- Email: [email protected]
Influence of Camber Angle on Rolling Radial Tire under Braking State
Available online at www.sciencedirect.com Available online at www.sciencedirect.com
Procedia Engineering
ProcediaProcedia Engineering 00 (2011) Engineering 15 000–000 (2011) 4310 – 4315 www.elsevier.com/locate/procedia
Advanced in Control Engineering and Information Science
Influence of Camber Angle on Rolling Radial Tire under Braking State Gang Chenga*, Weidong Wangb, Guoqun Zhaoc, Yanjin Guanc, Zhonglei Wanga a School of mechanical and electronic engineering, Shandong Jianzhu University, Jinan 250101, China Department of Engineering Mechanics，School of Civil Engineering，Shandong University，Jinan 250061, China c Key Laboratory of Liquid Structure and Heredity of Materials, Ministry of Education, Shandong University, Jinan 250061, China b
Abstract To study the rolling properties of a radial tire, an accurate 3D 195/60R14 tire model is established. The modal includes the geometric nonlinearity due to large deformation, material nonlinearity, the anisotropy of rubber-cord composites, the nonlinear boundary conditions from tire-rim contact and tire-pavement contact. The model can be used to simulate the changes of a rolling tire and calculate the tire deformation for various operating conditions. The profile of inflated tire is studied experimentally and numerically. The simulation result is in good agreement with the test result. Some contact problems, such as the tire deformation, the shape of contact area, the contact pressure distribution, are discussed in detail.
© 2011 Published by Elsevier Ltd. Selection and/or peer-review under responsibility of [CEIS 2011] Keywords: radial tire; belt, camber; braking state.
1. Introduction The pneumatic tire is the only component transferring the load between the vehicle and the road. The camber performance of the tire influences the steering and the proper selection of wheel positioning parameters. The tire behaviour is directly related to the vehicle/road interaction, the interface between the wheel (rim + tire) and the ground must be considered. Gim et.al. [1] establish a semi-physical model which experimentally formulates vertical force as a function of tire effect, camber angle and lateral force. Smith et.al. [2] uses the steady-state finite element model, in which a composite friction energy is
* Corresponding author. Tel.: +86-0531-86367273; fax: +86-0531-86361369. E-mail address: [email protected].
1877-7058 © 2011 Published by Elsevier Ltd. doi:10.1016/j.proeng.2011.08.809
Gang – 4315 GangCheng Chengetetal.al// Procedia ProcediaEngineering Engineering15 00(2011) (2011)4310 000–000
2
calculated from friction energy predictions at selected loading conditions taken from the drive file events. The composite friction energy profile is finally compared to laser measurements of the worn tire profile to examine the feasibility of a “virtual wear test”. Rao et al. [3] simulated the dynamic behavior of a pneumatic tire by using an explicit finite element, and discussed the effects of camber angle and grooved tread on tire cornering behavior. Lecomte et.al. [4] developed an integrated model which predict the interior noise due to the vibrations of a rolling tire structurally transmitted to the hub of a vehicle. In the modal the tire belt is modeled as an orthotropic cylindrical ring of negligible thickness with rotational effects, internal pressure, and pre-stresses included. The effects of internal pressure, prestress, curvature, and tire rotation on free waves are discussed. Liu [5] modeled a rolling passenger tire by explicit transient dynamic FEA (ABAQUS) and found the lateral force was quite insensitive to inflation and vertical load. Tire materials are multiplayer, asymmetric and anisotropic. This study presents a tire contact characteristics of a 195/60R14 radial tire on braking state under different camber angles. Different parts of the tire and their corresponding material properties, interference fitting of tire and rim, friction are taken into account in the finite element model. The effects of camber angle on the deformation and contact stresses of tread and belt in the contact area were calculated. 2. Finite Element Model of Radial Tire The tire is a complex composite structure, made up of rubber material and cord–rubber composite. Treatment of the rubber, laminate, and boundary contact conditions is the main problem to be considered seriously and cautiously to establish the finite element model. 2.1. Mesh Generation and Element Selection The radial tire mainly includes tread, shoulder, sidewall, carcass, belt and bead ring. Materials of sidewall, inside liner, apex, and tread are pure rubber with differing hardness. Belt, carcass, and bead ring are a single layer or multilayer cord-rubber composite. Crown
Inside liner
Belt
Cap ply Sidewall
Carcass Apex Bead ring
Chafer
Bead
