Abstract
A vacuum circuit breaker (VCB) operates with a mechanical mechanism that ensures rapid arc quenching, reliable protection, and current interruption in high-voltage electrical systems. Over the past few decades, numerous engineering teams and researchers have explored this issue. However, despite the importance of precise timing in VCBs, no analytical method currently exists to investigate the dynamic response of their mechanical mechanisms. Existing approaches rely heavily on numerical simulations or experimental testing, which are often time-consuming, computationally expensive, and impractical for extensive parametric studies. In this study, the time response of a VCB case study is investigated through multi-body dynamic analysis for both opening and closing conditions. Additionally, the optimal spring characteristics of the mechanism are explored, and a SolidWorks model of a manufactured VCB was created as a case study to achieve this objective. The angular relationships of the mechanism’s links were analyzed for both opening and closing actions. From these relationships, angular velocities were derived and incorporated into work-energy equations and boundary conditions from the SolidWorks model to determine the mechanism’s time response. The results indicate an opening time of 39.9 ms and a closing time of 60.5 ms.
Keywords: Medium voltage vacuum circuit breaker, Spring effects, Theoretical multibody dynamics, Opening time, Closing time
Subject terms: Mechanical engineering, Applied mathematics, Software
Introduction
Over the past decades, companies, institutions, and universities have focused on manufacturing switchgears and related equipment. However, recent research and development have shifted towards optimizing and redesigning these products within the framework of Industry 4.0. Supporting this claim, Matin et al.1 introduced a method for optimizing switchgears using artificial intelligence algorithms based on computational datasets. In another recent study, Alsumaidaee et al.2 proposed a method for fault detection in the switchgear industry. Additionally, significant developments have been made in continuous monitoring3, machine learning-based optimization of switchgear temperature rise4, remote switching systems in switchgears5, and advancements in protection, control, and power supply systems6. These advancements demonstrate that research and development in the manufacturing and monitoring systems of switchgears and essential equipment, such as VCBs, are pivotal in the industry.
In fact, VCBs are widely recognized as essential components in switchgear systems, as they must open and close all three phases within a very short duration7. To ensure a highly precise response, these devices must incorporate mechanisms that operate quickly while minimizing damage to their own components and other parts of the switchgear8. Moreover, the primary function of the VCB mechanism is to provide a fast, linear response that moves the device to open and close the contacts through linear displacement9,10. For decades, researchers have continuously sought to optimize the mechanism’s operation to achieve the best possible performance9. In fact, dynamic analysis plays a crucial role in understanding the motion behavior of components within VCBs, particularly in accurately determining the speed and acceleration of their mechanical links through energy-based formulations. While the specific dynamics of VCB mechanisms have received limited attention, similar modeling strategies have been widely applied in various engineering systems. For instance, dynamic and kinematic analyses have been used in motion platforms11 and in hybrid aerial vehicles through combined aerodynamic and control modeling approaches12.
The mechanical analysis of VCBs has been widely investigated by various engineering groups. For instance, Sun et al.13 investigated the dynamic behavior of marine circuit breakers (critical equipment on vessels) under vibrational conditions, while Li et al.14 employed finite element analysis (FEA) of various switching mechanism components to identify critical points of mechanical failure. Beyond mechanical optimizations, studies on the dynamic response of rotating systems have highlighted the impact of time-dependent misalignment on system stability. Aligned with performance troubleshooting, Choi et al.15 analyzed gas pressure within a vacuum interrupter (VI) using computational fluid dynamics in high-voltage VCBs, and Ma et al.16 aimed to reduce motor load torque by analyzing servo motor mechanism loads. Chen et al.17 explored dynamic arc parameters during short-circuit current interruption in VCBs. Additionally, Kang et al.18 optimized and analyzed a cam-spring linkage mechanism, and Zhang et al.19 enhanced solenoid valve mechanism performance and system operational speed by developing a dynamic fault analysis model for VCBs.
In VCBs, precise timing during closing and opening operations is critical to ensure proper electrical isolation and prevent faults20. Accurate timing guarantees that contacts open and close at optimal instants, thereby preserving system stability. While the velocity21 and forces22 involved in these operations are vital for effective arc extinguishing and mechanical integrity, temporal precision remains paramount for reliable operation and fault prevention. The motion mechanism, responsible for governing timing, velocities, and forces, must be rigorously engineered and maintained to ensure precise and efficient performance, ultimately enhancing the VCB’s operational efficacy and lifespan. Moreover, recent work by Matin et al.23 highlights the importance of such analysis by evaluating VCB cam stress using theoretical models, finite element simulations, and image processing of a cam deformed after 2500 cycles, revealing critical stress variations along the cam profile.
