Comparison of the traffic performance of a two-axle four wheel drive (4WD), rear wheel drive (RWD), and front wheel drive (FWD) vehicle on loose sandy sloped terrain

The traffic performances during driving and braking of a 5.88 kN weight wheeled vehicle with two-axle four wheel drive, rear wheel drive, and front wheel drive running up and down a loose sandy sloped terrain were compared by means of a simulation. For the given dimensions of the vehicle and the given terrain-wheel system constants, the relationship between the effective tractive and braking effort of the vehicle, the amount of sinkage of the front and rear wheels, the total amount of sinkage of the vehicle, and the slip ratio were calculated to estimate the optimum height of force of application and the optimum eccentricity of the center of gravity of the vehicle. It was observed that, during driving action, the maximum effective tractive effort of the four wheel drive vehicle (4WD) was larger than that of the rear wheel drive vehicle (RWD), which in turn was greater than that of the front wheel drive vehicle (FWD). During the braking action, the effective braking effort at skid -20% of the four wheel vehicle (4WB) was larger than that of the front wheel brake vehicle (FWB), in turn greater than that of the rear wheel brake vehicle (RWB), when the two-axle four wheel vehicle is moving up or down the loose sandy sloped terrain. The maximum terrain slope angle up which the two-axle wheeled vehicle is able to move during driving action was found to be about 0.067π rad for the 4WD vehicle, about 0.031π rad for the RWD vehicle, and about 0.017π rad for the FWD vehicle. The effective braking effort at skid-20% of 4WB, FWB and RWB was found to decrease with slope angle.     

The optimum height of application of force and eccentricity of a wheeled vehicle running on a loose sandy soil

In earthmoving sites, multi-wheeled vehicles are used to excavate a sandy soil or to pull other construction machinery. In this paper, the mechanism of a 5.88 kN weight, two-axle, four-wheel vehicle running on a loose sandy soil is theoretically analysed. For given terrain-wheel system constants, the combination of the effective braking force of the front wheel during pure rolling state and the effective driving force of the rear wheel during driving action will clarify the relation between effective effort of the vehicle and slip ratio and the relation between amounts of sinkage the front and rear wheels and slip ratio, etc. The maximum effective tractive effort of the vehicle varies with the height of application force and the position of the center of gravity of the vehicle. The optimum height of application of force and the eccentricity of the center of gravity to obtain the largest value of the maximum effective tractive effort can be explained with an analytical simulation program. Results of this study showed that the optimum height of application force should be 30 cm and the optimum eccentricity of the center of gravity is 0.05 for a vehicle considered for this study.     

Traffic performance of a rubber-tracked vehicle travelling up and down a sloped pavement

The tractive and braking performances of a 40 kN rubber-tracked vehicle travelling up and down a sloped pavement depend on the grouser shape. The purpose of this paper is to find the most suitable grouser shape to obtain the maximum optimum effective tractive effort and the maximum optimum effective braking force and to clarify the several traffic performances of the vehicle travelling up and down sloped concrete and asphalt paved roads. As results, it is verified that the most suitable shape of rubber grouser is an equilateral trapezoid type of contact length 3 cm for concrete pavement and another of contact length 5 cm for asphalt pavement, respectively, and that the effective tractive effort and the effective braking force decrease with the increment of slope angle.     

Further consideration of the shape-factor relationship for turbulent boundary layers

The lag-entrainment predictive scheme developed by Green et al. has been modified to include the pressure-gradient parameter Π₁. In the original model suggested by Green et al. the mass-flow shape factor H₁ is related to the common shape factor H, H₁ = f(H). In the present model H₁ is related to H, Reynolds number based on the local momentum thickness θ, and Π₁; thus H₁ = f(H, R_eθ, Π₁). The modified formula for H₁, is introduced into the original lag-entrainment integral model. Calculations are made to examine the present model for the predictions of the development of boundary layers approaching separation studied experimentally by the authors. Slightly improved predictions are obtained using the model developed by El Telbany et al. However, the present model proved to give an improved representation of the development of wall shear stress in cases the two-equation turbulence model proved to be unsuccessful.     