Fig. 1. (a) Finite element discretization of the tire cross section; (b) Finite element model of tire–pavement contact
Figure 1(a) depicts a schematic view of 2D tire section and mesh constructed for the current analysis of the tire. The tire is composed of a single-ply polyester carcass, a single cap ply, two belt layers, and several steel bead cords. In the static tire analysis, those parts are usually modeled using solid elements like rebar elements. The finite element software MARC affords the Rivlin and Ogden material models. After measuring the material parameter, it is easy to define the material model and properties. At the same time, the user can define the material stress–strain relation conveniently in the form of a user’s sub-routine or table. The
4311
4312
Cheng al. / Procedia Engineering 15 (2011) 4310 – 4315 GangGang Cheng et al et / Procedia Engineering 00 (2011) 000–000
non-linear mechanical properties of elastomers can be obtained by tests [6]. The corresponding material constants of elastomers are fitted from the testing data. The ply is the main stressed component of the tire. The rebar model describes the properties of belt, carcass, chafer, and bead. In the rebar model, rebar and solid elements are used to describe the reinforcing cord and the rubber, respectively. In order to fit the incompressibility of the rubber material, the rubber material element adopts the Herrmann incompressible element based on the incompressible Mooney material model. The cords are defined by a linear elastic model. 2.2. Treatment of Boundary Conditions Suppose the tire is a deformable body and the wheel rim is a rigid body. The actual wheel rim is separated into two parts (left and right rim) deliberately. At first, the axial distance of these two parts is longer than the standard width of the wheel rim. The two parts move in the axial direction. The wheel rim and the tire come into contact during the movement process until the distance of the two wheel rims reach the standard width of the wheel rim. Thus, the assembly of the tire and the wheel rim is realized virtually. Figure 1(b) is the boundary condition of the tire. The friction between the tire and the wheel rim is considered. The friction coefficient between them is 0.5. The contact between the tire and the road is a contact of large displacement and nonlinearity. Compared with the tire material, the road can be seen as a rigid body. The road is regarded as the rigid body in this study. The friction between the tire and the road is considered and the Coulomb for rolling friction model is adopted. 2.3. Loading Cases First, the axial movement of the left and right rim is controlled exactly until it reaches the standard width of the wheel rim. So the assembly and positioning load case between the wheel rim and the tire is realized. Secondly, applying even face pressure on the tire inner surface, the normal inflation pressure is 0.25 MPa. Then, the road is controlled to move to the tire axes, to make the tire produce definite deflection as the tire is loaded. One control node in the tire axes is defined. The node is incorporated with the road. The load rating 5194N of tire is applied on this node. The deflection under the load rating is controlled exactly by the load applied on the control node. Lastly, the rotation axis and rotation speed of the tire are defined. Meanwhile, the relative speed between the road and the tire is needed to be defined. 3. Analysis Result 3.1. Contact Stress Distribution Figure 2 is the analysis result of the contact area and the contact pressure distribution under different camber angles. The shape of the contact area is approximatively trapeziform when the camber angle is 5°under the load rating. The contact area becomes triangular at the camber angle 10°.With the increase of the camber angle, the contact pressure becomes increasingly non-uniform. The stress concentration of the tire shoulder becomes higher and the wear of the shoulder also becomes severe with single-sided wear. Under the camber state, the vertical deformation along the tire width in the contact area is different, which brings the difference of the normal contact pressure along the tire width in to the contact area. The contact pressure of the one-sided shoulder is larger. The high stress area extends to the opposite direction of motion direction under braking state. Figure 3 is the variation of maximum contact stress with the camber angle. The maximum contact stress of the contact area increases with the increase of the camber angle. The non-uniformity of the
3
Gang – 4315 GangCheng Chengetetal.al// Procedia ProcediaEngineering Engineering15 00(2011) (2011)4310 000–000
4
contact pressure and the different slippage along the tire width under the camber state can result in a longitudinal resistance and camber aligning torque. Meanwhile, the different normal deformation along the tire width under the camber state leads to the camber overturning torque.
