Calculation of Dynamic Tire Forces from Aircraft Instrumentation Data

2010 ◽  
Vol 38 (3) ◽  
pp. 182-193 ◽  
Author(s):  
Gary E. McKay
Keyword(s):  
System Performance ◽  
Equations Of Motion ◽  
Test Laboratory ◽  
Excellent Correlation ◽  
Friction Behavior ◽  
Aircraft Landing ◽  
Data Scatter ◽  
Tire Forces ◽  
Six Degree Of Freedom ◽  
Tire Friction

Abstract When evaluating aircraft brake control system performance, it is difficult to overstate the importance of understanding dynamic tire forces—especially those related to tire friction behavior. As important as they are, however, these dynamic tire forces cannot be easily or reliably measured. To fill this need, an analytical approach has been developed to determine instantaneous tire forces during aircraft landing, braking and taxi operations. The approach involves using aircraft instrumentation data to determine forces (other than tire forces), moments, and accelerations acting on the aircraft. Inserting these values into the aircraft’s six degree-of-freedom equations-of-motion allows solution for the tire forces. While there are significant challenges associated with this approach, results to date have exceeded expectations in terms of fidelity, consistency, and data scatter. The results show excellent correlation to tests conducted in a tire test laboratory. And, while the results generally follow accepted tire friction theories, there are noteworthy differences.

Tire Friction on Wet Roads

1976 ◽  
Vol 49 (3) ◽  
pp. 862-908 ◽  
Author(s):  
K. A. Grosch ◽  
A. Schallamach
Keyword(s):  
Hydrodynamic Lubrication ◽  
Vehicle Control ◽  
Critical Conditions ◽  
Frictional Properties ◽  
Road Surfaces ◽  
Road Friction ◽  
Tire Forces ◽  
The One ◽  
Tire Friction ◽  
Contact Pressures

Abstract Evidence accumulates that tire forces on wet roads, particularly when the wheel is locked, are determined by the dry frictional properties of the rubber on the one hand and by hydrodynamic lubrication in the contact area on the other. The probable reason why they are so clearly separable is that water is a poor lubricant, tending to separate into globules and dry areas under relatively small pressures. Road surfaces and tire profiles are, therefore, designed to create easy drainage and high local contact pressures. The influence of road friction on vehicle control well below the critical conditions is becoming more clearly understood; but more Investigations are required here, in particular under dynamic conditions.

Dynamic Rocking Response and Optimization of the Nonlinear Suspension of a Railroad Freight Car

1980 ◽  
Vol 102 (1) ◽  
pp. 86-93 ◽  
Author(s):  
M. Samaha ◽  
T. S. Sankar
Keyword(s):  
Equations Of Motion ◽  
Sine Wave ◽  
Optimization Techniques ◽  
Model Accuracy ◽  
Frequency Responses ◽  
Optimum Parameters ◽  
Freight Car ◽  
Six Degree Of Freedom ◽  
Railroad Freight ◽  
Rocking Response

A modified mathematical model of a large capacity railroad freight vehicle is presented. The model for this investigation is constructed in such a way to describe the bounce, sway and rocking modes of the system and also to account for most of the vehicle non-linearity effects. Equations of motion of the six degree of freedom nonlinear model are derived assuming that the excitations from the track in vertical and lateral directions are purely periodic in the form of a rectified sine wave. The solution for the time and frequency responses on digital computer are compared with available measured data to investigate the model accuracy. Multivariable optimization techniques are employed to find the optimum suspension parameters that minimizes the maximum car rocking response over the frequency range of interest. The optimum parameters are presented in different forms either for the existing or for stabilized vehicle configuration.

Added Fluid Mass and the Equations of Motion of a Parachute

1983 ◽  
Vol 34 (3) ◽  
pp. 226-242 ◽  
Author(s):  
John A. Eaton
Keyword(s):  
Equations Of Motion ◽  
Added Mass ◽  
Unsteady Forces ◽  
Fluid Mass ◽  
Mass Tensor ◽  
Body Shapes ◽  
The Stability ◽  
External Forces ◽  
Six Degree Of Freedom ◽  
Nonlinear Solutions

SummaryWhile it has long been known that added fluid mass may be important in the dynamics of parachutes, due to inadequate or incorrect derivation and/or implementation of the added mass tensor its full significance in the stability of parachutes has yet to be appreciated. The concept of added mass is outlined and some general conditions for its significance are presented. Its implementation in the parachute equations of motion is reviewed, and the equations used in previous treatments are shown to be erroneous. A general method for finding the equivalent external forces and moments due to added mass is given, and the correct, anisotropic forms of the added mass tensor are derived for the six degree-of-freedom motion in an ideal fluid of rigid body shapes with planar-, twofold- and axisymmetry, These derivations may also be useful in dynamic stability studies of other low relative density bodies such as airships, balloons, submarines and torpedoes. Full nonlinear solutions of the equations of motion for the axisymmetric parachute have been obtained, and results indicate that added mass effects are more significant than previously predicted. In particular, the component of added mass along the axis of symmetry has a strong influence on stability. Better data on unsteady forces and moments on parachutes are needed.

