Showing papers on "Slip ratio published in 2002"

Apparent fluid slip at hydrophobic microchannel walls

Abstract: Micron-resolution particle image velocimetry is used to measure the velocity profiles of water flowing through 30×300 μm channels. The velocity profiles are measured to within 450 nm of the microchannel surface. When the surface is hydrophilic (uncoated glass), the measured velocity profiles are consistent with solutions of Stokes’ equation and the well-accepted no-slip boundary condition. However, when the microchannel surface is coated with a 2.3 nm thick monolayer of hydrophobic octadecyltrichlorosilane, an apparent velocity slip is measured just above the solid surface. This velocity is approximately 10% of the free-stream velocity and yields a slip length of approximately 1 μm. For this slip length, slip flow is negligible for length scales greater than 1 mm, but must be considered at the micro- and nano scales.

Slip flow past a stretching surface

Abstract: The slip-flow of a Newtonian fluid past a linearly stretching sheet is considered. The partial slip is controlled by a dimensionless slip factor, which varies between zero (total adhesion) and infinity (full slip). An exact analytical solution of the governing Navier-Stokes equation is found, which is formally valid for all Reynolds numbers.

Transport of bubbles in square microchannels

Abstract: Liquid/gas flows are experimentally investigated in 200 and 525 μm square microchannels made of glass and silicon. Liquid and gas are mixed in a cross-shaped section in a way to produce steady and homogeneous flows of monodisperse bubbles. Two-phase flow map and transition lines between flow regimes are examined. Bubble velocity and slip ratio between liquid and gas are measured. Flow patterns and their characteristics are discussed. Local and global dry out of the channel walls by moving bubbles in square capillaries are investigated as a function of the flow characteristics for partially wetting channels. Two-phase flow pressure drop is measured and compared to single liquid flow pressure drop. Taking into account the homogeneous liquid fraction along the channel, an expression for the two-phase hydraulic resistance is experimentally developed over the range of liquid and gas flow rates investigated.

Nonlinear Smoluchowski slip velocity and micro-vortex generation

Abstract: When an electric field is applied across a conducting and ion-selective porous granule in an electrolyte solution, a polarized surface layer with excess counter-ions is created. The depth of this layer and the overpotential V across this layer are functions of the normal electric field j on the granule surface. By transforming the ionic flux equations and the Poisson equation into the Painleve equation of the second type and by analysing the latter's asymptotic solutions, we derive a linear universal j–V correlation at large flux with an electrokinetic slip length β. The flux-induced surface polarization produces a nonlinear Smoluchowski slip velocity that can couple with the granule curvature to produce micro-vortices in micro-devices. Such vortices are impossible in irrotational electrokinetic flow with a constant zeta-potential and a linear slip velocity.

Moving Boundary Models for Dynamic Simulations of Two-Phase Flows

Abstract: Two-phase flows are commonly found incomponents in energy systems such as evaporators and boilers. Theperformance of these components depends among others on thecontroller. Transient models describing the evaporation process areimportant tools for determining control parameters, and fast loworder models are needed for this purpose. This article describes ageneral moving boundary (MB) model for modeling of two-phase flows.The new model is numerically fast compared to discretized modelsand very robust to sudden changes in the boundary conditions. Themodel is a $7^th$ order model (7 state variables), which is asuitable order for control design. The model is also well suitedfor open loop simulations for systems design and optimization.It is shown that the average void fraction has a significant influenceon the system response. A new method to calculate the average voidfraction including the influence of the slip ratio is given. Theaverage void fraction is calculated as a symbolic solution to theintegral of the liquid fraction profile. (Less)

No-slip boundary condition switches to partial slip when fluid contains surfactant

Abstract: Physisorbed surfactant can change the hydrodynamic boundary condition of oil flow from “stick” to “partial slip”, provided that the shear stress on the wall exceeds a threshold level that decreases with increasing surface coverage of surfactant. To demonstrate this, Newtonian alkane fluids (octane, dodecane, tetradecane) were placed between molecularly smooth surfaces that were either wetting (muscovite mica) or rendered partially wetted by adsorption of surfactant (0.2 or 0.1 wt % hexadecylamine). The surface spacing was vibrated at spacings so large that the fluid responded as a continuum. The resulting hydrodynamic forces agreed with predictions from the no-slip boundary condition when flow rate, peak velocity normalized by surface spacing, was low but implied partial slip when it exceeded a critical level. In other words, the “slip length” depended on reduced velocity. When the reduced velocity was sufficiently high, a plateau shear stress was observed, ≈1.3 N m-2 for 0.2 wt % hexadecylamine, but also...

