KR101507136B1 - Method for obtaining Physical Quantities relating to Hydroplaning for a Tire in Thin Water using FEM and an Estimation Method - Google Patents

Abstract

It is a technical problem to provide a method of obtaining a physical quantity for a water film phenomenon in a thin water film using a finite element and a prediction method so that a physical quantity for a water film phenomenon in a thin water film can be obtained easily and quickly. To this end, a physical quantity acquisition method for a water film phenomenon in a thin water film by using the finite element and the prediction method of the present invention is characterized by using a finite element model for a tire and a water film to calculate at least two water film thicknesses in the first section Obtaining analytic physical quantities for each driving speed; Obtaining an exponential function of the thickness of the water film and the running speed by curve fitting through the asymptotic method; And obtaining a prediction physical quantity per driving speed for at least one water film thickness in the second section using the exponential function.

Description

[0001] The present invention relates to a method for acquiring a physical quantity of a water film phenomenon in a thin water film by using a finite element and a prediction method,

The present invention relates to a method for obtaining a physical quantity for a water film phenomenon in a thin water film.

The main parameters that lead to the hydrocephalus phenomenon identified by previous researchers are tire-related variables such as tire shape, internal pressure, structure of tires such as tire structure, road surface condition, drainage rate, etc., (Horn et al., 1986; Huebner et al., 1986).

The research of finding these hydrokinetic parameters has been done in earnest since 1960 by using NASA's Langley Research Center to investigate various phenomena of the meninges phenomenon using aircraft landing tracks. In this study, we investigated the shape and fluid behavior of the tire ground plane by using high-speed photographs of tires running on the water film of constant thickness with tempered glass on a part of the road surface (Suzuki and Fujikawa, 2001). Furthermore, the slip resistance, which is influenced by factors closely related to hydro-film phenomena such as running speed, type of tire, shape of tire tread, wheel load, surface characteristics of road surface, texture of road surface, (Rose and Gallaway, 1977; Anderson et al., 1998).

However, the experimental method requires a lot of time and money because it requires the production of experimental equipment and requires a separate test site. Therefore, the study of analytical methods has been continuing (Saal, 1936; Martin, 1996; Eshel, 1967; Grog-ger and Weiss, 1996; ZminDak and Grajcia, 1997; Nakajima et al. Koishi et al., 2001; Oh et al., 2008; Ong and Fwa, 2010).

Among these studies, Grogger and Weiss first introduced an analytical method using computational fluid dynamics (CFD) (Grogger and Weiss, 1996). In addition, Zmindak introduced a finite element method (FEM) for the analysis of water film phenomena (ZminDak, 1997). Since Nakajima, Okano and Koishi are commercial finite element method (FEM) codes, The water film phenomenon was analyzed for a water film thickness of 10 mm or more using Dytran (MSC. Dytran) (Nakajima et al., 2000), but analysis of the water film thickness of less than 10 mm was required. Therefore, Okano and Koishi simulated water film phenomena in consideration of water viscosity using another commercial code, LS-DYNA (Okano and koishi, 2001).

However, a Lagrangian element for a large number of tires and an Eulerian element for water are used, and a long analysis time is required because the simulations are performed several times for changes in the thickness of the water film. Therefore, a new simulation method has been proposed to study hydrodynamic phenomenon and slip resistance using mathematical model and finite element model (FE model) as a way to reduce analysis time (Oh and Jeong, 2008; Jeong, 2010; Ong and Fwa, 2010).

In particular, Oh and Jeong describe finite difference method (FDM) codes and finite element tire models developed based on Browne's mathematical formulations (Browne, 1975) FE tire model) for the first time.

Since this mathematical formulation becomes an illconditioned matrix when the thickness of the membrane is thin, we can obtain the pressure distribution and lift force by suggesting the asymptotic method. In addition, the simulation of the water film phenomenon was performed using the full FE simulation method of LS-DYNA and the two simulation methods were compared.

However, since the analysis method using FDM codes requires mathematical programming, a complicated series of repetitive processes is required. Also, in the simulation method using LS-DYNA, an abnormal case occurred in which a negative lift force occurred, and the vertical drag for the speed could not be clearly defined due to the oscillation .

In this way, several researches have been carried out on the hydrodynamic phenomenon.

