Mathematical Model Calculation of Loading of Wheels Pair of Diesel Locomotive UzTE16M at Wheel-shoe Braking

This article examines the calculation of the locomotive's wheelset load during wheel-blade braking. In this case, the bandage, together with the wheel center and the wheel axle, forms rigid joints, the deformations of which are not taken into account. As an example for the methodology, the UzTE16M2 locomotive strap was used, and a curve for the change in the braking force F_TORM during the clogging of the wheelset was presented.

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The traditional material for brake shoes of rolling stock for many decades has been grey friction cast iron, which has proven itself as a relatively reliable material under conditions of friction without lubrication on steel [1]. Recently, shoes have appeared made of more wear-resistant materials - metal, ceramics, and polymers [2,3], as well as various combinations of them with cast iron [3]. Nevertheless, cast iron remains a very promising material with a number of serious advantages: relatively low wear and low cost of the material, ease of manufacture, independence of braking efficiency from weather conditions, etc.

When a locomotive runs 12-18 thousand km, cast iron brake shoes wear out to half their mass; thus, tens of thousands of tons of cast iron are irretrievably lost every year. In this regard, scientific research aimed at finding ways to increase the operational durability of cast iron brake shoes is relevant.

One of the most important tasks for railway rolling stock is to increase the reliability and durability of braking systems, which is associated with ensuring strength and increasing wear resistance of the shoe-type brake unit.

A significant disadvantage of the shoe brake is that when the wheelset moves at high speeds and the braking distance is reduced, it is necessary to create a significant braking force, which leads to wheel skidding, i.e., movement of the wheelset without its rotation [4-6].

In addition, problems arise during operation related not only to increased wear of the pads, but also to damage to the associated wheel pair bandages. This is often due to poor-quality manufacturing of the pads. At the same time, an important quality of the friction material used is its compatibility with the steel bandage, eliminating its damage.

Research analysis. One of the main conditions imposed on the main elements of brake units is the requirement for high frictional heat resistance, i.e., the ability to maintain certain values ​​of the friction coefficient and the minimum amount of wear of the rubbing pair in the optimal range of speeds, temperatures, and loads.

With wheel-shoe braking, the braking force is created by radial pressure of the brake shoes on the wheels of the rolling stock. The mechanical action of the brake shoes on the wheel pairs is accompanied by frictional wear of the surface of the wheel rolling circles and the shoes themselves. The pressure of the brake shoes on the wheel pairs is two-sided [3,6]. The calculation scheme for the quasi-static calculation of the loading of a locomotive wheel pair during wheel-shoe braking is shown in Figure 1.

The following designations are introduced in the calculation scheme of Figure 1:

N_T- the force of pressing the brake shoe on the bandage;

dk – diameter of wheel

F_k1 and - friction forces arising when the brake shoe presses on the bandage with a force, while the sign changes depending on how the brake shoe is located (in front or behind the wheel in the direction of travel), which can be calculated using the formulas F_k2 N_T.

${\text{F}}_{\text{k}1}={\phi }_{\text{k}}{\text{ N}}_{\text{T}},{\text{ F}}_{\text{k}2}=-{\phi }_{\text{k}}{\text{ N}}_{\text{T}}\text{ (1)}$

Where φ_k - is the coefficient of friction of the shoe on the bandage; it depends on the type of the brake shoe, as well as on the speed of the train and the specific pressure of the shoe on the wheel [4,5]. To exclude the dependence of the friction coefficient on the pressing force, the conventionally accepted calculated brake pressure N_TP is used when performing brake calculations. The coefficient of friction for the calculated pressure is called the calculated coefficient of friction φ_kp. As the train speed decreases, the coefficient of friction increases. The values of the calculated pressure for different types of locomotives, cars, and their loading, shoe material are given in the tables; the values of the calculated coefficients of friction are calculated for speed intervals [4,5].

The friction force F_k1 is balanced by the reaction R₁, which occurs on the brake shoe, and the friction force F_k2 is balanced by the reaction R₂. These reactions, R₁ and R₂, are transmitted through the brake shoes and brake suspension to the frame, then to the spring suspension, and through it to the axle boxes and to the axles. At the same time, the reactions R₁ and R₂, together with the forces F_k1 and F_k2, create additional moments M1 and M2, unloading or loading the wheel depending on how the brake shoe is located (in front or behind the wheel in the direction of travel). The force of adhesion of the wheel to the rail is calculated using the formula F_RAIL.

