# Analysis of Asymmetric Wear of Brake Pads on Freight Wagons despite Full Contact between Pad Surface and Wheel

^{1}

^{2}

^{3}

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

_{hw}, is formed. The force, U, is distributed on this plane by the specific force, q

_{se}. Under the action of such forces, the friction force, F

_{ff}, is formed, and the force of resistance, B

_{rf}, to the rolling of the wheel arises and is realized during the wheel/rail contact.

_{ff}, during movement (rotation of the wheel, ω) is realized during the wheel/rail contact, which forms a harmful force of resistance to movement, i.e., F

_{ff}= B

_{rf}(Figure 3a) and, as a result, increases the energy consumption for train movement [10,50].

_{sp}, are redistributed unevenly along the pad. In the upper part of the pad, much larger specific braking pressures are concentrated, which gradually decrease towards its bottom. Due to this, the intensity of pad wear and the temperature of the tribotechnical steam during braking change proportionally. The resulting value of the braking force in the presence of clinodual pad wear takes the following form:

_{K}is the friction-coefficient brake pad, and ξ

_{D}is the friction area reduction factor due to clinodual pad wear.

_{hw}, also naturally increases. However, the thickness and bending stiffness of the brake pad decrease in braking modes under the influence of the brake-pad pressure, and thus it more easily assumes a more stable and balanced position (Figure 3b). In addition, any increase in the pad area, Q

_{hw}, relates to increasing the value of the specific contact pressure during braking, which approaches the nominal value.

_{hw}, appears (Figure 3). The presence of angle α accelerates this process because the effective area of the braking surface of the pad becomes smaller, and the contact frictional stress between the pad and the wheel increases. As a result, the upper worn part of the pad does not reach the wheel during braking, and it does not participate in the formation of the braking force. The frictional interaction of the pads with the wheels, and therefore the braking process, is significantly distorted due to the redistribution of specific pressures along the length of the pads. Therefore, this research proposed the force analysis approach as the solution to the problem in a disintegrated way by refining the method for quasi-static analysis.

^{2}. It corresponds to the wagon mileage of 48.38 thousand km.

_{ef}:

_{w}is the diameter of the rolling circle of the wheel in the plane that “cuts” the pad symmetrically, D

_{w}= 2∙R

_{w}; and dτ is the sectoral angle of discrete separation, Q

_{ef}, from the top, τ

_{t}, to the bottom, τ

_{b}, of the working surface of the pad in the sector, τ.

_{ef}:

_{t}− τ

_{b}) does not depend on the location of the site, dQ, nor does it depend on the change in the size of the sector (τ

_{t}− τ

_{b}) during operation (calculation of pad wear starts from angle τ

_{b}). Considering this, the lines of action of forces, dF, are tangent to the friction circle of radius r = |Oc| for any degree of wear within the braking sector (τ

_{t}− τ

_{b}). They form right angles with the corresponding radii:

_{f}, is called the circle of friction.

_{t}− τ

_{b}).

_{t}– τ

_{b}) are such that elementary reactions, dF, applied to elementary platforms, dQ, for all points of the braking sector converge practically in the middle of the arc, ∪ab, i.e., at point c. In other words, the composition of elementary reactions, dF, form a system of forces converging at one point. It follows that the resulting effect of this system of forces, F, is determined both by the magnitude and by the direction from the polygon of converging forces and it also passes through the midpoint of the arc, ∪ab, i.e., point c. Furthermore, the points similar to c considering the features of the occurrence of clinodual wear in brake pads are called unique points [50].

_{f}, as well as on some other indicators of the mechanical braking system of bogies. For example, they depend on the geometric parameters of the brake pad, in particular, from the position of the bisector, |OC|, which divides the angle of coverage of the pad into equal parts: (τ

_{t}− τ

_{b})/2.

_{w}= 0.25∙D

_{w}(Figure 6a). Figure 6a shows a circle described from the center, O

_{1}, which lies in the middle of the bisector, |OC|, of the braking sector, τ. It is called the circle of unique points, c.

