Longitudinal Slip Research Articles

Slip Constrained Torque Controller Using Incremental Backstepping with Integral Barrier Lyapunov Function*

This paper develops a speed controller for a rear-drive electric vehicle. A Barrier Incremental Backstepping strategy is proposed for tracking the desired speed, aiming to increase the robustness of the controller and avoid loss of traction due to excessive longitudinal slip. The solution is evaluated in simulation for different scenarios, showing satisfactory results in constraining the tire slip.

Basic Experiments on Longitudinal Creep Force in Model Wheel and Rail

Tangential forces caused by micro slippage between the wheels and rails of a railway vehicle are referred to as creep forces. Creep forces play a significant role in the dynamics of rolling stock, and therefore must be properly understood. Scale model wheel machines can simply measure the creep forces, however the problem is that the scale model rules of the creep force characteristics between the real and the model vehicles has not yet been established. In this study, longitudinal creep forces were measured using scale model wheels and rails as a basic study for establishing dynamically similar creep force characteristics in scale model wheels and rails. A device was developed to add micro running resistance torque by connecting a motor or electrical resistance to the axle, and the relationship between longitudinal slip rate and longitudinal creep force in the micro-slip region was investigated and is reported.

Coupled dynamic behaviours of the brake system considering wheel–rail interactions

ABSTRACT During vehicle operation, the brake system is influenced by wheel–rail interactions. To investigate the dynamic behaviours of the brake system, we propose a novel dynamic model of the brake system by considering the coupling effects between the disc–pad and the wheel–rail subsystems. Using the established model, the nonlinear coupled dynamic behaviours including wheel–rail adhesion characteristics, wheel–disc torsional vibrations and disc–pad stick–slip vibrations were comprehensively explored. The results showed that braking conditions remarkably influenced the longitudinal slip rate. The wheelset and brake units affect each other, and the wheels on one wheelset influence each other when they are asynchronous. The brake system is stable in the wheel–rail stick state, but becomes unstable in the wheel–rail stick–slip state or slip state. The limit cycle analysis showed that the brake pad stick–slip vibrations were easier to occur at a large slip rate.

A novel strain-based finite element family for mesh-independent analysis of the tensile failure of reinforced concrete bars

The paper presents a novel family of strain-based beam finite elements (FE) for analysis of tensile failure of a reinforced concrete bar (RC bar), with results of the analysis being independent of the applied FE mesh. The composite bar consists of a continuous longitudinal ductile reinforcing bar(s) surrounded by brittle concrete cover, which are considered separately in the model. Longitudinal slip at the contact between the concrete cover and reinforcing bars is allowed, while their relative displacements perpendicular to the axis of the RC bar are prevented. Cracks in concrete cover occur when tensile stress in concrete exceeds its tensile strength. Propagation of partially connected crack, that is, softening of the material at the crack, is described through constitutive law in form of nonlinear relationship between stresses in concrete at the crack and the width of the crack. Each separate crack is considered discretely as a discontinuity in geometry of the element. In the analysis of cracking of concrete, it is commonly assumed that the discrete crack can occur at the nodes of FE only. However, this assumption leads to dependence of the analysis results on the employed FE mesh. The presented family of FE enables occurrence of the crack anywhere along the FE. In order to achieve this, the discrete crack is excluded from equations of FE and additional boundary conditions are introduced at the discontinuity. This approach ensures that the location of the cracks, their number and their propagation are independent of the applied FE mesh. Advantages of the novel family of FE are thoroughly presented in a parametric study which investigates influence of number of FE as well as influence of degrees of interpolation and integration on the cracking of RC bar under tensile loading. Experimental results of tensile tests on the analysed bar are available in literature. It can be concluded that the results obtained with the minimal possible number of novel FE and sufficiently high degree of numerical integration scheme, applied for solving integrals in equations of FE, are considerably more accurate than the results of previous analyses with model of discrete crack at the nodes of FE only.

