Study on the Tire Uneven Wear Mechanism of the Running Wheel of Monorail Vehicles

Transcription

1 Journal of Applied Science and Engineering, Vol. 19, No. 4, pp (2016) DOI: /jase Study on the Tire Uneven Wear Mechanism of the Running Wheel of Monorail Vehicles Xiao-Xia Wen 1 *, Zi-Xue Du 2, Da-Yi Zhao 2, Zhou-Zhou Xu 2 and Yang Zhen 2 1 Institute of Urban Rail, ChongQing JiaoTong University, ChongQing , P.R. China 2 School of Electrical and Vehicle Engineering ChongQing JiaoTong University, Chong Qing , P.R. China Abstract In order to decrease the running wheels uneven wear, the finite element model of running wheels PC track beam of monorail vehicles is established. The monorail vehicle kinetic model is established on the basis of Newton Euler equation, and the boundary input parameter of the running wheel of straddle-type monorail vehicle curve negotiating working conditions is obtained. Based on the finite element model, the implicit algorithm is used to analyze the longitudinal and lateral shear and the slip velocity distribution between the wheel-track contact surface. The Uneven wear evaluation index of the running wheel is proposed, and the distribution law of the friction power density and friction power density Uneven within contact area is obtained. According to the research, when a monorail vehicle passes a track beam whose radius is 100 meters, the normal compressive stress, longitudinal and lateral shear of the running wheel in contact area will show clear gradient changes along the axle of the running wheel. There is no clear regularity change for the longitudinal and lateral slip speed along the axle of the running wheel. In accordance with the uneven wear evaluation index, quantitative analysis is conducted for the uneven wear phenomenon of the running wheel in the tire axle direction. Key Words: Straddle-type Monorail, Running Wheel, Uneven Wear Mechanism, Influential Factor, Uneven Index 1. Introduction Monorail transit belongs to one of the urban rail transit systems. Its running system is mainly composed by the running wheel, guide wheel, steady wheel and bogie, among which, the running wheel is a tubeless tire filled with nitrogen. After the straddle-type monorail transit is introduced to Chongqing of China, serious Uneven wear has occurred to the running wheel in the operation process, the contrast of which before and after the introduction of monorail transit is shown in Figure 1 below. *Corresponding author. wenxiaoxia150@163.com In addition to the sharp increase of the operation cost, severe Uneven wear of the running wheel will also lead to the significant reduction of the adhesion ability of the running wheel, the decrease of the vehicle driving efficiency, and the lengthening of the brake distance, thus seriously affecting the running safety and energy saving of monorail vehicles. Currently, few literatures have mentioned the mechanism study of the Uneven wear of the running wheel of straddle-type monorail vehicles by domestic and overseas scholars, but relatively in-depth studies on the Uneven wear of auto wheels have been conducted. Because the gas-filled rubber tire the same as that for autos is used

2 460 Xiao-Xia Wen et al. by the running wheel of monorail vehicles, the study method of auto wheel can play certain role in reference. The Uneven wear study on the Uneven wear of auto wheels is mainly conducted from three aspects: first, study from the perspective of tire structure and material characteristics; second, study from the characteristics and matching perspective of tires and the suspension system of vehicles; third, study from the external environment influential factors. For example, Walters M. H has drawn the conclusion by experiments that the toe-in angle of tires can have the biggest impact on Uneven wear, followed by the camber angle [1]. According to Yamazaki, the microcosmic slip between the tire and the ground plane caused by the lateral force change resulted from the running parameter change of vehicles is the main course for Uneven wear of tires. Based on the vehicle-tire-ground system, the Uneven wear mechanism of tires has been studied by Huang Haibo who pointed out that the uneven distribution of the slip force and slip speed of the tire on the tire axle and circumference is the root cause for its Uneven wear [2]. The car bogie structure form of straddle-type monorail vehicles is completely different from the chassis structure form of vehicles, thus leading to the huge difference between the inherent causes of tire Uneven wear and Uneven wear mechanism. By referring to research methods of tire Uneven wear of vehicles, the boundary input parameter of tires of the running wheel is abstracted by this paper through the analog computation of the monorail kinetic model. Based on the running wheel-pc rail beam finite element model, the distribution law of longitudinal and lateral shear forces and slip speed of the monorail running wheel on the wheel rail contact surface under the existing running state is obtained. In-depth researches on the generation mechanism of the tire Uneven wear of the running wheel of straddle-type monorail vehicles is carried out. 2. Establishment of the Model of the Running Wheel Figure 1. Structure of the running wheel of monorail vehicles and Uneven wear. 2.1 Geometric Model of the Running Wheel The tire diameter of the monorail running wheel is 2006 mm, the width is 340 mm, the aspect ratio of the cross section is 0.85, and the rim diameter is 424 mm. The geometric cross section of the running wheel is provided by some domestic tire manufacturer. The longitudinal groove pattern is used for the tire surface. The pattern structure of such tire is simple with even wear and large loading capacity. About 14 materials are used for the rubber running wheel, among which, there are 4 allsteel cord materials. For different regions, there are over ten rubber materials. The two-dimensional cross section and material distribution of the running wheel is shown in Figure 2. Figure 2. Two-dimensional cross section of the running wheel.