Multibody dynamics has been widely applied across various fields, including agricultural machinery design24, tribological modeling in clearance joints25, and motion reconstruction of human limbs26. These diverse applications demonstrate the flexibility and power of multibody dynamic methods in analyzing complex mechanical systems. To achieve the level of precision required in VCB operations, multi-body dynamics- the study of the dynamic behavior of mechanical systems composed of rigid and/or flexible bodies connected by joints27,28- plays a critical role in optimizing timing and force distribution. Yang et al.29 utilized multi-body dynamics theory and principal component analysis to simulate the dynamics of a high-voltage circuit breaker and determined the time and speed of the closing and opening processes. Jo et al.30 developed a multi-body dynamic model for VCBs, which they used to optimize the design mechanism involved in motion, enhancing the VCB’s opening speed by 35%. In another study, researchers improved a circuit breaker’s performance by optimizing its movement mechanism through dynamic simulation and multi-body dynamic analysis. They used Adams’s software for modeling and Visual Doc for optimization31. Another group used the multi-body dynamic method to study a circuit breaker and applied finite element analysis to enhance its durability and performance32. Duan et al.33 combined experimental testing with ADAMS-based simulation to investigate mechanical performance changes in aged 12 kV VCBs, showing that component faults correlated with speed dispersion over time. Similarly, Ahn et al.34 developed and validated a dynamic model of a spring-actuated cam mechanism, highlighting the critical role of friction in high-speed VCB motion behavior.
Despite extensive research on VCBs, there exists no analytical closed-form method that directly computes the opening and closing time responses of the spring-actuated mechanism based purely on mechanical formulations. This absence is mainly due to the complexity of modeling the dynamic interactions between links, springs, dampers, and boundaries in a multibody system—especially under realistic loading conditions. To address this gap, this study introduces, for the first time, an analytical energy-based approach that uses multibody dynamic principles to predict the time response of VCB mechanisms during both opening and closing operations. The formulation is derived from angular kinematics and implemented through the work-energy balance equations of the mechanism’s components. A notable advantage of this method is its independence from simulation tools and experimental calibration, enabling broader applicability and ease of validation. Unlike finite element or simulation-based approaches that require significant computational effort and are not suitable for extensive sensitivity analyses, the proposed analytical framework enables rapid evaluation of numerous design scenarios. Specifically, performing more than a thousand iterations by varying parameters such as spring stiffness, damping, and geometric configurations to obtain corresponding timing responses would be practically infeasible using conventional simulation or experimental techniques. However, with the developed closed-form expressions, such extensive parametric studies become computationally efficient and straightforward, allowing for a comprehensive understanding of the mechanism’s dynamic behavior. Analytical solutions like the one proposed in this study are inherently robust-they are free from numerical errors, offer clear insights into how mechanical parameters influence the dynamic response, and can serve as benchmarks for validating numerical models and experimental results. While prior works have employed experimental setups or black-box simulation models for dynamic timing analysis, these approaches often obscure the influence of individual mechanical parameters. By contrast, our closed-form analytical formulation explicitly relates timing performance to design variables, allowing for systematic design optimization. This work not only provides a methodologically sound alternative for time response prediction but also lays the foundation for future analytical investigations into high-speed mechanical actuators in power systems and beyond.
Research methods
The medium voltage VCB plays a critical role in electrical panels. Kerman Tablo Company undertook an analysis to design and manufacture a VCB switch with optimized performance. All the tasks performed in this study, focused on determining the operating time and identifying the key and critical parameters, both in formulating and fitting the appropriate equations to obtain the solution and in analyzing the results, are presented in the flowchart shown in Fig. 1, the switch designed and manufactured by our company is shown in Fig. 2. The main springs used in the VCB mechanism, which play a crucial role in the operation time, include a tension spring and two compression springs coupled in parallel. The spring stiffness was measured using a uniaxial testing machine, as shown in Fig. 3, the reported stiffness values are 18,248
and 24,637 
for the double compression springs and 6,364 
for the tension spring. To ensure the presented mechanism was consistent with the physical prototype, all components were manufactured according to the specified dimensions. The material assignment for each component in the model is shown in the Table 1.
Fig. 1.
Flowchart illustrating the methodology adopted in this study.
Fig. 2.
The case study of the VCB: (a) designed and modeled; (b) manufactured.
Fig. 3.
The tension and compression springs used in the case study subjected to uniaxial: (a) tension, (b) compression.
Table 1.