Study on Behavior of Steel Hoop Connections for Raw Bamboo Members.

Bamboo structures have various types of connections, such as bolting and lashing. One crucial issue in bamboo structures is that the connection with bolts and nails has a lower load-carrying capacity associated with the bamboo failure resulting from the bolt or nail invading them. This paper focuses on the connection for raw bamboo members with steel hoops (BHC), of which the two semi-circular steel hoops are fastened to the raw bamboo with high-strength bolts. The sliding friction is controlled by the interfacial pressure, which can be increased by tightening the bolts. A push-out experiment on thirty-six specimens was conducted considering the following two parameters: the different surface conditions of raw bamboo (with or without the epidermis) and the different interfacial pressure. The test results mainly showed the two failure modes of specimens under certain conditions: continuous longitudinal slip after the vertical load reached the peak; and the steel hoop stuck in the bamboo skin after a period of slip. It is found that the sliding friction was controlled by the interfacial pressure, and the difference in the anti-sliding capacity between the epidermal bamboo specimen and the non-epidermal bamboo specimen was magnified with the increase of interfacial pressure. The contact stress on the surface of bamboo is approximately uniformly distributed based on the finite element analyses. The interfacial pressure can be predicted by the torque value of the digital electronic torque wrench and the equations established by mechanical analysis, respectively. Moreover, the design formulae of bearing capacity for BHC under three guaranteed rates (50%, 95%, and 99.9%) were developed based on probability theory, while the fourth design formula was derived by regression analysis. The reliability indices of the four design formulae were up to 0.07, 1.44, 3.09, and 0.97, respectively, and the resistance partial coefficients were suggested accordingly.

Effect of tire slip losses on the energy demand and fuel consumption of a light-duty vehicle

The contribution of the tire-road slip of traction wheels to the total resistance opposing the motion of a light-duty commercial vehicle has been investigated through the simulation of several homologation and custom driving cycles. The calculation of the contribution of the tire slip losses was based on the estimation of the longitudinal tire slip, by means of Pacejka’s MF5.2 tire model. In this work, the computational steps required to evaluate this contribution were implemented in a previously developed fuel consumption simulation tool. Simulations were performed under several vehicle loading conditions and tire inflation pressures on traction and non-traction wheels, and considering different tire-road adherence conditions, in order to obtain a characterization of the tire slip losses over a wide range of working conditions. An analysis of the results shows that, although the contribution of tire slip losses to the total vehicle energy demand and fuel consumption may be relevant – especially under low-load, low adherence conditions – the sensitivity of the average on-cycle vehicle energy/fuel consumption to changes in the tire inflation pressure is only affected slightly by tire slip losses. Therefore, tire slip losses can be neglected in practice, when the aim of a simulation is to optimize the tire pressure to achieve average vehicle working conditions over a driving cycle.

A practical quantification of longitudinal slippage of robot platform wheels traversing on solid balls based uneven terrain

This research is spearhead for longitudinal slippage of robot platform wheels traversing on solid balls based uneven terrain. For this purpose, effects of solid ball diameter (0.0127–0.0508 m) accompanying with tire inflation pressure (20.68–55.16 kPa) and platform forward speed (0.17–0.50 m/s) on the slippage were practically quantified. Robotic experiments were executed in controlled test bed prepared by solid ceramic balls. Tentative data collected from the experiments indicate that the wheels experienced low (<30%), moderate (30–60%) and high slippage (>60%) under effects of independent variables. Results demonstrated that the increasing effect of the dominant variable of solid ball diameter on the slippage was 3.6 and 2.6 times greater than that of platform forward speed and tire inflation pressure, respectively. Meanwhile, the increasing linear effect of tire inflation pressure on the slippage was prevailed (1.4 times) than the decreasing linear effect of platform forward speed. Hence, to minimize the slippage as well as power loss of the platform traversing on each solid ball diameter, adjustment of tire inflation pressure should be enumerated as first priority. Overall, analytical results obtained in this research lead to open a new prospection for comprehending the slippage trends of off-road wheeled robots traversing on an uneven terrain composed of solid balls. Practicability of this type of the robots is remark in various industrial robotic operations, especially for process towers and reactors of oil, gas, petrochemical, and chemical industries. Hence, quantitative and qualitative information of this research are a rich source for relevant industrial investigators and experts who involved in this realm.