Traction performance of a pushed/pulled drive wheel

A comprehensive method for prediction of off-road driven wheel performance is presented, assuming a parabolic wheel–soil contact surface. The traction performance of a driven wheel is predicted for both driving and braking modes. Simulations show significant non-symmetry of the traction performance of the driving and braking wheels. The braking force is significantly greater than the traction force reached in the driving mode. In order to apply the suggested model for prediction of the traction performance of a 4WD vehicle, the load transfer effect was considered. Simulated traction performances of front and rear driven wheels differ significantly, due to the load transfer. In the driving mode, the rear driven wheel develops a net traction force greater than that of the front wheel. On the other hand, in the braking mode the front driven wheel develops a braking force significantly greater than that of the rear driven wheel due to a pushed/pulled force affected by the load transfer. The suggested model was successfully verified by the data reported in literature and by full-scale field experiments with a special wheel-testing device. The developed approach may improve the prediction of off-road multi-drive vehicle traction performance.     

Tractive performance and compaction effect of a road roller running on a weak sandy soil

This study aims to investigate the tractive performance of a two-axle, two-wheel vehicle with rear-wheel drive or brake and the compaction of a decomposed granite soil. The effects of traction or braking, the change of sinkage, the slip ratio of the front and rear roller, and the number of passes of the road roller were studied. A number of tests were conducted and the experimental data were compared with the theoretical analysis results. It was observed that the amount of sinkage on the front and rear roller took the minimum value when the front roller was in the unpowered rolling state and the slip ratio of the rear roller was almost zero. When the absolute value of the slip ratio of rear roller increased, the amount of sinkage on the front and rear rollers, the absolute value of the driven or braking force of the rear roller and the absolute value of effective tractive or braking effort of the road roller increased. When the front roller was in the unpowered rolling state and the rear roller was in the braking state at −5% skid, the compaction density of the soil was at a maximum.     

Correlations predicting frictional pressure drop and liquid holdup during horizontal gas-liquid pipe flow with a small liquid holdup

Experimental data and correlations available in the literature for the liquid holdup ε_L and the pressure gradient ΔP_TP/L for gas-liquid pipe flow, generally, do not cover the domain 0 < ε_L < 0.06. Reliable pressure-drop correlations for this holdup range are important for calculating flow rates of natural gas, containing traces of condensate. In the present paper attention is focused on reliable measurements of ε_L and ΔP_TPIL values and on the development of a phenomenological model for the liquid-holdup range 0 < ε_L < 0.06. This model is called the “apparent rough surface” model and is referred to as the ARS model. The experimental results presented in this paper refer to air-water and air-water + ethyleneglycol systems with varying transport properties in horizontal straight smooth glass tubes under steady-state conditions. The holdup and pressure gradient values predicted with the ARS model agree satisfactorily with both our experimental results and data obtained from the literature referring to small liquid-holdup values 0 < ε_L < 0.06. Further, it has been shown that in the domain 38 < < 72 mPa m the interfacial tension of the gas-liquid system has no significant effect on the liquid holdup. The pressure gradient, however, increases slightly with decreasing surface tension values.     

A new contact & slip model for tracked vehicle transient dynamics on hard ground

This study presents a new general transient contact and slip model for tracked vehicles on hard ground which is simple, accurate, and in agreement with the test results to a satisfactory level. Simulating zero track speed instances become possible with the new contact/shear model which is the major proposed improvement in addition to more accurate results for transient steering and tractive inputs. The model represents a general tracked vehicle having rear or front sprockets, with parameters for center of gravity, wheel positions, number of wheels, and track-pretention. To calculate longitudinal and lateral forces, a transient shear model is used. Shear stress under each track pad is assumed to be a function of shear displacement. The contact time formulation used in shear displacement calculation is improved to gain accuracy for transient and zero track speed conditions.The model is implemented on the Matlab/Simulink platform and verified with a comprehensive program of road tests composed of transient steering and tractive/braking scenarios. The results of the simulations and the road tests are satisfactorily similar for both constant and transient input maneuvers. Moreover, sensitivity simulations for vehicle parameters are conducted to show that the model responses are inline with the expected vehicle dynamics behaviours.     

