Fore-Aft Forces in Tire-Wheel Assemblies Generated by Unbalances and the Influence of Balancing

1991 ◽  
Vol 19 (3) ◽  
pp. 142-162 ◽  
Author(s):  
D. S. Stutts ◽  
W. Soedel ◽  
S. K. Jha
Keyword(s):  
Mathematical Model ◽  
Elastic Foundation ◽  
Torsional Oscillation ◽  
Vertical Direction ◽  
Torsional Stiffness ◽  
Rolling Motion ◽  
Vertical Force ◽  
Horizontal Force ◽  
Wheel Rim ◽  
Open Question

Abstract When measuring bearing forces of the tire-wheel assembly during drum tests, it was found that beyond certain speeds, the horizontal force variations or so-called fore-aft forces were larger than the force variations in the vertical direction. The explanation of this phenomenon is still somewhat an open question. One of the hypothetical models argues in favor of torsional oscillations caused by a changing rolling radius. But it appears that there is a simpler answer. In this paper, a mathematical model of a tire consisting of a rigid tread ring connected to a freely rotating wheel or hub through an elastic foundation which has radial and torsional stiffness was developed. This model shows that an unbalanced mass on the tread ring will cause an oscillatory rolling motion of the tread ring on the drum which is superimposed on the nominal rolling. This will indeed result in larger fore-aft than vertical force variations beyond certain speeds, which are a function of run-out. The rolling motion is in a certain sense a torsional oscillation, but postulation of a changing rolling radius is not necessary for its creation. The model also shows the limitation on balancing the tire-wheel assembly at the wheel rim if the unbalance occurs at the tread band.

scholarly journals Mathematical modeling of a self-propelled scraper at the beginning of soil set

2021 ◽  
Vol 1 (92) ◽  
pp. 154
Author(s):  
Sergii Kovalevskyi
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Degrees Of Freedom ◽  
Dynamic Change ◽  
Vertical Force ◽  
Horizontal Force ◽  
Small Influence ◽  
Rate Of Increase ◽  
Draw Conclusion ◽  
External Forces

The process of filling of scoop of dragshovel consists of a few operations which periodically repeat oneself in the working loop. Each of these stages is accompanied the different moving of dragshovel and his separate knots, conditioned actions of external forces, at cutting and load of soil in a scoop, that needs separate consideration of the tense state of dragshovel equipment in a few calculation positions. The analysis of the modes of ladening of metallokonstrukcii of dragshovel during implementation of basic operations of digging allows to define the rational modes of operations of machine. For the decision of the put tasks the calculation chart of self-propelled dragshovel was developed in the process of zaglubleniya of knife in soil, on the basis of which taking into account the grounded limitations and scope terms, a twomass mathematical model, having degrees of freedom in horizontal and vertical directions, is created. With the purpose of simplification of mathematical model the angular vibrations of tractor and dragshovel were not taken into account, in connection with their small influence on the operating loadings at zaglublenii of scoop. Realization of mathematical model allowed to get the charts of dynamic change of horizontal and vertical force, operating in the hinges of hauling frame. Swaying character of loadings rotined that maximal values were arrived at almost for the identical interval of time in the first semiperiod, and horizontal and vertical efforts increase with the increase of intensity of resistance digging. The results of researches rotined that forces operating in the front hinge of hauling frame grow with the increase of intensity of resistance digging, arriving at the maximal values of 195 and 78 kN. Horizontal efforts to a great extent exceed vertical and increased with growth of intensity of resistance digging. The rate of increase of maximums of horizontal force can be considered even, because at megascopic intensities from 150 to 250 kN/m, most values grow approximately on 32 %, that enables to draw conclusion about expedience of work with the less rates of movement of dragshovel, taking into account loading of metallokonstrukcii. The rate of growth of maximums of vertical force can be considered even, approximately on 7 %, with the increase of rate of climb of knife of dragshovel, that far fewer as compared to growth of efforts, operating in horizontal direction. Therefore diminishing of speed of zaglubleniya will not result in the substantial diminishing of loading on the hauling frame of dragshovel.

