Verification of the Simulation Model with Actual Research Vertical Stiffness Passenger Car Tire
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1 Machine Dynamics Research 03, Vol.37, No, 5-4 Verification of the Simulation Model with Actual Research Vertical Stiffness Passenger Car Tire Abstract Maciej Berdychowski, Konrad J. Waluś Poznan University of Technology The paper presents the possibilities of mathematical modeling of hyperelastic materials. Method of the composite hyperelastic medium modeling is presented. The rubber of the car's tire has been used as the example of such medium. Analysis of deformation is presented by numerical simulation with the use of Abaqus CAE software. The results obtained from calculation were discussed in terms of their practical use. Keywords: hyperelastic materials, rubber, CAE software. Introduction Road safety is constantly tackled the issue today. It depends on the skill of the driver, since the compliance with the traffic rules and environmental conditions and surfaces. Accidental and intentional response driver can cause a dangerous situation on the road, leading to a collision or accident. Increasing road safety infrastructure, enforce rules and behavior of road users, and the development and technological advances in vehicle design. Created systems and structures such as controlled crumple zones, airbags, seat belts, and others whose purpose is to protect human life during an accident. Finally, a system whose purpose is to mitigate the effects of, and even preventing an accident. These are mainly the ABS/ESP or any derivative of these systems. Their effectiveness depends to a large extent on the tire adhesion. This parameter is a value dependent on many variables and can undergo significant changes depending on the state and type of substrate. Effects on him to such parameters as: tire size, tire type, tire pressure, vehicle load, condition and surface, lying on the road contaminants such as sand, mud, water, snow, ice and more. All these parameters have an influence on the size of the contact area between the tire and road surface [Waluś K.J 009], which has a direct impact on the safety of the vehicle.this paper presents a comparative Chair of Machine Design Fundamentals
2 6 M. Berdychowski, K.J. Waluś analysis of experimentally obtained and the results of simulations based on tire deflection on the pressure and load, to verify the numerical model developed of tire.. Research For the purposes of analysis, numerical model to build tires. The tire is a composite element composed of a number of characteristic elements, each of which is made of another material having a linear or non-linear. The basic element of which is made tire (rubber) is a hyperelastic material (non-linear). In it is embedded cord, acts as a matrix or a belt. The matrix acts as a support element in the tire. It is constructed of cord strands arranged radially (radial) over the entire length of the cross-section of the tire. While belting acts as a strengthening of width equal to the width of the tread and just below it [Jurkowska B., 975]. The use of many different materials deposited in such a way to provide desired tire properties such as the shape, the deformation and deflection under load, toughness, adhesion to the rim, vibration damping, etc. [Jurkowska B.,975]. Modeling tires so complex structure with variable stiffness and thickness causes a lot of problems. An additional complication is the fact that different types of tires are different geometry, the type of rubber used, number of layers of the cord and the type of material from which it was made [Talaśka K., 0, Tarasiuk P., 008]. The analysis of tire sizes 65/80 R 4. The actual identification of the tire geometry was then mapped virtually geometry. Modeled everything except tire bead steel reinforcement. Replaced them through the selection of appropriate boundary conditions. The preliminary analysis of the substrate interacting with the tire was modeled as a rigid body, because the information about the state of stress and deformation of the substrate was not the purpose of these considerations. Defined and the pressure acting on the inner surface of the tank. Same tire received all degrees of freedom except for the vertical displacement. Geometry was modeled finite element discretization. Fig.. Construction of tires: bead, carcass, 3 belt, 4 tread [ABAQUS Technology Brief, 0]
3 Verification of the simulation model with actual research vertical stiffness passenger 7 Fig.. Geometric model of the tire and the ground: tire, - ground Fig. 3. Model tire and the ground with the applied FEM mesh: - carcass, - belts, 3 - tire Model includes hyperelastic rubber material and viscoelasticity (viscoelastic). Abaqus / CAE provides an assessment of hyperelastic material is automatically created by the response curves with selected potential strain energy. The potential energy of deformation (Strain energy potential) in the present task takes the form of a polynomial. According to [ ABAQUS 6.0 Documentation, 00 ] form of potential energy of deformation of the polynomial is as follows: N U = C i+ j= N i j el ij ( I 3) ( I 3) + ( J i= Di where: U is the energy per unit of reference, N is a parameter of the material, and D i the material parameters are dependent on temperature, I ) i () C ij I and are the first and second invariants of the stress deviator defined as [ ABAQUS 6.0 Documentation, 00 ]: I = λ + λ + and I = λ + λ + λ () λ3 3