The materials of VCB Components.
| Component | Material |
|---|---|
| Main Body and Primary Shafts | ST37 steel |
| Seats of the Shafts | CuFe3Al9 |
| Arms Linking the Shafts to the Interrupter | Aluminum |
| Push Button and Other Polymeric Components | Acrylonitrile Butadiene Styrene (ABS) |
| All springs | Stainless Steel CK75-1.1245 |
The model includes all manufactured components assembled according to their physical configuration. To simplify the computational model while maintaining fidelity to real-world behavior, the following mates were applied in SolidWorks:
Concentric mates: Used for shafts and pins to simulate rotational alignment. Coincident mates: Applied to planar faces and assembled sheet metal parts to eliminate relative motion.
Distance mates: Applied to components with fixed separations, such as parts mounted on the main shaft.
Limit mates: Used to restrict motion within predefined ranges, corresponding to mechanical stops.
Tangent mates: Applied to contacting surfaces to simulate sliding or rolling interactions.
This section first focuses on calculating the kinematic relationships between the links in the operating mechanism in Sect. 2.1, followed by the kinetic calculations for these links in Sect. 2.2. By deriving the kinematic relationships of the mechanism’s links in Sect. 2.1 and incorporating them into the energy equation developed in Sect. 2.2, the relative displacement and velocity of all links with respect to one another throughout the opening and closing processes can be determined.
Kinematic analysis in VCBs for closing and opening
Closing is a process in which the connection inside the VI is made, and the switch is in the closed position; in the opening process, the connection between the movable and fixed contacts is broken, placing the switch in the open position. Establishing contact within the VI requires the movable contact to approach the fixed contact, which depends on the motion of the mechanism’s links. The procedure begins by relating the angles within the switch mechanism using kinematic equations. In this context, the operating mechanism is analyzed differently for closing and opening processes.
This section presents a comprehensive derivation and explanation of the equations governing the closing process, which can also be generalized to describe the opening process. In both opening and closing processes, the objective is to establish a kinematic correlation among the levers of the mechanism. Ultimately, this enables the angular position and angular velocity of each lever in the closing phase to be expressed as functions of the linear displacement and linear velocity of the double compression springs, and in the opening phase, as functions of the linear displacement and linear velocity of the tension spring.
During closing, VCB is divided into four sub mechanisms, including two three-bar mechanisms and two four-bar mechanisms. For opening, the mechanism consists of one three-bar mechanism and two four-bar mechanisms. Figure 4 illustrates the case study during the closing process, highlighting the three-bar mechanism, which serves as the driver for the entire system. In this figure, the direction of motion for each link is indicated by an orange arrow. The length of the double compression springs in the three-bar mechanism is labeled as 
on the three-bar mechanism. To capture the main goal of this study, it was made to present the kinematic parameters of the mechanism were presented in terms of the length and the rate of the double compression springs. As shown in Fig. 4, 
, 
, and 
represent the lengths of the links, while 
and 
denote the angles of the links 
and 
was considered as ground. Applying the cosine law equation to the three-bar mechanism will give:
Fig. 4.
The driving mechanism in the switch is likened to a three-bar mechanism with a slider.
 |
1 |
 |
2 |
It is notable that using Eq. 1 parameters 
and 
are determined in terms of 
. Also, the time derivative of Eqs. 1 and 2 gives:
 |
3 |
 |
4 |
where 
, 
and 
are the linear velocity the angular velocity of the link 
and the angular velocity of the link 
, respectively. Using Eq. 2, the angular velocity 
is determined in term of the linear velocity 
.
Figure 5 illustrates the second mechanism in the closing process, modeled as a four-bar mechanism. In this mechanism, 
, 
, 
, and 
represent the lengths of the links, while 
, 
, and 
indicate the angles of links 
, 
, and 
relative to the ground. Here, since links 
and 
rotate on a single shaft, their angles maintain a constant relationship relative to each other. For this mechanism, 
is an input parameter, and it should determine two angles,
and 
.
Fig. 5.
The first four-bar mechanism in the switch for the closing process.
Two kinematic relations, parallel and perpendicular to the ground of the four-bar mechanism, can be expressed for this mechanism, as shown in Eqs. 5 and 6.
 |
5 |
 |
6 |
By eliminating the angle 
from the mentioned equations and using relations Eqs. 3 and 4, angle 
can be determined as a function of 
, and angle 
can be expressed in terms of angles 
and 
, as presented in Eqs. 7 and 8.
 |
7 |
 |
8 |
The time derivative of the Eq. 7 gives the angular velocity of the link e (Eq. 9) in terms of the angular velocity of the link 
and the angular velocity of the link 
(Eq. 10) in terms of the angular velocities of the links 
and 
and the other kinematics parameter of mechanism.
 |
9 |
Next, for the three-bar and four-bar sub mechanisms shown in Fig. 6, labeled as numbers 3 and 4, kinematic relationships can be derived similar to Eqs. 3–9, allowing the angles to be interconnected.