However, most of the above-mentioned analytical studies do not take into account the very thin film thicknesses (less than 1 mm) dominated by viscous effects, as they are the result of studies on water-film thicknesses greater than 5 mm. In particular, in the case of the extensional analysis method using a commercial explicit code such as LS-DYNA, a large number of Eulerian elements for water are used, Lt; RTI ID = 0.0 > factor < / RTI > In addition, when using complex pattern tires such as those of Kim and Jeong, the water element must have a size smaller than that of the tread pattern, It is very difficult to obtain the analytical results considering the very thin thickness of the water film.

A technical object of the present invention is to provide a method of acquiring a physical quantity for a water film phenomenon in a thin water film using a finite element and a prediction method so that a physical quantity for a water film phenomenon in a thin water film can be obtained easily and quickly.

In order to achieve the above object, a physical quantity acquisition method for a water film phenomenon in a thin water film by using a finite element and a prediction method according to an embodiment of the present invention is performed by using a finite element model for a tire and a water film, Obtaining an analytic physical quantity per driving speed with respect to at least two water film thicknesses; Obtaining an exponential function of the thickness of the water film and the running speed by curve fitting through the asymptotic method; And obtaining a prediction physical quantity per driving speed for at least one water film thickness in the second section using the exponential function.

The exponential function may be defined by equation (1), and equation (1) may be force = ch ^a v ^b . In the above equation (1), force is a force which is one of the physical quantities, h is the thickness of the water film, v is the running speed, and a, b and c are constants determined by the least squares method.

When the tire is a tire rolling model rotating on the water film, the analysis and prediction physical quantity may be a lift force, and the prediction physical quantity may be calculated by the equation (1) In the case of buoyancy, a, b and c in the above equation (1) can be determined using the least squares method as a constant of the prediction solution for buoyancy.

In the case of a tire sliding model in which the tire slides on the water film, the interpretation and prediction physical quantity may be a traction force or drag force, and the traction force or drag force may be calculated by the equation (1) (1) where the predicted physical quantity is the traction force, a, b and c in the equation (1) can be determined using the least squares method as a constant of the prediction solution for the traction force, A, b, and c can be determined using the least squares method as a constant of the prediction solution for drag.

The first section of the water film thickness may be greater than or equal to 5 mm, and the second section of the water film thickness may be less than 5 mm.

The step of acquiring the predicted physical quantity may include obtaining a lift force, a traction force and a drag force with the predicted physical quantity and then calculating a slip resistance value using the buoyancy force, And a step of calculating.

The buoyancy force, the traction force and the drag force can be obtained by the equation (1), respectively, and in the case of the buoyancy, a, b and c of the equation (1) are constants of the prediction solution for buoyancy, A, b, and c in equation (1) above can be constants of the predictive solution for the traction force and a, b, and c in equation (1) .

The slip resistance value can be calculated by the equation (2), and the equation (2)

일 수 있다. 상기 식(2)에서, SN_v는 미끄럼 저항 값이고, F_x은 타이어에 작용하는 수평 저항력으로 상기 견인력과 상기 항력의 합과 같고, F_z은 수직 하중으로 타이어와 노면 사이의 접촉력과 부력의 차이와 같다.

Lt; / RTI > (2), SN _v is a slip resistance value, F _x is a horizontal resistance force acting on the tire, equal to the sum of the pulling force and the drag force, F _z is a vertical load, The difference is the same.

As the running speed increases, the sliding friction coefficient between the tire and the road surface can be reduced.

As described above, by using the finite element and the prediction method according to the embodiment of the present invention, the physical quantity acquisition method for the water film phenomenon in the thin water film can have the following effects.

According to the embodiment of the present invention, the exponential function is obtained from the analytical physical quantity of the water film phenomenon acquired for the thickness of the water film in the first section by using the finite element model, and then the water film thickness The physical quantity of the water film phenomenon in the thin water film can be easily and quickly obtained through the exponential function.