Thawing soil strength measurements for predicting vehicle performance

The CRREL Instrumented Vehicle (CIV), shear annulus, direct shear and triaxial compression devices were used to characterize the strength of thawed and thawing soil. Strength was evaluated in terms of the Mohr-Coulomb failure parameters c′ and φ′, which can be used in simple models to predict the tractive performance of vehicles. Use of an instrumented wheel (like those of the CIV) is proposed for terrain strength characterization for traction prediction because the conditions created by a tire slipping on a soil surface are exactly duplicated. The c′ and φ′ values from a portable shear annulus overpredict traction because of the curved nature of the soil failure envelope in the region of low normal stress applied by a portable annulus. Of all the tests, the direct shear test yielded the highest φ′ value, due to its slow deformation rate and drained conditions. The triaxial test produced results closest to those of the instrumented wheel. For all methods, φ′ increases with soil moisture but decreases rapidly beyond the liquid limit of the soil. The φ′ measured with the vehicle was also found to be strongly influenced by the freeze-thaw layering of the soil.     

Experimental investigation of heat transfer and pressure drop characteristics of flow through spirally fluted tubes

Spirally fluted tubes are used extensively in the design of tubular heat exchangers. In previous investigations, results for tubes with flute depths e/D_vi < 0.2 were reported, with most correlations applicable for Re ≥ 5000. This paper presents the results of an experimental investigation of the heat transfer and pressure drop characteristics of spirally fluted tubes with the following tube and flow parameter ranges: flute depth e/D_vi = 0.1−0.4, flute pitch p/D_vi = 0.4−7.3, helix angle θ/90° = 0.3−0.65, Re = 500−80,000, and Pr = 2−7. The heat transfer coefficients inside the fluted tube were obtained from measured values of the overall heat transfer coefficient using a nonlinear regression scheme. The friction factor data obtained consisted of 507 data points. The proposed correlation for the friction factor predicts 96% of the database within ±20%. The heat transfer correlation for the range 500 ≤ Re ≤ 5000 predicts 76% of the database (178 data points) within ±20%, and the correlation for the higher Re range predicts 97% of the 342 data points within ±20%. Comparison of heat transfer and friction data show that these tubes are most effective in the laminar and transition flow regimes. The present results show that the increase of flute depth in the range considered does not improve heat transfer.     

Tractive performance of a bulldozer running on weak ground

To determine the tractive performance of a bulldozer running on weak ground in the driven state, the relations between driving force, drawbar pull, sinkage, eccentricity and slip ratio have been analysed together with each energy balance; effective input energy, sinkage deformation energy, slippage energy and drawbar pull energy. It is considered that the thrust is developed not only on the main straight part of the bottom track belt but also on parts of the front idler and rear sprocket, and the compaction resistance is calculated from the amount of slip sinkage. For a given vehicle and soil properties, it is determined that the drawbar pull increases directly with the slip ratio and reaches about 70% of the maximum driving force. The compaction resistance reaches about 13% of the maximum driving force. The sinkage of the rear sprocket, the eccentricity, and the trim angle increase with the increment of slip ratio due to the slip sinkage. These analytical results have been verified experimentally. After determining the optimum slip ratio to obtain a maximum effective tractive power, it is found that a larger optimum drawbar pull at optimum contact pressure could be obtained for a smaller eccentricity of vehicle center of gravity and a larger track length-width ratio under the same contact area.     

Tractive and braking performance of a flexible tracked tractor moving up and down weak sloped terrain

The objective of this study is to analyse the tractive and braking performance of a tractor travelling up and down a weak silty loam sloped terrain. The effects of track belt size on terrain-track system parameters were investigated experimentally, and the force and energy balances were clarified for the actual flexible tracked vehicle. The flexibility of the track belt has been precisely analysed as a function of track tension, loading and reloading properties of terrain, and contact pressure distributions. The results show that the optimum effective driving (or braking) force decreases with the increase of slope angle due to the decreasing vehicle weight component, while the thrust (or drag) decreases and the compaction resistance increases. The contact pressure distribution under the flexible track belt shows a triangular wavy pattern having peak values under each track roller. The shear resistance distribution has positive and negative peak values for the driving and braking states, respectively.     

