Research

Modeling and Simulation of the Maneuverability Performance in Articulated Trolleybus for Urban Transit Applications^z,2

Kai Ma 1

Zhixiong Gao 1,2

Qitai Liu 1

Xiao Wei 1

Ming Li 1

Qiang Li 2

Huihui Bian 2,3

uihui Bian 1

1 Baotou Beifang Chuangye CO., LTD 014030 Baotou China

2 Beijing Jiaotong University 100044 Beijing China

3 Shandong Labor Vocational and Technical College 250300 Jinan China

Kai Ma ¹, Zhixiong Gao ^1,2,*, Qitai Liu ¹, Xiao Wei ¹,Ming Li ¹,Qiang Li ²,Huihui Bian ^3,*

^z,2uihui Bian, 289543062@qq.com, Zhixiong Gao, zgcmk@126.com | Baotou Beifang Chuangye CO., LTD., Baotou, 014030, China; ²Beijing Jiaotong University, Beijing, 100044,China; ³Shandong Labor Vocational and Technical College, Jinan, 250300,China.

Abstract

The research paper presents a detailed study on the maneuverability performance of an articulated trolleybus, emphasizing its suitability for urban public transportation in constrained environments. It begins by contextualizing the limitations of traditional steel-wheel trams, such as large minimum curve radii and noise issues, and highlights the advantages of rubber-tired trams, including noise reduction, flexibility, and improved passenger comfort. The articulated trolleybus, featuring a three-body modular design with power units at the ends and a trailer in the middle, employs advanced steering control strategies integrating optical and magnetic sensing with virtual track guidance to achieve precise maneuvering. The study rigorously analyzes key maneuverability metrics—minimum turning radius, sweep path width, off-tracking, and yaw response—ensuring compliance with urban road design standards, particularly a minimum turning radius of 15 meters. Using MSC ADAMS multi-body simulation software, the paper models the trolleybus’s dynamic behavior negotiating tight horizontal curves (15 m radius), S-shaped curves, and steep vertical gradients (up to 13%), revealing critical articulation angles up to 28° between car bodies and up to 16.8° between the car body and bogie, which are essential for stability and stress distribution. Simulations confirm a minimum turning radius of approximately 14 meters, with swing-out, off-tracking, and swept path widths well within safety limits, demonstrating the vehicle’s capability to navigate tight urban spaces effectively. The articulated design’s rotational freedom about multiple axes accommodates complex road geometries and uneven surfaces, while the front-axle steering control strategy ensures superior tracking performance and stability compared to rear or combined axle control. The findings provide a theoretical and practical foundation for optimizing articulated trolleybus design, highlighting their potential to enhance urban transit capacity and flexibility by enabling higher passenger volumes and improved cornering ability. The study recommends further validation through extensive simulations and real-world testing to refine control algorithms and structural components, underscoring the articulated trolleybus as a promising solution for modern, efficient, and resilient urban public transportation systems.

Article Highlights

This paper presents the fundamental design of a novel articulated trolleybus and analyzes its maneuverability performance.

A nonlinear dynamic vehicle model incorporating transverse and vertical coupling is developed using MSC ADAMS multi-body dynamics software.

The study employs MSC ADAMS to investigate articulated trolleybus operation, focusing on parameters such as body yaw angle relative to curve tangent, turning radius, trajectory deviation, and sweep width. Steering performance is evaluated under various simulated conditions to empirically validate the kinematic advantages of the articulated design.

Keywords:

Articulated Trolleybus

Rubber-Tyred Tram

Rubber Tire Bogie

Maneuverability Performance

Articulated Vehicle

1.Introduction

Urban public bus networks constitute a hierarchical, multimodal system that facilitates seamless integration across various transportation modes, thereby delivering comprehensive services to metropolitan populations. In recent years, small-scale urban rail transit has garnered significant attention within China’s economic development framework, contributing substantially to urban modernization. Steel-wheel trams, also known as streetcars or light rail vehicles, represent a critical component of urban public transportation, offering several advantages. Their moderate passenger capacity ensures a comfortable travel experience by avoiding both overcrowding and underutilization. Additionally, their low energy consumption promotes environmental sustainability, and their investment costs are comparatively lower than those of alternative transit systems. Furthermore, tram systems provide considerable flexibility in route planning, with passenger capacities intermediate between conventional buses and heavier rail systems such as subways, thus offering a balanced solution in terms of volume and service frequency.

