computational methods of a kind of all-steel radial tyre, the method uses described formula to calculate The safety multiple of unit, tire belt general safety multiple takes the minimum of a value of its each unit safety multiple, draws tire Belt general safety multiple value, i.e. W=min w_i, i=1,2,3....n, n are carcass unit number.

The present invention, as a example by 10.00R20 all-steel radial tyre, utilizes tire material model and the structural capacity of independent research Learning finite element analysis technology, carcass cord/elastomeric material chooses C60-225HT and C60-175W bis-kinds, and air pressure is respectively 0.83Mpa, 0.93Mpa, carried out the carcass safety multiple under tyre inflating state and load on 3900kg state and calculated, point The difference of analysis tire safety multiple under inflation and load condition and Variation Features.Carry out Experimental Comparison by hydraulic pressure demolition, always Knot designs a set of brand-new carcass safety multiple computing formula.

Brief description

The ELEMENT MESH GRAPH of a certain tangent plane of Fig. 1 all-steel radial tire.

The enlarged drawing of a certain unit of Fig. 2 carcass.

Fig. 3 is that the change that the blowing pressure is 0.83Mpa, 0.93Mpa, C60-225HT carcass each unit safety multiple is intended to.

Fig. 4 is the variation diagram that the blowing pressure is 0.83Mpa, 0.93Mpa, C60-175HT carcass each unit safety multiple

Fig. 5 be the blowing pressure be 0.83Mpa, under load 3900kg operating mode, C60-225HT carcass ungrounded section each unit Safety multiple variation diagram.

Fig. 6 be the blowing pressure be 0.83Mpa, under load 3900kg operating mode, C60-175HT carcass ground connection section each unit Full multiple variation diagram.

Fig. 7 is that conventional security multiple calculates carcass schematic diagram.

Fig. 8 is finite element analysis computation solution procedure.

Fig. 9 is finite element analysis analysis and safety multiple calculation process.

Detailed description of the invention

1st, tire material model and tire construction mechanics finite element analysis general introduction

Here, first some theory and technologies developed involved by tire construction finite element analysis software are made briefly generally State.

1.1 model of element

Have employed two kinds of model of elements:Slotting unit and the six node pentahedron isoparametric elements such as eight node hexahedrons.

1.2 material model

Elastomeric material Incoercibility is solved by Lagrangian multiplier method, and its physical nonlinearity Mooney- Rivlin model is simulated, and strain energy density function describes：

W(I₁,I₂)=C₁₀(I₁-3)+C₀₁(I₂-3)

Wherein I1 and I2 is respectively strain the first and second invariants, C10 and C01 is the material constant being determined by experiment.

For rubber-base composite material, simulated by orthotropic material model, its corresponding Equivalent Elasticity mould Amount is determined by Halpin-Tsai equation by modulus and the volume fraction of elastomeric material and reinforcing fiber materials

1.3 geometrical model

For the large deformation of tire, using Lagrangian method to be described, strain tensor and stress tensor are taken as respectively Green-Lagrangian strain tensor E and Equations of The Second Kind Piola-Kirchhoff stress tensor S can be expressed as：

Wherein ∑ is first kind Piola-Kirchhoff stress tensor.Here, Green-Lagrangian strain tensor E can be shown as with offset table again：

1.4 equilibrium equation

Make q0 be the body force being defined in initial configuration, then use first kind Piola Kirchhoff stress tensor ∑ table The equilibrium equation showing is：

Div ∑+q0=0

1.5 constitutive equation

For elastic fluid, strain with Equations of The Second Kind Piola Kirchhoff stress tensor S and Green-Lagrangian and open The constitutive equation that amount E represents is：

S_ij=D_ijklE_kl

If tetradic D_ijklIt is the function of strain tensor E, then be nonlinear elasticity；If D_ijklIt is constant tensor, then It is linear elasticity.Sometimes non linear elastic constitutive relation equation Increment Matrix form represents：

