Abstract The dissipative rolling friction moment in a simple belt-drive system is estimated both experimentally and computationally while taking into account the detachment events at the belt-pulley interface. Shear traction is estimated based on measurements of the shear strain along the contact arc. It is shown that the dissipative moment can be approximated by taking the difference between the shear traction and the load carried by the belt. A model is developed for analyzing the contributions of different components to this dissipative moment by considering both the volumetric and surface hysteresis losses. The computed rolling friction moment is found to be in good agreement with that estimated based on the experiments. It is also found that while the shear- and stretching-induced energy losses contribute the most to the dissipation in the belt drive system, the losses associated with the Schallamach waves of detachment make up a considerable portion of the dissipation in the driver case.

The performance of a vehicle highly depends on the tire-terrain interaction characteristics. The terrain on which a vehicle operates can vary dramatically. This paper focuses on the evaluation of an in-plane truck tire performance running over the flooded surface. The truck tire is modeled using Finite Element Analysis (FEA) technique and validated against measured data. The water is modeled using Smoothed Particle Hydrodynamics (SPH), which includes water material properties. The tire-terrain interaction algorithm is defined using node-symmetric node-to-segment contact with edge treatment. The performance characteristics of the interaction include the rolling resistance coefficient, vertical, longitudinal tread and longitudinal tire stiffnesses. The simulations are repeated for several operating conditions such as inflation pressure, applied vertical load, and water depth. The flooded surface results are compared with previously published data. This work will be extended to include the prediction of the full in-plane and out-of-plane rigid ring tire model parameters while the tire is operating under various conditions.

The primary goal of this work is to implement a clutch and brake system on the single tire Terramechanics rig of Advanced Vehicle Dynamics Laboratory (AVDL) at Virginia Tech. This test rig was designed and built to study the performance of tires in off-road conditions on surfaces such as soil, sand, and ice. Understanding the braking performance of tires is crucial, especially for terrains like ice, which has a low coefficient of friction. Also, rolling resistance is one of the important aspects affecting the tractive performance of a vehicle and its fuel consumption. Investigating these experimentally will help improve tire models performance. The current configuration of the test rig does not have braking and free rolling capabilities. This study involves modifications on the rig to enable free rolling testing when the clutch is disengaged and to allow braking when the clutch is engaged and the brake applied. The first part of this work involves the design and fabrication of a clutch system that would not require major changes in the setup of the test rig; this includes selecting the appropriate clutch that would meet the torque requirement, the size that would fit in the space available, and the capability to be remotely operated. The test rig’s carriage has to be modified in order to fit a pneumatic clutch, its adapter, a new transmission shaft, and the mounting frame for the clutch system. The components of the actuation system consisting of pneumatic lines, the pressure regulator, valves, etc., have to be installed. Easy operation of the clutch from a remote location is enabled through the installation of a solenoid valve. The second part of this work is to design, fabricate, and install a braking system. The main task is to design a customized braking system that satisfies the various physical and functions constraints of the current configuration of the Terramechanics rig. Some other tasks are: design and fabrication of a customized rotor, selection of a suitable caliper, and design and fabrication of a customized mounting bracket for the caliper. A hydraulic actuation system is selected, since it is suitable for this configuration and enables remote operation of the brake. Finally, the rig is calibrated for the new testing configurations.

Different models for cycling power prediction have been presented and validated by different authors. The model validation processes have been performed in laboratory tests and field experimental tests. In field tests, different methods have been used, and in recent years, cycle-mounted power meters have been widely used for model validation and bicycle-cyclist set parameters determination. Field tests have been limited to the use of close spaces to avoid the high influence of external wind and to test in nearly flat surfaces. Although many studies have been carried out successfully in closed places, some advantages of the outdoor testing have not been exploited. This paper presents a methodology for performing outdoor tests while including the power delivered by the cyclist, the onboard measurement of wind speed and the accurate measurement of the road grade. The methodology seeks to determine the aerodynamic drag and rolling resistance coefficients based on experimental outdoor tests. A least squares method is used for identifying the model coefficients from the experimental data. A high correlation and significant similarity between the power measured and the power predicted by the model is found. These results suggest a good reliability of the wind speed measurement method and prove an improvement in the power prediction when including the onboard wind speed and road grade data. The coefficients found are in agreement with previous works presented in literature with similar bicycle-cyclist set characteristics.