However, steel-wheel trams face operational limitations, including a minimum curve radius exceeding 30 meters and a maximum climbing gradient below 60‰. These constraints limit their effectiveness in spatially restricted environments such as historic city streets, narrow alleys, pedestrian zones, and congested tourist areas. Moreover, noise generated at the wheel-rail interface, particularly on sharp curves, manifests as pronounced screeching due to increased vibrations, adversely affecting the urban acoustic environment and disturbing local residents.

In response, designers have increasingly advocated for the integration of rubber-tired trams within ground transportation systems. These vehicles offer benefits in noise reduction and enhanced passenger comfort, as demonstrated by innovations such as Toyo Rubber’s tires, which achieve a 75% noise reduction and maintain reliable performance across diverse road conditions. The replacement of metal wheels with rubber tires significantly attenuates noise at the rail contact interface by absorbing vibrational energy and interfacing effectively with steel components, thereby contributing to a quieter and more comfortable urban environment.

Currently, rubber-tired electric trams operate within three primary categories: monorail, automated guided rail, and track-guided rubber-tired electric tram systems. While monorail and automated guided rail systems are classified as medium-capacity rail transport modes integrating trams with dedicated track beams, they face challenges including extended construction periods, high costs, and large turning radii. Conventional buses in urban public transportation continue to encounter limitations such as restricted passenger capacity, operational complexity, and limited automation [1, 21–22]. To address these issues, Bombardier introduced the H-type guided rubber wheel tram (GLT) in 2000; NTL developed the V-type guided rubber-tired tram in 2006 [2–3]; and CRRC SIFANG Company launched the guided rubber-tired tram (GRT) in 2016 [4–6]. More recently, propelled by advances in sensor, positioning, and control technologies, several countries have investigated virtual-track-based autonomous rubber-tired electric trams. Notably, CRRC ZHUZHOU Company developed the autonomous rail transit (ART) in 2017; CRRC PUZHEN Company introduced the digital rail transit (DRT) in 2020; and CRRC ZHUJI Company created the super autonomous rail transit (SRT) in 2023, all employing virtual-track rubber-tired electric tram technology. The articulated trolleybus represents a high-capacity urban public transport solution that utilizes rubber tires on conventional roadways to provide rapid and efficient service. This system employs modular grouping technology for flexible configuration, integrates optical and magnetic sensing with computer-designed virtual tracks, and incorporates advanced control technologies to enable precise guidance and management.

Li Fu and colleagues [7–9] conducted an extensive investigation into the guiding principles of the GRT and rubber tire bogie, developing a steering system calculation model and rigorously evaluating steering equipment performance. Their results confirmed strict adherence to the Ackermann steering principle, exceptional smoothness on B-class roads, and superior curve negotiation capabilities.

Ren Lihui et al. [10–14] examined the guiding system and rubber wheel running gear of the GLT tram, simplifying the complex guide wheel-rail interaction as a unilateral spring force system with four contact points. Their study revealed that the guiding motion resembles a damped pendulum, with frequency primarily determined by the lateral stiffness of the running tires and guide rod length, and damping ratio influenced by these factors and vehicle speed.

Feng Jianghua and colleagues [15–19] studied autonomous rail transit (ART), detailing autonomous guidance components, trajectory-following control principles, and intelligent rail tram steering system modeling. Their findings demonstrated compliance with stringent response speed and trajectory accuracy requirements. They also proposed an intelligent rail virtual coupling model achieving following distances under 10 meters across speeds from 0 to 60 km/h, validated through experiments and simulations.

Hu Jihui et al. [20] investigated full-axle steering control technology for DRT, developing multi-track train models for single, double, and multi-section trams. MATLAB simulations showed that the proposed control strategy limited multi-track train trajectory deviations to within 10 cm.