Slip-aware driver assistance path tracking and stability control

This paper presents a novel integrated control framework that includes simultaneous vehicle lateral stabilization and path tracking by considering the combined-slip effect, wheel dynamics, and tire force nonlinearities for driver-assistance systems. Active front steering and brakes are the actuators of the developed slip-aware receding horizon control system, in which the loss of cornering forces caused by longitudinal slip dynamics is considered in the prediction model. The controller monitors tire capacities and normal forces, corrects driver’s input, and adjusts wheel torques and steering to provide safe performance in path tracking (e.g., lane-keeping) while stabilizing the vehicle within its handling limits. The main advantage of the developed slip-aware driver-assistance controller is the ability in handling multi-actuation vehicle systems through its more accurate prediction model. The performance and computational efficiency of the integrated strategy is evaluated in hardware-in-the-loop real-time experiments, in various pure- and combined-slip maneuvers, under different road friction conditions. Stability of the controller and longitudinal tire force observer is also investigated. The real-time experiments and simulations reveal that the proposed control framework outperforms the existing algorithms in dealing with reduced tire capacities in harsh maneuvers as a consequence of simultaneous vehicle and wheel stabilization, and path tracking.

Numerical Simulation on Seismic Behavior of Steel Fiber Reinforced Concrete Beam-Column Joints.

Steel fiber reinforced concrete (SFRC) is a novel material of concrete, which has a great potential to be used in practical engineering. Based on the finite element software Opensees, the main objective of this paper presented a numerical simulation method on investigating the seismic behavior of SFRC–beam-column joints (BCJs) through modifying the calculation method of joint shear and longitudinal reinforcement slip deformations. The feasibility and accuracy of the numerical modeling method were verified by comparing the computed results with experimental data in terms of the hysteresis curves, skeleton curves, feature points, energy dissipation, and stiffness degradation. And then, the influences of some key parameters on the seismic behavior of BCJs were investigated and discussed in detail. The parametric studies clearly illustrated that both adding the steel fiber and increasing the stirrup amount of joint core area could significantly improve the seismic behavior of BCJs. The axial compression ratio had limited influence on the seismic behavior of BCJs. Finally, based on the main factors (steel fiber volume ratio, stirrup amount, and axial compression ratio), a formula for predicting ultimate shear capacity is derived.

Damage identification of steel-concrete composite beams based on modal strain energy changes through general regression neural network

This paper presents a novel method for damage identification of steel-concrete composite beams based on modal strain energy (MSE) changes through general regression neural network (GRNN). A finite element (FE) model was developed using two Euler-Bernoulli beam elements as steel beam and concrete slab layers which are coupled by incorporating a deformable shear connection layer distributed at their interface. The connection layer was modelled as a uniform spring that enables both longitudinal slip and vertical uplift between the two components. The FE model was validated using experimental results of a full-scale composite beam in the laboratory. Three damage indices were defined as the elemental stiffness reduction in the steel, concrete and shear connection layers, respectively. A damage identification approach was developed to investigate the sensitivity of eigenvalues to damage in the composite interface. Then, MSEs change ratios were selected as the features for identifying structural damage in the composite layers. Principle component analysis was utilised to reduce the dimensionality of the large data features obtained from modal analysis leading to determining the main features for structural damage identification. The low dimensional data were employed as the input for the GRNN. Different damage cases were investigated, and the damage vectors were defined as the outputs of GRNN. The results show that the proposed method is efficient and reliable to identify damage in the composite beam with a few low vibration modes, even though small damage in the composite layers does not significantly affect these modes.

