Optimal Design of Dual Pantograph Parameters for Electrified Roads

Abstract

Electrified roads represent an emerging transportation solution in the context of global energy transition. These systems enable vehicles equipped with roof-mounted pantographs to draw power from overhead contact lines while in motion, allowing continuous energy replenishment. The effectiveness of this energy transfer—namely, the quality of pantograph–catenary interaction—is significantly influenced by the pantograph’s equivalent mechanical parameters. This study develops a three-dimensional overhead catenary model and a five-mass pantograph model tailored to electrified roads. Under conditions of road surface irregularities, it investigates how variations in equivalent pantograph parameters affect key contact performance indicators. Simulation results are used to identify a new set of equivalent pantograph parameters that significantly improve the overall quality of pantograph–catenary interaction compared to the baseline configuration. Sensitivity analysis further reveals that, under road-induced excitation, pan-head stiffness is the most critical factor affecting contact performance, while pan-head damping, upper frame stiffness, and upper frame damping show minimal influence. By constructing a coupled dynamic model and conducting parameter optimization, this study elucidates the role of key pantograph parameters for electrified roads in determining contact performance. The findings provide a theoretical foundation for future equipment development and technological advancement.

1. Introduction

Overhead-powered electrified roads enable electric vehicles to receive continuous electric power from overhead contact lines via onboard pantographs, supporting uninterrupted propulsion during motion. Outside the electrified sections, these vehicles switch to onboard energy storage systems such as batteries or capacitors to cover short non-electrified distances [1,2]. This emerging transportation solution integrates power supply infrastructure and vehicle electrification, offering clear advantages in energy efficiency, operational cost, and emissions reduction [3]. The power supply principle of electrified roads is illustrated in Figure 1, and selected operational electrical parameters are listed in

Table 1. Electrical Parameters of Electrified Roads.

Operating Parameters	Value	Operating Parameters	Value
Catenary Voltage	DC1500 V	On-board Battery Capacity	100 kWh
Loop Resistance	0.15 Ω/km	Substation Power	4 MW
Line current	1100 A	Pantograph current	240 A

.

Similarly to railway systems, the performance and safety of electrified roads depend heavily on stable and reliable contact between the pantograph and the overhead catenary system [4]. Among the factors influencing contact quality, the equivalent mechanical parameters of the pantograph—such as mass, stiffness, and damping—play a critical role in maintaining effective current collection and minimizing contact force fluctuations. The simplified parameters of the railway pantograph are illustrated in Figure 2.

Most scholars consider the pan-head mass (m₁) to be the most critical factor affecting pantograph–catenary interaction. For instance, Jin-Hee Lee et al. [5] used the response surface analysis method and the differential evolutionary algorithm to optimize the pantograph model and found that m₁ had the most significant impact on the standard deviation of the contact force among all examined parameters. J. Pombo et al. [6] applied finite element and multibody dynamics methods to construct a coupled pantograph–catenary model. Their findings indicated that increasing the m₁ led to a rise in both the maximum contact force and its standard deviation, whereas increasing the pan-head stiffness (k₁) and the lower frame damping (c₃) helped reduce the standard deviation. Jorge Ambrósio et al. [7] used a high-speed pantograph model combined with a genetic algorithm and found that increasing the m₁ raised the maximum contact force and its standard deviation, while a higher k₁ could reduce the standard deviation. Jiang et al. [8] derived the matching relationship between pantograph parameters and droppers’ natural frequencies and established a kinematic model of the pantograph–catenary system. They concluded that adjusting the m₁ and k₁ can significantly reduce pressure fluctuations between droppers and lower the standard deviation of contact pressure. Qi Wenyuan et al. [9] developed a dynamic model of a pantograph and a rigid catenary system and found that m₁ had the greatest influence on pantograph performance, followed by the upper frame mass (m₂) and stiffness (k₂), with the lower frame stiffness (k₃) having the least impact. Wu Mengzhen et al. [10] constructed a two-dimensional elastic chain suspension catenary and a three-mass pantograph model. They showed that changes in k₃ significantly affect the mean contact force; they further showed that reducing the m₁ or lower frame mass (m₃), decreasing the k₁ or k₂, and increasing damping (c₂) could improve current collection quality. Among these, the m₁ exhibited the highest sensitivity. Wang et al. [11] found that the optimal pantograph parameters varied with speed, with mass and stiffness having the most substantial impact, while damping ratio showed minimal influence. Wu et al. [12] concluded that the m₁ has a far greater influence on pantograph–catenary interaction quality than the other eight parameters. A reduction in m₃ leads to a negative change in the contact force standard deviation (Δσ), thereby improving stability. Reducing m₁ is also effective in minimizing contact force fluctuations. Ke Chen et al. [13] using finite element modeling combined with Sobol global sensitivity analysis and neural network optimization, highlighted m₁ and m₂ as key sensitive parameters, suggesting that reducing these masses can improve contact force characteristics.