Fig. 6.
The three-bar and four-bar mechanisms (3 and 4) used in the operation mechanism of the case study for the closing process.
Figure 7 illustrates the mechanisms involved in the switch operation during the closing process, which are identified in the case study. Now, by deriving the angular relationships of the mechanism, all angles are continuously related to each other from 
to 
, and angle 
is expressed as a function of 
, which represents the extension of the double.
Fig. 7.
The mechanisms of 1, 2 and 4 in the closing process, including the springs.
compression springs. As previously mentioned, the equations derived for the four-bar and three-bar sub-mechanisms in the closing process can similarly be applied to the opening process using the same approach. Figure 8 illustrates the two four-bar mechanisms and the one three-bar mechanism involved in the operating mechanism for the opening process, labeled as 1, 2, and 3. In this figure, the motion of each link is indicated by an orange arrow on each link.
Fig. 8.
The first and second four-bar mechanisms and the three-bar mechanism within the operating mechanism for the opening process.
Kinetic analysis in VCBs for closing and opening
The angles of the links and their angular velocities can be expressed in terms of the length and the spring extension rate, for both closing and opening processes. The only unknown is the spring release rate, denoted as 
for closing and 
for opening. At this point, by applying the principle of conservation of energy, which states that the energy in the initial state equals the sum of the stored energies in the secondary state, the angular relationships that expressed in terms of the parameter 
and 
for closing and opening, respectively, are related to the angular velocity relationships expressed in terms of 
and 
. Ultimately, deriving the velocity of links 
and 
results in the velocities of all the links.
The energy equation for the entire mechanism in the closing operation is expressed as:
 |
10 |
where 
and 
represent the energy at the initial moment before motion, and the energy at time 
. The energy at time 
includes: the total energy of the double compression springs, the tension spring, the spring inside the VI, and the spring mounted on the main shaft.
And the energy at the time 
is:
 |
11 |
where, 
,
,
and 
represent the total potential and kinetic energies of the first (three-bar), second (four-bar), third (three-bar), and fourth (four-bar) sub-mechanisms, respectively, at time . 
is the current energy of the double compression springs, the tension spring, the spring inside the VI, and the spring mounted on the main shaft, at time t. The energy equations corresponding to each link of the mechanism are presented in Table 2 for the closing process and in Table 3 for the opening process. The notation for each link or spring used in the tables is derived from the represented figures.
Table 2.
The energy equations for the links and springs involved in the mechanism during the closing process.
| Link label | Energy equation | ||
|---|---|---|---|
|
Gravitational potential energy | Kinetic energy | Spring energy |
| Sub-mechanism 1 | |||
|
|
|
|
|
|
|
|
|
|
|
|
| Sub-mechanism 2 | |||
|
|
|
|
|
|
|
|
|
|
|
|
| Sub-mechanism 3 | |||
|
|
|
|
|
|
|
|
|
|
|
|
| Sub-mechanism 4 | |||
|
|
|
|
|
|
|
|
|
|
|
|
| Damper | |||
|
|
||
| Vacuum interrupter’s spring | |||
|
|
||
Table 3.
The energy equations for the links and springs involved in the mechanism during the opening process.
| Link label | Energy equation | ||
|---|---|---|---|
|
Gravitational potential energy | Kinetic energy | Spring energy |
| Sub-mechanism 1 | |||
|
|
|
|
|
|
|
|
|
|
|
|
| Sub-mechanism 2 | |||
|
|
|
|
|
|
|
|
|
|
|
|
| Sub-mechanism 3 | |||
|
|
|
|
|
|
|
|
|
|
|
|
| Damper | |||
|
|
||
| Vacuum interrupter’s spring | |||
|
|
||
In which 
represents the mass of the link; 
is the height relative to the initial position; 
shows the mass moment of inertia; 
demonstrates the angular velocity; 
is the stiffness of the corresponding spring; 
shows the amount of deformation in the double compression springs or other relevant springs; 
is the linear velocity of the double compression springs, and 
denotes the displacement of the link’s center of mass.
