The influence of AAR coupler features on estimation of in-train forces

A railway coupling is a mechanism used to connect railroad vehicles (coaches/wagons) to form a train, with functional objectives of transmission and dissipation of in-train forces. Inadequate force management in coupler systems leads to longitudinal discomfort [1‐3], running instability [4, 5], failures and disengagement of vehicles [6, 7]. Thus, accurate estimation of in-train forces is critical to assess structural and operational safety of vehicle elements or train as a whole. A rail vehicle coupler system typically includes inter-connection elements and energy-absorbing elements, often referred as couplers and draft gears, respectively.

This study is concerned with Association of American Railroads (AAR) standard, automatic coupler systems. AAR automatic coupler systems are globally, the most widely used coupling mechanisms for freight trains [8] till date. Couplers of AAR coupler systems require some slack (clearance) to facilitate automatic inter-connection through their integrated component called knuckle (Fig.  1b). While, slack is desirable for freight trains to control starting dynamics [9], it is disadvantageous in case of passenger trains, as it induces significant longitudinal jerks and running instability during acceleration/declaration [10]. Therefore, a very low slack design, “H” type, called tight-lock coupling [11] is being used in passenger trains in various countries, including India, due to heavy haul capacity and economic benefits of AAR couplers [12].

While, coupler connects vehicles and transmits in-train forces, draft gear provides stiffening and buffering actions against impacts and vibrations [13]. Thus, characteristics of coupler systems govern the dynamics of train, as whole [14, 15]; especially longitudinal train dynamics (LTD). LTD studies involve estimation of relative motions and in-train forces between vehicles [16]. Besides laboratory and field tests, numerical simulations are the backbone of railway research community, as these experiments involve high cost, large development time and most importantly the regulations. Therefore, most of the scientific studies on LTD are based on numerical simulations, which require accurate description of railroad vehicle elements. As dynamic in-train forces are transferred through and managed by coupler systems, their modeling is crucial for accurate prediction of relative motions and forces [17].

Early studies ignored couplers and mathematically modeled the coupling system as a linear spring-damper element [18, 19], directly connected between two vehicles, to represent equivalent draft gear characteristics, which shows substantially different hysteresis behavior than that of a draft gear. However, these models ignored coupler slack, which is an important aspect of railway coupling system. Later studies considered nonlinearity of the system by including coupler slack, for instance Ahmed et al. [20] used clearance dead-band along with linear spring-damper elements. A slightly better representation of draft gear hysteresis was developed in Ref. [21]. Although this model considers bilinear stiffness to characterize nonlinear stiffening of spring toward the end of loading stage, the simulated characteristics differ significantly from experimental characteristics. A better model [22] was proposed by adding additional cubic term of displacement for improved approximation of nonlinear stiffening. This model can simulate close value of peak force and energy absorption; however, overall force variation significantly deviates from the actual trend. Hsu et al. [23] developed an improved model, incorporating frictional hysteresis by replacing cubic term with a velocity dependent exponential function. It also incorporated preload of draft gear. No separate models were developed till then, for different draft gear types. With further advancements in modeling approaches, lately various advanced models relating to different draft gear types have been developed.

A major breakthrough in longitudinal dynamic simulations came with more sophisticated friction draft gear model, friction wedge model, developed by Cole [24]. In this analytical approach, draft gear characteristics can be completely defined through its well-known physical attributes: friction coefficients, wedge angles, spring stiffness, etc. Cole’s model [24] has been widely used in various railway dynamic studies [25‐27]. An advanced model of double stage friction draft gear was given by Wu et al. [28], which assumes four working stages of the draft gear. This model has been extensively used in the studies of dynamics of trains in which double stage friction draft gear based coupler systems are used [29‐31]. All these mathematical models can be implemented readily in numerical simulations; however, commercial MBD software widely use look-up table method [5, 32‐38]. It requires a large set of experimental dynamic characteristics (force–deflection) at various loading rates and the approaches to solve discontinuity during transition velocity, to connect loading and unloading paths [39].

The hysteresis characteristics of friction draft gears can be accurately described through its well-defined physical attributes. However, precise description of damping mechanism of polymers is not well-established, hence, their hysteresis models are presently developed using experimental dynamic characteristics. Modern approaches of modeling polymer draft gears, in general, include look-up table [4, 32, 40‐43] and polynomial fitting methods [44, 45]. The common approach to model polymer draft gear characteristics is, fitting experimental characteristics with higher-order polynomials [44, 45] and developing deflection and velocity dependent empirical relations.