Dynamic Analysis of a Nonlinear Torsional Flexible Coupling With Elastic Links

2003 ◽  
Vol 125 (3) ◽  
pp. 509-517 ◽  
Author(s):  
Charles W. Bert ◽  
Shiyuan Wu
Keyword(s):  
Dynamic Analysis ◽  
System Performance ◽  
Power Transmission ◽  
Angular Displacement ◽  
Rotational Velocity ◽  
Equations Of Motion ◽  
Flexible Coupling ◽  
Elastic Links ◽  
Lagrange’S Equation ◽  
Power Transmission Systems

Torsional oscillations in mechanical power transmission systems are a significant source of dynamic loads which are harmful to the system performance. The effects can cause a drive shaft to become unstable and self-destructive at critical speeds. This research focuses on dynamic analysis of a nonlinear torsional flexible coupling with elastic links. The equations of motion are derived by means of Lagrange’s equation. These equations are used to obtain the quasi-static performance of torque vs. angular displacement at constant rotational velocity. An exact solution is also found for the phase-plane representation for free oscillation torque. The fluctuation ratios of input velocity vs. output velocity of the system are obtained for determining the system performance. The results of the analyses of steady running and transient oscillation performance are applied to the determination of optimum proportions of the couplings. Results are compared with those of rigid-link couplings to show the influence of elasticity of the link on dynamic behavior of the system.

Adaptive Virtual Autobalancing for a Magnetic Rotor With Unknown Mass Imbalance: Part II — Dynamic Balancing

1995 ◽  
Author(s):  
Kai-Yew Lum ◽  
Sanjay P. Bhat ◽  
Dennis S. Bernstein ◽  
Vincent T. Coppola
Keyword(s):  
Equations Of Motion ◽  
Magnetic Actuation ◽  
State Equations ◽  
Mass Imbalance ◽  
Unbalanced Rotor ◽  
Statically Unbalanced Rotor ◽  
Multiple Plane ◽  
Control Forces ◽  
Six Degree Of Freedom ◽  
Adaptive Control Algorithm

Abstract In Lum et al. (1995), an adaptive control algorithm for the stabilization of a rigid, statically unbalanced rotor moving in the plane was proposed. The control strategy consisted in emulating a mechanical autobalancer using magnetic actuation so as to directly cancel the effects of static mass imbalance. In this present paper, this strategy is extended to the case of a rigid, dynamically unbalanced rotor in six degree-of-freedom motion. The state equations of the controller are based on the equations of motion of a multiple-plane autobalancer, and the control forces partially emulates the interaction between rotor and autobalancer. It is shown in simulation that the adaptive virtual autobalancing control can achieve stabilization of rotor motion as well as adaptation to changes in imbalance.

Dynamic Inversion Control for Performing Herbst Manoeuver with Lateral Center-of-Gravity Offset

2017 ◽  
Vol 67 (2) ◽  
pp. 198
Author(s):  
Bijoy K. Mukherjee ◽  
Manoranjan Sinha
Keyword(s):  
Reference Frames ◽  
Equations Of Motion ◽  
Computation Time ◽  
Center Of Gravity ◽  
Dynamic Inversion ◽  
Time Step ◽  
Highly Nonlinear ◽  
Dynamics And Control ◽  
Body Reference ◽  
Six Degree Of Freedom