3-D Mechanical Analysis of Magnetic- Pneumatic Microfabrication Stage

2010 ◽  
Vol 44-47 ◽  
pp. 186-189
Author(s):  
Xue Peng Liu ◽  
Dong Mei Zhao
Keyword(s):  
Magnetic Flux ◽  
Dynamic Characteristic ◽  
Analytical Method ◽  
Vertical Direction ◽  
Mechanical Analysis ◽  
Air Gap ◽  
Vertical Force ◽  
Air Bearing ◽  
Horizontal Force ◽  
Supporting Force

3-D mechanics of magnetic- Pneumatic microfabrication stage includes X, Y-direction horizontal force and vertical direction force. Horizontal force can be resolved by analytical method with magnetic equation while vertical force can be done by isentropic equations.The acceleration is expected to be 8m/s2, and working gap of air bearing is to be 10 um. Experiments show that magnetic flux air gap is below 3.9mm with the current of 2A and working gap of air bearing is 20um with the supporting force of 16kgf to match the dynamic characteristic requirements.

scholarly journals Report of the Kew Committee for the fourteen months ending December 31, 1891

1892 ◽  
Vol 51 (308-314) ◽  
pp. 152-182
Keyword(s):  
Vertical Force ◽  
Horizontal Force ◽  
Increased Activity

The operations of The Kew Observatory, in the Old Deer Park, Richmond, Surrey, are controlled by the Kew Committee, which is constituted as follows: The magnetographs have worked satisfactorily all through since last report. The curves obtained, representing Declination, Horizontal Force, and Vertical Force, have shown a marked increased activity in terrestrial magnetic changes as compared with the preceding year, although no very large disturbances have been registered.

Impact of Electric Vehicle Lateral Dynamics on the Battery Pack

2014 ◽  
Vol 590 ◽  
pp. 451-457
Author(s):  
Sen Nan Song ◽  
Fa Chao Jiang ◽  
Hong Shi
Keyword(s):  
Mathematical Model ◽  
Angular Acceleration ◽  
Simulation Software ◽  
The Body ◽  
Battery Pack ◽  
Vehicle Body ◽  
Rolling Motion ◽  
Rolling Angle ◽  
On The Road ◽  
The Mathematical Model

The present work is concerned with the rolling motion of the battery pack when EV travelling on the road. First McPherson suspension system was regarded as the research object with detailed analysis of its structural features and motion characteristics. Establish the mathematical model which could apply to calculating the rolling motion of the vehicle body. Through MATLAB/Simulink simulation software, we could calculate the rolling angle on passive suspension. On this basis, assume that the battery pack mounted on the vehicle body and make it passive connection and PID connection. When the body rolls, the battery pack will produce a certain angle then. Next establish the mathematical model to summarize the relationship between the two variables. Then we set the parameters and calculate the roll angle of battery pack in both cases for comparison. Simulation results show that road irregularities will make battery rotate an angle and PID controller can effectively reduce the angle, especially angular acceleration. This paper put forward a new idea that battery is connected with body by active control on EV, and proves the superiority in reducing the rolling angle.

scholarly journals World Experience in Creating Mathematical Models of Air Springs: Advantages and Disadvantages

2021 ◽  
pp. 25-42
Author(s):  
A. Y Kuzyshyn ◽  
S. A Kostritsia ◽  
Yu. H Sobolevska ◽  
А. V Batih
Keyword(s):  
Mathematical Model ◽  
Finite Element ◽  
Mathematical Models ◽  
Dynamic Behavior ◽  
High Speed ◽  
Vertical Direction ◽  
Rolling Stock ◽  
Air Spring ◽  
Advantages And Disadvantages ◽  
Mechanical Models