However, some scholars hold differing views. Jin-Woo Kim et al. [14] used an orthogonal experimental design and identified c₃, m₃, and k₂ as the dominant factors affecting pantograph–catenary coupling. Ning Zhou et al. [15] developed a finite element model to study the influence of design parameters on contact force. Their results indicated that proper optimization of k₁ and pan-head damping (c₁) can enhance contact performance and increase allowable operating speeds. Wang Ying et al. [16] developed a multi-body pantograph–catenary coupled dynamic model using Laplace transform and numerical methods. Through single- and multi-variable optimization, they identified k₁ and frame mass as the most sensitive parameters affecting contact force fluctuations. Liu Yang et al. [17] employed a genetic algorithm targeting the reduction in the standard deviation of contact force to optimize sensitive parameters, including k₁, k₂, and c₃. Their results demonstrated a significant improvement in the dynamic performance of the pantograph–catenary system after optimization. Chen Yang et al. [18], based on a flexible pan-head finite element model, it is recommended to reduce k₂, increase k₁, and appropriately adjust m₁ and m₂ while keeping damping constant to optimize contact force performance.

It is evident that previous studies on pantograph parameter optimization have not reached a consensus, and most research efforts have focused on railway systems. These studies largely neglect the effects of road surface irregularities on pantograph–catenary interaction and do not address the unique characteristics of electrified roads. However, the inherent differences between electrified roads and railway systems impose new requirements on the operating environment of the pantograph–catenary system for electrified roads.

Table 2. Comparison of Key Differences Between Electrified Road and Railways.

	Road Surface Smoothness	Vehicle Deformation Level	Pantograph–Catenary Design
Railway System
	High smoothness	Relatively small	Single pantograph–single wire
Electrified Road System
	Inevitably uneven	Relatively large	Dual pantograph–dual wire

presents a comparative analysis of pantograph–catenary characteristics between the two systems.

As shown in Table 2, railway systems typically exhibit high track smoothness and minimal vehicle deformation. Their single pantograph–single wire configuration, combined with a stable operating environment, ensures reliable pantograph–catenary contact quality. In contrast, electrified road systems feature lower road surface smoothness, greater vehicle deformation, and a dual pantograph–dual wire structure, making them more susceptible to disturbances from road surface irregularities. Consequently, optimizing pantograph parameters becomes particularly critical for improving contact performance in electrified road applications.

To address this gap, this paper develops a five-mass pantograph model and a three-dimensional dual-contact-wire catenary model that reflect the distinct features of electrified roads. The study investigates how variations in the equivalent parameters of the pantograph affect the quality of pantograph–catenary interaction under uneven road conditions.

2. Methods

2.1. Catenary Model

The overhead catenary system continuously supplies electric power to transport vehicles and consists of components such as contact wires, messenger wires, and droppers. Its structure is complex and exhibits strong nonlinear characteristics. Finite element modeling is widely used due to its ability to capture the dynamic behavior of such systems.

In the model, Beam188 elements are used to represent the contact wire and messenger wire, while Link8 elements—which bear only tensile forces—are used to simulate the droppers. Accessories such as clamps are modeled using Mass21 point mass elements. Since the catenary system does not include lateral displacement constraints in this case, steady arms are not included in the model.