(a) Camber angle 3°
(d) Camber angle 10°
(b) Camber angle 5°
(c) Camber angle 7°
(e) Camber angle 12°
(f) Camber angle 15°
Fig. 2. Footprints and normal stress (MPa) distribution in contact area under different camber angles at braking state
Max normal stress (MPa)
1.2 1.1 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0
3
6
9
12
15
18
Camber angle (°) Fig. 3. Variation of maximum normal stress in contact area with the camber angle
3.2. Stress distribution of belt When the tire is rolling, the elastic ply of the tire along with the road and the whole tire enters into deformation status. Figure 4 shows the stress distribution of the tire cross-section in contact zone under different camber angles at braking state. Figure 5 shows variation of maximum equivalent stress in contact area with the camber angle. The larger stress concentrates on the edge of the belted layer with the
4313
4314
Cheng al. / Procedia Engineering 15 (2011) 4310 – 4315 GangGang Cheng et al et / Procedia Engineering 00 (2011) 000–000
increase of the camber angles during the braking state. The maximum equivalent stress of belt goes up when the camber angle is in the range of 3-10º. The maximum equivalent stress of belt changes slightly when the camber angle is 10-15º.
(a) Camber angle 3°
(c) Camber angle 7°
(e) Camber angle 12°
(b) Camber angle 5°
(d) Camber angle 10°
(f) Camber angle 15°
Fig. 4. Stress distribution of the tire cross-section in the contact zone under different camber angles at braking state.
5
Gang – 4315 GangCheng Chengetetal.al// Procedia Procedia Engineering Engineering 15 00 (2011) (2011) 4310 000–000
6
M ax eq uiv al ent st ress (M Pa)
150 145 140 135 130 125 120 0
3
6
9
12
15
18
Camber angle (°)
Fig. 5. Variation of maximum equivalent stress in contact area with the camber angle
4. Conclusions The 3D nonlinear FEM modeling techniques of rolling of radial tire under braking state is discussed in detail in this study. The contact performance of the radial tire is analyzed numerically. Influence of the camber angle on the radial tire under rolling states is studied. Numerous results, such as the normal stress distribution in contact zone and stress distribution of the belt are obtained visually. The analysis results show: (1) The normal stress in the contact zone increases with the increase of the camber angle. The area of the high normal stress increases with the increase of the camber angle and concentrates at the one-side shoulder. (2) The stress of the radial tire concentrates on the edge of the belted layer. The variation of the stress along the cross-section is not monotonous. Acknowledgements The research work was supported by the national science foundation of China (50775132), Shandong Outstanding Young Scientist Research Award Foundation（BS2009CL047） and the science foundation of Shandong province (ZR2010EM032). References [1] Gim G, Choi Y, Kim S. A semi-physical tire model for a vehicle dynamics analysis of handling and braking. Vehicle System Dynamics 2007; 45(suppl):169-190. [2] Smith KR, Kennedy RH, Knisley SB. Prediction of tire profile wear by steady-state FEM. Tire Science and Technology 2008; 36:290-303. [3] Rao K, Kumar R, Bohara P. Transient Finite Element Analysis of Tire Dynamic Behavior. Tire Science and Technology 2003;31:104–127. [4] Lecomte C, Graham WR, O'Boy DJ. Validation of a belt model for prediction of hub forces from a rolling tire. Tire Science and Technology 2009;37:62-102. [5] Liu HH. Load and inflation effects on force and moment of passenger tires using explicit transient dynamics. Tire Science and Technology 2007;35:41-55. [6] Guan YJ, Zhao GQ, Cheng G. Influence of belt cord angle on radial tire under different rolling states. Journal of Reinforced Plastics and Composites 2006;25:1059-1077.