Motion dynamics of a rover with slip-based traction model

Abstract: This paper investigates kinetic behavior of a planetary rover with attention to tire-soil traction mechanics and articulated body dynamics, and thereby study the control when the rover travels over natural rough terrain. Experiments are carried out with a rover test bed to observe the physical phenomena of soils and to model the traction mechanics, using the tire slip ratio as a state variable. The relationship of load-traction factor versus the slip ratio is modeled theoretically then verified by experiments, as well as specific parameters to characterize the soil are identified. A dynamic simulation model is developed considering the characteristics of wheel actuators, the mechanics of tire-soil traction, and the articulated body dynamics of a suspension mechanism. Simulations are carried out to be compared with the corresponding experimental data and verified to represent the physical behavior of a rover.

Slip velocity and lift

Abstract: equilibrium position with a unique, slightly positive equilibrium angular slip velocity. The angular slip velocity discrepancy defined as the difference between the angular slip velocity of a migrating particle and the angular slip velocity at its equilibrium position is positive below the position of equilibrium and negative above it. This discrepancy is the quantity that changes sign above and below the equilibrium position for neutrally buoyant particles, and also above and below the lower equilibrium position for heavy particles. The existence and properties of unstable positions of equilibrium due to newly identified turning point transitions and those near the centreline are discussed. The long particle model of Choi & Joseph (2001) that gives rise to an explicit formula for the particle velocity and the velocity profile across the channel through the centreline of the particle is modified to include the effect of the rotation of the particle. In view of the simplicity of the model, the explicit formula for Up and the velocity profile are in surprisingly good agreement with simulation values. The value of the Poiseuille flow velocity at the point at the particle's centre when the particle is absent is always larger than the particle velocity; the slip velocity is positive at steady flow.

Slip Flow Convection in Isoflux Rectangular Microchannels

Abstract: Laminar forced convection in thermally developing slip flow through isoflux rectangular microchannels is analytically investigated. Local and fully developed Nusselt numbers, fluid temperatures, and wall temperatures are obtained by solving the continuum energy equation for hydrodynamically fully developed slip flow with the velocity slip and temperature jump condition at the walls. Heat transfer may increase, decrease, or remain unchanged, compared to nonslip flow conditions, depending on aspect ratios and two-dimensionless variables that include effects of the microchannel size or rarefaction and the fluid/wall interaction. The transition points that separate heat transfer enhancement from reduction are acquired for different aspect ratios

To Slip or Not to Slip: Water Flows in Hydrophilic and Hydrophobic Microchannels

Abstract: The slip effects of water flow in hydrophilic and hydrophobic microchannels of 1 and 2 μm depth are examined experimentally. Fabrication processes for silicon/Pyrex microchannels were chosen to ensure good control of the channel height and to obtain atomically smooth surfaces. Hydrophilic surfaces were prepared with an RCA-1 cleaning, while hydrophobic surfaces were created by coating the channel surface with the self-assembled monolayer of octadecyltrichorosilane (OTS). The flow rates of pure DI water at various applied pressure differences for each surface condition were measured using a high precision flow metering system and it was observed that the flow rates in hydrophobic channels is larger than in the same hydrophilic channel. The increase of the flow rate can be explained by assuming a slip velocity at the wall. The slip effects become more pronounced as the channel height decreases and the wall shear rate increases. The slip length was found to vary as approximately the square root of the shear rate and had values of approximately 40 nm in the hydrophobic channels and 15 nm in the hydrophilic channels at a shear rate of 105 s−1 .Copyright © 2002 by ASME

Motion dynamics and control of a planetary rover with slip-based traction model

Abstract: This paper investigates kinetic behavior of a planetary rover with attention to tire-soil traction mechanics and articulated body dynamics, and thereby study the control when the rover travels over natural rough terrain. Experiments are carried out with a rover test bed to observe the physical phenomena of soils and to model the traction mechanics, using the tire slip ratio as a state variable. The relationship of load-traction factor versus the slip ratio is modeled theoretically then verified by experiments, as well as specific parameters to characterize the soil are identified. A dynamic simulation model is developed considering the characteristics of wheel actuators, the mechanics of tire-soil traction, and the articulated body dynamics of a suspension mechanism. Simulations are carried out to be compared with the corresponding experimental data and verified to represent the physical behavior of a rover. Finally, a control method is proposed and tested. The proposed method keeps the slip ratio within a small value and limits excessive tire force, so that the rover can successfully traverse over the obstacle without digging the soil or being stuck.