Based on the topological structure of a simple chain-type catenary, the global finite element model is constructed by assembling the mass and stiffness matrices of each component. The dynamic equation of the catenary system is expressed as:

$$M_c{\ddot{U}}_c+C_c{\dot{U}}_c+K_c{U}_c=F_c$$

(1)

In Equation (1), M_c, C_c, and K_c represent the mass, damping, and stiffness matrices of the catenary, assembled from the elemental mass and stiffness matrices of the messenger wire, contact wire, droppers, and clamps in the finite element model. F_C is the external load vector of the nodes on the catenary. $\ddot{\mathbf{U}}c$, $\dot{\mathbf{U}}c$, and $\mathbf{U}c$ denote the acceleration, velocity, and displacement vectors.

The initial shape of the catenary is determined using the negative sag method [19] to ensure the system remains in a balanced state. A schematic diagram of the established finite element catenary model is shown in Figure 3.

2.2. Pantograph Model

The pantograph is an onboard electrical device used by vehicles to collect power from the overhead contact line. It consists of contact strips, an upper frame, a lower frame, a base, and a driving mechanism.

Based on the principles of energy transfer and efficiency, the pantograph can be modeled as a dynamic system composed of lumped masses, springs, and dampers. A five-mass model is adopted to represent the dynamics of the left and right pan-heads, the upper frame, and the vehicle body, effectively capturing the system’s behavior under external excitation. The five-mass model is shown in Figure 4.

To incorporate the vehicle’s motion degrees of freedom into the pantograph model and accurately describe the dynamic response to road-induced excitations, an additional beam element is introduced beneath the lower frame mass. This element simulates the vertical displacement z of the pantograph base and the vehicle’s roll angle α, as caused by road irregularities.

Among the resulting motion components, vertical displacement z and roll angle α were selected as the dominant excitations for two reasons:

• z governs the global vertical separation between the pantograph and the catenary, directly affecting the contact force magnitude.
• α captures left–right asymmetry in dual-head, dual-wire systems, since road-induced roll motions tilt the pantograph base and cause differential displacements at the two contact points.

Other degrees of freedom, such as lateral motions, showed a smaller influence on the contact force dynamic. This selection ensures both physical relevance and model efficiency. The model is illustrated in Figure 5.

The motion equation for the five-mass pantograph model is given by:

$$M_p{\ddot{U}}_p+C_p{\dot{U}}_p+K_p{U}_p=F_p$$

(2)

In Equation (2), M_p, C_p and K_p denote the mass, damping, and stiffness matrices of the pantograph, respectively, while $\ddot{\mathbf{U}}$_p, $\dot{\mathbf{U}}$_p and U_p represent its acceleration, velocity, and displacement matrices.

2.3. Pantograph–Catenary Interaction Solution

The pantograph–catenary contact interaction is commonly solved using the penalty function method [20], in which a spring element is introduced between the pantograph and the catenary to simulate the switching behavior of the contact state. When the spring is compressed, the system is considered to be in contact; otherwise, it is considered to be separated. The penalty function is defined as:

$$F_f=\left\{\begin{array}{ll}{k}_c(z_1-z_c)\hfill & z_1>z_c\hfill \\ 0\hfill & z_1\le z_c\hfill \end{array}\right.$$

(3)

where

• F_f is the pantograph–catenary contact force,
• k_c is the stiffness of the penalty spring element, and k_c = 50,000 Nm⁻¹,
• z₁ is the vertical displacement of the pantograph head,
• z_c is the vertical displacement of the contact node on the catenary.

The equation of motion for the interacted pantograph–catenary system can be written as:

$$\left(\begin{array}{cc}{M}_p& 0\\ 0& M_c\end{array}\right)\left(\begin{array}{c}{\ddot{U}}_p\\ {\ddot{U}}_c\end{array}\right)+\left(\begin{array}{cc}{C}_p& 0\\ 0& C_c\end{array}\right)\left(\begin{array}{c}{\dot{U}}_p\\ {\dot{U}}_c\end{array}\right)+\left(\begin{array}{cc}{K}_p& 0\\ 0& K_c\end{array}\right)\left(\begin{array}{c}{U}_p\\ U_c\end{array}\right)=\left(\begin{array}{c}{F}_p\\ F_c\end{array}\right)$$

(4)

$$M\ddot{U}+C\dot{U}+KU=F$$

(5)

In this equation:

• M, C, and K are the generalized mass, damping, and stiffness matrices of the system,
• $\ddot{\mathbf{U}}$, $\dot{\mathbf{U}}$ and U are the displacement, velocity, and acceleration matrices,
• F is the generalized external force vector applied to the system.

