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The bulk of automobiles are equipped with ABS currently. Having of automatic devices that prevent vehicle wheels from locking and skidding does not require consideration of the normal reactions on the front and rear vehicle axles wheels’ changes dynamics. However, ABS malfunction is possible for various reasons, and in this case the braking system must provide the safety vehicle braking. To provide this, it is necessary to return to the problem of choosing the rational braking forces distribution between the wheels of the front and rear axles.

New solutions for actual problems of determination the efficient distribution of braking forces between the axles of the vehicle, and the stability and drivability of two-axles vehicles at service braking are received in the thesis. It permitted for the first time to determine the Law of distribution of the braking forces between the axles, that ensuring straight-running stability of two-axle vehicle at service braking, to obtain the ideal characteristics for the braking system of two-axle vehicle at service braking and to determine possible values for the distribution of braking force on the front axle. The drivability criterion at service braking obtained further development; it is offered to use boundary at gripping front or rear wheels angular vehicle acceleration on the road.

One of the reasons for the large number of road accidents on highways in Ukraine [1] is the instability of the braking properties due to the unstable characteristics of the brake mechanisms’ friction pairs. The manufacturer produces new automobiles with installed brake pairs (brake pads and their counter bodies), which have passed long-term tests for the stability of the friction coefficient and braking forces distribution of between the axles. This ensures the compatibility of the friction pairs characteristics for front and rear brake mechanisms according to the criteria of heat resistance. During operation, instead of worn-out brake pads, brake discs and drums, drivers can purchase new ones, manufactured as spare parts. However, in the well-known literature there are no methods that allow to check the compatibility of the friction pairs characteristics for front and rear brake mechanisms according to the criteria of heat resistance.

The solution to the problem of stability of a multi-axle vehicle during braking is connected with the determination of the dynamic distribution of normal road reactions between the axles. To assess the stability of the vehicle is used as an indicator of the stability factor representing the ratio of the stabilizing moment to moment, the perturbing skid. When the values of the stability coefficient is greater than or equal to unity, the movement is stable, and otherwise it is unstable. For a multi-axle vehicle, determining the dynamic normal road reactions on the axles is possible after disclosing the static uncertainty of the physical model of the car, which is a multi-support beam. The solution to this problem involves the use of the "three sigma" rule.