Recent advances in power and efficiency of computerized modeling methods has made it easier to develop accurate tire models. These newer models are now created with such accuracy that it has become easy to predict the experimental tire’s behavior and characteristics. These models are helpful with determining tire, tire-road, and tire-soil interaction properties. By creating virtual models, the overall capital for research and development can be reduced as well as replacing unavailable experimental tires for research. This research paper mainly focuses on the validation of computer generated FEA tire models which are then used for the prediction of the experimental tire’s rolling resistance, static and dynamic characteristics. Experimental data, such as rolling resistance and vertical acceleration are used in validation simulations in order to tune the virtual model to match the experimental tire’s behavior. The tire that was used for this research is a six-groove 445/50R22.5 FEA truck tire, which was constructed and validated over the course of this research.

This work presents a methodology for the evaluation of energy cost on cycling through on-road tests. The proposed methodology consists on the measurement of the power delivered by the cyclist on the pedals when riding on a real circuit. The aim of the methodology is to generate indexes for the direct evaluation of the effect on energy cost generated by an arbitrary modification implemented on a bike. The modification can include the variation of multiple parameters. The proposed indexes for the evaluation of the energy cost are the mean input power and the mechanical work per distance during the test. The proposed methodology intends to evaluate the energy cost for a given bike-rider set on a given circuit. A case study is presented for the evaluation of tire pressure influence on energy cost. For the application of the methodology, one cyclist rode on the circuit of interest with a set of different tire pressures. The power delivered by the cyclist was measured on the pedals. Several tests were conducted for each pressure in order to achieve a good level of significance. The results obtained for the case study with the proposed methodology are compared with the results of a method based on rolling resistance coefficients reported in literature.

Pneumatic tires play a greater role in vibration control of vehicles with stiff or no suspension systems. The challenge is to find an approach that enhances vibratory damping in the tires without increasing the power losses due to rolling resistance effects. This paper presents a novel tire damping enhancement that allows for improved damping within the tire while maintaining the rolling resistance found in a typical pneumatic tire. The damping enhancement was evaluated by testing an apparatus/demonstrator that simulates a pneumatic tire. The experiment was initially configured to measure the damping ratio of the conventional tire design using a calibrated external excitation and analyzing the decay of the vibration. The damping enhancement presented in the paper was then subjected to the same test and analysis procedure. Results of the analysis show that the proposed damping enhancement measurably decreased the time of the vibratory oscillation.

One of the technical problems in wheel dynamics is to establish and control the relationship between the tire kinematic and force characteristics related to tire slippage and thus to tire-soil power losses and wheel mobility estimation. This problem has been attracting a lot attention from the research community for decades. The electronization of modern vehicles can enhance their performance in complex and severe vehicle-road/terrain environments by implementing agile control decision within the scale of milliseconds. Thus, agility requires new approaches when considering and analyzing the tire slippage process. This paper presents an analysis of the tire slippage process in stochastic terrain conditions for the purpose of agile tire slip modeling, estimation and control. Based on the introduced relations between the rolling radii of the tire, circumferential wheel force/wheel torque, wheel kinematic parameters and tire slippage, a set of agile tire-terrain characteristics is offered in the paper. The proposed characteristics take in consideration the rate of change of the listed parameters and thus allow a user to estimate the agile dynamics of the tire slip and evidence the closeness to the peak friction coefficient and hence estimate potential mobility loss. The characteristics establish relationships between the stochastic peak friction coefficient, rolling resistance coefficient, and wheel kinematic/force parameters. The characteristics are illustrated by computer simulation results in several terrain conditions.

Military vehicles have been experiencing high rollover rates over the last few years of deployment. There have been several hundred rollovers, of which approximately fifty percent are categorized as fall based. Fall based rollover occurs when the road gives way underneath the vehicle on one side as the soil is unable to support the vehicle load. To reduce fatalities, a real-time driving simulator can be used to simulate fall-based rollover for the driver training as well as for validating the effectiveness of advanced suspension technologies. The driver training can help prepare drivers with the varying degrees of terrain difficulties, by applying optimal steering and speed strategies in a simulated environment. The fall-based rollover occurs mainly due to combination of the tire sinkage and the lateral bulldozing. In the current research, equations for the tire-soil model are developed based on the Bekker’s equations and Mohr-Coulomb equations that compute the tire sinkage into the soil, the lateral and longitudinal forces from the soil deformation, rolling resistance due to the soil compaction, and the lateral plowing effects. The tire-soil model is incorporated into a commercial real-time multi-body code to simulate fall-based rollovers for various slopes and soil conditions. Results indicate rollover propensity changes depending the type of soil and the steering strategy used.