Due to the strong nonlinearity of the pantograph–catenary interaction, analytical solutions are generally unattainable. Therefore, the Newmark-β method is employed for numerical integration [21]. This method discretizes time into small steps and recalculates the system stiffness matrix K and the contact force F_c at each time increment. The procedure is as follows:

$$U_{t+\Delta t}=U_t+{\dot{U}}_t\Delta t+[(0.5-\beta ){\ddot{U}}_t+\beta {\ddot{U}}_{t+\Delta t}]\Delta t^2$$

(6)

$${\dot{U}}_{t+\Delta t}={\dot{U}}_t+[(1-\alpha ){\ddot{U}}_t+\alpha {\ddot{U}}_{t+\Delta t}]\Delta t$$

(7)

where

• U_t and U_t+Δt are the displacement matrices at time t and t + Δt,
• α and β are weighting parameters controlling numerical damping and stability.

When α = 0.5 and β = 0.25, the method corresponds to the average acceleration method, which is unconditionally stable. By iterating these steps over time, the dynamic contact forces between the pantograph and the catenary can be effectively simulated.

3. Experiments and Simulation Results

3.1. Model Validation of the Pantograph–Catenary System

Electrified roads are still in the early stages of development. Establishing validation standards or test sections that reflect the excitation characteristics of road surfaces requires extensive preparation and verification. Consequently, at the current stage, the model validation of the pantograph–catenary system faces certain challenges. Considering that the structural design of pantographs and overhead contact lines for electrified roads heavily draws from railway systems—particularly in aspects such as contact strip materials, mechanical configuration, stiffness settings, tension levels, and wiring layouts—existing railway modeling and validation standards can serve as valuable references for current research. In accordance with the EN 50318 standard [22], the validity of the developed pantograph–catenary model is verified. The specific parameters used for the pantograph and catenary models are listed in

Table 3. Equivalent parameters of the pantograph.

Pantograph Head Parameter	Value	Upper Frame Parameter	Value	Lower Frame Parameter	Value
m1 (kg)	7.94	m2 (kg)	8.22	m3 (kg)	5.9
k1 (N/m)	6650	k2 (N/m)	13,181	k3 (N/m)	74
c1 (N·s/m)	85.31	c2 (N·s/m)	11.9	c3 (N·s/m)	67.41

and

Table 4. Parameters of the catenary model.

Contact Wire		Messenger Wire		Dropper
Young’s modulus (GPa)	120	Young’s modulus (GPa)	120	Young’s modulus (GPa)	105
Poisson’s ratio	0.3	Poisson’s ratio	0.3	Poisson’s ratio	0.3
Linear density (kg/m)	1.35	Linear density (kg/m)	1.07	Linear density (kg/m)	0.089
Tension (kN)	20	Tension (kN)	16	Catenary span (m)	50
Cross-sectional Area(m2)	151 × 10−6	Cross-sectional Area(m2)	147 × 10−6	Height between wires (m)	1.6
Dropper spacing (m)		5, 8, 8, 8, 8, 8, 5

.

Simulation results at speeds of 250 km/h and 300 km/h are compared with the tolerance ranges specified in the standard. The results confirm that the simulation model meets the standard criteria, validating the accuracy and reliability of the proposed pantograph–catenary model.

3.2. Pantograph–Catenary Contact Force Under Road Excitation

The electrified road vehicle considered in this study is a heavy-duty truck equipped with a pantograph. Vehicle dynamic responses were collected from heavy-duty coal transport trucks operating on asphalt roads near a coal mine. Based on these data, the road surface roughness was reconstructed using an inverse modeling approach. An electrified vehicle dynamics model was established in Trucksim, where the motion of the pantograph base was decomposed into translational and rotational components to obtain the excitation inputs z and α. The newly established five-mass pantograph model simulates these excitations by applying vertical displacement z and roll α to the beam element beneath the pantograph base. Under a simulation vehicle speed of 60 km/h, base excitation data collected from a section of uneven road is applied to the beam element. A comparison of the pantograph–catenary contact force before and after applying the base excitation is shown in Figure 6, while the quantitative evaluation of the contact force is summarized in

Table 5. Contact force evaluation before and after base excitation.