Flow in a cylinder driven by rotating split-disk endwalls

Flow of an incompressible viscous fluid contained in a cylindrical vessel (radius R, height H) is considered. Each of the cylinder endwalls is split into two parts which rotate steadily about the central axis with different rotation rates: the inner disk (r < r₁) rotating at Ω₁, and the outer annulus (r₁ < r < R) rotating at Ω₂. Numerical solutions to the axisymmetric Navier-Stokes equations are secured for small system Ekman numbers E ( v/(ΩH²)). In the linear regime, when the Rossby number Ro

Full-size image (1K)

, the numerical results are shown to be compatible with the theoretical prediction as well as the available experimental measurements. Emphasis is placed on the results in the nonlinear regime in which Ro is finite. Details of the structures of azimuthai and meridional flows are presented by the numerical results. For a fixed Ekman number, the gross features of the flow remain qualitatively unchanged as Ro increases. The meridional flows are characterized by two circulation cells. The shear layer is a region of intense axial flow toward the endwall and of vanishing radial velocity. The thicknesses of the shear layer near r = r₁ and the Ekman layer on the endwall scale with E and E , respectively. The numerical results are consistent with these scalings.     

An optimum design method for robotic tracked-vehicles operating over fresh concrete during straight-line motion

This paper addresses the general problem of the design of tracked base travel systems for special purpose vehicles and/or robotic machines that may be required to move over weak surfaces or over a lightly bonded terrain composed of fresh concrete. For the special case of a vehicle travelling on a very soft fresh concrete during construction, the paper presents detailed comparative studies of the tractive performance of several tracked vehicles with alternative slump values and mean contact pressure configurations. To complete these studies a detailed simulation-analytical method was used. From this, it was established that the simulation analysis method is useful for predicting land locomotion performance of specially designed small tracked vehicles running over fresh concrete of different consistencies during driving and braking action. This work was done for straight-line motion. Some possibilities for the real-time optimum control method of the tractive and braking performance of automated and robotic vehicles are also outlined.     

The effect of velocity on rigid wheel performance

A simulation model to predict the effect of velocity on rigid-wheel performance for off-road terrain was examined. The soil–wheel simulation model is based on determining the forces acting on a wheel in steady state conditions. The stress distribution at the interface was analyzed from the instantaneous equilibrium between wheel and soil elements. The soil was presented by its reaction to penetration and shear. The simulation model describes the effect of wheel velocity on the soil–wheel interaction performances such as: wheel sinkage, wheel slip, net tractive ratio, gross traction ratio, tractive efficiency and motion resistance ratio. Simulation results from several soil-wheel configurations corroborate that the effect of velocity should be considered. It was found that wheel performance such as net tractive ratio and tractive efficiency, increases with increasing velocity. Both, relative wheel sinkage and relative free rolling wheel force ratio, decrease as velocity increases. The suggested model improves the performance prediction of off-road operating vehicles and can be used for applications such as controlling and improving off-road vehicle performance.     

Fluid flow in a rotating cylindrical container with a rotating disk at the fluid surface

Fluid flow in a rotating cylindrical container of radius R_w and height H with a co-axially rotating disk of radius R_d at the fluid surface is numerically investigated. The container and the disk rotate with angular velocities Ω_w and Ω_d, respectively. We solve the axisymmetric Navier-Stokes equations using a finite-volume method. The effects of the relative directions and magnitudes of the disk and container rotations are studied. The calculations are carried out with various ratios of Ω_w and Ω_d for H/R_w = 2 and R_d/R_w = 0.7. Streamlines and velocity vectors in the meridional plane and azimuthal velocities are obtained. The flow fields in the meridional plane are discussed with relation to azimuthal velocities in the interior of the container. The numerical results are also compared with experimental data.     