4 8 M. Berdychowski, K.J. Waluś where: the tensile stress deviator takes the form 3 λi = J λ, J expresses the total el volume, J elasticity of the total volume in the main directions. The initial shear modulus and bulk modulus determined by the relation (3) [ABAQUS 6.0 Documentation, 00]: µ = ( C 0 C ), o + 0 i K 0 = (3) D In this work, the following parameter values: C0 = 0000, C0 = 0, D = 0 Between the surfaces of the tire and the ground contact is defined characteristics of a surface to surface. Identified properties of tangent and normal. The tangential contact forces are calculated using an algorithm with the ability to define the penalty coefficient of friction. In the normal direction used the "hard contact". The tire cord occurs, in which we can distinguish two main layers: the belt and the matrix. Belt layers occurs in the middle of the tank just below the tread and composed of thin threads. Strengthens the tire cap ply for impact and helps maintain an even contact patch with the road surface. However, the inner layer of the matrix is composed of a thin tire wire and fabric, which is to increase the strength of the pressure. Also prevents against excessive distortion of the sidewalls of the address inequalities. The model takes into account the occurrence of tire reinforcement described. They were modeling in the form of finite element type "shell", embedded in solid elements "solid" (Fig. 3). Properties cord layers defined in the "Rebar layers" and assigned to the respective finite element. Table shows the material values assigned. Material Table. The material properties of the cord wrap and carcass Young's modulus Area per bar Spacing Poisson ratio [Pa] [m] [m] Carcass *0 9 0,3,96E Belts *0 9 0,3 7E Modeling cord also needs to give adequate bond between the finite elements that define the cord, and the FEM mesh defining the rubber material. To define appropriate depending on the binding used "embedded" that is used to define an element or group of elements submerged / embedded in other finite elements. 3. Research results The model number on the definition and application of material data FE mesh is analyzed. The calculation was performed for three cases tire inflation pressures of 0.5, 0. and 0.5 MPa. For each of these pressures were analyzed tank deflection under load. Adopted values of forces in the range of 50kg to 450kg at 50kg. The
5 Verification of the simulation model with actual research vertical stiffness passenger 9 exact values of the performed calculations are summarized in Table, and shown in Fig Force [kg] Table. Comparison of the results obtained from the numerical analysis of the experimental results 0,5 MPa 0,0 MPa 0,5 MPa Research Research Research ,5 6,34 4,5 5,54 4 4,9 00 9,5, , ,79 3,7 9,5, , 4 6, 4, ,55 7 8,47 4,5 6, ,8 9,5 0, ,9 3,7 9, ,5 7,8 4,5 5,,5 3, ,5 9,68 7 7,33 3,5 5, ,5 MPa Force [kg] Experimental studies Fig. 4. Graph the relationship between the deflection and load tire pressure in the tires 0,5 MPa
6 0 M. Berdychowski, K.J. Waluś ,0 MPa Force [kg] Experimental studies Fig. 5. Graph the relationship between the deflection and load tire pressure in the tires 0,0 MPa ,5 MPa Force [kg] Experimental studies Fig. 6. Graph the relationship between the deflection and load tire pressure in the tires 0,5 MPa 4. Research analysis The results of simulation based on the pressure of tire deflection and load were analyzed statistically determine the standard deviation of a single measurement. For the standard deviation of the normal distribution (using Type A evaluation of standard uncertainty [EA-4/0, PN ISO 3534-:00]), the following equation: n σ x = xi x the standard deviation of a single measurement ( ) i = n
7 Verification of the simulation model with actual research vertical stiffness passenger where: n number of measurements, x i the value of a single measurement, x average value or expected value, x i x the measurement error, maximum deviation from the expected value. Deflections obtained experimentally, in order to verify the developed model, it is considered as a model, which enabled the calculation of basic deviation from the expected value. The measurement results obtained were not observed excessive errors. After performing this analysis, the relative error percentage was calculated. The results of the statistical analysis are shown in Tables 3 to 5. Results of simulation with respect to the actual characteristics of the deflection tank characterized by the values of the relative error of.5 bar pressure from 0.9 to 6.8%,.0 bar pressure is in the range from. to 3.%, and the relative error for the pressure of.5 bar from 7. to 4.8%. Force [kg] Table 3. Comparative analysis of experimental measurements and simulations for the pressure of 0.5 MPa Experimental studies 0,5 MPa x i x The relative error percentage [%] ,5 6,34 0,706 5,3 00 9,5,,56 6, ,79 3,04 3, ,, 6, ,55 0,30, ,8 0,04 0, ,9 0,504, ,5 7,8,89 5, ,5 9,68 7,95 8,7 The standard deviation of a single measurement,467
8 M. Berdychowski, K.J. Waluś The standard deviation of a single measurement for the results of simulation deflection tire pressure of 0.5 MPa was σ = 0,5MPa,467[ mm] : and the maximum relative error MPa 6,8%. Following the modification of the Student-t 0,5 = distribution for 0 measurements and 95% confidence level designation of tire deflection error was worth σ 0,5MPa T studenta = 3,374[ mm]. Table 4. Comparative analysis of experimental measurements and simulations for pressure 0.0 MPa Force [kg] Experimental studies 0,0 MPa x i x The relative error percentage [%] ,5 5,54,08 3, ,5 50 3,7 5,53 0, , 4, ,47,6 8, ,5 0,9,96 7, 350 3,7,369 5, ,5 5, 0,49, ,33 0,09, The standard deviation of a single measurement,404 The standard deviation of a single measurement for the results of simulation deflection tire pressure of 0.0 MPa was σ = 0,0MPa,404[ mm] : and the maximum relative error MPa 3, %. Following the modification of the Student-t 0,0 = distribution for 0 measurements and 95% confidence level designation of tire deflection error was worth σ 0,0MPa T studenta = 3,8[ mm].