Static Contact Force: 80 N Speed: 60 km/h	Without Excitation	With Excitation
	Pantograph (N)	Left Pantograph (N)	Right Pantograph (N)
Contact Force during Raising (N)	91.14	155.74	128.51
Average Contact Force (N)	79.13	69.86	80.98
Standard Deviation (N)	3.25	21.96	21.74
Maximum Contact Force (N)	92.85	155.74	127.53
Minimum Contact Force (N)	72.55	22.62	21.41
Contact Loss Rate (%)	0	0	0

.

The contact force indicators show a significantly lower average contact force on the left pantograph head compared to the right. This discrepancy is primarily attributed to the uneven road surface elevation, with the left side of the vehicle experiencing a generally lower elevation than the right. This unevenness induces a vehicle roll motion, which is transmitted through the vehicle body to the pantograph base, resulting in asymmetric contact forces between the left and right pantograph heads. Such differences caused by lateral road irregularities provide a meaningful basis for evaluating the effectiveness of parameter optimization in the pantograph design.

By analyzing the contact force imbalance before and after optimization, the improvements in pantograph performance under realistic excitation conditions can be intuitively demonstrated.

3.3. Pantograph Parameter Optimization

For pantographs used in electrified roads, the increasing complexity of both the structural topology and operating conditions necessitates a re-optimization of design parameters to ensure high-quality pantograph–catenary interaction under new transportation environments. Based on the established simulation model, variations in contact force under different parameter values can be rapidly and cost-effectively evaluated. This approach enables the identification of suitable pantograph configurations tailored to the operational conditions of electrified road freight vehicles.

The DSA380 pantograph, configured with a 1600 mm extension height, is adopted as the baseline for comparison. The parameter ranges for optimization are determined based on industry experience, as summarized in

Table 6. Parameter ranges for pantograph modeling.

Pantograph Head Parameter	Range	Upper Frame Parameter	Range	Lower Frame Parameter	Range
m1 (kg)	3~12	m2 (kg)	5~14	m3 (kg)	3~18
k1 (N/m)	3000~16,000	k2 (N/m)	8000~18,000	k3 (N/m)	0.1~130
c1 (N·s/m)	0~100	c2 (N·s/m)	0~50	c3 (N·s/m)	10~210

.

The optimization of pantograph parameters should consider three major aspects: Contact force performance, Left-right contact force balance, and Engineering feasibility.

• From the perspective of contact force performance evaluation, the selection of pantograph parameters should aim to: Reduce the maximum contact force F_max, to avoid hard impacts between the pantograph and catenary, which may cause fatigue damage to the contact wire and abnormal wear of the pantograph strip; Lower the pan-up contact force F_r, in order to minimize transient disturbances to the catenary system during pantograph lifting; Decrease the standard deviation Δδ, to suppress fluctuations in the contact force; Increase the minimum contact force F_min, to reduce the risk of loss of contact (dewirements) and ensure continuous current collection.
• From the perspective of balancing left–right contact force, as shown in

  Table 7. Optimization logic for each parameter.

  Optimization Goal	Consideration Items	Optimization Trend
  1. Performance Indicators	Maximum contact force	↓ Lower is better
  	Minimum contact force	↓ Lower is better
  	Contact Force during Raising	↓ Lower is better
  	Standard deviation of contact force	↓ Lower is better
  2. Balancing Left–Right Contact	Left Pantograph Head
  	Maximum contact force	↓ Lower is better
  	Contact Force during Raising	↓ Lower is better
  	Average contact force	↑ Higher is better
  	Right Pantograph Head
  	Maximum contact force	↑ Slight increase acceptable
  	Contact Force during Raising	↑ Slight increase acceptable
  3. Engineering Feasibility	Cost of production and maintenance	Consider economical viability

  , the left pantograph head exhibits a higher pan-up contact force F_r and maximum contact force F_max, but a lower average contact force F_m than the right pantograph. Therefore, to reduce the left pantograph’s F_r and F_max, and simultaneously increase its average contact force F_m, it is acceptable to slightly increase the right pantograph’s F_r and F_max to balance the bilateral contact performance.
• From the perspective of engineering feasibility, parameter selection should also consider practical manufacturability and maintainability, aiming to reduce production and maintenance costs.