A study of properties of vortex stretching and enstrophy generation in numerical and laboratory turbulence

Dynamically relevant alignments are used in order to show that regions with weak vorticity are not structureless, non-Gaussian and dynamically not passive. for example, the structure of vorticity in quasi-homogeneous/isotropic turbulent flows is associated with strong alignment between vorticity ω and the eigenvectors of the rate of strain tensor λ_i (especially — but not only — between ω and λ₂) rather than with intense vorticity only. Consequently, much larger regions of turbulent flow than just those with intense vorticity are spatially structured. The whole flow field — even with the weakest measurable enstrophy — is strongly non-Gaussian, which among other things is manifested in strong alignment between vorticity and the vortex stretching vector W_i ≡ ω_jS_ij. It is shown that the quasi-two-dimensional regions corresponding to large cos(ω, λ₂) are qualitatively different from purely two-dimensional ones, e.g. in that they possess essentially nonvanishing enstrophy generation, which is larger than its mean for the whole field.     

Stress state of compound polygonal plate

The constructions made of bars and plates with holes, openings and bulges of various forms are widely used in modern industry. By loading these structural elements with different efforts, there appears concentration (accumulation) of stress whose values sometimes exceeds the admissible one. The durability of the given element is defined according to the quantity of these stresses. Since the failure of details and construction itself begins from the place where the stress concentration has the greatest value.

Therefore the exact determination of stress distribution in details (bars, plates, beams) is of great scientific and practical interest and is one of the important problems of the solid fracture.

Compound details (when the nucleus of different material is soldered to the hole) are often used to decrease the stress concentration.

In the present paper, we study a stress–strain state of polygonal plate weakened by a central elliptic hole with two linear cracks info which a rigid nucleus (elliptic cylinder with two linear bulges) of different material was put in (soldered) without preload.

The problem is solved by a complex variable functions theory stated in papers [Theory of Elasticity, Higher School, Moscow, 1976, p. 276; Plane Problem of Elasticity Theory of Plates with Holes, Cuts and Inclusions, Publishing House Highest School, Kiev, 1975, p. 228; Bidimensional Problem of Elasticity Theory, Stroyizdat, Moscow, 1991, p. 352; Science, Moscow (1996) 708; MSB AH USSR OTH 9 (1948) 1371].

Kolosov–Mushkelishvili complex potential (z) and ψ(z) satisfying the definite boundary conditions are sought in the form of sums of functional series.

After making several strict mathematical transformations, the problem is reduced to the solution of a system of linear algebraic equations with respect to the coefficients of expansions of functions (z) and ψ(z).

Determining the values of (z) and ψ(z), we can find the stress components σ_r, σ_θ and τ_rθ at any point of cross-section of the plate and nucleus on the basis of the known formulae. The obtained solution is illustrated by numerical example.

Changing the parameters A₁, m₁, e, A₂, and m₂ we can get the various contour plates.

For example, if we assume m₁=0, A₁=r, then the internal contour of L₁ becomes the circle of radius r with two rectilinear cracks (for the nucleus––a rectilinear bulges).

Further, if we assume a small semi-axis of the ellipse b₁ to be equal to zero (b₁=0), then a linear crack becomes the internal contour of L₁ (and the nucleus becomes the linear rigid inclusion made of other material). For m₂=0; A₂=R, the external contour L₂ turns into the circle of radius R.

The obtained method of solution may be applied and in other similar problems of elasticity theory; tension of compound polygonal plate, torsion and bending of compound prismatic beams, etc.     

Uniformly valid approximations for non-linear oscillations with small damping

A uniformly valid zeroth-order approximation is obtained for the general equation y + εH(y)y + M(y)y = 0, where ε is a small parameter. The notion of multiple scaling is utilized to set up a systematic approximation scheme. Examples are given for simple polynomials for H(y) and M(y), which lead to results involving elliptic integrals. Further restrictions allow progress to be made in terms of gamma functions.     

Multi-pass effect on off-road vehicle tractive performance

The paper presents an analysis and qualitative and quantitative evaluation of the multi-pass effect on off-road vehicle tractive performance in different soils. A literature review and the results of this study indicated that to accurately predict a vehicle’s tractive performance, the multi-pass effect should be taken into account. A new method has been developed on how to calculate the effect in given soil and operating conditions. The method includes consecutive calculation of the tractive performance: (a) for the first vehicle pass using an analytical model with soil input including an initial soil parameters set, (b) for the following vehicle passes using the same analytical model with corresponding soil input for each pass which can be obtained using the new procedure.