KIM Kyong-il et al. [23–30] systematically outlines the research trajectory of improving the overall performance of articulated heavy vehicles (such as tractor-semi-trailers) through Active Steering Control technology. The core lies in resolving the inherent conflict between a vehicle's low-speed maneuverability and high-speed stability: counter-phase steering of the trailer wheels reduces the turning radius at low speeds, while in-phase steering suppresses yawing and rollover, thereby enhancing stability at high speeds. Evolving from early theories on self-steering axles (LeBlanc et al.) and explorations of electronic system applications (Kusters et al.), the research progressively deepened into the analysis of the mechanisms behind vehicle roll dynamics and lateral load transfer (Kamnik et al.). Building on this foundation, scholars focused on validating the effectiveness of active semi-trailer steering in improving roll stability (Cheng & Cebon) and enhancing overall safety (Cheng). This led to the development of comprehensive control strategies capable of balancing both low and high-speed performance (Kim et al.). Ultimately, through high-speed real vehicle tests (Roebuck et al.), this technology transitioned from theoretical simulation to practical engineering application, demonstrating its feasibility and significant potential as a key technology for enhancing the safety and handling of articulated vehicles.

Maciej Marcin Michałek et al. [30–31] propose a modular algorithmicapproach to kinematic modelling of nonholonomic (multi-)articulated buses, including theN-trailer vehicles as a special case, comprising a car-like prime-mover passivelyinterconnected with arbitrary number of segments (wagons/trailers) equipped with fixed orsteerable wheels, and with various locus of a driving axle in a kinematic chain. Kinematicmodels are valid under an assumption of a pure rolling of all the vehicle wheels (no skid/slipmotion), which is practically justified for the low-speed maneuvering conditions. Theproposed approach leads to compact nonlinear models which, thanks to their modularconstruction, preserve clear geometrical interpretation of velocity couplings between thevehicle segments. Derivations of kinematic models for popular structures of articulated andbi-articulated urban buses are presented for various driving-axle locus and steeringcapabilities. Experimental model validation, conducted with a full-scale wagon-drivenarticulated bus, illustrates utility of the approach.

Research on rubber-tired trams primarily addresses vehicle performance and guide wheel-rail interactions, with a central challenge being the elucidation of factors affecting guiding stability. Articulated trolleybuses, as an emerging category of rubber-tired trams, face analogous kinematic challenges, including mechanical compatibility with track-following control strategies, longitudinal force distribution, and integrated drive system development. These represent promising avenues for future research in tire-type rail transit vehicles.

This study examines the motion dynamics of articulated trolleybuses using MSC ADAMS multi-body simulation software. The degrees of freedom in vehicle movement were assessed under three conditions: negotiating a minimum horizontal curve radius of 15 meters, traversing an S-shaped curve, and ascending a 13% incline on a minimum transition curve radius of 200 meters.

2. Requirements for Maneuverability Performance

To ensure vehicular safety, maneuverability performance is engineered to comply with roadway specifications, emphasizing critical features essential for tram operation. Key metrics include turning radius, sweep path width, off-tracking behavior, and yaw rate/response characteristics.

The minimum turning radius is defined as the tightest curve traced by the centerline of the outermost front wheel at full steering lock. Sweep path width denotes the minimum clearance width required for the tram to complete a turn. Off-tracking quantifies the lateral deviation between the trajectories of the foremost leading axle center and the rearmost axle center. Yaw characterizes the angular difference between the path of the outermost wheel’s centerline and the trajectory of the vehicle body’s leading or trailing extremity. Articulated trams exhibit both front-swing and rear-swing motions during complex maneuvers.

Design Specification* (CJJ 37-2012), required curb turning radii for intersections across all road classifications are detailed in Table 1.

Table 1

Parameters of Urban Road Intersection Radii
Road Gradient	Main Road	Secondary Road	Bypass Road
Secondary road	15	15	10
Bypass Road	10	10	10

Fig. 1

Diagram Illustrating Turning Radius and Tram Turning Width

According to the *Urban Road Intersection Design Specification* (CJJ 152–2010) and the *Urban Road Engineering

This study focuses on articulated trolleybuses operating on urban arterial and secondary roads, establishing that the minimum turning radius—measured from the centerline of the outer front wheel track—should not exceed 15 meters.