3 Study on the Tire Uneven Wear Mechanism of the Running Wheel of Monorail Vehicles Constructive Model of Rubber Materials of the Running Wheel Mechanical behavior of rubber materials is very complex. To accurately establish running wheel tire finite element model, An accurate constitutive model of rubber must be established to describe the mechanical properties. Most of the rubber elasticity continuous mechanical behavior is based on isotropic continuum mechanics, the strain energy density of super-elastic material is determined by three invariants, according to the tensile test. The strain energy function is used to expressed as the function U(I 1, I 2, I 3 ) of three Uneven strain constants I 1, I 2 and I 3. The relationship between three Uneven strain constants and three main elongation ratio is as follows [2]: In Equations (1, 2, 3), the main elongation ratio is: (1) (2) (3) (4) where, i means the strain on the principal axis, and i = 1, 2, 3. To get the nominal stress value, the virtual work equation when establishing the rubber material load is: (5) According to Equations (1), (2), (3) and (5), the relationship between the principal stress T i and the main elongation ratio i can be inferred. When the rubber material is set as the incompressible material: (9) Based on the above theory, the running wheel rubber materials is super-elastic, which is set as incompressible material, so the strain energy function can be used to refer to the function U(I 1, I 2 ). According to the Mooney- Rivlin model, its constructive relation [3] is shown below: (10) where, U means strain energy; N refers to material parameters, C ij refers to temperature-dependent material parameters; I 1 / I 2 is the first and second Uneven strain constant. By making N = 1, the model can be simplified to: (11) In order to determine the Mooney-Rivlin model parameters C 10 and C 01, rubber biaxial tensile test was carried out. the three-dimensional stress and three main elongation ratio are: (12) (13) Equations (12),(13) are brought into Equations (6), (7) and (8), 1 and 2 isasshowninequation(14): (6) (7) Because: (14) (15) (8) Fitting coefficients C 10, C 01 in the Mooney-Rivlin model are:

4 462 Xiao-Xia Wen et al. (16) According to the biaxial drawing experimental test, the stress-strain parameters of the cord thread glue, apex and sidewall rubber can be got. By making use of the Mooney-Rivlin model, the fitting coefficient C 10 and C 01 can be obtained. The stress-strain of rubber materials is shown in Figure Running Wheel-PC Rail Beam Finite Element Model When establishing the running wheel-pc rail beam finite element model, the two-dimensional cross section of the running wheel is established according to the axial symmetry, in which, the rebar reinforcing rib unit simulation is adopted for the all-steel cord. The steel wire diameter, steel wire spacing and steel wire distribution of the cord is shown in Table 1. CGAX3H and CGAX4H super-elastic unit simulation is adopted for rubber materials of all regions [4,5]. The rim is defined as the analytical rigid. The density of the PC rail beam concrete material is 2450 (Kg/m3), the elasticity modulus is (MPa), and the Poisson s ratio is 0.2. The established two-dimensional model of the running wheel has 791 nodes and 655 units in total. By making use of the rotation function, the two-dimensional section is rotated to three-dimensional finite element model of the running wheel. Through the combination of the three-dimensional model and the rail beam model, the finite element model of the wheel track can be obtained, as shown in Figure Verification of the Running Wheel-PC Rail Beam Model The deformation degree of the tire after loaded can directly affect the wheel track contact status and tire surface wear. Therefore, the tire stiffness is an important index to measure the accuracy of the running wheel-pc rail beam finite element model. The stiffness fitting of the running wheel obtained by calculation is shown in Figure 5. The lateral, vertical and longitudinal stiffness analog computation result of the running wheel is compared Figure 4. Running wheel-pc rail beam finite element model. Figure 3. The stress-strain relationship of four rubber materials of the running wheel. Table 1. The diameter, spacing and distribution of the cord steel wire Parameter of the cord layer Steel wire angle ( ) Steel wire spacing (mm) Steel wire diameter (mm) Carcass cord Belt layer Belt layer Belt layer Null belt Figure 5. Three-way stiffness fitting curve of the running wheel.