A slip model with molecular dynamics

Abstract: In this paper we present analytical investigations of the slip flow in a hard disk drive where the flying head is approximately 25 nm above the rotating disk. A new slip velocity model is developed, incorporating molecular dynamics to take into account the impact of molecular collisions which play an important role in the interactions between molecules and the solid surface. A modified Reynolds equation is derived based on the modified slip model. Analytical solutions for velocity distribution and flow rate, using the modified Reynolds equation are obtained. Non-dimensional flow rate for plane Poiseuille flow, pressure distributions and load-carrying capacities for slope flow are compared with those available in the literature. Comparison with first-order, second-order and 1.5-order slip models shows that the new model agrees reasonably well with the solution obtained from the linearized Boltzmann equation.

A fuzzy logic controller design for vehicle abs with a on-line optimized target wheel slip ratio

Abstract: For a vehicle Anti-lock Braking System (ABS), the control target is to maintain friction coefficients within maximum range to ensure minimum stopping distance and vehicle stability. But in order to achieve a directionally stable maneuver, tire side forces must be considered along with the braking friction. Focusing on combined braking and turning operation conditions, this paper presents a new control scheme for an ABS controller design, which calculates optimal target wheel slip ratio on-line based on vehicle dynamic states and prevailing road condition. A fuzzy logic approach is applied to maintain the optimal target slip ratio so that the best compromise between braking deceleration, stopping distance and direction stability performances can be obtained for the vehicle. The scheme is implemented using an 8-DOF nonlinear vehicle model and simulation tests were carried out in different conditions. The simulation results show that the proposed scheme is robust and effective. Compared with a fixed-slip ratio scheme, the stopping distance can be decreased with satisfacto교 directional control performance meanwhile.

Rheology of yogurt during pipe flow as characterized by magnetic resonance imaging

Abstract: Flow behavior of yogurt during pipe flow was investigated using a magnetic resonance imaging (MRI) viscometer. The technique utilizes a velocity profile and independent pressure drop measurement to evaluate rheological parameters. The yield stress and slip velocity were obtained directly from the MR images; the Herschel-Bulkley consistency index, K, and the flow behavior index, n, were obtained through curve fitting procedures for product temperatures of 25C and 35C, over a shear rate range of 0.5 - 40 s -1 . At 25C, the average value of the yield stress was 14 Pa; the values of K and n were 5.6 Pa s n and 0.36, respectively. As the wall stress increased from 15 to 42 Pa, the slip velocity increased linearly from 13 to 54 mm s -1 . At 35C, the average value of the yield stress was 10 Pa; the values of K and n were 1.1 Pa s n and 0.88, respectively. As the wall stress increased from 12 to 31 Pa, the slip velocity increased linearly from 14 to 59 mm s -1 . These rheological parameters and slip velocities are relevant to the postfermentation cooling process performed in a continuous heat exchanger.

Stress-density ratio slip-corrected Reynolds equation for ultra-thin film gas bearing lubrication

Abstract: The direct simulation Monte Carlo method is used to evaluate the improved slip boundary condition and slip-corrected Reynolds equation for gas lubrication in magnetic recording storage system. The study shows that in transition regime, the slip velocity is affected not only by shear stress, but also by density itself. In this ultra-thin film lubrication environment, the slip velocity has a linear relationship with the ratio of shear stress to density near the wall. This observation is particularly true when Knudsen number is around 1 or larger. Through this study, the authors have developed a new slip velocity model, named stress-density ratio model, particularly suitable to transition regime. Based on this novel model, a slip-corrected Reynolds equation is also derived and solved numerically. The stress-density ratio model is confirmed to offer a better applicability than the previous slip-flow models for modern computer magnetic storage device, where the Knudsen number of slider air bearing is in the range of unity or larger.