FIG. 1 is a schematic view of a finite element model for simulation of a water film phenomenon among a physical quantity acquisition method for a water film phenomenon in a thin water film according to an embodiment of the present invention.
FIG. 2 is a graph of time showing improved behavior by controlling the process of pressurization, load, and acceleration without increasing the analysis time.
3 is a graph showing the lift force according to the running speed with respect to the water film thickness.
FIG. 4 is a graph showing the buoyancy of a 2.5 mm water film thickness according to the running speed, and comparing the buoyancy by the buoyancy analysis with the finite element model and the prediction through the exponential function.
FIG. 5A is a graph showing the traction force by the running speed with respect to the thickness of the water film.
5B is a graph showing the drag force according to the running speed with respect to the thickness of the water film.
FIG. 6A is a graph showing the traction force of the running speed for a 2.5 mm water film thickness, and comparing the traction force by the finite element model and the traction force by the prediction through the exponential function.
FIG. 6B is a graph showing the drag force according to driving speed for a 2.5 mm water film thickness, and comparing the drag force by prediction through the drag and exponential function by the analysis through the finite element model.
FIG. 7A is a graph showing the traction force by the driving speed with respect to the thickness of the water film of 0.5 mm, which is predicted by the exponential function.
FIG. 7B is a graph showing the drag according to the running speed with respect to the thickness of the water film of 0.5 mm, which is the drag due to the prediction through the exponential function.
8A is a graph showing a slip resistance value (SN) versus running speed, which is a graph comparing the slip resistance values calculated by the equation without considering the slip resistance values and the friction coefficient changes measured through the equipment.
8B is a graph showing a slip resistance value (SN) with respect to the running speed, which is a graph comparing the slip resistance values calculated through the equation in consideration of the slip resistance value and the friction coefficient variation measured through the equipment.

Hereinafter, embodiments of the present invention will be described in detail with reference to the accompanying drawings, which will be readily apparent to those skilled in the art to which the present invention pertains. The present invention may, however, be embodied in many different forms and should not be construed as limited to the embodiments set forth herein.

FIG. 1 is a schematic view of a finite element model for a water film phenomenon simulation in a physical quantity acquisition method for a water film phenomenon in a thin water film according to an embodiment of the present invention. FIG. , And the graph showing the time when the acceleration process is controlled to show the improved behavior.

FIG. 3 is a graph showing the lift force according to the running speed with respect to the water film thickness, and FIG. 4 is a graph showing the buoyancy of the running speed with respect to the water film thickness of 2.5 mm. This is a graph comparing the buoyancy by the prediction through.

FIG. 5A is a graph showing a traction force with respect to a water film thickness, and FIG. 5B is a graph showing a drag force according to a running speed with respect to a water film thickness.

FIG. 6A is a graph showing the pulling force of a 2.5 mm water film thickness according to the running speed, which is a comparison of the traction force by an analysis through a finite element model and a prediction by an exponential function. FIG. It is a graph comparing the drag force by the prediction by the drag and exponential function by the analysis through the finite element model.

FIG. 7A is a graph showing the traction force by the predicted value through the exponential function, and FIG. 7B is a graph showing the drag force according to the running speed with respect to the thickness of the water film of 0.5 mm. Which is a graph showing the drag due to the predicted through.

8A is a graph showing a slip resistance value (SN) versus running speed, which is a graph comparing the slip resistance values calculated through the equation without considering the slip resistance values and the friction coefficient changes measured through the equipment, 8B is a graph showing a slip resistance value (SN) with respect to the running speed, which is a graph comparing the slip resistance values calculated through the equation in consideration of the slip resistance value and the friction coefficient variation measured through the equipment.

Hereinafter, a method of acquiring a physical quantity for a water film phenomenon in a thin water film using a finite element and a prediction method according to an embodiment of the present invention will be described in detail with reference to FIGS. 1 to 8. FIG.

Recent research on slip resistance has shown that the change in the slip resistance for changes in water thickness less than 5 mm is greater than the water thickness between 5 mm and 10 mm (Ong and Fwa, 2010). In addition, in the case of the ASTM test method (ASTM) E274, which is used in many countries, the amount of water having a water film thickness of 1 mm or less is used to perform a sliding resistance test .

Therefore, in the present invention, a full-FE simulation method using LS-DYNA is used to simulate the water film phenomenon for the thicknesses of 5 mm, 7.5 mm, and 10 mm, and Oh et al. The lift force for each 2.5mm thin film thickness was obtained by using the asymptotic method proposed in this paper. The accuracy of the asymptotic method was verified by comparing the obtained results with the results obtained by the full FE simulation method for the thickness of 2.5 mm.