5 Study on the Tire Uneven Wear Mechanism of the Running Wheel of Monorail Vehicles 463 with the experimental result provided by the wheel manufacturer, as shown in Table 2. As can be seen from Table 2, the error of the corresponding experimental data of the tire stiffness computation result of the running wheel is within the allowable scope. In this way, the accuracy of the running wheel- PC rail beam finite element model is verified. If the wear situation of the running wheel is to be confirmed, it will be need to get the force parameters and movement parameters working on the running wheel when monorail vehicles are in operation. According to the early-stage study, the Uneven wear of auto wheels is mainly shown on the working conditions of the curve driving, and the tire Uneven wear and the vehicle suspension structure form are closely related to suspension parameters. Compared to the operation condition of the auto wheel, monorail vehicles cannot realize the differential speed of the internal and external running wheel due to the lack of differential speed structure and suspension parameters. Therefore, the load status of the running wheel of vehicles when the curve passes the working condition is severer. To get the boundary condition parameter of the running wheel under the curve working condition, it is needed to establish a dynamic curve of monorail vehicles through the kinetic model. When the monorail vehicles pass the curve rail beam whose radius is R and ultrahigh angle is S, the impact of the transition curve and curve elevation should be considered [6]. The kinetic model of monorail have 35 degree total. The model is shown in Figure 6(a), (b), (c). Due to article length restrictions, kinetic equations of bogie three freedom degrees is only as follows, including the lateral movement, shaking movement and inclination movement. 3.1 Kinetic Equation of Bogie Lateral, Shaking and Inclination Motion Respectively Bogie lateral kinetic equations: 3. Boundary Conditions of the Running Wheel Model Bogie inclination kinetic equations : Table 2. Contrast of the experimental data and analog result Parameter Lateral stiffness (N/m) Vertical stiffness (N/m) Longitudinal stiffness (N/m) Computation result Experimental data Error 3.51% 5.08% 3.04%

6 464 Xiao-Xia Wen et al. Bogie shaking kinetic equations: where K 1ijlk /C 1ijlk air spring vertical stiffness/damp; K 2ijlk /C 2ijlk running wheel radial stiffness/damp; K 3ijlk / C 3ijlk steering wheel radial stiffness/damp; K 4ijlk /C 4ijlk stability wheel radial stiffness/damp; K 5ij /C 5ij air spring transverse stiffness/damp; d w Lateral distance between running wheel; d s air spring lateral distance between running wheel; 2L c stability wheel longitudinal distance between front and rear bogie; 2L g longitudinal distance of steering wheel; 2L w longitudinal distance of running wheel; h 1i vertical distance between body center and air spring upper plane; h 2i vertical distance between bogie center and air spring bottom plane; h gi vertical distance between bogie center and steering wheel; h si vertical distance between bogie center and stability wheel; h r vertical distance between the bogie and running wheel center; h t vertical distance between the bogie and beam top surface; Y ci /Y tij body /bogie lateral displacement, Y sij11 /Y sij12 lateral displacement of left and right stability wheel, Y gij11 /Y gij12 lateral displacement of left and right steering wheel; Z gij11 /Z gij12 vertical displacement of steering wheel; Z wijl1 /Z wijl2 vertical displacement of running wheel; Z sijl1 /Z sijl2 vertical displacement of stability wheel; M tij /J t ij /J t ij the mass of bogie/x-axis moment of inertia of bogie/z-axis moment of inertia of bogie; ci / tij body/bogie inclination angle; tij shaking angle of bogie; sec Track beam ultra angle; i represent number of train, j = 1, 2 represent front and rear bogie respectively; l = 1, 2 represent front and rear wheel respectively, k = 1, 2 represent rigth and left wheel respectively; k aw /k ag /k as Cornering Stiffness Figure 6. Monorail vehicles kinetic model.