The Influence of the Slip Flow on Steady-State Load Capacity, Stiffness and Damping Coefficients of Elastically Supported Gas Foil Bearings

Abstract: The slip flow effect is considered to estimate the load capacity and the dynamic coefficients of an elastically-supported gas foil hearing when the local Knudsen number for the minimum film thickness is greater than 0.01. The compressible Reynolds equation with slip flow conditions is used to evaluate the load capacity. The linearized dynamic coefficient equations are obtained by the perturbation method. Numerical predictions compare the static and dynamic force performances considering slip flow at room-to-high temperate with the performance of elastically-supported foil bearing without slip flow for a range of bearing compliances and bearing numbers. It has been shown that the slip flow effect on the load capacity and the dynamic coefficients at high temperature is significant in the region of low bearing numbers. Presented as a Society of Tribologists and Lubrication Engineers Paper at the ASME/STLE Tribology Conference in Cancun, Mexico October 27–30, 2002

Device for estimating maximum road friction coefficient forms product of defined coefficient with ratios of reaction force and vertical load and of changes in reaction force and slip ratio

Abstract: The device has a devices for computing a reaction force of the road on the tire of the wheel based on a tire mode, the vertical load on the tire, the ratio of the reaction force and vertical load, the ratio of the change in reaction force to the change in slip ratio computed using the tire model and the maximum road friction coefficient based on the product of a predefined coefficient with the first and second ratios. The device has a first device for computing a reaction force of the road on the tire of the wheel based on a tire mode, a second device for computing the vertical load on the tire, a third device for computing the ratio of the reaction force and vertical load, a fourth device for computing the ratio of the change in reaction force to the change in slip ratio computed using the tire model and a fifth device for computing a maximum road friction coefficient based on the product of a predefined coefficient with the first and second ratios. An Independent claim is also included for a method of estimating maximum friction coefficient between a tire and a road.

The effect of water saturation on gas slip factor by pore scale network modeling

Abstract: A pore scale network model is presented to describe the flow of gas in tight porous media. The Adzumi’s approach of dual mechanism for transport of gas through the capillary is incorporated in this model. The treatment of the microscopic flow mechanism gives an insight into the Klinkenberg effect, where the effective permeability of the tight porous media is a function of the mean pressure. From the simulation, it shows that the slip factor decreased with the increase of the permeability of the porous media and was affected by the variation of the distribution function of the capillary radius. In the process of gas flow through water-saturated porous media, the slip factor is not a constant any more; it will decrease with the increase of the water saturation.

Examination of the Slip Boundary Condition by µ-PIV and Lattice Boltzmann Simulations

Abstract: This work examines the slip boundary condition by Lattice Boltzmann simulations, addresses the validity of the Navier’s hypothesis that the slip velocity is proportional to the shear rate and compares the Lattice Boltzmann simulations to the experimental results of Tretheway and Meinhart (Phys. of Fluids, 14, L9-L12). The numerical simulation models the boundary condition as the probability, P, of a particle to bounce-back relative to the probability of specular reflection, 1P. For channel flow, the numerically calculated velocity profiles are consistent with the experimental profiles for both the no-slip and slip cases. No-slip is obtained for a probability of 100% bounce-back, while a probability of 0.03 is required to generate a slip length and slip velocity consistent with the experimental results of Tretheway and Meinhart for a hydrophobic surface. The simulations indicate that for microchannel flow the slip length is nearly constant along the channel walls, while the slip velocity varies with wall position as a results of variations in shear rate. Thus, the resulting velocity profile in a channel flow is more complex than a simple combination of the no-slip solution and slip velocity as is the case for flow between two infinite parallel plates.

Brake control device, brake control method, and recording medium

Abstract: The invention provides a brake control device for a vehicle, a brake control method and a recording medium having a program causing a computer to perform the brake control method. A tire friction characteristic with respect to a vehicle velocity or a wheel velocity is memorized in advance. When a brake is put on to the vehicle, a current slip ratio or a current slip velocity is found and an optimum slip ratio or an optimum slip velocity is calculated using the tire friction characteristic. Then, a difference between the optimum slip ratio and the found current slip ratio or a difference between the optimum slip velocity and the found current slip velocity is compared with a predetermined value. According to a result of the comparison, a braking force applied to the vehicle is controlled.