In addition, using a full FE simulation method and an Estimation Method using the LS-DYNA tire sliding model, the sliding resistance against a very thin film thickness of less than 1 mm Respectively. Therefore, in order to simulate the ASTM E274 slip resistance measurement method, a simulation was carried out using a tire sliding model. Through the traction force generated at the contact surface between the tire and the road surface and the dynamic pressure of the water, A drag force is generated in the contact surface. That is, as the driving speed increases, the frictional force between the tire and the road surface gradually decreases. The skid number (SN), which is the skid resistance value, was obtained by dividing the obtained result by the wheel load and compared with the test result using the ASTM E274 equipment. Hereinafter, the above-described physical quantity obtaining method will be described in more detail.

1. Methodology using LS-DYNA (hereinafter referred to as "LS-DYNA")

In order to simulate the hydrodynamic phenomenon using LS-DYNA, the tires were modeled by finite element method (FEM) consisting of Lagrangian elements and the meniscus was modeled by finite volume method consisting of Eulerian elements (FVM; Finite Volume Method). Therefore, a coupling function is required to transmit strain and pressure between two kinds of elements. In the present invention, a water-film phenomenon was simulated using LS-DYNA's multi-material ALE (Arbitrary Lagrangian-Eulerian) formulations to deal with the tire-fluid coupling problem (Olovsson and Souli, 2000, Okano and Koishi, 2001).

1.1. FE model of hydroplaning simulation of water film phenomenon simulation

The simulation model of the water film phenomenon used in the present invention is a smooth plane surface modeled as a rigid body and having a zero micro texture as shown in FIG. 1 and a smooth plane surface having a zero micro texture, and ASTM E501-08 slip resistance test standard ribs A tire model modeled on a tire (Rib tire) was used. Therefore, the water film simulation simulated tire model was modeled as a G78-15 tubeless type and consisted of a tire tread width of 148.6mm and a cross sectional radius of 393.7mm when the internal pressure was applied . The tire model also has seven plain ribs with 16.8 mm each and six straight grooves with 5.08 mm, each groove having a skid depth of 9.8 mm depth and an under-tread thickness of 2.5 mm (ASTM E501-08).

Tires are composite materials composed of various parts such as belts, carcass, treads, and beads, and belts are thin composite materials with high elastic modulus. If this is modeled using a continuum element, the time-increment is reduced to increase the analysis time. Thus, thin composite materials such as belts were modeled using multi-layered shell elements. Since the bead core has a high modulus of elasticity, it is modeled as a rigid body to shorten the analysis time, and the reference node of the bead core is moved in the direction The speed and vertical load were applied respectively.

The water-film model uses 8-node solid elements to create Eulerian elements in a range that can be flowed on the road surface, Was modeled as an empty element called "Void " to allow water to flow. The density and viscosity of water were assumed to be 998 kg / m ³ and 1.002 × 10 ^-3 Ns / m ³ , respectively.

In order to increase the numerical accuracy and reduce the analysis time, the hydrodynamic model is divided into small parts evenly in contact with the tire, and the element size is increased as the distance from the contact surface increases. The smallest element of the water element that meets the tire section is 40mm in the traveling direction, 2mm in the width direction, and 2.5mm in the height direction. The total number of elements used in tires is 30,800, and the total number of elements used in the hydro-model is 143,400.

1.2 Method for simulating the hydrodynamic phenomenon [tire rolling model and tire sliding model]

Several previous studies have used a model in which tires rotate in place and water and road surface flow in opposite directions (Okano and Koishi, 2001; Oh et al., 2008). Using this simulation model of water film phenomenon, the number of water elements can be reduced and the analysis time can be greatly reduced. However, unlike the actual phenomenon, the speed of the tire is the same as that of the water and the road surface, so the friction between the tire and the road surface can not be considered properly. Therefore, in the present invention, a simulation model is used in which a tire runs on a road surface with a water film until a water speed is generated (Nakajima, 2000; Huebner et al., 1986; Janajreh et al., 2001). In the present invention, this model is called a tire rolling mode.

However, to compare with the test results of the ASTM E274 (Pavement Friction Tester) slip resistance measuring device, a model that allows the tire to slide on the road surface while restricting the rotation of the tire should be used. In other words, the principle of ASTM E274 is to measure the friction force between the tire and the road surface by injecting a certain amount of water into the tire of the trailer while dividing it by the effective wheel load, And determines a skid number (SN) value as a resistance.