After multiple rounds of simulation experiments and significance testing for each parameter variation, the sensitivity curves of the pantograph head, upper frame, and lower frame parameters are presented in Figure 7, Figure 8 and Figure 9, respectively.

As shown in Figure 7, both the pan-up contact force F_r and the maximum contact force F_max exhibit significant sensitivity to changes in the pantograph head mass m₁. Considering optimization objectives 1 and 3, values of 4.5 kg and 6.5 kg represent non-dominated solutions for the left pantograph, while 7 kg appears to be the optimal solution for the right pantograph. When additionally considering optimization objective 2 (balancing bilateral contact force), the optimized value of the pantograph head mass m₁ is determined to be 6.5 kg.

The pan-up contact force F_r, maximum contact force F_max, and standard deviation Δδ are all highly sensitive to variations in pantograph head stiffness. Reducing pantograph head stiffness can effectively improve contact performance, which is consistent with findings in the railway field. Based on the optimization objectives, the equivalent stiffness k₁ of the pantograph head is selected as 3000 N/m. However, previous studies have shown that a decrease in k₁ leads to increased wear of carbon strips and higher electrical losses [23]. Under stochastic vibration conditions, the friction coefficient of carbon strips decreases significantly as the relative pantograph–catenary speed approaches 80 km/h [24]. Therefore, under favorable road conditions, increasing the operating speed to around 80 km/h and moderately enhancing pantograph head stiffness can effectively reduce carbon strip wear.

In contrast, a decrease in pantograph head damping increases the pan-up contact force F_r. Therefore, the equivalent damping coefficient c₁ of the pantograph head is retained at its original value of 85.31 N·s/m to maintain system stability.

As shown in Figure 8, the influence of upper frame mass m₂ on contact force is relatively complex. Considering optimization objectives 1 and 3, both 6 kg and 12 kg can be regarded as non-dominated solutions for the equivalent upper frame mass. Taking into account optimization objective 2 (balancing bilateral contact force), the optimized value of m₂ is selected as 6 kg.

To increase the average contact force on the left pantograph and reduce the standard deviation Δδ, the equivalent stiffness k₂ of the upper frame is set to 8000 N/m based on optimization objective 2.

The variation in the damping coefficient c₂ has a negligible impact on the contact force performance. Therefore, the equivalent damping is maintained at its original value of 11.9 N·s/m.

As shown in Figure 9, the variation in the lower frame equivalent mass m₃ significantly affects both the maximum contact force F_max and the rising contact force F_r. When considering only optimization objective 1, the optimal value of m₃ is 3 kg. However, under optimization objective 3, 5.9 kg and 14 kg are identified as non-dominated solutions for the left pantograph, while 5.9 kg and 13 kg serve the same role for the right pantograph. Taking optimization objective 2 into account (balancing bilateral contact force), the selected optimized value of m₃ is 14 kg.

The equivalent lower frame stiffness k₃ shows a negative correlation with the average contact force F_m. Given that the average contact force is relatively low, reducing k₃ is beneficial for improving F_m. Therefore, k₃ is set to 0.1 N/m.

The equivalent damping coefficient c₃ of the lower frame has a notable influence on both the raising contact force F_r and the maximum contact force F_max on the left pantograph. Accordingly, the optimized value of c₃ is chosen as 210 N·s/m.

3.4. Analysis of Optimization Effect

After updating the parameters m₁, m₂, m₃, k₁, k₂, k_3, and c₃ to their optimized values, the final parameter settings of the pantograph system are summarized in

Table 8. Optimized pantograph parameter values.

Pantograph Head Parameter	Optimized Value	Upper Frame Parameter	Optimized Value	Lower Frame Parameter	Optimized Value
m1 (kg)	6.5	m2 (kg)	6	m3 (kg)	14
k1 (N/m)	3000	k2 (N/m)	8000	k3 (N/m)	0.1
c1 (N·s/m)	85.31	c2 (N·s/m)	11.9	c3 (N·s/m)	210

. A comparison of parameter values before and after optimization is illustrated in Figure 10, while the changes in contact force evaluation metrics are presented in

Table 9. Comparison of contact force evaluation metrics before and after optimization.