<!--?xml version="1.0" encoding="UTF-8"?--><div class="abstract"><div class="abstract_label">The present study addresses the effects of lateral center-of-gravity (CG) movement, resulting from asymmetric firing of some of the onboard stores, on the dynamics and control of a combat aircraft while attempting the highly demanding Herbst manoeuver. The complete six degree-of-freedom equations of motion of the aircraft for such lateral CG offset are derived in two different body reference frames attached either to the symmetric nominal CG location or to the shifted asymmetric CG location. The Herbst manoeuver is first simulated using nonlinear dynamic inversion based control to handle the highly nonlinear post stall flight dynamics considering the standard equation of motion without considering any lateral CG variation. Thereafter, it is observed that if the same controller is retained, the manoeuver performance deteriorates significantly even when the CG undergoes a moderate lateral shift. To overcome this shortfall, closed loop controllers are next designed incorporating both the models of asymmetric dynamics as derived in this paper. It is validated through MATLAB simulations that both the controls, thus designed, can recover the original manoeuver performance almost completely; however, the first one requires more complex computations and hence increased computation time while the second one requires that all the measurements be transformed to the new body reference frame at every time step.</div></div>

Modeling and Validation of a Roll Simulator for Recreational Off-Highway Vehicles

2011 ◽  
Author(s):  
Scott B. Zagorski ◽  
Dennis A. Guenther ◽  
Gary J. Heydinger ◽  
Anmol S. Sidhu ◽  
Dale A. Andreatta
Keyword(s):  
Experimental Data ◽  
Degrees Of Freedom ◽  
Close Agreement ◽  
Energy Equation ◽  
Equations Of Motion ◽  
Excellent Correlation ◽  
Motor Systems ◽  
Non Linear ◽  
Entrapped Air ◽  
Three Degrees Of Freedom

A model of a roll simulator for recreational off-highway vehicles (ROV) is presented. Models of each sub-system are described including the equations of motion, the braking, hydraulic and roll motor systems. Derivation of the equations of motion, obtained using Lagrange’s energy equation, demonstrates that they have three degrees-of-freedom (two dynamic, one static) and are coupled and highly non-linear. Results from the hydraulic sub-system illustrated that the amount of entrapped air in the system can significantly influence the response. Comparisons of the model with experimental data from the actual roll simulator showed close agreement. The greatest difference was with motor pressure. The acceleration levels and roll motions for both the model and experimental data showed excellent correlation.

Should a Vehicle Always Deviate to the Tire Blowout Side? - A New Tire Blowout Model with Toe Angle Effects

2021 ◽  
Author(s):  
Ao Li ◽  
Yan Chen ◽  
Xinyu Du ◽  
Wen-Chiao Lin
Keyword(s):  
Road Safety ◽  
Experimental Results ◽  
Vehicle Stability ◽  
Ground Vehicles ◽  
Test Vehicle ◽  
Friction Forces ◽  
Toe Angle ◽  
Tire Forces ◽  
Tire Friction ◽  
First Time

Abstract As a severe tire failure, tire blowout during driving can significantly threaten vehicle stability and road safety. Tire blowout models were developed in the literature to conclude that a vehicle always deviates to the tire blowout side. However, this conclusion is proved to be inaccurate in this paper, since one important factor was largely ignored in the existing tire blowout models. Toe angle, as a basic and widely-applied setup on ground vehicles, can provide preset and symmetric lateral tire forces for normal driving. However, when tire blowout occurs, different toe angle setups can impact vehicle motions in different ways. For the first time, the toe angle is explicitly considered and integrated into a tire blowout model in this paper. For different tire blowout locations, driving maneuvers, and drivetrain configurations, the impacts of different toe angle setups on the variations of tire friction forces and vehicle motions are analyzed. The developed tire blowout model with toe angles is validated through both high-fidelity CarSim® simulation results and experimental results of a scaled test vehicle. Both simulation and experimental results show that a vehicle may not deviate to the tire blowout side, depending on the toe angle setups and driving maneuvers. Moreover, the experimental results also validate that the proposed tire blowout model can accurately evaluate the tire blowout impacts on vehicle dynamics.

The Dynamics of Ball Bearings

1971 ◽  
Vol 93 (1) ◽  
pp. 1-10 ◽  
Author(s):  
C. T. Walters
Keyword(s):  
Fourth Order ◽  
Ball Bearing ◽  
Equations Of Motion ◽  
Numerical Results ◽  
Degree Of Freedom ◽  
Spin Axis ◽  
General Analysis ◽  
Ball Bearings ◽  
High Speeds ◽  
Six Degree Of Freedom

The details of the dynamics of the elements of a ball bearing become increasingly important at high speeds. A comprehensive general analysis of the motions of balls and a ball separator with realistic lubrication is summarized. The equations of motion consider four degree-of-freedom balls and a six degree-of-freedom separator and are integrated numerically with a fourth order Runge Kutta scheme. Numerical results are presented for a particular spin axis gyro bearing configuration.

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