A new framework is developed in this paper for the efficient implementation of semi-empirical terramechanics models in multibody dynamics environments. In this approach, for every wheel in contact with soft soil, unilateral contact constraints are added to the solver in both the normal direction and the tangent plane. The forces associated with the tangent plane, like traction and rolling resistance, are formulated in this approach as set-valued functions, whose properties are determined by deregularization of the above-mentioned terramechanics relations. As shown in this paper, this leads to the dynamics representation in the form of a linear complementarity problem (LCP). With this formulation, stable simulation of rovers is achieved even with relatively large time steps. In addition, a high-resolution height-field is employed to model terrain-surface deformations and changes in hardening of soil under the wheel. As a result, the multi-pass effect is also captured in our approach. In addition, an extensive set of experiments was conducted using a version of the Juno rover (Juno II). The experimental results are analyzed and compared with the model developed in the paper.

The advancement of computerized modeling has allowed for the creation of extensive pneumatic tire models. These models have been used to determine many tire properties and tire-road interaction parameters which are either prohibitively expensive or unavailable with physical models. This paper focuses on the prediction of tire-ground interaction with emphasis on individual and combined effect of tire slip angle and camber angle at various operating parameters. The forces generated at tire contact such as rolling resistance, cornering force, aligning moment and overturning moment can be predicted and used to optimize the tire design parameters. In addition to above stated, the three-groove FEA truck tire model representing radial-ply tire of size 295/75R22.5 was used in vertical load deflection test to determine enveloping characteristics under various load conditions and inflation pressures.

Recently, the development of non-pneumatic tires (NPT) such as the Michelin Tweel is receiving increased attention due to potential advantages over pneumatic tires, including characteristics of rolling resistance (RR). This study focuses on the design of a NPT based on properties of vertical stiffness and rolling energy loss. Using a finite element (FE) model, a parametric study is conducted to study the effect on vertical stiffness and RR response considering two design variables; (a) thickness of the spokes, and, (b) the shear band thickness of the NPT. Using the two geometric variables, a design of experiments (DOE) is performed to study the effect on both RR and vertical displacement. Results from the DOE are used to create response surface models (RSM) for both the objective function (minimal RR) and a constraint on vertical deflection. The analytical RSM function is optimized for minimizing the rolling loss subjected to the given constraint. In addition a design sensitivity study is performed to evaluate the influence of the design variables on the output response. Results indicate that both variables have significant effect on RR, with the shear band thickness having the greater effect.

The design requirements of a low rolling loss non-pneumatic wheel are determined through a systematic optimization approach. In order to reduce the rolling resistance, linear elastic materials are considered instead of elastomers. To achieve an adequate compliance level, a metamaterial needs to be designed. The required metamaterial properties are determined as a result of an optimization where the metamaterial tensor components as well as the geometric dimensions are the design variables. This way the metamaterial can be designed such that the overall behavior of the non pneumatic wheel achieves the best performance in terms of compliance and contact patch pressure distribution. The resulting constitutive metamaterial properties of the shear layer can be used as prescribed constitutive properties to tailor the periodic mesostructure of a material by means of topology optimization.

A novel off-road tire model for planetary rover applications is created to investigate the mobility of such exploration vehicles. A volumetric contact model in series with a hyperelastic Bekker soil model is used to derive the contact forces between a deformable tire and soft soil. The volumetric off-road tire model is derived for a cylinder rolling on flat ground, and the rolling resistance can be directly calculated from the volumetric contact model. The longitudinal and lateral tire forces are calculated by integrating the shear stress over the contact patch. To check the consistency of the tire model, it is simulated using a simplified 14 degree of freedom model often used in vehicle dynamics simulations. The results are compared against those of a conventional rigid tire simulated under the same conditions. The deformable tire is shown to generate a 34 % higher traction force than the rigid tire. In another steering scenario, the feasibility of this model for handling anyalses is verified.