Figure 1a illustrates interconnection between two rail vehicles, by means of AAR coupler system and important components of the assembly. Details are presented for the general case, for instance, during curve negotiation. The close representation of equivalent elements for vibration model of coupler system is illustrated in Fig. 1b. Coupler interconnection is, however, a complex interaction involving various design slacks. Important features associated with coupler interconnection are presented in Fig. 2a. Also, draft gear action is highly nonlinear. A typical nonlinear dynamic characteristic of draft gears is presented in Fig. 2b. While main features of draft gear can be identified as masses, equivalent nonlinear stiffening and damping (Fig. 2b), those in coupler include masses, structural stiffness and slacks (Fig.  2a). Illustrated slack between buffing shoulders during fully stretched condition of knuckles, shown in Fig.  2a, has been referred to as knuckle slack in this study, while, the slack between coupler and knuckle contours is referred as contour slack. Total design slack is thus the sum of knuckle slacks and contour slack. Slack between faces of horn and wing of either side couplers is referred as lateral coupler slack.

Most recent mathematical models of draft gears incorporate nonlinear stiffening and damping with good accuracy [8, 39] (dynamic effects due to draft gear mass is ignored); however, coupler slack is the only feature of couplers, that is included in the form of a dead-zone. It is usually combined in the draft gear model itself, to represent a coupling unit. Some of the models also include structural stiffness of coupler and knuckle. Such a simplified model, shown in Fig.  3a, is widely used in LTD studies involving curve negotiation and emergency braking [4, 32] scenarios, while that shown in Fig.  3b is extensively used in simulations for vehicles running on tangent tracks [26, 38]. Couplers are combined and modeled as a massless link of twice the length of individual coupler, to estimate the coupler angle to compute tangential forces.

Studies addressing effect of clearance on various mechanisms [46‐49] show that actual acceleration or force transfer is considerably different than those considered without clearance. Noteworthy deviations in transmitting forces between connected bodies are caused by intermittent impacts and frictional rubbing during metal-metal contact; hence dynamic aspects of presence of clearance in a mechanism should not be overlooked. To the authors’ knowledge, no significant work is found, addressing actual dynamic interactions between couplers due to the slack and inertia except in Refs. [50‐53]. Although Lu et al. [50] considered normal contact and frictional forces between coupler heads, inertia and structural stiffness characteristics are disregarded. Yao et al. [51] and Cole et al. [52] though mentioned the effect of coupler inertia; slack induced impacts and frictional transitions between couplers are not incorporated. The inertial effects of coupler contribute in interaction between coupler heads, giving rise to intermittent impacts and frictional rubbing actions [54]. Recently, Yadav et al. [53] developed a mathematical model of such a coupling system, incorporating masses of couplers. It has been shown that, there is significant difference in the estimation of in-train forces and jerks, with and without consideration of coupler masses. However, they did not accommodate relative rotation between couplers to estimate the lateral forces. Also, interaction between couplers and their respective knuckles are not modeled.

This study develops multi-body dynamic model of AAR automatic coupler systems, for numerical simulations to analyze the actual dynamics of coupling system. An attempt has been made in this study to address the implications of various slacks and inertial effects of couplers on longitudinal dynamics of rail vehicles. Multi-body dynamic models of two coupling types have been developed to incorporate rotational degree of freedom of the couplers for improved analysis of interactions between the contours of couplers and knuckles within slack regime. Knuckle clearance is also incorporated. It includes more details of a coupler system than the existing mathematical models and is able to capture the frictional transitions and the resulting lateral reaction.

Two types of AAR standard coupling systems have been analyzed. For convenience in discussions, following nomenclature is defined:Focus is on differences in dynamic behavior, predicted with and without consideration of couplers inertia. The effects of important design parameters are investigated for abovementioned couplings, and compared with those predicted using respective conventional coupling model, used in earlier studies. Particularly, the steep variations in draft gear reaction forces are analyzed, due to the intermittent impacts and friction actions, occurring in the vicinity of clearance zone. Detailed multi-body dynamic models of these couplings, incorporating inertial, geometrical and contact properties, are developed to investigate the expected dynamic behaviors of these coupler systems. Conventional mathematical models are not modeled mathematically, but they are replicated by manually assigning very small masses to the components of detailed models itself, discarding knuckles and locking together the two couplers.

An automatic coupler provides a three-dimensional mechanism to form inter-connection between rail vehicles, through its integrated component called knuckle. AAR standard automatic couplers are designated as types, “E”, “F” and “H”, based on different design (contour profiles and coupler heads) and permissible slack. AAR coupler systems can broadly, have four possible slacks: (a) contour slack, (b) knuckle slack, (c) yoke connection slack, and (d) draft gar slack. Yoke connection slack and draft gear slack arise due to wear and tear but contour and knuckle slacks are design intended slacks to deliver the desired actions. E-type couplers are characterized by highest slack, with typical design slack (contour + knuckle slack) up to 20 mm, followed by F-type couplers with design slack up to 10 mm. Both these couplers are primarily used in freight trains. In H-type couplers, popularly known as tight-lock couplers, used in passenger trains, a maximum design slack up to 3.2 mm is allowed.