Therefore, in the present invention, two simulation models of water film phenomena were used. That is, a tire rolling model in which a reference node of a bead core element is provided with a speed in a direction in which the tire advances, a tire rolling model that rotates on a water surface, And a tire sliding model that travels while restraining and resting on the road surface is used.

The tire sliding analysis model that restrains the rotation of the tire can be interpreted in the same way as the test method of ASTM E274 (Pavement Friction Tester) which measures the frictional force generated on the contact surface with the road surface by applying the temporary braking have.

1.3 Load and Speed Time History ( Loading and speed time histories )

When a water film development simulation is performed for a 10 mm water film thickness, the time increment is approximately 1 × 10 ^-6 sec. Therefore, the simulation of the water film phenomenon requires a long analysis time. Therefore, in order to perform the analysis efficiently, it is only necessary to set the internal pressure of the tire in a very short time, accelerate the load, and accelerate it (Oh et al. In this process, the tire is considerably oscillated. As shown in FIG. 2, the improved behavior can be obtained by appropriately adjusting the pressurization, load and acceleration processes without increasing the analysis time.

The internal pressure and the vertical load were 165kPa and 4826N (ASTME274), respectively, and the running speed of the tire was constantly increased from 0 to 140km / h. The interpretation of a single film thickness takes about 23 hours with 3.06GHz CPU speed and 12GB memory computer.

2. Estimation Method

Lagrangian elements for a large number of tires and Eulerian elements for water are used when simulating hydro-film phenomena using LS-DYNA. In particular, the tire rolling method, which can simulate actual phenomena well, requires a long analysis time because a large number of elliptical elements are used to model the water.

In addition, for a very thin water film thickness of less than 1 mm, a full FE simulation of a water film phenomenon requires a very small elliptical element, so it takes about 150 hours of analysis time. In addition, if the thickness of the water film is different, a simulation model for each water film thickness is required, and a proper method for reducing the analysis time is needed because the simulation must be performed several times.

Therefore, in the present invention, the asymptotic method first proposed in Oh and Jeong's research can be applied to shorten the time required for the water film analysis (Oh and Jeong, 2008).

First, using LS-DYNA, we can simulate the water film phenomenon for the three water film thicknesses of 5mm, 7.5mm and 10mm, and then obtain the lift force for each driving speed. It is possible to show the lift force as an exponential function of the thickness of the water film and the speed as shown in Equation (1) by curve fitting the lift force thus obtained as shown in Fig.

(1)

(One)

Where h is the thickness of the water film and v is the running speed. The constants a, b, and c of the prediction solution for the vertical drag can be easily determined using the least squares method, which are 0.576, 1.98, and 0.182, respectively. However, these constants depend on the structure and shape of roads and tires. Therefore, using the equation (1), a lift force for a water film thickness of 2.5 mm was easily obtained. The results are shown in FIG. 4 for comparison and verification with the lift force obtained for 2.5 mm membrane thickness using the LS-DYNA full FE simulation method. The dotted line is the prediction result obtained by the estimation method (Estimation method), and the solid line is the analysis result obtained by the full FE simulation method. The two results show that the lift force obtained by using the estimation method is a reasonable result because the change of the lift force value is very similar as the driving speed increases.

In order to obtain the accuracy of the analytical results and the prediction results quantitatively, the Ratio of sum of squares (R2) was obtained, and R2 of 0.952 was obtained. Since R2 is very close to 1, it can be said that the prediction results obtained using the estimation method are very similar to the analysis results. Therefore, very thin film thicknesses, which require a lot of analysis time when performing various FE thickness simulations (Full FE simulation) using Estimation method, which is an exponential function of water film thickness and running speed, For example 1 mm or less) or for various driving speeds.

3. Simulation Result

The ASTM E274 (Pavement Friction Tester) test method uses a water film thickness of 0.5 mm (ASTM E274, Ong and Fwa, 2010) with a water injection rate of 600 mL / min.mm at a running speed of 65 km / h. Also, since the amount of water per mm of spraying width sprayed on the vehicle is directly proportional to the running speed, it maintains a constant water film thickness regardless of the speed change (ASTM E274). Therefore, in the present invention, a sliding resistance simulation is performed using a tire sliding model at a constant thickness of 0.5 mm as a method for obtaining the frictional force between the tire and the road surface when the measuring wheel is braked at an arbitrary running speed Respectively. In addition, the change of the slip resistance value SN (skid number) with respect to the running speed change of 40 km / h, 60 km / h and 80 km / h was confirmed by using the estimation method.