DS=DT De

1.6 contact problems

Tire contacts process with ground

How to process the difficult point that contact area is Nonlinear Analysis of Tires.Effect between tire and ground is a large deformation Contact problems.The outstanding feature of contact problems is that contact boundary condition cannot be determined in advance.It is well known that linear contact problem Solution is to obtain after the shape having made contact area supposes and contact force distribution pattern supposes, here it is famous Hertz is false Fixed.And for nonlinear large deformation contact, it is impossible to understand the shape of contact zone and the distribution form of contact force in advance.For Problem above, uses variable bound and the concept of constraint increment.Its basic thought is:Be given monolateral before each step calculates execution The constraint knots modification of displacement constraint being substituted in increment equilibrium equation calculates, at any time according to constraint reaction with freely save Restrained boundary is changed in some displacement.As free node displacement increment can be with superposition, constraint increment also can superposition.Last Restrained boundary obtains in the lump with global displacement field；The advantage of the method is that computational accuracy is high, fast convergence rate.

Tire contacts process with wheel rim

Research Literature seldom having and mentions what wheel rim retrained, being also only the use of simple fixed constraint process hand even if having Method^[6].And in practical situation, between tire and wheel rim, there is interference fit relation, and when tire is installed to wheel rim, bead part Displacement and " lock ring " effect to wheel rim of one " interior receipts " will be produced.Due to wire loop and adjacent material, in modulus, difference is huge Greatly, will be inevitably generated an area of stress concentration at tyre bead portion, this area of stress concentration will produce shadow to tire construction Ring.It is not that nature is closely sealed additionally, due to bead part outer rim shape with rim base, thus first when being contained in tire on wheel rim First between tyre bead with wheel rim, exist for large deformation to contact.Simultaneously because rim surface has hyperbolicity structure, this contact is asked Topic is than contacting more complicated and being difficult to process between tire with ground.Here variable constraint method is used to solve.This problem It is performed such:The constraint reaction that will be located in every bit on contact surface is divided into tangential and two components of normal direction, if ratio between two Less than a certain number set in advance, then this point is stayed fixed motionless, and otherwise this point is creep setpoint, and slippage is constraint increment, and about The tangential component of Shu Fanli is in opposite direction and is directly proportional.Point after sliding also should be positioned at containment surfaces.Constantly iterative computation is simultaneously The position adjusting creep setpoint makes tangential force less, when all of obligatory point is all stayed and decided or move about in little scope, just closely Seemingly obtain without wheel rim Contact Boundary during friction.

1.7 tire construction finite element analysis flow processs

Finite element analysis computation solution procedure is as shown in Figure 8.

Finite element analysis analysis and safety multiple calculation process are as shown in Figure 9.

2nd, the calculating of finite element safety multiple

Finite element is the numerical method that approximation seeks general continuous domain problem, is a branch of Computational Mechanics, solves differential A kind of numerical method of equation problem.For tire, it is simply that by discrete for one piece tyre for up to ten thousand unit individualities (such as Fig. 1, certain One tangent plane tire divide grid chart), then as tire a part of framework material carcass be composed of multiple units equally (as Fig. 2, the enlarged drawing of a certain carcass unit), by finite element analysis, we can obtain unit and stress field, strain field.

The safety multiple of carcass each unit should be equal to the strength suffered tension force actual with monofilament of carcass monofilament Ratio.

Therefore, the safety multiple computing formula of carcass unit is expressed as：

Wherein B single cord Fracture Force (N/ root), L_elemUnit circumferential lengths (cm), a₀Cord density coefficient, u_endsCord Calendering density (root/cm), E_elemUnit cord-thread direction tensile stress (N/cm²), S_elemUnit cord-thread direction sectional area (cm²).

Fracture Force B of carcass individual wire can obtain data by tension test, and (steel wire producer and tire enterprise are conventional Test event), L_elem、S_elemFor stress and strain model basic parameter, E_elemCan be calculated by finite element dynamics and obtain, wherein

I.e. assembly drum radius R_dumWith unit radius of gravity center R_elemRatio, the change of the different cord density of reflection cell position Change.

Destroy first in weak spot in view of carcass, usually occur in tire shoulder and sidewall transitional region, namely The quick-fried position of tire slide fastener.Therefore carcass general safety multiple takes the minimum of a value of its each unit safety multiple, i.e.

W=min w_i, i=1,2,3....n, n are carcass unit number. (3)

Fig. 3～Fig. 6 sets forth the safety times when inflation pressure of tire is 0.83Mpa, 0.93Mpa for the carcass each unit Count numerical value, and the blowing pressure is the change in 3900kg ground area safety multiple for the 0.83Mpa load, have studied safety multiple (tradition is the safety times calculating under inflated condition based on the calculating of boundary-layer theory in change under inflation and different applying working condition Number, it is impossible to carry out calculating under different applying working condition).