Knuckle slack is provided on all AAR type couplers to avoid load transfer through knuckle pin, which is the weakest component of the assembly. Improved design and precisely machined mating surfaces of coupler and knuckle allow H-type couplers to form inter-connection utilizing knuckle slack itself, and ideally it does not require additional contour slack. The reason for avoiding excessive slack in passenger train couplers (H-type) is that slack induces longitudinal jerks and running instability during acceleration/declaration [10]. On the other hand, in freight train couplers (E and F type), additional slack in the form of contour slack is provided to control starting dynamics [9]. Moreover, excessive slack may lead to very high magnitude of jerks, sufficient to cause failure of vehicle and coupling components and may also cause train-parting. In addition, large slack can also induce additional lateral force, coupled with longitudinal in-train force. Hence, accurate analysis of influence of slacks is essential.

Various design slacks and resulting interactions of coupler components during operation are illustrated in Fig. 4. Top row of figures displays front sectional views and bottom row displays top views. Left side coupler and corresponding knuckle are omitted in front sectional views for clarity. Once, couplers are interconnected, knuckles are locked to prevent the knuckle rotation (clockwise for K2 and counter-clockwise for K1). However, a small amount of rotation of knuckles is possible in the opposite directions (counter-clockwise for K2 and clockwise for K1) because of available small slack d\(_3\), as shown in Fig. 4d. Figure 4a illustrates a random position of couplers. It can be seen that the outer diameter of knuckle pin is provided with some tolerance (knuckle slack). Although, lock inhibits unlocking of knuckle, small translational movements (Fig. 4d) of knuckles are also possible within the cavity inside respective coupler heads, due to presence of slacks d\(_1\) (omitted in Fig. 4d for clarity) and d\(_2\). A small amount of slack between faces of horn of one coupler and the corresponding cavity (wing pocket) on other coupler (Fig. 1c), allows a very small amount of relative rotation between couplers. These horn and wing features are though present in H-type and F-type couplers, there are no wing pockets in E-type couplers, allowing comparatively larger rotation between couplers, constrained by the amount of contour slack. During buff mode, knuckle transfers the force by interacting with coupler on matching contour, called buffing shoulders (Fig. 4b) and through the faces of pin protector regions. In draft mode, it transfers the load through its pulling lug contacting the pulling lug on coupler (Fig. 4c) and through the faces of pin protector regions. Thus, coupler pin does not stake any buff or draft load in a defect-free coupler system and its only function of it is to assist knuckle to rotate during mating of couplers. In this study, only design slack (contour + knuckle) has been considered. Thus, numbers of interactions are possible within coupling regime: (i) interaction of buffing shoulder (in buff mode: Fig. 4b) or pulling lug (in draft mode: Fig. 4c) of a knuckle with its own coupler, along with pin protector (ii) interaction of knuckle head with opposite coupler head (in buff mode Fig. 4e) and (iii) interaction of knuckle nose with opposite knuckle nose (in draft mode: Fig. 4f).

The focus of this study is to address the influence of coupler’s features on estimation of in-train forces, rather analyzing full train dynamics. This work is thus restricted to modeling and analysis of coupler system only. Simulations are performed using MSC ADAMS platform, using fixed time-step with sample time of \(1 \times 10^{-3}\) s.

Because of discontinuous features (slacks and dry friction) of AAR couplers, steep variations are expected in the in-train forces. Therefore, it is important to estimate the actual forces being transmitted through coupler system to the vehicles and components of coupler system.

AAR coupler systems are complex three dimensional vibration systems, with design intended slack (clearance) and comparable components masses. A railway coupler system experiences a wide range of excitation frequency, from quasi-static to dynamic. Although, at lower excitation frequencies, inertial effects are negligible, but at higher excitation frequencies, inertia of coupling components, more importantly the masses of couplers have noticeable influence. Also, the slack in these couplers induces intermittent impacts and rubbing actions. Coupler masses have noticeable effect on longitudinal reaction of draft gear, transmitted to its connected vehicle. It induces significant overshoot, almost same magnitude as applied external force, under the assumed constraints in this study. Neglecting this additional component gives under-estimated in-train forces and may provide incorrect assessment of operational and structural safety of vehicles and components. This study demonstrates the importance of consideration of important features of coupler systems for design and operational assessment of rail vehicles. Such detailed models of coupler systems, coupled with full train can be used to determine the accurate forces for structural design of couplings and vehicles.