7 Study on the Tire Uneven Wear Mechanism of the Running Wheel of Monorail Vehicles 465 of running wheel/steering wheel/stability wheel respectively; a g lateral distance between steering wheel center and bogie center; a s lateral distance between stability wheel center and bogie center; b gt lateral distance between steering wheel surface and bogie center; b st lateral distance between stability wheel surface and bogie center. Now, the kinetic computation is carried out by taking the 36 km/h monorail vehicles passing the 100-meter curve radius rail beam as the working condition, the main parameter of the kinetic model of the monorail is shown in Table 3. the boundary input parameter of the running wheel is abstracted from the kinetic computation result. The time process of the wheel core vertical force, lateral deflection angle and lateral roll angel of the running wheel is abstracted, as shown from Figure 7. To get a steady value on the curve section of monorail vehicles, the abstracted parameters need to be cut off and be processed through equalization [7], as shown in Figure 7. As can be seen from Figure 7(a), (b), (c), the running wheel is at the state of combined slip and lateral inclination when the monorail vehicle passes the 100-meter curve radius track beam at the speed of 36 km/h. When driving to the curve section and driving away from the curve section, there is certain slight acceleration and slight brake. The curve negotiating work condition of the running wheel is with the integration of the driving/ brake, slip and lateral inclination. When the monorail vehicle passes the 100-meter curve radius rail beam, the boundary input parameter of the running wheel after the section and equalization treatment is as shown in Table Analysis on the Uneven Wear of the Running Wheel 4.1 Wear Model and Uneven Wear Evaluation Index Tire surface wear is a very complicated process with fatigue wear, grind wear and mechanical-chemical corrosive wear. The wear speed is generally used in projects to represent the wear of tires [8]. With the study on the tire wear mechanism, some tire wear models have been proposed gradually, among which, the friction power density in the power exponent model of the wear quality m and the friction power density can reflect the coupling effect of many factors, so it can well represent the tire wear. Therefore, the application is extensive. The power exponent model is used for the wear model of the running wheel [9] Wear Model of the Running Wheel (17) (18) (19) Table 3. The main parameter of the kinetic model of the monorail Sign Sign meaning Value K 1ijlk /C 1ijlk Air spring vertical stiffness (N/m -1 )/ damp (Ns/m -1 ) 2.45E6/4E4 K 2ijlk /C 2ijlk Running wheel radial stiffness (N/m -1 )/damp (Ns/m -1 ) 2.45E6/4E4 K 3ijlk /C 3ijlk Steering wheel radial stiffness (N/m -1 )/damp (Ns/m -1 ) 9.8E5/3120 K 4ijlk /C 4ijlk Stability wheel radial stiffness s(n/m -1 )/damp (Ns/m -1 ) 9.8E5/3120 K 5ij /C 5ij Air spring transverse stiffness s(n/m -1 )/damp (Ns/m -1 ) 2d w Lateral distance between running wheel (m) d s Air spring lateral distance between running wheel (m) L c Stability wheel longitudinal distance between front and rear bogie L g Longitudinal distance of steering wheel (m) L w Longitudinal distance of running wheel (m) h 1i Vertical distance between body center and air spring upper plane (m) h 2i Vertical distance between bogie center and air spring bottom plane (m) h gi Vertical distance between bogie center and steering wheel (m) h si Vertical distance between bogie center and stability wheel (m) h r Vertical distance between the bogie and running wheel center h t Vertical distance between the bogie and beam top surface (m) 0.503