9 Verification of the simulation model with actual research vertical stiffness passenger 3 Force [kg] Table 5 Comparative analysis of experimental measurements and simulations for the pressure of 0.5 MPa Experimental studies 0,5 MPa x i x The relative error percentage [%] ,9 0,88, ,, 5,7 50 9,5,86 5,569 4,8 00 4,5 6,5 0,8 50 4,5 6,94 5,954 6, , ,6 4,666,4 400,5 3,3 3,4 8, ,5 5,,89 7, The standard deviation of a single measurement,96 The standard deviation of a single measurement for the results of simulation deflection tire pressure of 0.5 MPa was σ = 0,5MPa,96[ mm] : and the maximum relative error MPa 4,8%. Following the modification of the Student-t 0,5 = distribution for 0 measurements and 95% confidence level designation of tire deflection error was worth σ 0,5MPa T studenta = 4,50[ mm]. 5. Summary Task modeling tires that were made, it was difficult because they did not have accurate data in material test tires. The numerical model in the case was treated as a "black box". Knowing the input data (accepted test conditions) and output data (results), a numerical model in such a way that the selected input data giving as close as possible to the experimental results. The results obtained were compared with the simulation results obtained in experimental studies. Presented graphically in Chapter 3, the results show the convergence of the calculated deflection tire model developed with the values obtained experimentally. The calculated standard deviations for a single measurement taken in the analysis of pressures and loads do not exceed
10 4 M. Berdychowski, K.J. Waluś σ = 0,5MPa,96[ mm]. The maximum relative error percentage was 4.8%. The values of the error above 5% refer to the values for the imposition of pressure: 0.5 MPa - up to 00 kg, 0.0 MPa - up to 00 kg, 0.5 MPa - up to 50 kg. For the adopted model with tires of size 65/80 R4 operating pressure for a passenger vehicle Dacia Logan is 0.0 MPa and the single wheel load zwarzeniu vehicles ranges from about 50 kg (rear end) to about 30 kg (front of the vehicle). For the simulation calculations performed, pressure 0.0 MPa, and the load 50, 300 and 350 kg, the relative percentage error is in the range from 5.3 to 8.7%. The scope of the calculated values of the relative error suggests that results of simulations are consistent with experimental studies. Tire model was built in order to further analyze the issues of cooperation with the ground. It will assess the size of the contact area, which is important for the safety of the vehicle and directly related to the deflection of the tire, which is reflected in the value of the loading forces and pressure in the tire. References This work has been supported by National Science Centre grant ABAQUS Technology Brief, 0: An Integrated Approach for Transient Rolling of Tires TB-03-TRT-, January 0. ABAQUS 6.0 Documentation, 00. EA-4/0 Wyrażanie niepewności pomiaru przy wzorcowaniu, wydanie elektroniczne, 999, Jurkowska B., Jurkowski B. 975, Production of tires and tubes (Produkcja opon i dętek), WNT Warszawa 975. PN ISO 3534-:00, Statystyka, Terminologia i symbole Część : Ogólne terminy z zakresu rachunku prawdopodobieństwa i statystyki. Talaśka K., Waluś K. J., Berdychowski M. 0, Modeling car tires using FEM software (pilot study) [Modelowanie opon samochodowych z wykorzystaniem oprogramowania MES (badania pilotażowe)]; Technika Transportu Szynowego 9/0, s , Tarasiuk P. 008, FEM calculation of slow-moving vehicle wheels - tire model and the accuracy of the numerical solution (Obliczanie MES kół pojazdów wolnobieżnych - model opony a dokładność rozwiązania numerycznego), Acta mechanica et automatica, vol. no. 4, 008. Waluś K. J., Wolniewicz R. M., Olszewski Z., Drożyński M. 009, Analysis of pressure and load influence on geometric parameters of tire under static conditions, 7th French- Polish Seminar of Mechanics, , Lille, Francja, p
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