_{t}− τ

_{b}), which is as follows:

_{t}− τ

_{b})/2. The angle is a straight line, and the straight line, |cC|, is tangent to the friction circle. Therefore, the point, c, can be observed as a point of an intersection of the friction circle with the circle built on the axis as on the diameter. This circle is a circle of unique points that change their location due to changes in the friction coefficient, φ

_{f}.

## 3. Results

_{f}= 0.05; φ

_{f}= 0.28; and φ

_{f}= 0.34. For the clarity and simplicity of the description of the procedure of determining unique points (for different φ

_{f}), the calculation-graphical method of constructing polygons of forces acting on of quasistatic-equilibrium objects was applied.

_{f}) a friction circle, which marks the middle points, C

_{1}and C

_{2}, of the contact arcs of the friction surfaces of the brake pads and wheels of the wheelset. Here, circles of unique points for the front (right) and rear (left) in the course of movement of the pads on segments |OC

_{1}| and |OC

_{2}| as on diameters are constructed [50]. Then, the points of intersection of the friction circles with the wheels are the unique points c

_{1}, c

_{2}, …, c

_{8}, for the right and left pads when the wheel rotates clockwise. During the rotation of the wheel in the opposite direction, the unique points are ${c}_{5}^{\prime}$, ${c}_{6}^{\prime}$, ${c}_{7}^{\prime}$, and ${c}_{8}^{\prime}$ for the right pad and ${c}_{1}^{\prime}$, ${c}_{2}^{\prime}$, ${c}_{3}^{\prime}$, and ${c}_{4}^{\prime}$ for the left pad.

_{X}are the arms of action of the moments of the respective forces, while the arm |pe| for simplicity is denoted by a.

_{G}is the arm of action of the moments of the corresponding forces, which equals |dm|. The arm, |dm|, is denoted as b for simplicity; M

_{ff}is the moment of friction forces, which is positive at the kinematic node of point d when the pad is located in front of the wheel rotating clockwise and negative when the pad is located behind the wheel rotating counterclockwise.

_{1}= |ej| is the distance from point j to point e, and l

_{2}= |jd| is the distance from point j to the kinematic node at point d (Figure 8).

_{f}is the friction coefficient between the wheel and the pad; and 2∙α is the angle of coverage of the wheel pad, 2∙α = τ.

_{b}, of wear does not coincide with the center, C, of the contact ∪AB pad. Regarding this, the reaction, F, in the form of the force, F

_{t}, applied at point H

_{t}adds the moment relative to point C. At this moment, M

_{t}causes the formation of a wedge in the upper part of the pad (Figure 8b):

_{b}, is also calculated according to Formula (19), and only the value for the lower part of the pad, H

_{b}, is substituted.

_{v}is denoted as ${M}_{t}^{\prime}$ when the moment acts on the pad during the rotation of the wheel clockwise, and as ${M}_{t}^{\u2033}$ when against it.

_{t}and M

_{b}depend on many parameters, such as the nominal size of the pad; its one-sided wear, Δc, coordinates of the center of gravity of the pad; the angle, α, of the axis of the pendulum suspension; and the magnitude and the direction of the force, F, during braking. Of course, the analysis of all factors affecting the performance of brake pads is very difficult. At the same time, the influence of several named parameters on M

_{t}and M

_{b}is weak. This study examined the effect of these moments, with the main one being one-sided damaging pad wear at the upper end of Δb.

_{t}, acting on the pad after wearing it by Δb were performed. This meant that the type of dependence for a symmetrical brake pad of a freight-wagon bogie for Δb = 0, b = b

_{0}(where b

_{0}is the thickness of the new pad, Figure 9) was determined.