8 466 Xiao-Xia Wen et al. Figure 7. Time history curve of the running wheel passing though rail beam. Table 4. Boundary condition parameters of the running wheel Curve Radius (m) 100 Running speed (Km/h) FN (N) Slip angle Normal radial load, roll angle (20) In the equation, m refers to the quality loss unit area; k 1, k 2 means wear parameters related to rubber components, roughness of the contact surface and temperature; w means the friction power density of unit contact area; w x means the longitudinal friction power density of the unit contact area; w y means the lateral friction power density of unit contact area; M means the tire wear quality; T(s) means the flow line width; and ds means the flow line arc length Uneven Wear Index of the Running Wheel As can be learnt from the kinetic computation result, the roll angle of the running wheel is large when the monorail vehicle curve passes, which will lead to the uneven distribution of the normal compressive stress in the tire axle direction as well as the shear force in the x-direction and y-direction of the running wheel. As a result, the Uneven wear of the running wheel will occur. To measure the Uneven wear degree of the running wheel, the Uneven value of the friction power in the wheel rail contact area can be used to measure the Uneven wear degree of the running wheel. The total longitudinal and lateral friction power [9, 10] can be expressed as: (21) (22) where, W x is the total longitudinal friction power; W y is the total lateral friction power; V is the driving speed of the vehicle; r is the rolling angular velocity; R ix is the rolling radius; is the slip angle; F x is the longitudinal force, and F y is the lateral force. The average longitudinal and lateral friction power density of unit contact surface w x and w y is: where, A refers to the contact area of the wheel rail. (23)

9 Study on the Tire Uneven Wear Mechanism of the Running Wheel of Monorail Vehicles 467 The Uneven value of the friction power p: (24) 4.2 Analysis on the Uneven Wear Result of the Running Wheel As can be seen from the kinetic analysis, there is slight acceleration, slip, lateral inclination and slight brake for the running wheel when the monorail vehicle curve passes, which is a superimposed and combined work condition. The slight acceleration, slip, lateral inclination and slight brake work condition of the running wheel is gradually superimposed when the monorail vehicle curve passes by this paper, so as to simulate the wear process of the running wheel after running for 400 hours on the track. The status of contact between the running wheel and the wheel track of its surface contact area is obtained. The normal compressive stress of the contact surface node of the running wheel is abstracted, thus getting the normal compressive stress contour map of the running wheel (as shown in Figure 8). Seen from Figure 8, the distribution of the normal compressive stress of the running wheel in the tire width direction is uneven and shows significant gradient changes. In the entire wheel track contact area, the large compressive stress is concentrated on the outer side of the running wheel and the inner side of the 20 mm-wide narrow bar zone. The maximum compressive stress is Mpa, which is located in the middle area of the outer side of the running wheel grounding area, and the minimum compressive stress is Mpa, located at the inner side of the running wheel in the wheel track contact area. Seen from Equation (19), the rubber wheel wear is not only related to the normal compressive stress, but also in direct proportion to the longitudinal and lateral friction stress working on the running wheel as well as the corresponding slip speed product. Therefore, by abstracting the longitudinal and lateral friction stress on the contact surface node of the running wheel, its contour line distribution figure in the whole contact area can be shown in (a) and (b) of Figure 9. The abstracted longitudinal and lateral slip speed as well as the slip speed contour map in the whole contact area is shown in (a) and (b) of Figure 10. According to the wear evaluation index, the friction power density distribution of the grounding area can be obtained via the calculation of Equation (12), as shown in (a) and (b) of Figure 11. As can be seen from Figure 11, large values of the friction power density are concentrated in the area whose longitudinal length is -50 mm~ -120 mm and lateral length is 0 mm~35 mm away from the center of the wheel track contact area. In other words, after crossing the central point 0 of the wheel track contact area, the running Figure 8. Normal pressure contour line of the ground tread of the running wheel. Figure 9. Distribution of the friction stress on the contact surface of the running wheel.