First, a full FE simulation method is used to estimate the drag force generated on the tire by the traction force generated between the tire and the road surface and the dynamic pressure of the water for 5 mm, 7.5 mm, . The coefficient of dynamic friction between the tire and the road surface used in this analytical model was calculated from the mean dynamic friction coefficient obtained at a speed of 40 km / h, 60 km / h, and 80 km / h using ASTM E274 (Pavement Friction Tester) 0.51 was used (Lee, 2010). The result thus obtained can be expressed as a function of the running speed and the thickness of the water film by curve fitting to minimize the error as shown in FIGS. 5A and 5B.

FIGS. 6A and 6B are graphs comparing the traction force and the drag force with respect to the 2.5 mm thickness of the membrane according to the analysis results obtained by the full FE simulation method and the prediction results obtained by the estimation method. It is. The constants a, b and c of the prediction solution used are 0.545, 1.82 and 0.150 for the traction force and 0.937, 1.24 and 0.223 for the drag force, respectively. Therefore, the traction force and the drag force using the tire sliding model are the exponential functions of the running speed and the thickness of the water film as the lift force of the tire rolling model It can be shown well.

7A and 7B are results of predicting the traction force and the drag force for a very thin water film thickness h of 0.5 mm using the estimation method. Therefore, when the thickness of the water film of 0.5 mm is constantly maintained as in the measurement method of the ASTM E274 (Pavement Friction Tester) equipment, the sliding speed changes at 40 km / h, 60 km / h and 80 km / h traction force and drag force can be easily obtained.

From the obtained results, the slip resistance at each sliding speed was calculated as shown in Equation (2).

(2)

(2)

Where Fx is the horizontal resistance force acting on the tire and Fz is the vertical load. That is, the horizontal resistance force Fx is equal to the sum of the traction force and the drag force, and the vertical load Fz is the difference between the contact force and the lift force between the tire and the road surface (Ong and Fwa, 2010).

Table 1 shows the traction force and drag force obtained by the full FE simulation method and the estimation method using the LS-DYNA tire sliding model as the running speed The values are expressed as quantitative values.

Speed (km / h) 40 60 80 Traction force (N) 2434.27 2333.03 2202.83 Drag force (N) -12.67 -20.79 -29.57

As a result, it can be seen that the traction force in the horizontal direction between the tire and the road surface decreases as the running speed increases at a constant water film thickness, and the drag force generated in the tire by the dynamic pressure of the water increases have. That is, as the driving speed increases, a lift force due to the dynamic pressure of water occurs, so that the traction force acting between the tire and the road surface gradually decreases. On the other hand, as the driving speed increases, the water drag force acting on the tire increases in the direction opposite to the running direction. Therefore, the frictional force, which can be expressed by the sum of the traction force and the drag force, decreases with an increase in the running speed at a very thin water film thickness of 0.5 mm.

The SN (Skid Number) was calculated as shown in Equation (2), and the result was compared with the test result as shown in FIG. 8A. 8A is a prediction result obtained by a full FE simulation and an estimation method, and a box plot is a result of ASTM E-274 (Pavement Friction Tester) . The test results show that the slip resistance is measured 8 times on the road surface of 4 sections using 40 km / h, 60 km / h and 80 km / h. The average slip resistance values (SN) obtained from the test results measured eight times in each section in all four sections are 52.97, 48.05 and 43.99 for 40km / h, 60km / h and 80km / h, respectively. The predicted results are 50.13, 47.91, 45.03. For reference, the SN (40) R shown in FIGS. 8A and 8B is 40 Km / h, the SN (60) R is 60 Km / h and the SN (80) R is 80 Km / h.

