Topic
Self aligning torque
About: Self aligning torque is a research topic. Over the lifetime, 520 publications have been published within this topic receiving 8286 citations.
Papers published on a yearly basis
Papers
TL;DR: The Magic Formula model as mentioned in this paper provides a set of mathematical formulae from which the forces and moment acting from road to tyre can be calculated at longitudinal, lateral and camber slip conditions, which may occur simultaneously.
Abstract: An account is given of the latest version 3 of the Magic Formula tyre model. The model provides a set of mathematical formulae from which the forces and moment acting from road to tyre can be calculated at longitudinal, lateral and camber slip conditions, which may occur simultaneously. The model aims at an accurate description of measured steady-state tyre behaviour. The coefficients of the basic formula represent typifying quantities of the tyre characteristic. By selecting proper values, the characteristics for either side force, aligning torque or fore and aft force can be obtained. The new version of the model contains physically based formulations to avoid the introduction of correction factors. Double-sided, possibly non-symmetric pure slip curves are employed as the basis for combined slip calculations. Suggestions are given to estimate the driving part of the longitudinal slip curve and to represent the characteristic at rolling backwards.
1,187 citations
1 Feb 1987
TL;DR: In this paper, a new way of representing tyre data obtained from measurements in pure cornering and pure braking conditions has been developed in order to further improve the Dynamic Safety of vehicles, making use of a formula with coefficients which describe some of the typifying quantities of a tyre, such as slip stiffnesses at zero slip and force and torque peak values.
Abstract: A new way of representing tyre data obtained from measurements in pure cornering and pure braking conditions has been developed in order to further improve the Dynamic Safety of vehicles. The method makes use of a formula with coefficients which describe some of the typifying quantities of a tyre, such as slip stiffnesses at zero slip and force and torque peak values. The formula is capable of describing the characteristics of side force, brake force and self aligning torque with great accuracy. This mathematical representation is limited to steady-state conditions during either pure cornering or pure braking and forms the basis for a model describing tyre behaviour during combined braking and cornering.
1,084 citations
TL;DR: In this article, the steady-state empirical "Magic Formula" tire model was used to model the acceleration and braking properties of the Delft Tyre 97, and a full set of equations of the steady state part of the model of the new version was presented.
Abstract: The tyre force and moment generating properties connected with the vehicle's horizontal motions are considered. Knowledge of tyre properties is necessary to properly design vehicle components and advanced control systems. For this purpose, mathematical models of the tyre are being used in vehicle simulation models. The steady-state empirical ‘Magic Formula tyre model’ is discussed. The aligning torque description is based on the concepts of pneumatic trail and residual torque. This facilitates its combined slip description. Following Michelin, weighting functions have been introduced to model the combined slip force generation. A full set of equations of the steady-state part of the model of the new version ‘Delft Tyre 97’ is presented. The non-steady state behaviour of the tyre is of importance in rapid transient maneuvres, when cornering on uneven roads and for the analysis of oscillatory braking and steering properties. A relatively simple model for longitudinal and lateral transient responses...
522 citations
Patent•
6 Nov 1986
TL;DR: In this paper, a force and torque converter is provided that senses forces and torque applied to the device by a Cartesian coordinate system, with respect to a fixed number of relays.
Abstract: A force and torque converter (1) is provided that senses force and torque applied to the device (1). The converter (1) includes a base (10), a grip (9), resilient connection members (2, 4, 6) that extend radially and coplanarly from a central hub (8), located within the grip (9), and that connect to the grip, and sensing mechanisms to sense the displacement of the connection members (2, 4, 6). The displacements are resolved to determine the force and torque that is applied to the device (1), with respect to a Cartesian coordinate system.
210 citations
Journal Article•
TL;DR: In this paper, an analytical approach for determining tyre dynamic properties is presented for braking/traction and steering manoeuvres with a varying camber angle on regular or irregular terrains.
Abstract: This study presents an analytical approach for determining tyre dynamic properties in a sequence of three papers. Most of the necessary parameters are determined using tyre geometry, orientation and some experimental data. Explicit formulations are derived analytically for the tyre dynamic properties as functions of the slip ratio, slip angle, camber angle and other tyre dynamic parameters. These formulations can be used for the general vehicle simulations in braking/traction and steering manoeuvres with a varying camber angle on regular or irregular terrains. In the first paper a brief review of some previous studies is given. Tyre modelling, contact, slip and friction properties are also studied. Tyre forces and moments due to pure slips are investigated. An algorithmic procedure is provided, in the summary for computational purposes. In the second paper, tyre forces and moments due to comprehensive slips are studied. Finally, in the third paper these analytical models are validated against some experimental data.
180 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2021 | 2 |
| 2020 | 8 |
| 2019 | 12 |
| 2018 | 8 |
| 2017 | 12 |
| 2016 | 14 |