${\text{F}}_{\text{RAIL}}=\Psi {\text{ P}}_{\text{T}}\text{ (2)}$

Where P_T– load from the wheel to the rail;

Ψ– coefficient of adhesion between the wheel and the rail.

Under normal conditions, the reactive force F_TORM of braking (braking force) and the force of adhesion of the wheel to the rail F_RAIL are equal to each other and mutually balanced (Figure 1), and it is obvious that

${\text{F}}_{\text{TORM}}=2{\phi }_{\text{k}}{\text{ N}}_{\text{T}}.\text{ (3)}$

In this case, the braking force cannot be increased indefinitely, since its value is limited by the inequality.

${\text{F}}_{\text{TORM}}\le {\text{F}}_{\text{RAIL}}=\Psi {\text{ P}}_{\text{T}}\text{ (4)}$

i.e., at any moment in time, the braking force F_TORM cannot exceed the force of adhesion of the wheel to the rail F_RAIL.

In this case, jamming of wheel pairs, or skidding, is possible, in which the wheel stops rotating and slides along the rail while the train continues to move. As a rule, jamming of wheel pairs does not occur instantly; it is preceded by its slippage, as a result of which the speed of the wheel pair becomes less than the forward speed of the rolling stock unit. This leads to an increase in the braking force F_TORM due to an increase in the friction coefficient φ_k and jamming. In this case, at the point of contact of the wheel with the rail, kinetic energy is intensively converted into heat, and due to abrasion and the effect of high temperature on the surface, a slider (oval platform) is formed on the rolling surface of the wheel. This phenomenon is characterized by a characteristic shift of metal at the place of formation of the slider.

To prevent skidding during braking, the permissible braking pressure (braking force) is taken such that the friction force arising when two brake shoes are pressed on the bandage with a force of N_T-F_TORM = 2φ_k N_T exceeds the adhesion force F_RAIL= ψ PT (Figure 1).

The braking force F_TORM is limited by the coefficient of adhesion of the wheel to the rail ψ. To ensure skid-free braking of the locomotive wheel pair, the following condition must be met:

$\text{n}\cdot {\phi }_{\text{kp}}\cdot {{\displaystyle \sum }}^{\text{}}{\text{N}}_{\text{TP}}\le {\Psi }_{\text{p}}\cdot {\text{P}}_{\text{T}},\text{ (5)}$

Where n is the number of pads on the wheel (usually n = 1 or n = 2). The pressure of the brake pads on the wheel pairs is two-sided; therefore, in our case, n = 2 [3,6] (Figure 2.1);

ϕ_kp– the calculated coefficient of friction of the shoe on the tire; it depends on the type of brake shoe, as well as on the speed of the train and the specific pressure of the shoe on the wheel;

Σ N_TP- total calculated force of pressing of brake pads on the axle, kN (tf);

Ψ_p- calculated coefficient of wheel-rail adhesion;

P_T– axle load on rail, kN (tf).

Figure 2 shows the curve of the change in braking force F_TORM during wheelset lockup.

The ratio of the total calculated pressure to the weight of the train is called the calculated braking coefficient.

${\text{υ}}_{\text{p}}=\frac{{\text{N}}_{\text{TP}}}{\left(\text{P}+\text{Q}\right)},\text{ (6)}$

where ${\text{υ}}_{\text{p}}$ -is the calculated braking coefficient;

Р- weight of the locomotive;

Q -is the weight of the train cars.

The estimated braking coefficient characterizes the train's provision of braking pressure. The value of braking pressure per 100 t of train weight is numerically equal to the estimated braking coefficient, expressed as a percentage. The train must be provided with braking pressure according to the standard for its category [1,3].

In calculations where the use is taken into account emergency braking, the calculated braking coefficient is taken to be equal to its full value. If the application of full service braking is taken into account, the calculated braking coefficient is taken to be equal to 0.8 of its calculated value [3,7-16].

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