This paper presents a structural and topological analysis of braking mechanisms in railway vehicles. The braking force is transmitted from the piston rod of a pneumatic cylinder to the axle of the railway vehicle through a lever mechanism. In case of a single cylinder, the braking mechanism has a complex topological structure, being composed of three plane cinematic chains: a central, horizontal chain and two vertical cinematic chains. By highlighting the component cinematic chains, the present paper shows the sequential operation of a multi-mobile mechanism with a single conducting element. Most passenger vehicles have four axles, meaning two two-axle bogies. The modern trend is to use disk brakes, with one or two disks for every axle. This way, the braking mechanism becomes less complicated, but requires more brake cylinders, at least one per axle.
1. General considerations
The braking mechanisms of railway vehicles (rail cars and locomotives) are called by railway operators brake beam mechanism [1]. These brake beam mechanisms are made up of plane articulated beams through which the motion and force of the brake cylinder piston is transmitted to the brake shoes.
The brake shoe beam mechanism is made up of a central brake beam mechanism, which operates horizontally, and an axle brake beam mechanism, which operates vertically.
If the brake shoes exert pressure on the wheel from two opposite sides, the brake beam mechanism operates symmetrically; if they exert pressure from only one side, the brake beam mechanism operates asymmetrically [1, 2].
In case of a symmetric brake beam mechanism, the pressure on the axle is exerted from two opposite sides, thus holding the axle in a slanted position – perpendicular on the direction of the pressure force.
By using two symmetrical brake shoes on each wheel, the pressure exerted on one of the brake shoes is reduced, thus reducing the wear of the brake shoes and increasing the friction coefficient and the effect of the braking action.
On the other hand, the asymmetrical brake beam mechanism is less complicated and exerts less pressure.
Most brake shoe beam mechanisms are symmetrical and they are used on four-axle freight and passenger rail cars (two two-axle bogies).
The asymmetrical brake beam mechanism is used on certain types of freight rail car bogies, whose specific frame design allows brake shoes to be installed only on the inside of the bogie wheels.
In case of certain railway vehicles such as: locomotives, motorised and special rail cars, because of the small space, the brake beam mechanism has to be divided in several brake disk mechanism, which operate individually, using a brake cylinder.
In case of diesel-hydraulic, diesel-electric and electric locomotives, specific brake beam mechanisms are used, which have brake cylinders on every wheel. In the following paragraphs, we will analyse only the symmetrical and asymmetrical brake beam mechanisms used for freight and passenger rail cars.
2. The topological structure of the brake shoe mechanism
The automated braking mechanism (fig. 1) is made up of two distinct components, which operate as mechanical subsystems [3]:
– the command mechanism, called central brake beam mechanism, made up of a plane articulated mechanism (fig. 1), which operates horizontally (xy) underneath the rail car frame and
– the execution mechanism, called axle brake beam mechanism, made up of a plane articulated mechanism (fig. 1), which operates vertically (xz), perpendicular on the axis of the axle.
The central brake beam mechanism and the two axle brake beam mechanisms (in case of two-axle rail cars) are connected through a beam 1(Os) and respectively 1(Od), which have a relatively high length (2 – 3 m). Through this beam, the motion is transmitted from the horizontal plane xy (where the central brake beam mechanism operates) to the vertical plane xz (where the brake mechanism of every axle operates). The two articulations of the longitudinal beam 1 (fig. 1) have perpendicular axes, one is vertical (in Ds respectively Dd when exiting the horizontal cinematic chain) and the other axis – A – is horizontal (when entering the vertical cinematic chain).
3. The central brake beam mechanism
The central brake beam mechanism (fig. 2) is made up of a fixed cylinder 0, where the mobile rod piston 1 moves, beam 2 (with three cinematic thimbles A, B and D) with a mobile joint A to the conducting rod 1, rod 3 (with two joints B and C) and beam 4, which is geometrically identical to beam 2 and has a fixed joint C0 and two mobile joints C and D’.