- The output data of the problem, which include the following parameters, such as the radius of the rolling circle, R
_{w}; the pad width, m; friction coefficients between the wheel and the pad, φ_{f}; angle of coverage of the pad, τ; and initial configuration of the location of the CBP (points A, B, e, d), are formed. - The radius of the friction circle corresponding to the specified friction coefficient is calculated using Formula (6).
- Then, the unique points (c
_{0.5}; c_{2}; c_{4}; ${c}_{0.5}^{\prime}$; ${c}_{2}^{\prime}$; ${c}_{4}^{\prime}$) as a result of the intersection of friction circles for the initial friction coefficients (φ_{f}_{1}= 0.05; φ_{f}_{2}= 0.28; and φ_{f}_{3}= 0.34) with a circle of unique points described with the center at point O_{1}and radius r_{w}= 0.25∙D_{w}are geometrically determined. - Furthermore, an arc, ${O}^{\prime}$, and marking the intersection points ${O}_{1}^{\prime}$, ${O}_{2}^{\prime}$ with circles of radius R
_{w}are geometrically drawn from point B with the radius R_{w}. Then, the centers ${A}_{1}^{\prime}$ and ${A}_{2}^{\prime}$ located on ∪AA_{0}and formed by the radius AB with the center at point B are drawn. Points ${O}_{1}^{\prime}$ and ${O}_{2}^{\prime}$ determine the position of the center of the wheel relative to the clinodual-worn pad. - The next step is to draw arcs with the radii ${O}_{1}^{\prime}$d and ${O}_{2}^{\prime}$d from point O to the intersection with the trajectory of kinematic node movement d. The intermediate positions occupied by the kinematic node, d, relative to the center of point O (points D
_{1}and D_{2}are marked in Figure 9) are determined. This is the result of pad upper-end wear by the amounts of Δb and 2∙Δb. - Then, the corresponding points, B
_{1}and B_{2}, on the rolling circle of the wheel are determined when they intersect with arcs of radius Ad drawn from the centers D_{1}and D_{2}. - When the positions of points B
_{1}and B_{2}are determined, the centers C_{1}and C_{2}on the ∪AB braking sector of the clinodual-worn pad are determined. To conduct this, the points on the same rolling circle of the wheel with arcs are marked. Their radii are equal to the chords, which are in the contacts of the arcs ∪BA_{1}/2 and ∪BA_{2}/2. These arcs are drawn from centers B_{1}and B_{2}, respectively. - The wear of the pads during wheel rotations clockwise and counterclockwise is observed at their intersection points, ∪AB, with lines c
_{4}j, c_{4}j_{1}, and c_{4}j_{2}and ${c}_{4}^{\prime}$j, ${c}_{4}^{\prime}$j_{1}, and ${c}_{4}^{\prime}$j_{2}for the centers H_{b}and H_{t}(the points H_{b}and H_{t}are not presented in Figure 9). At the same time, the coordinates of point j are represented by Formula (16) for the variable location of the pendulum suspension of the brake pad, |ed|. These points are not marked in Figure 9 because they will have constantly different coordinates due to the braking process, which is a time function. - Furthermore, the moments M
_{t}and M_{b}are calculated using Formula (19). The force, F, is determined for each value, Δb, from the force’s polygon (Figure 10). The arms Δt and Δb are determined directly by their measuring from Figure 9. The lengths of the perpendiculars descend from the centers C, C_{1}, and C_{2}on the line of action of the force. - The cycle is repeated for the next value of the friction coefficient according to the initial data up to the last of the available φ
_{f}. - At the final stage, the graphoanalytical solution of the problem in the form of dependencies for moments M
_{t}and M_{b}for two-way wheel movement is obtained together with the various friction coefficients, φ_{f}, under the condition of clinodual wear in the upper-pad part.

_{0}and 1/3∙b

_{0}, respectively (Figure 11).

_{t}and M

_{b}and, therefore, wear of the pads during the two-way movement of the wheels are different [50].

_{b}and H

_{t}relative to the centers of the contact arc of the pad AB. The results of the calculations are presented in the form of graphs in Figure 11. With the help of this graphical solution, it is possible to determine the dependences for the values of excess moments as functions of the value Δb of one-sided wear of the brake pads acting on the new (Figure 12a) and on the worn (Figure 12b) pads with different coefficients of friction:

_{b}and H

_{t}located symmetrically to the center, C [10,50].

