A METHOD OF EVALUATING VEHICLE CONTROLLABILITY ACCORDING TO THE DYNAMIC FACTOR

A . T u r e n k o Doctor of technical sciences, Professor, Rector*** Е-mail: rector@khadi.kharkov.ua M . P o d r y g a l o Doctor of technical sciences, Professor, Head of a Department* Е-mail: pmikhab@rambler.ru D . K l e t s Doctor of Technical Sciences, Professor Department of Automobiles and Transport Infrastructure N. E. Zhukovsky National Aerospace University "Kharkiv Aviation Institute" Chkalova str., 17, Kharkiv, Ukraine, 61070 Е-mail: d.m.klets@gmail.com V . G a t s k o PhD* Е-mail: ivanovich87.90@mail.ru M . B a r u n Candidate of Economic Sciences** Е-mail: masha.barun@gmail.com *Department of Mechanical Engineering Technologies and Motor Vehicle Repairs*** **Department of Ecology*** ***Kharkiv National automobile & highway university Petrovskogo str., 25, Kharkiv, Ukraine, 61002 Запропоновано метод оцінки керованості автомобіля у сталому режимі руху за допомогою коефіцієнта динамічності. Визначено, що зміна тиску повітря у шинах, з використанням розробленого алгоритму, дозволяє підвищити стійкість автомобіля проти рискання і, відповідно, безпеку дорожнього руху. Отримані результати можуть бути використані як у процесі експлуатації, так і при проектуванні нових конструкцій машин Ключові слова: керованість, стійкість, коефіцієнт динамічності, сталий рух, автомобіль


Introduction
Handling and driving stability are the most important performance characteristics that influence road traffic safety.When driving in a steady mode, control is one of the features of a more general (complex) property -stability of the vehicle.Manageability at a steady motion allows the driver to promptly and accurately stabilize the azimuth angle and the vehicle turning radius.
The stability and manageability properties should be formed both at the stage of designing new vehicles and during operation of existing vehicles.This issue is especially urgent for trucks with understeer.Development and implementation of specific scientific and technical recommendations based on design and operational parameters of vehicles will increase the efficiency of their operation and road safety in general.

Analysis of previous studies and statement of the problem
The problem of ensuring stability of vehicles has been extensively considered in numerous studies published in Ukraine [1] and abroad [2,3].These studies, however, express different opinions on the relationship between the most important performance properties -the stability and controllability of a vehicle, indicating absence of a common approach to their establishment and evaluation.
A steady rectilinear motion of a wheeled car takes place at regular periodic vibrations of the guide wheels [4], which relates to the need to ensure the course stability by correcting the yaw rate [5].However, the published studies insufficiently specify the criteria for handling the rectilinear movement of the vehicle, i. e. the course control criteria.
The authors of [6,7] describe a wheeled car in the road plane as a resilient oscillating system producing forced oscillations.The equation for these oscillations is the following [6]: h sin pt, dt dt where ψ is a course angle of the vehicle at any given time; where ω 1 is a circular natural frequency of the elastic system; where p is an angular frequency of the forced oscillation (in this problem -the frequency of the driver's actions or those of the automatic control device on the steering); 2n is a relation of the damping coefficient damp α to the moment of inertia M Z I .Forced oscillations occur with a frequency of a disturbing force (in this problem -the torque); and if the circular natural frequency is bigger than the frequency of the disturbing force, there is no phase shift between the oscillations and the force (torque).If the frequency of the disturbing force exceeds the natural frequency, there is a phase shift π (180°) [6].This method can be used to determine the natural frequencies of single vehicles, but it does not provide an assessment of dynamic oscillations in transient modes of movement.
It is known that the biggest instability of vehicles is revealed during braking [8] and in motion within road trains [9].When the frequencies of natural and forced oscillations coincide, there is a sharp increase in the amplitude of the forced oscillations, known as resonance.In the absence of damping ( damp α =0 and 2n 0 = ), the amplitude A of the forced oscillations increases to infinity.In the vicinity of the resonance point, the value of the forced oscillation amplitude is determined by a dynamic factor F dyn [6].
where 0 A is a static turn of the system at the amplitude value of torque equal to M torq .
If there is damping (viscous friction forces of resistance), the value of the amplitude of the oscillations is determined by the following correlation: This approach is used to determine the amplitude of the vehicle's oscillations, but it does not evaluate the impact of structural and operational factors and the technical condition of the vehicle on its directional control.
Thus, adaptation of frequency methods for evaluating resistance to the vehicles' yaw is an expedient issue that requires further research.

Research aim and objectives
The aim of the study is to improve the stability and manageability of vehicles at a steady motion by adjusting the air pressure in the tires, which helps reduce the dynamic factor of the vehicle's yaw.
To achieve this aim, it is necessary to solve the following tasks: -to determine the dynamic factor of the vehicle's yaw; -to analyse the dependence of the dynamism on the design and operational parameters of the vehicle.