During curve negotiation, each wheel follows a distinct trajectory; the inner rear wheel exhibits the smallest turning radius, while the outer front wheel exhibits the largest. Consequently, the lane width required for curved travel exceeds that for straight travel. To accommodate inward tracking of rear wheels on horizontal curves, the Urban Road Engineering Design Specifications mandate pavement widening for curves with radii less than 250 meters. Small-radius curves are common in urban road designs due to land preservation or avoidance of building demolition. Symmetrical widening relative to the design centerline is preferred, with each side receiving half of the total required widening.

3. Structural Design of the Articulated Trolleybus

3.1 Tram Composition

The articulated trolleybus features a three-body configuration: the first and third cars serve as power units equipped with steering drive axles, while the second car functions as a trailer. A gate-type steering axle is installed in the lower section of the gate-type articulated frame.

The vehicle employs a 750V DC electrical traction system with dual traction capability and a low-floor chassis design to facilitate barrier-free passenger movement. It operates autonomously on standard roadways, dedicated routes, and pedestrian zones via concealed wire guidance. Key performance parameters include a minimum turning radius of 15 meters, a maximum climbing gradient of 130‰, a maximum speed of 80 km/h, and an axle load below 11 tons.

Figure 2 illustrates the articulated trolleybus, and Table 2 details its main technical specifications.

Fig. 2

Configuration of the Articulated Trolleybus

Table 2

Principal Technical Parameters of the Articulated Trolleybus
Parameters	Technical
Maximum Operating Speed (km/h)	80
Length of the basic unit (mm)	Approximately 7,000
Width of tram (mm)	2500
Height of tram (mm)	≤ 3400
Floor height of the guest room (mm)	Approximately 220
Width of Side Door (mm)	Greater than or equal to 1300
Distance Between Bogies (mm)	The value is less than or equal to 7000.
Axle Load (t)	≤ 11

3.2 Car Body Composition

The car body comprises multiple modular units connected by a gate-type articulated frame situated between the power cars and the trailer, as shown in Fig. 3.

Fig. 3

Structure of the Multi-Body Articulated Car Body

Rubber-tire bogies are classified into steering drive axles and gate-type steering axles. The steering drive axle connects to the Mc car body via suspension and tie rods (left side of Fig. 3), whereas the gate-type steering axle mounts to the swing frame through suspension and tie rods (right side of Fig. 4).

Fig. 4

Relationship between the Car body and the Bogie

Figures 2–4 demonstrate that the Mc car body’s posture adjustment depends on steering drive axle control, while the swing frame’s attitude is regulated by steering of the driving tires via the door steering axle. The trailer body (Tp car body) connects to the swing rack via a hinge, with an electric power cylinder installed between the Mc car body, swing rack, and trailer body to lock the swing rack to the car body.

3.3 Articulation Operational Principles

The articulated trolleybus primarily operates on urban roadways where bituminous concrete compaction quality influences pavement smoothness and density. As the vehicle traverses uneven asphalt surfaces, the three interconnected car bodies experience sequential lateral tilting—front, middle, then rear—resulting in significant torsional angles at articulation points. These joints require substantial rotational freedom about the longitudinal axis to mitigate concentrated stress.

Additionally, when negotiating inclined ramps, one car body may ascend while adjacent bodies remain level, producing considerable vertical angular displacement. Thus, articulation points must permit substantial rotational freedom about the transverse axis to accommodate relative movement.

Consequently, the articulated bearing primarily enables rotation about the vertical axis while providing necessary compliance around longitudinal and lateral axes, ensuring reliable navigation through complex roadway geometries such as curves and inclines.

Fig. 5

Fixed Hinge Installation Mechanism.

Figure 5 depicts the bottom hinge with articulated bearing connections: the fixed hinge seat rotates freely about the vertical axis via Articulated Bearing 1, while Articulated Bearing 2, supported by the intermediate cradle, facilitates pivotal rotation about the same axis. This configuration affords critical rotational flexibility in horizontal and lateral directions, enabling smooth navigation.