Purpose. Taking into account the production and commissioning of modern high-speed rolling stock, the authors are aimed to analyze the currently created mathematical models describing the dynamic behavior of the air spring, systematize them and consider the advantages and disadvantages of each model type. Methodology. For the analysis, a comparative chronological method was used, which makes it possible to trace the development of several points of view, concepts, theories. In accordance with the adopted decision equations, the existing models of air springs were divided into three groups: mechanical, thermodynamic and finite-elements. When analyzing mathematical models, the influence of a number of parameters on the dynamic behavior of the air spring, such as disturbing force frequency, heat transfer, nonlinear characteristics of materials, the shape of the membrane, etc., was considered. Findings. A feature of mechanical models is the determination of input parameters based on the analysis of experimental results, requires access to complex measuring equipment and must be performed for each new model of an air spring separately. Unlike mechanical models, which allow taking into account the damping effect of an air spring in the horizontal and vertical direction, thermodynamic models are mainly focused on studying the dynamic behavior of an air spring in the vertical direction. The use of the finite element method makes it possible to most accurately reproduce the dynamic behavior of an air spring, however, it requires significant expenditures of time and effort to create a finite element model and perform calculations. Originality. Mathematical models of the dynamic behavior of an air spring are systematized, and the importance of their study in conjunction with a spatial mathematical model of high-speed rolling stock is emphasized. Practical value. The analysis of the mathematical models of the dynamic behavior of the air spring shows the ways of their further improvement, indicates the possibility of their use in the spatial mathematical model of the rolling stock in accordance with the tasks set. It will allow, even at the design stage of high-speed rolling stock, to evaluate its dynamic characteristic and traffic safety indicators when interacting with a railway track.

scholarly journals The Observed Relationships Between Some Solar Rotation Parameters and the Activity Cycle

1983 ◽  
Vol 102 ◽  
pp. 99-111
Author(s):  
Robert Howard ◽  
Barry J. LaBonte
Keyword(s):  
Solar Activity ◽  
Solar Rotation ◽  
Rotational Velocity ◽  
Torsional Oscillation ◽  
Periodic Oscillation ◽  
Activity Cycle ◽  
Solar Activity Cycle ◽  
Solar Activity Minimum ◽  
Activity Maximum ◽  
Open Question

Several parameters of the solar rotation show variations which appear to relate to the phase of the solar activity cycle. The latitude gradient of the differential rotation, as seen in the coefficients of the sin2 and sin4 terms in the latitude expansion, shows marked variations with the cycle. One of these variations may be described as a one-cycle-per-hemisphere torsional oscillation with a period of 11 years, where the high latitudes rotate faster at solar activity maximum and slower at minimum, and the low latitudes rotate faster at solar activity minimum and slower at maximum. Another variation is a periodic oscillation of the fractional difference in the low-latitude rotation between north and south hemispheres. The possibility of a variation in the absolute rotational velocity of the sun in phase with the solar cycle remains an open question. The two-cycle-per-hemisphere torsional waves in the solar rotation also represent an aspect of the rotation which varies with the cycle. We show that the amplitude of the fast flowing zone rises a year before the rise to activity maximum. The fast zone seems to be physically the more significant of the two zones.

scholarly journals V. Discussion of Kew magnetic data, especially the diurnal inequalities of horizontal force and vertical force, from ordinary days of the eleven years 1890 to 1900

1916 ◽  
Vol 216 (538-548) ◽  
pp. 187-277 ◽  
Keyword(s):  
Diurnal Variation ◽  
Regular Part ◽  
Annual Reports ◽  
Magnetic Data ◽  
Vertical Force ◽  
Horizontal Force ◽  
The Absolute