Flexural strength test on new profiled composite slab system

This research presents an experimental study on the flexural strength and failure behaviour of a newly developed composite metal decking system. The newly developed metal decking system with a thickness of 0.75 mm and 1.0 mm produced by the industry requires a detailed study in strength and performances before it is launched for commercialization. A simply supported conventional reinforced concrete slab is used as the control specimen and two composite slabs with different metal thickness of steel sheet profiles were constructed and tested under a four points flexural strength test. The strength and behaviour of the slabs are recorded and comparisons with conventional slabs with composite deck slabs are made to achieve the objectives. The recorded results of three different slabs were then used to plot a load-displacement graph and deflection profiles are to be analysed and compared. The yield flexural capacity and average yield displacement of specimens for the composite slabs were 28.0 kN and 0.80 mm respectively. The 1.0 mm metal thickness composite slab has the highest ultimate flexural capacity among all specimens which is 84 kN followed by a 0.75 mm metal thickness composite slab with 58 kN and ends with the lowest 9.1 kN of conventional slab. Two cracking patterns were found during the experimental test which includes shear cracking and flexural cracking`. Besides that, two major failure modes under bending which are flexure failure at the centre point of the specimen and bond or longitudinal slip failure along the side of the specimen were found in the experimental test. Bond failure results in slippage between the concrete and metal deck, which can result in cancellation of the composite action at interface. In conclusion, the strength of slabs improved, and ductility was remarkably increased when slabs acted as a composite structure.

Self-Adaptive Path Tracking Control for Mobile Robots under Slippage Conditions Based on an RBF Neural Network

Wheeled mobile robots are widely implemented in the field environment where slipping and skidding may often occur. This paper presents a self-adaptive path tracking control framework based on a radial basis function (RBF) neural network to overcome slippage disturbances. Both kinematic and dynamic models of a wheeled robot with skid-steer characteristics are established with position, orientation, and equivalent tracking error definitions. A dual-loop control framework is proposed, and kinematic and dynamic models are integrated in the inner and outer loops, respectively. An RBF neutral network is employed for yaw rate control to realize adaptability to longitudinal slippage. Simulations employing the proposed control framework are performed to track snaking and a DLC reference path with slip ratio variations. The results suggest that the proposed control framework yields much lower position and orientation errors compared with those of a PID and a single neuron network (SNN) controller. It also exhibits prior anti-disturbance performance and adaptability to longitudinal slippage. The proposed control framework could thus be employed for autonomous mobile robots working on complex terrain.

Effect of geometric lath orientation on fatigue crack propagation via out-of-plane dislocation glide in martensitic steel

Strain accumulation ahead of the fatigue crack tip in the martensite lath of a medium-carbon steel was examined using a three-dimensional electron backscatter diffraction (3D-EBSD) technique. The objective of this study is to explain the crack propagation mechanism due to the activation of out-of-plane slips with their Burgers vectors having no component of the crack growth direction, which exhibits high resistance to fatigue crack growth. The 3D-EBSD analysis revealed little misorientation in the crystal, concurrent with the fatigue crack propagation in the coarse laths oriented favourably for dislocation glide in their longitudinal directions. This suggests that these laths contributed to strain accommodation. In contrast, strain preferentially accumulated in the coarse laths oriented unfavorably for the longitudinal slip, promoting crack propagation. These indicate that the geometrical anisotropy and distribution of martensite laths dominate the fatigue crack propagation resistance in martensitic carbon steel.

Test and Numerical Model of Curved Steel-Concrete Composite Box Beams under Positive Moments.