Static Contact Force: 80 N Speed: 60 km/h	Left Pantograph Head (N)			Right Pantograph Head (N)
	Before	After	Improvement	Before	After	Improvement
Contact Force during Raising (N)	155.74	102.34	34.29%	128.51	103.96	19.11%
Average Contact Force (N)	69.86	75.21	7.61%	80.98	83.01	2.51%
Standard Deviation (N)	21.96	16.20	26.23%	21.74	16.34	24.84%
Maximum Contact Force (N)	155.74	128.17	17.7%	128.51	119.70	6.85%
Minimum Contact Force (N)	22.62	39.54	74.89%	21.41	30.48	43.36%
Contact Loss Rate (%)	0	0	0%	0	0	0%

.

As shown in Table 9, the optimized pantograph parameters exhibit favorable results. The lift-off contact force (F_r), maximum contact force (F_max), and standard deviation (δ) for both the left and right pantographs are significantly reduced, while the average contact force (F_m) and minimum contact force (F_min) are substantially increased. These improvements enhance the interaction performance of the pantograph–catenary system under uneven road conditions and improve the overall current collection quality.

When the static contact force is increased to 110 N, the comparison of pantograph–catenary contact forces before and after optimization is shown in Figure 11, and the corresponding performance indicators are summarized in

Table 10. Comparison of contact force evaluation metrics before and after optimization at 110 N static contact force.

Static Contact Force: 110 N Speed: 60 km/h	Left Pantograph Head (N)			Right Pantograph Head (N)
	Before	After	Improvement	Before	After	Improvement
Contact Force during Raising (N)	196.22	127.10	35.22%	166.56	141.74	14.90%
Average Contact Force (N)	97.96	105.12	7.31%	109.05	112.77	3.41%
Standard Deviation (N)	22.97	17.27	24.81%	22.64	17.44	23.0%
Maximum Contact Force (N)	196.22	168.75	14.00%	166.56	152.73	8.31%
Minimum Contact Force (N)	49.41	54.09	9.47%	51.87	45.08	−13.1%
Contact Loss Rate (%)	0	0	0%	0	0	0%

.

According to the simulation results, under a static contact force of 110 N, the optimized pantograph parameters significantly improved most evaluation metrics. Although the minimum contact force of the right pantograph slightly decreased, overall pantograph–catenary interaction performance was further enhanced.

When the operating speed of the electrified vehicle decreases from 60 to 40 km/h, the optimization results are shown in Figure 12 and

Table 11. Comparison of contact force evaluation metrics before and after optimization at 40 km/h.

Static Contact Force: 80 N Speed: 40 km/h	Left Pantograph Head (N)			Right Pantograph Head (N)
	Before	After	Improvement	Before	After	Improvement
Contact Force during Raising (N)	133.91	104.49	22.04%	87.98	78.09	11.24%
Average Contact Force (N)	69.36	75.59	9.00%	80.69	83.32	3.26%
Standard Deviation (N)	21.23	14.84	29.91%	20.59	14.56	29.29%
Maximum Contact Force (N)	142.25	117.46	17.43%	147.07	112.66	23.04%
Minimum Contact Force (N)	30.45	43.26	42.07%	25.29	35.42	39.98%
Contact Loss Rate (%)	0	0	0%	0	0	0%

.

As shown, the new parameter set continues to effectively improve the contact force performance, even under varying vehicle speeds.

The lifted displacement is also an important indicator for assessing contact quality. The figure below presents the contact node displacements at a speed of 60 km/h with a pantograph uplift force of 80 N.

As shown in Figure 13, the contact nodes exhibit a downward shift at higher positions, which helps reduce contact wear, while at lower positions, the node displacement increases, thereby decreasing the probability of pantograph detachment and further improving contact quality.

3.5. Sensitivity Analysis of Pantograph Parameters

Sensitivity analysis quantifies how each pantograph parameter influences contact force fluctuations, helping to identify and eliminate parameters with negligible impact on system performance. Based on the variations shown in Figure 9, the ranges of each parameter within its respective value interval were compiled, and their relationships with the contact force evaluation metrics are illustrated in Figure 14.

As shown in Figure 14, the pantograph head stiffness (k₁) exhibits the highest sensitivity within its value range, significantly affecting all evaluation metrics. In contrast, the pantograph head damping (c₁), the upper frame stiffness (k₂), and its damping coefficient (c₂) show minimal changes, indicating low sensitivity. The sensitivity ranking of each pantograph parameter is summarized in

Table 12. Sensitivity ranking of pantograph parameters.