10 468 Xiao-Xia Wen et al. Figure 10. Distribution of the slip speed on the contact surface of the running wheel. wheel and track beam surface gradually starts to get rid of the contact area. The maximum friction power density is (W/mm 2 ), located in the place whose grounding length is -105 mm and width is mm. The minimum friction power density is (W/mm 2 ), located in the place whose grounding length is -165 mm and width is mm. The friction power density distribution characteristic in the wheel track contact area is completely consistent with the movement characteristic law of the running wheel. When the running wheel is rolling, it rolls into the track surface from the wheel and cross the wheel contact center to gradually increase the slip components between the running wheel and the track surface and to increase the slip speed. Therefore, compared to the front side of the contact area of the running wheel and the track surface, the friction power density of the back contact area is larger. It can also be learnt from Figure 11 that the distribution of the friction power density is uneven along the width direction of the running wheel, which shows the regular gradient change. As the friction power density is in direct proportion to the wear amount, it can be inferred that the wear of the cyclic annular bar area whose width is about 35 mm outside the running wheel is rather more serious in the region. Uneven wear status will occur for the running wheel in the width direction. If the switch-switch passes the curve, the other side of the running wheel will also show the same wear. According to the Uneven wear evaluation index in Equation (13), the longitudinal and lateral friction power density value of the grounding area and the average power density of the entire grounding area is subtracted and squared, thus getting the distribution of the Uneven value of the entire grounding area, as shown in Figure12. Through the quadrature of Uneven values in the whole area, the evaluation index of the Uneven wear of the running wheel is To verify this conclusion, after making the running wheel run for 400 hours, abstract the central nodal displacement change process curve along the tire width in the wheel track contact area, as shown in Figure 13. As can be seen from Figure 13, when the monorail Figure 11. Distribution of the friction power density of the running wheel.

11 Study on the Tire Uneven Wear Mechanism of the Running Wheel of Monorail Vehicles 469 Figure 12. Distribution of the Uneven value of the friction power density of the running wheel. vehicle passes the rail beam whose curve radius is 100 m, the displacement of the running wheel along the axle and the external side of the central node is significantly higher than the inner nodal displacement of the running wheel after running for 400 hours. Wear of the wheel track contact area close to the external side of the curve beam is significantly higher than that close to the inner contact area. Clear Uneven wear has occurred to the external side of the running wheel. 5. Conclusions Specific to the severe Uneven wear of the running wheel of straddle-type monorail vehicles, the following studies have been carried out: (1) Based on the rubber constructive model and the exponent wear model of the tire, the running wheel wear of the monorail vehicle in curve negotiating is analyzed, and the topological characteristics of the running wheel and the curve track beam contact area are obtained. Studies have found out that the normal compressive stress, longitudinal shear force and lateral shear force in the wheel track contact area show clear gradient change in the wheel width direction when monorail vehicles pass the track beam whose curve radius is 100 m, and no significant law has shown for the longitudinal and lateral slip speed along the axle direction change of the running wheel. (2) Based on the running wheel-pc rail beam finite element model, the distribution law of the longitudinal and lateral shear force and slip speed on the wheel track contact surface is obtained when the monorail running wheel is under certain running status. The Uneven wear evaluation index of the running wheel Figure 13. Changes of the central nodal displacement in the wheel track contact area. is proposed, and the distribution law of the friction power density and friction power density Uneven value of the running wheel in the wheel tract contact area is calculated. According to the friction power density Uneven index, quantitative evaluation is conducted for the Uneven wear of the running wheel. The above research achievement can inspire Chines rail vehicle enterprises to conduct rational design of the first suspension and secondary suspension parameters as well as the structure parameters like the bogie guide wheel and vertical steady wheel distance of monorail vehicles when designing the straddle-type monorail bogie, so as to reduce the roll angle of the monorail vehicle curve negotiating and alleviate the Uneven wear of the running wheel. Acknowledgement Fund Project: National Natural Science Foundation of China, Project Name: Research on The Mechanism and Control Method of Monorail Trains Running Tires Shoulder Wear, Project Number: References [1] Walters, M. H., Uneven Wear of Vehicle Tires, Tire Science and Technology, Vol. 4, No. 21, pp (2003). doi: / [2] Yi, Z. X., Experimental Study Based on Rubber Stretch [D], [Master], China: ChongQing Jiaotong University (2012).

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