Compared with straight steel–concrete composite beams, curved composite beams exhibit more complicated mechanical behaviors under combined bending and torsion coupling. There are much fewer experimental studies on curved composite beams than those of straight composite beams. This study aimed to investigate the combined bending and torsion behavior of curved composite beams. This paper presents static loading tests of the full elastoplastic process of three curved composite box beams with various central angles and shear connection degrees. The test results showed that the specimens exhibited notable bending and torsion coupling force characteristics under static loading. The curvature and interface shear connection degree significantly affected the force behavior of the curved composite box beams. The specimens with weak shear connection degrees showed obvious interfacial longitudinal slip and transverse slip. Constraint distortion and torsion behavior caused the strain of the inner side of the structure to be higher than the strain of the outer side. The strain of the steel beam webs was approximately linear. In addition, fine finite element models of three curved composite box beams were established. The correctness and applicability of the finite element models were verified by comparing the test results and numerical calculation results for the load–displacement curve, load–rotational angle curve, load–interface slip curve, and cross-sectional strain distribution. Finite element modeling can be used as a reliable numerical tool for the large-scale parameter analysis of the elastic–plastic mechanical behavior of curved composite box beams.

Distributed Formation Control of Nonholonomic Wheeled Mobile Robots Subject to Longitudinal Slippage Constraints

This paper investigates the distributed formation control problem of multiple nonholonomic wheeled mobile robots within real environments. The formation pattern of the system adopts leader–follower structure and the communication topology among the multirobot system is modeled by a directed graph. Slippage is hard to avoid due to the possible existence of ice, sand, or muddy roads. To overcome the effect of slippage, an adaptive trajectory tracking controller for leader robot is designed, such that the leader robot can keep up with the virtual reference trajectory and estimate the real value of unknown slipping ratio accurately. In addition, it is difficult for each follower robot to obtain leader’s states in a large formation system, so distributed formation controllers are designed based on distributed observers. It is shown that the proposed controllers can realize formation objective and overcome the slippage constraints at the same time. Finally, the effectiveness of the proposed controllers is verified by simulation results.

A Strain-Based Method to Estimate Longitudinal Force for Intelligent Tires by Using a Physics-Based Model

Tires are essential components of vehicles and the only vehicle components in contact with the road. The tire longitudinal force originating from the contact between the tire and road can enhance traction and braking and contribute to the directional stability of vehicles. If the longitudinal tire force can be accurately estimated, vehicle safety can be improved. This study established a longitudinal tire physics-based model combining the brush model with the flexible ring model to develop a strain-based intelligent tire system for estimating the longitudinal tire force. The developed longitudinal dynamic model was used to study tire strain characteristics under pure longitudinal slip conditions. An algorithm was developed for estimating the longitudinal tire force through feature extraction and data fitting of the tire strain. A finite-element tire model was established to simulate the longitudinal force. Comparing the simulated and estimated forces indicated that the proposed algorithm can accurately predict the longitudinal force of intelligent tires and thus provide useful information to vehicle stability control systems.

Control of Vehicle’s Mixed Longitudinal and Lateral Stability with Engine Dynamics Using Super Twisting Control Algorithm

Vehicle stability control is one of the most important subjects in the control engineering field. Many research activities have been done to develop more comfort and safe travel for passengers. In this paper, vehicle mixed stability in longitudinal and lateral motion has been investigated. Four-wheel seven degrees of freedom model of vehicle is considered to extract the dynamic equations and closed-loop system simulation. Dugoff’s nonlinear model has been used to simulate the behavior of tires and road, and Cho’s engine model with two state variables has been used for vehicle power system simulation, so it makes the input torque to wheels to be more realistic. Because of the good robustness properties of sliding mode control, the second-order sliding mode with a super-twisting algorithm has been used for calculation of control inputs. This method is proved to be so appropriate and useful in the case of uncertainty in a complicated vehicle dynamic model and multiple disturbances in vehicle motion. Engine throttle angle and yaw moment have been considered as a longitudinal system and lateral system control inputs respectively. The longitudinal slip coefficient and yaw rate are considered as system output. Simulation results show the effectiveness of the proposed method.