1. In 1901 the development of electrical traction in West London rendered it clear that unless conditions altered in an unexpected direction, no further magnetic records from Kew Observatory would be sufficiently free from artificial disturbances to be an altogether satisfactory medium for the minute study of phenomena such as the regular diurnal variation. The time seemed to have come for taking stock of the records obtained. The measurement of magnetic curves formed no regular part of the work at Kew Observatory until 1890. Prior to that date the Annual Reports contained only a summary of the results of the absolute observations. Since 1890 the programme of work has included the measurement of the magnetic curves for 5 “quiet" days a month.

scholarly journals Extract from a letter from M. Kämtz addressed to Colonel Sabine (Translation)

1854 ◽  
Vol 6 ◽  
pp. 300-303
Keyword(s):  
Vertical Force ◽  
Horizontal Force ◽  
Terrestrial Magnetism

I have just completed the memoir on terrestrial magnetism which I mentioned to you in former letters. It would follow from the materials which I have employed, that the horizontal force requires constants which differ from those for the vertical force, and the differences, although for the most part not considerable are sometimes too large, as it appears to me, to be overlooked: it is for observers to decide in this matter.

scholarly journals I. On the diurnal variations of the disturbances of the magnetic declination at Lisbon

1876 ◽  
Vol 24 (164-170) ◽  
pp. 373-375
Keyword(s):  
Diurnal Variations ◽  
Short Paper ◽  
Total Force ◽  
Vertical Force ◽  
Horizontal Force ◽  
Magnetic Declination ◽  
The Subject

The Observatory of Infante D. Luiz has possessed since 1863 a set of magnetographs giving continuous records similar to those at Kew. In 1870 the results of the declination magnetograph, from the year 1864 to 1867, were published; and in 1874 the results for the same period of the bifilar and balance magnetographs (results embracing the horizontal force, vertical force, total force, and inclination) were published. At present the results of the declination for 1868 to 1871 are in course of publication. The subject of this short paper is the diurnal variations of the disturbances of the declination. The method which has been adopted for reducing the disturbances is that of Sir Edward Sabine. I have taken ± 2 millimetres, or 2'·26, as the limits, beyond which limits all readings are regarded as disturbed.

Static and Dynamic Buckling of a Compressed Narrow Rectangular Plate on an Elastic Foundation

2008 ◽  
Author(s):  
Leonid Srubshchik ◽  
Issac Herskowitz ◽  
Irina Peckel ◽  
Edward Potetyunko
Keyword(s):  
Rectangular Plate ◽  
Elastic Foundation ◽  
Isotropic Plate ◽  
Vertical Direction ◽  
Dynamic Buckling ◽  
Initial Time ◽  
Asymptotic Formulas ◽  
Surface Load ◽  
Small Surface ◽  
Asymptotic Values

In this paper we consider a thin narrow rectangular isotropic plate subjected to a small surface load and supported laterally by a continuous nonlinear elastic foundation. The both short ends of plate are clamped while the longitudinal sides are completely free, so that their points can move along the boundary, along the normal to the boundary, and in a vertical direction. At initial time the uniformly distributed in-plane compressive stresses are suddenly applied to the short ends in the longitudinal direction. Our goal is to find the asymptotic formulas for values of static and dynamic buckling load in the case of the narrow elastic plate and estimate their values as function of the imperfection parameter. We apply the geometrically nonlinear theory for the thin rectangular isotropic plate laterally supported by the continuous softening or stiffening foundation to formulate an associated nonlinear spectral problem for the load parameter. This problem contains a small natural parameter δ - the ratio of the width of the rectangular plate to its length and can be integrated using the asymptotic method developed in the work by Srubshchik, Stolyar and Tsibulin [1]. Accordingly we approximate the solution of the original problem by the leading term of the finite expansion in δ which is described by the motion equations of an axially compressed elastic column on the nonlinear continuous elastic foundation which has only one spatial dimension and can be investigated more comprehensively. The formulas for asymptotic values of the static and dynamic buckling compressive loads are obtained by means of the perturbation theory and by one-term Fourier’s approximation respectively. The specific numerical results for these asymptotic values are presented.

Sign in / Sign up

Export Citation Format

Share Document