Due to the fixed hinge’s unrestricted roll flexibility, an anti-roll device is installed between the tram body end and cradle to reduce relative roll angle. The intermediate car body exhibits considerable roll flexibility at both ends, with a triangular elastic tie rod hinge limiting relative roll motion between body and cradle. The Mc car body permits pitch movement about its cradle, with a free hinge and anti-roll device rigidly restricting roll, as shown in Fig. 6. One end of the elastic articulation attaches firmly to the intermediate car body, the other to the cradle via a joint bearing. During horizontal curve negotiation, articulation rotation occurs smoothly about bearing 1; in vertical curves, rubber deformation accommodates rotation about bearing 2.

Fig. 6

Elastic Articulation and Anti-Rolling Installation Mechanism

3.4 Steering Control Principles

Figure 7 illustrates an articulated trolleybus turning left with the front electrical power cylinder fixed and the rear cylinder free to extend and retract. The first axle controls steering; the second axle actively adjusts tire angle to follow the front axle’s trajectory, while the third and fourth axles employ passive follower steering. This constitutes the front axle control strategy.

Fig. 7

Relationship between the Car body and the Bogie.

Figure 8 shows the vehicle turning left with the rear electrical power cylinder fixed and the front cylinder free. The first axle governs steering; the second and third axles use passive follower steering, while the fourth axle actively adjusts tire angle to align with the front axle’s path. This is the rear axle control strategy.

Fig. 8

Relationship between the Car body and the Bogie.

Figure 9 depicts the vehicle turning left with Car 2’s electrical power cylinder locked and those of Cars 1 and 3 free. The first axle controls steering; the second and third axles use passive follower steering; the fourth axle adjusts tire angle to follow the front axle’s trajectory.

Fig. 9

Relationship between the Car body and the Bogie.

This analysis reveals that the four steering control forces applied to the front and rear axles correspond precisely to the four steering degrees of freedom. Each body module achieves static equilibrium, effectively decoupling lateral body movements and reducing the risk of race conditions and instability. The front axle control strategy is symmetrical, ensuring consistently high tracking performance regardless of direction. During front axle tracking, the front wheels pull the tram, enhancing stability, with all wheel tracks converging toward the front wheel, improving tracking. Conversely, rear axle tracking involves pushing the tram, compromising stability, with wheel tracks converging toward the rear wheel and degraded tracking performance. Tracking errors originating at the front axle propagate rearward, complicating correction. In combined front and rear axle tracking, the middle axles act as a boundary: the front section exhibits superior tracking, the rear section inferior. Therefore, front axle tracking is the primary control strategy, with rear and combined tracking serving as redundancies.

4. Simulation of the Car Body Movement

4.1 Theoretical Analysis

Considering the front axle, as Car No. 1 enters a horizontal curve, its portal steering axle adjusts wheel orientation. Simultaneously, the upper body rotates about the horizontal axis via the elastomeric bearing, and the lower body pivots around the horizontal rotation axis via the fixed hinge, resulting in complete body rotation (Fig. 10).

As the leading tram body enters the curve, the portal steering axle aligns wheels and body to coordinate trajectories across axles (Fig. 11), enabling subsequent sections to enter the curve sequentially and facilitating smooth exit.

At the end of vertical curve negotiation, the fixed hinge seat rotates about its bearing, the elastomeric bearing accommodates angular displacement, and the Z-shaped free hinge rotates vertically under load. This coordinated kinematic behavior permits relative vertical rotation between end and central bodies, facilitating traversal of vertical curves and smooth exit (Fig. 12).

Fig. 10

Diagram of Tram Body Entering a Horizontal Curve (1).

Fig. 11

Diagram of the Tram Body Entering a Horizontal Curve (2).

Fig. 12

Diagram of the tram body entering a vertical curve.

4.2 Simulation Analysis

A multi-unit model was developed using MSC ADAMS multi-body software. Rotary joints simulate longitudinal drawbar connections; contact elements represent frictional rolling between rubber tires and ground; springs model pneumatic suspension via air springs; elastic hinges characterize connections between elastic rubber components and free hinges.

Simulation analysis of a Tram Negotiating a Flat Curve with a radius of 15 m Radius (R15m).

Figures 10(a) and 10(b) show a maximum rotation angle of 16.7° between car body and bogie, and a peak 27.6° angle between two bodies, providing a basis for car body analysis.

Simulation of Tram Traversing a Vertical Curve with 200 m Radius.