Nonlinear Model Predictive Control for Integrated Energy-Efficient Torque-Vectoring and Anti-Roll Moment Distribution

This study applies nonlinear model predictive control (NMPC) to the torque-vectoring (TV) and front-to-total anti-roll moment distribution control of a four-wheel-drive electric vehicle with in-wheel-motors, a brake-by-wire system, and active suspension actuators. The NMPC cost function formulation is based on energy efficiency criteria, and strives to minimize the power losses caused by the longitudinal and lateral tire slips, friction brakes, and electric powertrains, while enhancing the vehicle cornering response in steady-state and transient conditions. The controller is assessed through simulations using an experimentally validated high-fidelity vehicle model, along ramp steer and multiple step steer maneuvers, including and excluding the direct yaw moment and active anti-roll moment distribution actuations. The results show: 1) the substantial enhancement of energy saving and vehicle stabilization performance brought by the integration of the active suspension contribution and TV; 2) the significance of the power loss terms of the NMPC formulation on the results; and 3) the effectiveness of the NMPC with respect to the benchmarking feedback and rule based controllers.

Profound insight into tractor energy dissipation through inevitable interaction inside wheel-soil interface for the period of plowing works

Inevitable interaction between soil and pneumatic tires of an off road vehicle in a rectilinear motion leads to experience of energy dissipation. Rolling resistance force and longitudinal slip of wheels are responsible for the energy dissipation inside wheel-soil interface. Attention of current study is paid to methodically elucidate the energy dissipation by wheels of front wheel assist tractor for the period of plowing works. To achieve this goal, the energy dissipation dependency on draft force requirement of plow implement as well as tractor drive mode (rear wheel drive (RWD) and front wheel-assisted drive (FWAD)) was quantitatively ascertained. Results disclosed that the energy dissipation ascended in domain of 3.18-17.66 and 3.14-21.04 MJ/ha for the RWD and FWAD mode, respectively, as the draft force requirement proliferated from 3.85 to 23.04 kN. Whilst, energy expenditure for plowing works ranged from 12.45 to 74.85 MJ/ha. It means that the energy dissipation was approximately equal to quarter of energy expenditure for plowing works. When the draft force requirement augmented, portion of the energy dissipation caused by the slip of the wheels raised in range of 12.15-82.51% and thereby, that of rolling resistance force of the wheels dropped in range of 87.85-17.49%. Hence, to reduce the energy dissipation, for both drive modes at the higher draft force requirement, activation of slip control system for preservation of the slip of the wheels in a particular range is sufficient enough. For both drive modes at the lower draft force requirement, not only activation of the system, but also decrement of rolling resistance force of the wheels by overinflating the tires must be prescribed. In case of the FWAD mode, overinflating the tires must be accomplished based on generation of driving lead of front wheels in allowable range.

Enhancing brush tyre model accuracy through friction measurements

Accurate tyre models are important to ensure valid and reliable simulation of vehicle behaviour. To this purpose, the Magic Formula (MF) became the de facto standard for vehicle dynamics simulations, despite requiring many empirically derived coefficients. This paper shows how the accuracy of a simple physical-based brush-type tyre model can be enhanced to simulate tyre behaviour that closely matches MF results. To do so, the real, highly complex rubber friction characteristics are incorporated into the brush model. The friction characteristics were obtained from friction measurements with a tread rubber block. The developed model is validated against experimental tyre data obtained on a flat-track test rig and the corresponding MF model. Results show that the inclusion of friction characteristics allow accurate simulation of longitudinal and lateral slip conditions over a wide range of normal loads with the simple brush model. At extreme loading scenarios, the simulation accuracy deteriorates because of the significant influence of highly nonlinear deformation behaviour of the tyre that is not accounted for in the brush model formulation.