4315
Procedia Engineering
ProcediaProcedia Engineering 00 (2011) Engineering 15 000–000 (2011) 4310 – 4315 www.elsevier.com/locate/procedia
Advanced in Control Engineering and Information Science
Influence of Camber Angle on Rolling Radial Tire under Braking State Gang Chenga*, Weidong Wangb, Guoqun Zhaoc, Yanjin Guanc, Zhonglei Wanga a School of mechanical and electronic engineering, Shandong Jianzhu University, Jinan 250101, China Department of Engineering Mechanics，School of Civil Engineering，Shandong University，Jinan 250061, China c Key Laboratory of Liquid Structure and Heredity of Materials, Ministry of Education, Shandong University, Jinan 250061, China b
Abstract To study the rolling properties of a radial tire, an accurate 3D 195/60R14 tire model is established. The modal includes the geometric nonlinearity due to large deformation, material nonlinearity, the anisotropy of rubber-cord composites, the nonlinear boundary conditions from tire-rim contact and tire-pavement contact. The model can be used to simulate the changes of a rolling tire and calculate the tire deformation for various operating conditions. The profile of inflated tire is studied experimentally and numerically. The simulation result is in good agreement with the test result. Some contact problems, such as the tire deformation, the shape of contact area, the contact pressure distribution, are discussed in detail.
© 2011 Published by Elsevier Ltd. Selection and/or peer-review under responsibility of [CEIS 2011] Keywords: radial tire; belt, camber; braking state.
1. Introduction The pneumatic tire is the only component transferring the load between the vehicle and the road. The camber performance of the tire influences the steering and the proper selection of wheel positioning parameters. The tire behaviour is directly related to the vehicle/road interaction, the interface between the wheel (rim + tire) and the ground must be considered. Gim et.al. [1] establish a semi-physical model which experimentally formulates vertical force as a function of tire effect, camber angle and lateral force. Smith et.al. [2] uses the steady-state finite element model, in which a composite friction energy is
* Corresponding author. Tel.: +86-0531-86367273; fax: +86-0531-86361369. E-mail address: [email protected].
1877-7058 © 2011 Published by Elsevier Ltd. doi:10.1016/j.proeng.2011.08.809
Gang – 4315 GangCheng Chengetetal.al// Procedia ProcediaEngineering Engineering15 00(2011) (2011)4310 000–000
2
calculated from friction energy predictions at selected loading conditions taken from the drive file events. The composite friction energy profile is finally compared to laser measurements of the worn tire profile to examine the feasibility of a “virtual wear test”. Rao et al. [3] simulated the dynamic behavior of a pneumatic tire by using an explicit finite element, and discussed the effects of camber angle and grooved tread on tire cornering behavior. Lecomte et.al. [4] developed an integrated model which predict the interior noise due to the vibrations of a rolling tire structurally transmitted to the hub of a vehicle. In the modal the tire belt is modeled as an orthotropic cylindrical ring of negligible thickness with rotational effects, internal pressure, and pre-stresses included. The effects of internal pressure, prestress, curvature, and tire rotation on free waves are discussed. Liu [5] modeled a rolling passenger tire by explicit transient dynamic FEA (ABAQUS) and found the lateral force was quite insensitive to inflation and vertical load. Tire materials are multiplayer, asymmetric and anisotropic. This study presents a tire contact characteristics of a 195/60R14 radial tire on braking state under different camber angles. Different parts of the tire and their corresponding material properties, interference fitting of tire and rim, friction are taken into account in the finite element model. The effects of camber angle on the deformation and contact stresses of tread and belt in the contact area were calculated. 2. Finite Element Model of Radial Tire The tire is a complex composite structure, made up of rubber material and cord–rubber composite. Treatment of the rubber, laminate, and boundary contact conditions is the main problem to be considered seriously and cautiously to establish the finite element model. 2.1. Mesh Generation and Element Selection The radial tire mainly includes tread, shoulder, sidewall, carcass, belt and bead ring. Materials of sidewall, inside liner, apex, and tread are pure rubber with differing hardness. Belt, carcass, and bead ring are a single layer or multilayer cord-rubber composite. Crown
Inside liner
Belt
Cap ply Sidewall
Carcass Apex Bead ring
Chafer
Bead
Fig. 1. (a) Finite element discretization of the tire cross section; (b) Finite element model of tire–pavement contact