This paper presents a theoretical and experimental study on the effects of rolling friction between balls and the racer on ball positioning for an automatic ball balancer (ABB). The performance of an ABB, which is characterized by residual vibration of the rotor, relies heavily on balls’ positions. However, the magnitude of rolling friction determines the ball position of the balancing system, which in turn affects the performance of the ABB. In this study, a set of ball balancers are fabricated including ceramic balls and the associated PTFE and ceramic ball races for the purpose of investigating the validity of the mathematical model of the rolling friction. The driving-force equation associated with the dynamic equations of motion of the balls is developed to determine the ball positions as well as the performance of the balancing system. Two sets of experimental apparatus are constructed. One is aimed to verify the mathematical model of the rolling friction of the ball balancer. The other applies an optical-disc drive system together with a high-speed camera to record the ball positions and verify the results obtained from computer simulation.

Mobility aids that are currently available in developing countries do not fully meet users’ needs. People require a device that is maneuverable within the home and that can travel long distances on rough roads. To address this problem, we have designed the Leveraged Freedom Chair (LFC), a wheelchair-based mobility aid capable of navigating virtually any terrain by optimally utilizing upper body power for propulsion through a variable-speed lever drivetrain. The lever system achieves a 4:1 change in mechanical advantage, equating to leverage that ranges from 0.42X to 1.65X a standard wheelchair hand rim. In comparative trials, the LFC demonstrated capabilities that far exceed those of any mobility aid currently available in the developing world; it was able to cruise on smooth surfaces at 2m/s (5mph), climb muddy, grassy hills with a 1:3 slope, and navigate terrain with a coefficient of rolling resistance as high as 0.48. This operational flexibility should make the LFC usable on any terrain, from rural walking paths to tight indoor confines, and greatly increase the mobility of people with disabilities in developing countries. The LFC may also be attractive to wheelchair users in developed countries, as its performance breadth exceeds that of currently available products.

Currently legislation is in place to encourage a reduction in energy usage. As such there is an increased demand for machinery with higher efficiencies, not only to reduce the operational costs of the machinery, but also to cut capital expenditure. The power losses associated with the gear mesh can be divided into speed and load dependant losses. This paper reviews some of the mathematical models proposed for the individual components associated with these losses, such as windage, churning, sliding and rolling friction loses. A mathematical model is proposed which predicts the power losses on helical gears highlighting the major contributor to losses in the gear mesh. Furthermore, the mathematical model is validated with a case study.

The motion and vibration of a moving body running on the complicated 3 dimensional trajectory considering the running resistance are investigated in this paper. A roller coaster is treated with here as the concrete example of a moving body. The equations of motion of a roller coaster in which a trajectory and a vehicle are coupled are derived by using the differential-algebraic equation (DAE). The dynamic behavior of a roller coaster which moves forward due to the gravity acceleration neglecting the running resistance has been reported in our former papers. In this paper, we take the effect of an air resistance and a rolling resistance into consideration. The influences of these resistances on the required time from the starting point to the arriving one and the vibration response of a vehicle are investigated. Moreover, it is shown that the numerical solutions have a better coincidence with the experimental results which have been obtained by measuring an actual roller coaster.

In this paper, a model is developed to analyze the longitudinal forces of interaction between the vehicles within a train consist. The track geometry is described in a preprocessor in terms of an arc length parameter. A single degree of freedom vehicle model is developed, in which the nonlinear equation of motion of the vehicle is expressed in terms of the track arc length using a velocity transformation. The velocity transformation matrix is obtained by expressing the Cartesian and angular velocities in terms of the time derivative of the arc length. Models are developed for representing; braking forces from a typical air brake system, coupler reactions from draft gear or end-of-car cushioning devices, and the rolling resistance acting on each vehicle. An example of a 10-car train is used to demonstrate the use of the formulations presented in this paper. Different simulation scenarios, including varying track configurations and brake failure, are presented.

A novel contact model is presented which includes normal contact force and damping, rolling resistance torque and tangential friction force. This model is appropriate for the simulation of robotic tasks involving contact between objects of any shapes, occurring at relatively low velocities. It features a contact stiffness proportional to the contact area and leads automatically to the correct selection of the point of action of the force. The contact force magnitude is shown to be proportional to the interpenetration volume. A numerical simulation of a sphere impacting on the inside surface of a cylinder is presented.