_{G}, and ${h}_{G}^{\prime}$ change. This means that the input parameter is changed in the Formula (17). Therefore, the coordinates of point j change during the operation of the pads. Probably, the clinodual wear of the brake pad cannot be eliminated by choosing the initial position of the hinge point, d, of the new pad.

## 4. Discussion

## 5. Conclusions

- 1.
- The method of quasi-static analysis was applied to determine the harmful wear of the composite brake pads of freight wagons. This method made it possible to carry out a geometrical analysis of the pendulum suspension system of CBPs with clinodual wear and its interaction with the wheel. Moreover, this approach made it possible to establish that the unique point is the point of intersection of the friction circle. The position of the point on the axis of the pendulum suspension makes it possible to determine the mathematical values for the arms of the moments of forces during braking for the upper and lower parts of the CBP.

- 2.
- The force factors that ensure the quasi-static equilibrium of the articulated elements of the suspended pad during the braking of the freight-wagon bogie were determined, which made it possible to create the prerequisites for solving the problems related to the clinodual wear of CBPs. Based on the performed quasi-static analysis, it was determined that the moments for the upper and lower parts of the CBP depended on many parameters. Excessive values of the moments lead to the formation and increase in the intensive wedge dual wear of pads during the movement of freight wagons. It was established that, due to the clinodual wear of the pad, the braking area of its upper part decreased with the increase in the mileage of wagons, which negatively affected both the braking efficiency of the freight train and the safety of train traffic.
- 3.
- The methodology and procedure for an analytical solution to the problem of the quasi-static balance of forces and moments acting during braking of a wheel with a pad brake in the case of two-way traffic, if identical events occur during braking, were presented. Based on the results of this study, it was established that, to eliminate the clinodual wear of the pads, the excess torque should be equal to zero. A rational place for mounting the block was determined, which made it possible to eliminate its abnormal wear in operational conditions.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Nomenclature

a | Distance from the hinge, d, of the pendulum suspension to hinge c, a = d + c |

b | Distance from the hinge, c, to the point of action of force G, b = c |

b_{0} | Thickness of the new pad, b = b_{0} |

B_{rf} | Force of resistance to rolling |

c | Circle of unique points |

|cd| | Dynamic eccentricity |

d | Kinematic node |

D_{w} | Diameter of the rolling circle of the wheel in the plane that “cuts” the pad symmetrically, D_{w} = 2∙R_{w} |

dF | Form of distributed discrete forces |

dτ | Sectoral angle of discrete separation, Q_{ef}, from the top, τ_{t}, to the bottom, τ_{b}, of the working surface of the pad in the sector, τ |

e | Fixed point of the hinge |

F | Opposing reaction |

F_{ff} | Friction force |

G | Gravitational force generated by the weight of the bogie-brake-system parts |

h | Distance between the point of concentrated friction force application (point C) and point H |

H | Point center of wear of the brake-pad working surface |

h_{G} | Arm of action of the moments |

h_{X} | Arm of action of the moments of the respective forces |

K | Pressure force on the pad |

l | Length of the pendulum suspension, l = |ed| |

l_{1} | Distance from point j to point e, l_{1} = |ej| |

l_{2} | Distance from point j to the kinematic node at point d, l_{2} = |jd| |

m | Width of a brake pad |

M_{b} | Moment that causes the formation of a wedge in the lower part of the pad |

M_{ff} | Moment of friction forces |

M_{t} | Moment that causes the formation of a wedge in the upper part of the pad |

P | Force that acts on the brake pad from the triangle side during braking |

Q_{ef} | Working (brake) pad area |

Q_{шcm} | Area of harmful abrasion |

q_{se} | Specific force |

r | Circle with radius |

R_{w} | Radius of the rolling circle |

s | Center of gravity |

T | Force reactions of the pendulum suspension |

U | Force of pressing the top of the block to the wheel |

α | Angle between the horizontal axis that passes through the center of the wheel and the middle of the brake pad, C |