Figure 1(a) depicts a schematic view of 2D tire section and mesh constructed for the current analysis of the tire. The tire is composed of a single-ply polyester carcass, a single cap ply, two belt layers, and several steel bead cords. In the static tire analysis, those parts are usually modeled using solid elements like rebar elements. The finite element software MARC affords the Rivlin and Ogden material models. After measuring the material parameter, it is easy to define the material model and properties. At the same time, the user can define the material stress–strain relation conveniently in the form of a user’s sub-routine or table. The
4311
4312
Cheng al. / Procedia Engineering 15 (2011) 4310 – 4315 GangGang Cheng et al et / Procedia Engineering 00 (2011) 000–000
non-linear mechanical properties of elastomers can be obtained by tests [6]. The corresponding material constants of elastomers are fitted from the testing data. The ply is the main stressed component of the tire. The rebar model describes the properties of belt, carcass, chafer, and bead. In the rebar model, rebar and solid elements are used to describe the reinforcing cord and the rubber, respectively. In order to fit the incompressibility of the rubber material, the rubber material element adopts the Herrmann incompressible element based on the incompressible Mooney material model. The cords are defined by a linear elastic model. 2.2. Treatment of Boundary Conditions Suppose the tire is a deformable body and the wheel rim is a rigid body. The actual wheel rim is separated into two parts (left and right rim) deliberately. At first, the axial distance of these two parts is longer than the standard width of the wheel rim. The two parts move in the axial direction. The wheel rim and the tire come into contact during the movement process until the distance of the two wheel rims reach the standard width of the wheel rim. Thus, the assembly of the tire and the wheel rim is realized virtually. Figure 1(b) is the boundary condition of the tire. The friction between the tire and the wheel rim is considered. The friction coefficient between them is 0.5. The contact between the tire and the road is a contact of large displacement and nonlinearity. Compared with the tire material, the road can be seen as a rigid body. The road is regarded as the rigid body in this study. The friction between the tire and the road is considered and the Coulomb for rolling friction model is adopted. 2.3. Loading Cases First, the axial movement of the left and right rim is controlled exactly until it reaches the standard width of the wheel rim. So the assembly and positioning load case between the wheel rim and the tire is realized. Secondly, applying even face pressure on the tire inner surface, the normal inflation pressure is 0.25 MPa. Then, the road is controlled to move to the tire axes, to make the tire produce definite deflection as the tire is loaded. One control node in the tire axes is defined. The node is incorporated with the road. The load rating 5194N of tire is applied on this node. The deflection under the load rating is controlled exactly by the load applied on the control node. Lastly, the rotation axis and rotation speed of the tire are defined. Meanwhile, the relative speed between the road and the tire is needed to be defined. 3. Analysis Result 3.1. Contact Stress Distribution Figure 2 is the analysis result of the contact area and the contact pressure distribution under different camber angles. The shape of the contact area is approximatively trapeziform when the camber angle is 5°under the load rating. The contact area becomes triangular at the camber angle 10°.With the increase of the camber angle, the contact pressure becomes increasingly non-uniform. The stress concentration of the tire shoulder becomes higher and the wear of the shoulder also becomes severe with single-sided wear. Under the camber state, the vertical deformation along the tire width in the contact area is different, which brings the difference of the normal contact pressure along the tire width in to the contact area. The contact pressure of the one-sided shoulder is larger. The high stress area extends to the opposite direction of motion direction under braking state. Figure 3 is the variation of maximum contact stress with the camber angle. The maximum contact stress of the contact area increases with the increase of the camber angle. The non-uniformity of the
3
Gang – 4315 GangCheng Chengetetal.al// Procedia ProcediaEngineering Engineering15 00(2011) (2011)4310 000–000
4
contact pressure and the different slippage along the tire width under the camber state can result in a longitudinal resistance and camber aligning torque. Meanwhile, the different normal deformation along the tire width under the camber state leads to the camber overturning torque.