Evaluation Metrics	Sensitivity Ranking of Parameters
Contact Force during Raising	c3 > m1 ≫ k1 ≈ m3 > m2 > k3 ≈ c1
Maximum Contact Force	k1 > c3 > m2 ≈ m3 > m1 > k3
Minimum Contact Force	k1 ≈ m2 > k3 > k2 ≈ c3
Average Contact Force	k1 > k3 ≫ c3
Standard Deviation	k1 ≫ k2 > m2 ≈ c3 ≈ m1 > m3

.

Table 12 summarizes the parameters that have a relatively significant influence on each contact force evaluation metric. Parameters not included in the ranking are considered to have negligible effects. The following observations can be drawn from Table 12:

• The lower frame damping (c₃) has the most significant impact on the rising contact force (F_r), followed by the pantograph head mass (m₁), which is clearly distinguishable from subsequent parameters. The pantograph head stiffness (k₁) and the lower frame mass (m₃) have comparable effects, while the influence of upper frame mass (m₂), lower frame stiffness (k₃), and pan-head damping (c₁) is relatively minor, with k₃ and c₁ exhibiting similar levels. Therefore, optimizing the raising contact force should focus primarily on tuning c₃ and m₁.
• The k₁ and c₃ exhibit the greatest influence on the maximum contact force (F_max), while m₂ and m₃ have comparable but lesser impacts. Other parameters show progressively weaker effects. Since F_max reflects the extreme conditions of pantograph–catenary interaction, k₁ and c₃ play a critical role in controlling it. Proper selection of these parameters is necessary to avoid excessive force that could damage components or insufficient force that could disrupt current collection.
• The k₁ and m₂ are the dominant factors influencing the minimum contact force (F_min), with significantly greater impact than k₃, upper frame stiffness (k₂), and c₃. Maintaining F_min within an appropriate range is essential for ensuring uninterrupted current collection. Optimizing k₁ and m₂ helps reduce the risk of contact loss due to insufficient force.
• The average contact force (F_m) is most strongly affected by the k₁, followed by k₃, which shows a clear difference from the influence of c₃. As F_m is a fundamental indicator of current collection performance, it is primarily governed by stiffness-related parameters such as k₁ and k₃. Adjusting these parameters can optimize F_m, balancing current quality and mechanical wear, and serving as a critical basis for parameter matching.
• The standard deviation (δ) of contact force is most affected by k₁, followed by k₂. Other parameters (m₂, c_3, and m₁) have similar but lesser effects, with the least impact observed from m₃ relatively. Since δ reflects the stability of current collection, k₁ plays a central role in minimizing force fluctuations. Optimizing k₁ is therefore critical to improving dynamic current quality and reducing the risk of contact loss.

4. Conclusions

• This study addresses the impact of road surface irregularities on pantograph–catenary interaction performance in electrified roads by developing a coupled dynamic model of the pantograph and catenary system. Road-induced excitation is integrated into the pantograph parameter optimization framework. Simulation results identify a new set of pantograph parameters that significantly improve contact force indicators under both 80 N and 110 N static contact forces, thereby enhancing system adaptability and robustness.
• Sensitivity analysis under road excitation conditions revealed that pantograph head stiffness (k₁) is the most critical factor affecting pantograph–catenary interaction, while head damping (c₁), upper frame stiffness (k₂), and upper frame damping (c₂) were found to be insensitive. Among various evaluation metrics, the raising contact force (F_r) is most influenced by the lower frame damping (c₃) and pantograph head mass (m₁), with effects far exceeding those of other parameters. With the exception of k₁ and lower frame stiffness (k₃), other parameters had negligible influence on the average contact force (F_m). Moreover, only k₁ showed a notable impact on the standard deviation (δ), underscoring its importance in ensuring stable current collection. This finding not only provides a theoretical basis for pantograph parameter design but also offers an important reference for engineering optimization of the power collection system in electrified roads.

Given the limited validation methods of the pantograph–catenary model in this study, future work will incorporate field measurements from a dedicated test section, providing a more comprehensive and reliable basis for model validation. At the same time, it is necessary for the electrified road community to gradually establish validation standards tailored to road-induced excitation characteristics.