Beams 2 and 4 (fig. 2a) are also connected through a stressed helicoidal spring (a24), which serves to brig rod 1 in its initial position. The cinematic chart (fig. 2b) does not display the helicoidal spring because it is not considered a cinematic element. Through beams 5 and 6 the translation movement of rod 1 is transmitted to the braking execution mechanisms of every axle. The mobility of this mechanism (fig. 2b), which is made up of a closed cinematic chain (0, 1, 2, 3 and 4), can be calculated using the following formula [4]:
(3.1)
introducing the numeric values of parameters:
Using this formula (3.1) we can obtain the numeric value of the mobility:
(3.1’)
The two mobilities show that the central brake beam mechanism (fig.3) that have a single conducting element operate differentially, putting in motion first beam 1(Os), in stage I, a situation in which beam 4 remains fixed (point C, the centre of the joint, acts as a fixed joint). After putting in motion the brake shoe (S1 and S2) and the tyre of the left axle wheel Os (fig. 3a), the movement of rod 1 is transmitted through beam 4 to beam 1 (Od) (fig. 1) and from here to the braking execution mechanism of the right axle Od.
4. The axle brake beam mechanism
We have considered a first alternative of the axle brake beam mechanism (on the left) as a structural chart (fig. 3a), where the fixed joints are located on longeron 0 of the two-axle rail car.
The structural chart of the symmetrical braking mechanism (fig. 3a) corresponds to a specific cinematic chart (fig. 3b), which identifies the mobile cinematic elements (1, 2, 3, 4, 5, 6, 7, 8, 9, 10 and 11), as well as the cinematic thimbles, presented as fixed (B0, D0, E0, F0 and H0) and mobile joints (A, B, C, D, E, F, G and H). The physical modelation of the mechanism can be obtained using a mobile lever m (fig. 4a), through which a cinematic element and two cinematic thimbles are introduced (Om, Am).
The geometrical mobility of the plane mechanism (fig. 4a), which is made up of several closed cinematic chains [3, 4], can be calculated using the following formula:
(4.1)
where the numerical values of the structural parameters are:
Using this formula (4.1) we can calculate the numerical value of the geometrical mobility:
M = 3×12 – 2×17 – 0 = 2 (4.1’)
Considering the braking mechanism of an axle (fig. 3a), the two independent motions correspond to the sequential motion through which the two brake shoes (S1, S2) are successively pushed towards the rim of the wheel. This operation includes two phases.
In phase I, when joint B is immobile (fig. 4b), beam 4 rotates clockwise and brake shoe S1 is pushed towards the tyre of the wheel through dyadic chain LD(3, 4), after which joint D is immobilised (fig. 4c).
The structural and topological formula of the MM[4] motorised mechanism in phase I, using level m as acting element (fig. 4b) is:
MM=MF(0,m)+LD(1,2)+LD(3,4)
(4.2)
In phase II (fig. 3c), the structure of the mechanism is modified and the structural and topological formula is as follows [4]:
MM=MF(0,m)+LTr(1,2,3,5)+LD(6, 7)+LD(8,9)+LD(10,11)
(4.3)
This formula (4.3) highlights a triadic chain LTr(1,2,3,5) and three dyadic chains LD(6,7), LD(8,9) and LD(10,11). By continuing the trigonometrical rotation of level m (fig. 4c), joint D is blocked and the motion is transmitted to beam 11, which rotates clockwise, pushing joint H and brake S2 towards the tyre of the wheel.
Version 2 of the single-axle braking mechanism with symmetrical brake shoes is shown in fig. 5. Here, there are fewer cinematic elements (fig. 3).
Considering the physical model of the plane mechanism (fig. 6a), by adding a lever m and two joints (Om, Am) within another closed cinematic chain, the mobility can be calculated using the following formula [4]:
(4.4)
where the numerical values of the structural parameters are:
n =10, C5 = 14, C4 = 0
Using this formula (4.4) we can calculate the numerical value of mobility:
M=3 x 10 – 2 x 14 – 0 =2 (4.4’)
The two independent motions correspond to the sequential motion of the two brake shoes (S1, S2) which implies the operation of the single-axle braking mechanism (fig. 5a) in two phases.
In phase I, when joint B is immobile (fig. 6b), beam 4 rotates clockwise and brake shoe S1 is pushed towards the tyre of the wheel through dyadic chain LD(3, 4), after which joint D is immobilised (fig. 6c).
The structural and topological formula for phase I, using lever m as acting element (fig. 6b) is:
MM=MF(0,m)+LD(1,2)+LD(3,4) (4.6)
In phase II (fig. 6c), the structure of the mechanism is modified and the structural and topological formula becomes:
MM=MF(0,m)+LTr(1,2,3,5)+LD(6, 7)+LD(8,9)
(4.7)
Formula 4.7 identifies one triadic chain LTr(1,2,3,5) and two dyadic chains LD(6,7) and LD(8,9). By continuing the trigonometrical rotation of lever m (fig. 6c), joint D is blocked and the motion is transmitted to beam 9, which rotates clockwise and pushes joint G and brake shoe S2 towards the tyre of the wheel.