As can be seen from the results of FIG. 8A, in the test results obtained by using the estimation method and the test results using the ASTM E274 (Pavement Friction Tester) equipment, the same tendency that the slip resistance value SN decreases as the running speed increases . That is, the average slip resistance value (SN) of the test result decreases almost constantly by a difference of 4.92 and 4.06, respectively, when the running speed increases by 20 km / h. Similarly, it can be seen that the slip resistance SN of the predicted results also decreases by a constant difference of 2.22 and 2.88, respectively.

However, the slip resistance value of the predicted result is slightly different from the average slip resistance value of the test result according to the running speed. That is, as the driving speed increases, the decrease in the slip resistance value is smaller than the average slip resistance value in the test result. This is because the prediction result obtained by the estimation method from the analysis result using LS-DYNA can not consider the change of the sliding friction coefficient between the tire and the road surface as the running speed increases.

In general, as the driving speed increases on a dry road surface, the sliding friction coefficient between the tire and the road surface decreases (McLean AJ, et al 1994). Therefore, in the present invention, in order to consider the change of the sliding friction coefficient as the running speed increases, three additional analyzes of the friction coefficient change are performed, and the results are shown in FIG. 8B. Here, '+' denotes a friction coefficient of 0.55, '*' denotes a friction coefficient of 0.48, and '×' denotes a sliding resistance value obtained by using a coefficient of friction of 0.51 as a predicted result of FIG.

As can be seen from the above results, the slip resistance values for the three friction coefficient changes all decrease to the same tendency as the driving speed increases. If the reduction of the sliding friction coefficient between the tire and the road surface is considered as the driving speed increases, the slip resistance value of a larger difference than the result predicted by only the influence of the dynamic pressure of the water will be obtained. That is, assuming that the slip friction coefficient of 0.55, 0.51, and 0.48 changes at 40 km / h, 60 km / h, and 80 km / h, respectively, as shown in the above prediction results, The difference between the two values is very similar to 1.42, 0.14 and 1.26 at 40km / h, 60km / h and 80km / h, respectively.

Therefore, the traction force and the drag force can be estimated by using the full FE simulation method and the estimation method using the LS-DYNA and the exponential function of the water film thickness (h) and the running speed The change of the slip resistance SN can be easily confirmed.

In addition, LS-DYNA full FE simulation method solves the problem that analysis time of more than 150 hours is required when analyzing a model for a thickness of 0.5 mm. That is, the analysis time required for the three water film thicknesses of 5 mm, 7.5 mm, and 10 mm is 21, 23, and 26, respectively, by the full FE simulation method. The time required to predict the obtained result using the estimation method (Estimation Method) is less than 1 hour including the data arrangement time. Therefore, it takes a total of 71 hours to obtain the results for a very thin film thickness of 0.5 mm using the full FE simulation method and the Estimation Method. Therefore, the full FE simulation ) Method can shorten the analysis time by more than two times than obtaining the result.

In addition, if a prediction solution is obtained by using the method proposed in the present invention, the lift force or the skid resistance value SN (skid number) for various thicknesses of the water film can be easily and quickly Can be obtained.

4. Conclusion

In the present invention, full three-dimensional FE simulation was performed on three water film thicknesses (5 mm, 7.5 mm, and 10 mm) that can consider the viscosity of water using LS-DYNA.

The lift force was obtained by the running speed for the thickness of the water film and the buoyancy for a thin film thickness of 2.5 mm was estimated using the Estimation Method which can be expressed as a function of the water thickness and running speed lift force can be easily predicted.

The predicted results are very similar to the results of a full FE simulation method using a tire rolling model for the same 2.5 mm of water thickness. In other words, as the driving speed increases, the change in the lift force also increases equally, so it is not only qualitatively reasonable, but also a result of squaring the ratio of sum of squares (R2) From the result of 0.952, the accuracy of the prediction result and the analysis result was obtained.

Therefore, various membrane thicknesses, especially full FE simulation, can be achieved by using full FE simulation method and estimation method using LS-DYNA tire rolling model. It is possible to predict very thin water film thicknesses (for example, 1 mm or less) or various driving speeds, which require a lot of analysis time.

Furthermore, a full FE simulation method and an estimation method using the LS-DYNA tire sliding model are used to estimate the traction force for a very thin film thickness of 0.5 mm A drag force could be obtained.

The results are shown in terms of the sliding resistance value (SN) and compared with the test results using ASTM E274 (Pavement Friction Tester) equipment. As a result of the test results and the simulation results, the same tendency was obtained that the friction force between the tire and the road surface decreased and the slip resistance value (SN) decreased as the driving speed increased.

