Freight train air brake models

Figures & data

Figure 1. Typical freight train air brake systems.

Figure 2. Basic triple valve actions: (a) release, (b) brake and (c) lapping.

Table 1. Typical features of modern air brake systems.

Valve type	ABDX [107]	KE [79]	WF 5 [110]	120–1 [94]	KAB60 [115]
Feature	(AAR)	(UIC)	(AUS)	(CHN)	(RUS)
Service brake	YES	YES	YES	YES	YES
Quick action	YES	YES	YES	YES	YES
Quick service	YES	YES	YES	YES	YES
Lapping	YES	YES	YES	YES	YES
Release	YES	YES	YES	YES	YES
Accelerated release	YES	NO	YES	YES	YES
Retarded recharge	YES	YES	YES	YES	YES
Graduated release	NO	YES	NO	NO	YES
Emergency portion	YES	NO	NO	YES	NO

Figure 3. Brake pipe lumped parameter model [56].

Figure 4. Brake pipe lumped parameter model [84].

Table 2. Methods to solve brake pipe models.

Representative reference	Method	Mesh size/ step-size
[54]	Finite Difference
[56]	Method of Characteristics
[52]	Finite Difference and Finite Element	One element per vehicle
[53]	Finite Element	One element per vehicle
[60]	Finite Element	4–7 m
[35]	Finite Difference	1 millisecond
[69]	Differential method and operator splitting
[71]	Finite Difference
[77]	3^rd order Taylor expansion	1 m
[81]	Finite Element	~1.2 m (10 elements per vehicle)
[90]	Method of Characteristics	1–2 m, variable step-size
[100]	Method of Characteristics
[98]	Operator splitting
[115]	Method of Characteristics
[101]	Method of Characteristics	1 m, variable step-size
[107]	Finite Difference	One element per vehicle
[117]	Separation of variables

Figure 5. Empirical function: (a) pressure drop and vehicle speed to vehicle deceleration [84], and (b) brake cylinder pressure to brake pipe pressure [77].

Figure 6. Interconnection logics of railway brake control valve (revised from [53]).

Figure 7. Wagon brake system diagram [101], ${\mathrm{\varnothing }}_1\sim {\mathrm{\varnothing }}_{17}$ are various orifices.

Figure 8. Stages in empirical models for valve motions [52].

Figure 9. Simple example of a quasistatic valve motion model.

Figure 10. Orifices: (a)square and sharp edged orifices and (b) orifice flow [48].

Figure 11. Brake rigging and wheel-rail adhesion, where $F_{ad}$ is the adhesion force; $r_w$ is wheel radius; $v_{st}$ is wheel translational speed; $\omega$ is wheel rotational speed; $N_b$ is brake shoe normal force; $F_b$ is brake shoe friction force; and $P_b$ is brake cylinder pressure.

Figure 12. Brake simulations with wheel-rail adhesion [45].

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