(a) Camber angle 3°
(d) Camber angle 10°
(b) Camber angle 5°
(c) Camber angle 7°
(e) Camber angle 12°
(f) Camber angle 15°
Fig. 2. Footprints and normal stress (MPa) distribution in contact area under different camber angles at braking state
Max normal stress (MPa)
1.2 1.1 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0
3
6
9
12
15
18
Camber angle (°) Fig. 3. Variation of maximum normal stress in contact area with the camber angle
3.2. Stress distribution of belt When the tire is rolling, the elastic ply of the tire along with the road and the whole tire enters into deformation status. Figure 4 shows the stress distribution of the tire cross-section in contact zone under different camber angles at braking state. Figure 5 shows variation of maximum equivalent stress in contact area with the camber angle. The larger stress concentrates on the edge of the belted layer with the
4313
4314
Cheng al. / Procedia Engineering 15 (2011) 4310 – 4315 GangGang Cheng et al et / Procedia Engineering 00 (2011) 000–000
increase of the camber angles during the braking state. The maximum equivalent stress of belt goes up when the camber angle is in the range of 3-10º. The maximum equivalent stress of belt changes slightly when the camber angle is 10-15º.
(a) Camber angle 3°
(c) Camber angle 7°
(e) Camber angle 12°
(b) Camber angle 5°
(d) Camber angle 10°
(f) Camber angle 15°
Fig. 4. Stress distribution of the tire cross-section in the contact zone under different camber angles at braking state.
5
Gang – 4315 GangCheng Chengetetal.al// Procedia Procedia Engineering Engineering 15 00 (2011) (2011) 4310 000–000
6
M ax eq uiv al ent st ress (M Pa)
150 145 140 135 130 125 120 0
3
6
9
12
15
18
Camber angle (°)
Fig. 5. Variation of maximum equivalent stress in contact area with the camber angle
4. Conclusions The 3D nonlinear FEM modeling techniques of rolling of radial tire under braking state is discussed in detail in this study. The contact performance of the radial tire is analyzed numerically. Influence of the camber angle on the radial tire under rolling states is studied. Numerous results, such as the normal stress distribution in contact zone and stress distribution of the belt are obtained visually. The analysis results show: (1) The normal stress in the contact zone increases with the increase of the camber angle. The area of the high normal stress increases with the increase of the camber angle and concentrates at the one-side shoulder. (2) The stress of the radial tire concentrates on the edge of the belted layer. The variation of the stress along the cross-section is not monotonous. Acknowledgements The research work was supported by the national science foundation of China (50775132), Shandong Outstanding Young Scientist Research Award Foundation（BS2009CL047） and the science foundation of Shandong province (ZR2010EM032). References [1] Gim G, Choi Y, Kim S. A semi-physical tire model for a vehicle dynamics analysis of handling and braking. Vehicle System Dynamics 2007; 45(suppl):169-190. [2] Smith KR, Kennedy RH, Knisley SB. Prediction of tire profile wear by steady-state FEM. Tire Science and Technology 2008; 36:290-303. [3] Rao K, Kumar R, Bohara P. Transient Finite Element Analysis of Tire Dynamic Behavior. Tire Science and Technology 2003;31:104–127. [4] Lecomte C, Graham WR, O'Boy DJ. Validation of a belt model for prediction of hub forces from a rolling tire. Tire Science and Technology 2009;37:62-102. [5] Liu HH. Load and inflation effects on force and moment of passenger tires using explicit transient dynamics. Tire Science and Technology 2007;35:41-55. [6] Guan YJ, Zhao GQ, Cheng G. Influence of belt cord angle on radial tire under different rolling states. Journal of Reinforced Plastics and Composites 2006;25:1059-1077.
4315