However, the predicted results obtained by the analytical method do not consider the decreasing sliding friction coefficient as the running speed increases, so the amount of decrease in the sliding resistance is smaller than the average sliding resistance of the test result. Therefore, we confirmed the decrease of the sliding resistance value by simulating the decrease of the sliding friction coefficient as the running speed increases, and the results are very similar to the average sliding resistance of the test results.

Therefore, it is considered that the same results as the test results can be obtained if the change of the sliding friction coefficient can be considered as the driving speed increases in the analytical method prediction results. In addition, when the sliding resistance simulation is performed using the full FE simulation method and the estimation method, the analysis time is reduced to twice as much as that using the full FE simulation only can do.

Therefore, when the estimation solution is obtained by using the method proposed in the present invention, it is possible to estimate the physical quantities for various water film thicknesses, that is, lift forces, traction forces, drag forces drag force can be easily and quickly obtained, and the change of the slip resistance value between the tire and the road surface can be confirmed using the drag force.

While the present invention has been particularly shown and described with reference to exemplary embodiments thereof, it is to be understood that the invention is not limited to the disclosed exemplary embodiments, Of the right.

Lift force: Buoyancy h: Thickness
FE simulation: Finite element simulation
Estimation: Prediction Traction force: Traction force
Drag force: Drag SN: Slip resistance value

Claims (9)

delete delete delete Obtaining an analytic physical quantity for each of the at least two water film thicknesses in the first section using the finite element model for the tire and the water film;
Obtaining an exponential function of the thickness of the water film and the running speed by curve fitting through the asymptotic method; And
Obtaining a prediction physical quantity per driving speed for at least one water film thickness in the second section by using the exponential function,
The exponential function is defined by equation (1)
The above equation (1)
force = ch ^a v ^b ,
In the above equation (1), force is a force which is one of the physical quantities, h is the thickness of the water film, v is the running speed, a, b and c are constants determined by the least squares method,
In the case of the tire sliding model in which the tire slides on the water film,
The analysis and prediction physical quantity is a traction force or a drag force,
The traction force or drag force is calculated by the above equation (1)
If the predicted physical quantity is a traction force, a, b and c in the equation (1) are determined using a least squares method as a constant of the prediction solution for the traction force,
Wherein a, b and c in the equation (1) are determined by using a least square method as a constant of a prediction solution for drag when the predictive physical quantity is a drag force. 5. The method of claim 4,
The first section of the thickness of the water film is 5 mm or more,
Wherein the second section of the water film thickness is less than 5 mm. Obtaining an analytic physical quantity for each of the at least two water film thicknesses in the first section using the finite element model for the tire and the water film;
Obtaining an exponential function of the thickness of the water film and the running speed by curve fitting through the asymptotic method; And
Obtaining a prediction physical quantity per driving speed for at least one water film thickness in the second section by using the exponential function,
The step of obtaining the predicted physical quantity includes:
Calculating a sliding resistance value using the buoyancy force, the pulling force and the drag force after obtaining a lift force, a traction force and a drag force with the predicted physical quantity, Method of obtaining physical quantity. The method of claim 6,
The exponential function is defined by equation (1)
The above equation (1)
force = ch ^a v ^b ,
In the above equation (1), force is a force which is one of the physical quantities, h is the thickness of the water film, v is the running speed, a, b and c are constants determined by the least squares method,
The buoyancy, the traction force and the drag force are respectively obtained by the above-mentioned equation (1)
In the case of buoyancy, a, b and c in equation (1) are constants of the prediction solution for buoyancy,
In the case of the traction force, a, b and c in the above equation (1) are constants of the prediction solution for the traction force,
(A), (b) and (c) are the constants of the predictive solution for the drag. 8. The method according to claim 6 or 7,
The slip resistance value is calculated by equation (2)
The formula (2)

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(2), SN _v is a slip resistance value, F _x is a horizontal resistance force acting on the tire, equal to the sum of the pulling force and the drag force, F _z is a vertical load, A method of acquiring a physical quantity for a water film phenomenon such as a difference. 9. The method of claim 8,
Wherein the sliding friction coefficient between the tire and the road surface is reduced as the running speed increases.

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