On the wall slip of polymer blends

Abstract: The slip flow of the polypropylene (PP)/poly[ethylene-co-(vinyl acetate)] (EVA) system was studied in a capillary rheometer for shear rates of 40–1000 s−1 at four temperatures. Three dies made of aluminum with a length/diameter (L/D) ratio of 15 and diameters of 1.59, 1.19, and 0.79 mm provided the flow data. Calculations of the slip velocity by the Mooney method showed power-law behavior with the stress. Blends were prepared at various proportions of PP and EVA for observation of the variation of the slip velocity for different compositions and temperatures. Direct microscopic observations of the slip layer on extruded samples showed domains of the dispersed phase unevenly distributed between the slip layer and the core and provided estimates of the thickness of the layer adjacent to the capillary wall. Results showed that the viscosity in the slip layer was 10–100 times lower than that in the bulk for the same value of the shear stress. In terms of the extrapolation length, the development of the slip layer was the result of different disentanglement dynamics of the molecules in the slip layer in comparison with those in the bulk. © 2002 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 40: 303–316, 2002

Quantification of the slip phenomenon and the effect of shear thinning in the capillary flow of linear polyethylenes

Abstract: The slip phenomenon in the capillary flow of linear polyethylenes and its relation to their shear-thinning behavior was studied in this work. A simple macroscopic analysis that allows a description of the trend of the slip length and the contribution of slip to the average fluid velocity as functions of the shear stress is presented. From this analysis it is shown that an increase or decrease of the slip length for increasing shear stress is determined by the polymer architecture and the competition between slip and shear thinning. A similar behavior is observed for the ratio between the slip and whole average fluid velocities. The analysis is validated using experimental data obtained during the continuous extrusion of linear low-density polyethylene melts under strong slip conditions in a brass die.

Squeeze flow of a power-law fluid between two rigid spheres with wall slip

Abstract: The effect of wall slip on the squeeze flow of a power-law fluid between two rigid spherical particles has been examined based on the Reynolds lubrication theory. It is shown that the viscous force arising from the squeeze flow with wall slip may be resolved to the noslip solution by introducing a slip correction coefficient. An expression for the slip correction coefficient of force is derived which is related to the slip parameter, the flow index and the upper limit of integration. Generally, wall slip results in a reduction in the viscous force. The reduction in the viscous force increases as the flow index increases, suggesting that wall slip has a more profound effect on shear thickening material. However, such reduction decreases as the upper limit of integration increases from finite liquid bridges to fully immersed systems. The reduction in the viscous force also increases as the slip parameter increases, which is the expected behaviour.

Stokes slip flow through a grid of circular cylinders

Abstract: The Stokes flow through a row of equally spaced circular cylinders with partial slip on the boundaries is studied by domain decomposition and matching. The pressure drop or resistance across the grid is found for various slip and normalized cylinder radii. Asymptotic formulas are found for sparcely and closely spaced cylinders.

Road surface friction coefficient estimating method, signal multiplex transmission method and signal multiplex transmission device

Abstract: A method of directly and efficiently estimating a road surface friction coefficient independently of slip ratio by measuring tangential force and vertical force acting on the elastic body (3) of an elastic wheel (1), and calculating the road surface friction coefficient on the basis of the measured values of these forces and the measured value of wheel angular velocity.

Hydrodynamics of Trickle-Flow Reactors: Updated Slip Functions for the Slit Models

Abstract: A new set of velocity ( f v ) and shear ( fs ) slip correlations was proposed for improving the prediction, by the extended and the double-slit trickle-bed mechanistic models, of the liquid hold-up, the total pressure drop, the wetting efficiency, and the gas-liquid interfacial area in the trickle flow regime. Amendment of the original f s and f v slip correlations 3 ’ 6 was motivated by the following incentives: (i) a much wider trickle flow regime database currently at disposal with in excess of 5,100 experimental data; (ii) application of a traceablity protocol to guarantee no corruption and normalization of the compiled data in the database; (iii) contrary to previous formulations, reduction to one single set of f s and f v slip functions applicable to both the extended and the double-slit models. The slip functions were correlated in terms of gas Reynolds ( Re L ) , liquid Reynolds ( Re L ) , Froude ( Fr L ) , Weber ( We L ) , Lockhart-Martinelli ( X L ) , and Stokes ( St L ) numbers. Implementation of the slip functions in the extended slit model yields liquid hold-up and pressure drop with an average absolute relative error (AARE) of 17% and 19.5%, respectively. Similarly, the double-slit model predicts wetting efficiency, gas-liquid interfacial area, liquid hold-up, and total pressure drop with AARE = 11%, 34.7%, 20%, and 18%, respectively.