2α | Angle of coverage of the wheel pad, 2∙α = τ |

β | Suspension angle |

γ | Friction angle |

δ | Shift |

Δ_{c} | One-sided brake-pad wear |

$\Delta M$ | Excess moment of forces |

$\Delta v$ | One-side harmful wear |

ξ_{D} | Friction-force-reduction factor due to clinodual pad wear |

τ | Angle of coverage of the pad |

${\phi}_{K}$ | Friction-coefficient brake pad |

ω | Rotation of the wheel |

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**Figure 1.**Clinodual wear of a CBP: (

**a**) pads removed from a wagon with large remaining working mass; (

**b**) overtime clearances between the “pad–wheel” tribotechnical pair.

**Figure 2.**A model of a brake lever transmission system of a two-axle wagon with brake pads: 1, 2—vertical lever; 3—triangle; 4—brake pad; 5—pad holder; 6—pendulum suspension; 7—delimiter of clearance; 8—spacer triangle; and 9—bracket with a lock (a device for uniform pad wear).

**Figure 3.**A scheme of the formation of clinodual frictional wear of the brake pad: (

**a**) reproduction of the initial center of abrasion of the brake-pad upper end during movement without braking; (

**b**) braking with a pad brake with the development of its clinodual frictional wear.

**Figure 4.**A 3D model of the CBP with clinodual wear: 1—harmfully worn pad surface; 2—a line of separation of planes; 3—a plane of brake (working)-pad wear; 4—a block body; 5—the result of brake wear; and 6—the result of harmful wear.

**Figure 5.**A scheme of the reaction formation of the wheel, F = K = P∙cosα, as the sum of the forces, dF, acting on the sections, dQ, of the working surface of the CBP, Q

_{ef}.

**Figure 6.**A scheme of the construction of unique points: (

**a**) circles; (

**b**) front and rear brake pads in the direction of movement.

**Figure 8.**A scheme of the interaction of the CBP with the wheel during braking: (

**a**) coincidence of the center of wear with the center of the contact arc of the pad; (

**b**) determination of the excess moment for the deviation of the center of wear from the center of the pad.

**Figure 11.**The dependence of the moments M

_{t}and M

_{b}on the Δv for a symmetrical pad: (

**a**) when b = b

_{0}; (

**b**) when b = 2/3∙b

_{0}; and (

**c**) when b = 1/3∙b

_{0}.

**Figure 12.**The dependence values of the excess moments $\Delta {M}^{\prime}\left(\Delta t\right)$ and $\Delta {M}^{\u2033}\left(\Delta t\right)$ on the parameter, Δb, for a symmetrical pad: (

**a**) when b = b

_{0}; (

**b**) when b = 2/3∙b

_{0}; and (

**c**) when b = 1/3∙b

_{0}.

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## Share and Cite

**MDPI and ACS Style**

Panchenko, S.; Gerlici, J.; Lovska, A.; Ravlyuk, V.; Dižo, J.; Blatnický, M.
Analysis of Asymmetric Wear of Brake Pads on Freight Wagons despite Full Contact between Pad Surface and Wheel. *Symmetry* **2024**, *16*, 346.
https://doi.org/10.3390/sym16030346

**AMA Style**

Panchenko S, Gerlici J, Lovska A, Ravlyuk V, Dižo J, Blatnický M.
Analysis of Asymmetric Wear of Brake Pads on Freight Wagons despite Full Contact between Pad Surface and Wheel. *Symmetry*. 2024; 16(3):346.
https://doi.org/10.3390/sym16030346

**Chicago/Turabian Style**

Panchenko, Sergii, Juraj Gerlici, Alyona Lovska, Vasyl Ravlyuk, Ján Dižo, and Miroslav Blatnický.
2024. "Analysis of Asymmetric Wear of Brake Pads on Freight Wagons despite Full Contact between Pad Surface and Wheel" *Symmetry* 16, no. 3: 346.
https://doi.org/10.3390/sym16030346