3rd, test case

First, tire material performance test, the foundation of material model.

Including sizing material, steel-wire carcass material, steel wire/rubber composite etc., set up material property input file.

Remarks：Steel-wire carcass testing of materials i.e. obtains Fracture Force B of carcass cord.

2nd, tire product design and material distribution drawing are drawn.

Remarks：This part will obtain u_endsCarcass ply calendering density (root/cm), a₀Cord density coefficient, reflects not coordination Put the change of cord (unit) cord density.I.e. assembly drum radius R_dumWith unit radius of gravity center R_elemRatio,

3rd, the simulation analysis software utilizing independent research carries out finite element analysis computation to product.Including various aerated worts Calculate and inflate lower carry calculation etc..Through pre-treatment, calculating, last handling process, obtain the stress of carcass each unit, strain, position Shifting, geological information etc..Refer to above-mentioned " finite element analysis analysis and safety multiple calculation process ".

Remarks：This part can obtain, as the inflation pressure of tire P of input parameter；The geometry of the carcass unit extracting Information, element length L_elem, unit cord-thread direction cross-sectional area S_elem；FEM calculation obtains carcass each unit cord-thread direction (i.e. Warp-wise) tensile stress E_elem, so far, all parameters that the present invention calculates all obtain.

4th, the calculating of carcass safety multiple

The safety multiple computing formula of carcass each unit

The destruction of carcass first occurs at weak spot, and therefore tire belt general safety multiple takes its each unit The minimum of a value of safety multiple.

Therefore carcass general safety multiple takes the minimum of a value of its each unit safety multiple, i.e.

W=min w_i, i=1,2,3....n, n are carcass unit number.

4th, the main feature of the present invention and technical advantage

1) development of mechanics of tire is developed into present finite element analysis technology by boundary-layer theory, theory of thin shell, and tire has Finite element analysis technology is more advanced mechanics of tire analysis means, and therefore its computational accuracy is substantially improved.

2) present invention is based on the tire construction mechanics finite element analysis technology of independent intellectual property right and material model, to carcass Safety multiple calculate and give finite element formula, the overall carcass safety multiple of tire can not only be given, and can give Go out the safety multiple at each position of carcass (finite elements), the safety multiple under different applying working condition, contrast can also be described simultaneously Conventional security multiple computing formula has huge advantage, and conventional security multiple can only calculate the safety times of tire integral inflating operating mode Number.

3) hydraulic bursting test, finite element safety multiple calculate, conventional security multiple calculate three's correction data show (see Table 1), finite element carcass safety multiple and actual test error control about 5%, and tradition carcass safety multiple calculates than reality Test value bigger than normal 10%～20%, therefore, the present invention substantially increases the computational accuracy of carcass safety multiple, all-steel radial tire tire It is the basic parameter that tire product designs that body safety multiple calculates, and industry theory development is significant by the present invention.

Table 1 hydraulic bursting test test, safety multiple of the present invention calculate, the contrast of conventional security multiple evaluation

Claims (2)

1. the safety multiple computational methods of a carcass unit, it is characterised in that the method uses below equation to enter Row calculates：

$W_i=\frac{B.L_{elem}.a_0.u_{ends}}{E_{elem}.S_{elem}}---\left(1\right);$

Wherein：B is belt single cord Fracture Force, and unit is N/ root；

L_elemFor element length, unit is cm；

a₀For cord density coefficient；

u_endsCord rolls density, and unit is root/cm；

E_elemUnit cord-thread direction is the tensile stress of circumference, and unit is N/cm²；

S_elemUnit cord-thread direction cross-sectional area, unit is cm²；

Described

I.e. assembly drum radius R_dumWith unit radius of gravity center R_elemRatio.

2. the carcass safety multiple computational methods of an all-steel radial tyre, it is characterised in that the method uses claim 1 Described formula carries out calculating the safety multiple of unit, and tire belt general safety multiple takes its each unit safety multiple Minimum of a value, draw tire belt general safety multiple value, i.e. W=minw_i, i=1,2,3....n, n are carcass unit Number.