5. The asymmetrical brake shoe mechanism
The asymmetrical brake shoe mechanism (fig. 7) is used for the bogies of some of the freight cars which can be found in CFR’s vehicle exploitation fleet.
The physical modelation of the mechanism (fig. 7a) allows beam 1 to be put in motion by lever m, which is equipped with two joints, one fixed Om and one mobile Am.
The mobility of this mechanism (fig. 7a) can be calculated using the following formula [4]:
(4.7)
where the numerical values of the structural parameters are:
n =10, C5 = 14, C4 = 0
Using this formula (4.7) we can calculate the numerical value of mobility:
M=3 x 10 – 2 x 14 – 0 =2 (4.7’)
The two independent motions correspond to the sequential motion of the two brake shoes (S1, S2), which implies the operation of the braking mechanism for one axle (fig. 7) in two phases.
In phase I, joint E is fixed and the structural topological formula is:
MM=MF(0,m)+LTr(1,2,3,4)+LD(5, 6)
(4.8)
This chart allows the rotation of beam 6 clockwise (fig. 7b), which implies the motion of joint D (brake shoe S1) from left to right.
In phase II, joints D and B are fixed (fig. 7c) and the structural topological formula is:
MM=MF(0,m)+LD(1,2)+LD(4,7)+LD(8,9) (4.9)
which implies the rotation of beam 9 clockwise, and joint G (brake shoe S2) will move towards the left.
6. The brake disk mechanism
The topological structure of the brake disk mechanisms (fig. 8) is similar to the structure of the central braking mechanism (fig. 2) used in the brake shoe mechanism for two and four-axle rail cars.
The usage of the brake disk mechanism is very modern and it tends to be used more and more. The solution is to use one (fig. 8a) or two disks (fig. 8b) which are installed in a rigid position on every axle of the rail car. This way, the braking mechanism is mess complicated, but it requires a higher number of brake cylinders, at least one per axle. Based on the structural chart of the disk brake mechanism (fig. 8a), we can create the cinematic chart of the plane mechanism (fig. 9a) – brake disks 5 and 6.
The mobility of the mechanism can be calculated using the following formula:
M=3n – 2C5 – C4
(6.1)
The cinematic chart identifies the specific structural-topological numeric parameters:
n=6, C5=7, C4=0
Using formula (6.1) we can calculate the mobility when the mechanism is in a neutral position (fig. 9):
M= 3 x 6 – 2 x 7 – 0 =4
(6.1’)
Two of the four mobilities correspond to the free rotation movements of elements 5 and 6 around joints D and E. The other two geometrical mobilities represent the movement of the two disks (connected to elements 5 and 6) until they reach brake disk Df.
In phase I, joint C is fixed (fig. 9b), and the motorised mechanism (MM) with the fundamental mechanism MF(0,1) operate within a single closed chain, based on the following structural-topological formula:
MM=MF(0.1) + LD(2,3)
(6.2)
In phase II, joint C becomes mobile and plate 5 translates radially on the plane surface of the brake disk, creating a translation thimble (fig. 9c). The structural-topological formula of the motorised mechanism (MM), with the cinematic chart made up of two closed chains, becomes:
MM=MF(0.1)+ LD(2,5)+LD(3,4)
(6.3)
Bibliography
1. Sebeşan, Şt., Contribuţie în problema determinării poziţiei levierelor şi lungimii barelor la timoneriilr frânelor cu acţiune simetrică şiasimetrică, Revista Probleme feroviare, Nr. 7, 1956, pag. 3-8;
2. Tilea, D., Aparate şi instalaţii pe vagoane, Ed. Didactică şi Pedagogică, Bucureşti, 1961;
3. Antonescu, P., Buda, L., Manolescu, N. I., Contribuţii la analiza structurală şi cinematică a mecanismelor de frânare a vagoanelor, Lucrările SYROM’73, Vol. B-2, p. 11-23;
4. Antonescu, P., Mechanism and Machine Science, Printech Publishing House Bucharest, 2005.
by [Mihai SÂRBULESCU, Ovidiu ANTONESCU]
Share on: 