Determination of the dynamic factor at the vehicle yaw
To ensure the stability and controllability of a vehicle at a steady rectilinear motion, it is necessary to satisfy the condition max v , the amplitude A increases (5).After the transition from the circular frequencies p and ω 1 to the oscillation frequencies, expressions (4) and ( 5) will look as follows:

Analysis of the dynamic factor dependence on the design and operational parameters of the vehicles
As v poss increases, there is an increase in the dynamic factor [6], which is determined by the following dependence: Since the action of the torque moment M torq is disturbing, the increase in the amplitude А of forced oscillations results in an imbalance between the control action and the vehicle's reaction to it.Therefore, when poss nat v v , < the closer the value of the dynamic factor F dyn to 1, the better the controllability and, hence, the stability of the steady rectilinear movement of the vehicle.
Let us consider the worst case in which in expression (8) n 0.
= This expression will be reduced to the following: In [10], a formula is suggested to determine the frequencies of natural oscillations of a vehicle in the road plane:  Let us estimate the possibility of obtaining the maximum frequency of natural oscillations of the vehicle in the road plane.The analysis of equation (10) shows that an increase of poss v is possible either at a higher We assume that the ratio of the total lateral stiffness of the front and rear wheels of the vehicle is equal to the ratio of the coefficients of resistance to lateral withdrawal, i. e.:  The analysis of the graphs given in Fig. 1 shows that in vehicles with a neutral steering an increase in the parameter a/L (a displacement of the centre of mass to the front axis) increases the natural frequency of oscillations in the road plane.
When expression ( 10) is added to equation ( 9), we obtain the following: The analysis of expression (16) shows that with a higher poss v there is an increase of the F dyn .If poss v 0, = the value of F dyn =1.With an increase in the vehicle base L, there is a lower dynamic factor F dyn , whereas with a bigger overall weight, the F dyn increases.The F dyn also increases with a bigger radius of inertia of the automobile Z i in relation to the vertical axis and with a lower C y1 .In Fig. 2, there are graphs of the dependence for the vehicle Ural-4320 at different values of C y1 (the benchmark data for the plotting of the graphs are shown in Table 1).The analysis of these graphs shows the presence of a minimum value of F dyn .On achieving the neutral steering of the vehicle (C y1 /C y2 = =b/a), the right side of expression (16) becomes reduced.Therefore, expression (16) becomes as follows: We assume that v poss =v max poss =0.7 Hz.Equation (17) becomes as follows: Table 1 The geometric parameters and the weight of the vehicle Ural-4320 The  The analysis of the graphs in Fig. 3 reveals that in a fully loaded vehicle Ural-4320 the dynamic factor is higher than in an equipped vehicle.
When the C y1 value increases at the described loads of the vehicle Ural-4320, the difference of the values dyn F * * decreases.
The right side of equation ( 16) is minimal if When equation ( 19) is integrated into equation ( 16), the result is the following: The minimal value (F dyn ) min can be determined by integrating the expression ( ) The results are a basis for further research on the yaw stability of multi-axial vehicles and multi-unit automobile trains.F .F = at a neutral steering of the vehicle.At equal lateral rigidities in all six wheels in this case C y1 /C y2 =1/2, which is close to 0.531.
2. The design and operational parameters have a significant influence on the vehicle's dynamic factor.With a fully loaded vehicle Ural-4320, C y1 should be increased relatively to C y2 by adjusting the internal air pressure in the tires.For trucks Ural-4320 with dual tires on the equalizer trolley and with equal lateral rigidity of the tires, the ratio C y1 /C y2 =1/4 allows having (F dyn ) min when the vehicle is loaded.If the vehicle is loaded, it is necessary to reduce the air pressure in the tires of the wheels of the equalizer trolley with respect to the air pressure in the tires of the front wheels.This helps bring the ratio C y1 /C y2 to the value of 0.47, which can allow obtaining (F dyn ) min .For two-axial vehicles to have a neutral steering, it is necessary to control and adjust the ratio of the air pressure in the tires of the front and rear wheels.
is an angular velocity of the vehicle in the road plane; is an angular acceleration of the vehicle in the road plane; h is the ratio between the amplitude of the driving torque M torq of the wheeled vehicle and the vehicle's moment of inertia in the road plane in relation to the vertical axis stretching through the centre of elasticity torque moment M torq should not exceed the natural frequencies of the vehicle oscillations in the road plane nat v .Under the condition of max poss the value of nat total lateral stiffness indices of the wheels of the front and rear axes of the vehicle; a m is the mass of the automobile; L is the longitudinal wheel base of the vehicle; a and b denote the distance from the front and rear axes to the projections of the vehicle centre of gravity in relation to the horizontal surface; z i is the vehicle inertia radius in relation to the vertical axis.

. 1 ,
expresses the condition for a neutral steering of the vehicle, when the neutral steering of the vehicle is 1 2 .δ = δ Thus, the neutral steering of the vehicle allows getting the maximum value of the frequency of natural oscillations is less than under condition (11).This means that vehicles with understeer and oversteer have their natural frequency lower than automobiles with neutral steering.It is obvious that the operation of two-axial vehicles with single wheels on the driving axes at changing their centre of mass position, it is possible to satisfy condition (11) by adjusting the internal air pressure in the tires of the front and rear wheels.Equation(10) with regard to the correlation there are graphs of the dependence nat a v L       at m а =8,100 kg; L =4.2 m; B =2.0 m; 1 y C =1.475×10 5 N/m (curve 1) and 2 y C =2.264×10 5 N/m (curve 2).

Fig. 3
Fig. 3 also contains graphs of the dependence 1 2 y min yn y d C ( ) C F       for the vehicle Ural-4320 when it is equipped and fully loaded.For the Ural-4320, the ratio of the lateral rigidity of the tires

1 .
The dynamic factor of the vehicle yaw (F dyn ) min only slightly differs from dyn F * * .However, the correlations C y1 /C y2 differ greatly.For an equipped vehicle, C y1 /C y2 = =0.531at a neutral steering.With F dyn =(F dyn ) min , the value (C y1 /C y2 )* is equal to 0.47.For a fully loaded vehicle, these values are 0.414 and 0.22, respectively.Therefore, for the ) min C y1 , N/m loaded truck Ural-4320 having single tires on all wheels, it can be recommended to ensure that dyn d n * y