Investigation of the Wall Slip Effect in Highly Concentrated Disperse Systems by Means of Non-Invasive UVP-PD Method in the Pressure Driven Shear Flow1

Abstract: A novel in-line UVP-PD non-invasive rheological measuring technique was introduced for rheological analysis of highly concentrated disperse systems. The method is based on a combination of the Ultrasonic Pulsed Echo Doppler technique (UVP, Ultrasound Velocity Profiler) and the pressure difference (PD) method. The rheological properties were derived from simultaneous recording and on-line analysis of the velocity and related radial shear stress profiles across a circular channel. Wall slip velocity was extrapolated from the on-line fit and monitored on-line simultaneously with the flow index. Two effects were found and preliminarily analyzed. The first effect refers to a transition from strongly non-Newtonian to Newtonian flow velocity profile while increasing in the absolute flow velocity. The second flow effect refers to an abrupt reduction of the wall slip velocity while increasing the absolute flow velocity. Considerable discrepancy was found between the results of the in-line UVP-PD measurement in pressure driven shear flow and the results of the conventional rheometry.

Low Reynolds Number Slip Flow in a Curved Rectangular Duct

Abstract: The radially symmetric, steady, slow viscous slip flow through a curved duct of rectangular cross section is studied. The Stokes equation is solved using eigenfunction expansions and Navier's slip condition. As slip is increased, the location of the maximum velocity moves from near center to the outer wall. The minimum velocity occurs at the inside corners. It is found that both slip and curvature promote the flow rate but not necessarily the mean velocity. ©2002 ASME

Phenomenological model of propagation of the elastic waves in a fluid-saturated porous solid with nonzero boundary slip velocity

Abstract: It is known that a boundary slip velocity starts to play an important role when the length scale over which the fluid velocity changes approaches the slip length, i.e., when the fluid is highly confined, for example, fluid flow through porous rock or blood vessel capillaries. Zhu and Granick [Phys. Rev. Lett. 87, 096105 (2001)] have recently experimentally established the existence of a boundary slip in a Newtonian liquid. They reported typical values of the slip length of the order of few micrometers. In this light, the effect of introduction of the boundary slip into the theory of propagation of elastic waves in a fluid-saturated porous medium formulated by Biot [J. Acoust. Soc. Am. 28, 179–191 (1956)] is investigated. Namely, the effect of introduction of boundary slip upon the function F(κ) that measures the deviation from Poiseuille flow friction as a function of frequency parameter κ is studied. By postulating phenomenological dependence of the slip velocity upon frequency, notable deviations in the domain of intermediate frequencies in the behavior of F(κ) are introduced with the incorporation of the boundary slip into the model. It is known that F(κ) crucially enters Biot’s equations, which describe dynamics of fluid-saturated porous solid. Thus, consequences of the nonzero boundary slip by calculating the phase velocities and attenuation coefficients of both rotational and dilatational waves with the variation of frequency are investigated. The new model should allow one to fit the experimental seismic data in circumstances when Biot’s theory fails, as the introduction of phenomenological dependence of the slip velocity upon frequency, which is based on robust physical arguments, adds an additional degree of freedom to the model. In fact, it predicts higher than the Biot’s theory values of attenuation coefficients of the both rotational and dilatational waves in the intermediate frequency domain, which is in qualitative agreement with the experimental data. Therefore, the introduction of the boundary slip yields threefold benefits: (1) better agreement of theory with experimental data since the parametric space of the model is larger (includes effects of boundary slip); (2) the possibility to identify types of porous medium and physical situations where boundary slip is important; and (3) constrain model parameters that are related to the boundary slip.

Method and apparatus for judging road surface conditions, and program for setting threshold for judging road surface conditions

Abstract: A method for judging road surface conditions, comprising the steps of: detecting rotational information of tires; storing the rotational information of the respective tires; calculating a vehicle velocity; calculating an acceleration/deceleration of the vehicle; calculating a slip ratio of left-sided front and rear wheels and right-sided front and rear wheels and a slip ratio of front and rear wheels, respectively; calculating an amount of fluctuation in differences in slip ratios between the right and left wheels; obtaining a linear regression coefficient and a correlation coefficient between the slip ratio of the front and rear wheels and the acceleration/deceleration of the vehicle; and setting a threshold for judging road surface conditions.