Figures 11(b) and 11(c) indicate a minimum ground clearance of 10.4 mm at the rear body end oriented oppositely, and a maximum cradle twist angle of 2.03°, informing car body design and joint bearing selection.

Simulation of Tram Navigating an S-Shaped Curve with 15 m Radius.

Figs. 12

(a) and 12(b) reveal a maximum 16.8° angle between tram body and bogie at the front end, and a largest 28.0° twist between rear and intermediate bodies, critical for car body analysis.

Fig. 10

Simulation Results. (a) The variation in the rotational angle between Carbody No. 2 and the bogie., (b) The variation in the rotational angle between Car Body No. 1 and Car Body No. 2.

Fig. 11

Simulation analysis of the vertical curve. (a) The minimum displacement of the front damper relative to the ground clearance., (b) The junction between the end body and the cradle.

Figure 12. Simulation results of the S-shaped curve. (a) The change in the rotational angle between the first body and the bogie., (b) The variation in the rotational angle between the third body and the intermediate carbody.

(4) Simulation of a Tram Navigating an S-Curve with a Radius of 15 m Radius

Simulations assessed tram trajectory and maneuverability (Fig. 1). At maximum steering angle of 28°, results are shown in Figs. 15–18. Urban road design standards specify a lane width of 3.5 m for speeds above 60 km/h; for curves with 20 m radius, lane widening of at least 1.5 m is required to meet minimum standards.

Fig. 15

Simulation results of the calculated turning radius.

Fig. 16

Simulation results of swing-out width

Fig. 17

Simulation results of off-tracking width

Fig. 18

Simulation of the calculated swept path width.

5 Conclusion

This study employed numerical simulation to investigate the maneuverability of an articulated trolleybus, yielding the following principal findings:

- The maximum rotation angle between car body and running gear reaches 16.8°, critical for resisting lateral forces and maintaining stability during maneuvers. The articulation between two car bodies attains a maximum rotation of 28°, facilitating smooth transitions in multi-section trams. During vertical curve negotiation, the car body exhibits a minimal torsion angle of 2.03° about the cradle, indicating negligible deformation and preserving structural integrity.

- Comprehensive simulation indicates a minimum turning radius of 14.02 m, enabling efficient navigation of tight urban turns and confined spaces. Calculated parameters include an outer swing width of 0.73 m, trajectory deviation of 1.17 m, and sweep width of 3.13 m. These values demonstrate operation well within safety limits, fully complying with road safety standards regarding stability and clearance.

The findings provide a theoretical foundation for the design and optimization of articulated trolleybuses by integrating mechanical engineering and control theory concepts to address challenges such as stress distribution and energy consumption. Future research should focus on validating and refining articulated tram models through extensive testing, including simulations and on-road experiments in diverse urban environments. Demonstrations of successful path-tracking algorithms and stability control underscore the potential of these vehicles. Articulated trolleybuses offer significant promise for urban public transportation by increasing traffic capacity through higher passenger volumes per trip and enhancing operational flexibility via tight cornering and adaptability to variable demand, thereby improving efficiency and resilience in urban transit systems.

Funding

Not applicable.

Data Availability

Data sets generated during the current study are available from the corresponding author Kai Ma on reasonable request.

Clinical Trial

Not applicable.

Ethics Approval and Consent to Participate

Not applicable.

Consent for publication

Not applicable.

Competing Interests

The authors declare that they have no competing interests.

Author Contribution

Author Contributions:Conceptualization, Kai Ma and Huihui Bian; Methodology, Qiang Li; Software, Ming Li; Validation, Zhixiong Gao and Xiao Wei; Formal Analysis, Kai Ma and Huihui Bian; Investigation, Huihui Bian; Resources, Zhixiong Gao; Data Curation, Kai Ma and Huihui Bian ; Writing – Original Draft Preparation, Huihui Bian; Writing – Review & Editing, Kai Ma and Huihui Bian; Visualization, Huihui Bian; Supervision, Qiang Li; Project Administration, Xiao Wei; Funding Acquisition, Zhixiong Gao and Kai Ma.

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Modeling and Simulation of the Maneuverability Performance in Articulated Trolleybus for Urban Transit Applications 1