In which 
is the linear displacement of the tension spring, and 
represents the linear velocity of the tension spring, while the other parameters are similar to those in the closing process, except that they are denoted with a prime symbol, indicating that they correspond to the opening process. In the energy equations used, the only unknown is the velocity of 
in the closing process and the velocity of 
in the opening process. Once these velocities are determined, the angular velocities of all other links in both processes can be obtained, since, as previously mentioned, all the equations, whether related to angular positions or their derivatives (i.e., angular velocities), are continuously interconnected.
Results and discussion
In this study, the operating time of a VCB is obtained using an analytical method, providing precise calculations of the time required for both closing and opening processes. This method offers a reliable approach for evaluating the performance of the mechanism, ensuring accuracy in the timing of each link. The analytical results serve as a reference point for comparing other research works, allowing for the verification and validation of their findings. using this method, discrepancies in previously reported operating times can be identified, ensuring the consistency and reliability of VCB performance studies.
In research methods, the angular relationships and velocities in the switch mechanism were derived for both the closing and opening processes. For example, the definition of velocity will yield:
 |
12 |
where 
, 
and 
represent angular velocity, angular displacement, and time interval, respectively. By having the values of the velocity in terms of kinematics for each of the mechanism’s links, the operational time for each link can be calculated and compared.
Figure 9 illustrates the curve 
versus 
for link 
in the second sub-mechanism during the closing process. Similarly, Fig. 10 presents the curve of 
versus 
for link 
in the first sub-mechanism during the opening process, where the area under the curve represents the system’s operating time. For a shaded element in the Figs. 9 and 10, its area represents 
, and by integrating over the entire area under the curve, the operating time can be obtained. Using the mentioned method for all the effective links in the closing and opening processes, the operating times for all links are obtained, which are equal. This consistency confirms the accuracy of the equations used, and the operating time was determined to be 60.5 ms for the closing process and 39.9 ms for the opening process across all links.
Fig. 9.
Time extraction method from the 
vs. 
. curve for the second four-bar sub-mechanism during the closing process.
Fig. 10.
Time extraction method from the 
vs. 
curve for the first four-bar sub-mechanism during the opening process.
In general, numerous studies have been carried out in this field. Due to variations in the displacement stroke of both the vacuum interrupter and the operating mechanisms of the switches, the operating times differ to some extent. Nevertheless, the available literature indicates that, in most cases, the closing time is less than 100 ms, while the opening time is less than 60 ms. These values are broadly consistent with the findings of the present study, which determined operating times of 60.5 ms for closing and 39.9 ms for opening. A number of these studies, which have determined the operating time either in VCBs or in circuit breakers using software-based and experimental approaches, are summarized in Table 4.
Table 4.
Closing and opening times of the mechanism as reported in selected studies.
Li et al.14 investigated the operating performance of different spring arrangements in the operating mechanism of a VCB. Yang et al.32 presented the results of their research on the operating performance of VCB. Chen and Xin35 handled dynamic analysis and end link velocity mounted on the VI of a 12 kV VCB. Fei et al.36 investigated the operating performance of high-voltage VCB. Duan et al.37 carried out experimental studies on a VCB. Ahn and Kim34 employed the ADAMS software simulation to investigate a high-speed circuit breaker in another work. Kang et al.38explained the operating performance of a 170 kV VCB, and Tang et al39. performed experiments on a 35 kV VCB, obtaining results very similar to the current study.
The variations in operating times quoted in different studies (Table 4) are due to several reasons. The rated voltage and circuit breaker class are the initial factors. Higher-voltage VCBs have larger sizes and heavier mechanisms, so they take more time to operate. Second, the character and design of the operating mechanism matter. Spring-actuated, hydraulic, or pneumatic mechanisms affect performance, as do the preloading and stiffness of springs. Third, differences arise from the nature of the inquiry. Experimental measurements are influenced by friction, clearances, and ambient conditions. In contrast, numerical simulations tend to provide more idealized and faster responses. Fourth, requirements such as link dimensions, the weight and inertia of moving parts, and material quality differ between studies, leading to different outcomes. Fifth, the intended operational demands are not always the same. Some circuit breakers are designed for fast operation, while others prioritize longevity and reliability over speed. Finally, test and environmental conditions-such as temperature, humidity, and mechanical wear-can also contribute to these differences.
Among the studies that examined the operating time for both opening and closing processes, one was identified40 in which the VI travel stroke measured 0.022 m, close to the 0.025 m used in the present work. In this study, the displacement-time curve of the moving contact during the closing process was obtained experimentally. This curve was extracted and compared with the displacement-time curve of the moving contact of the VI in the present study, and the percentage of error or the difference between the two curves is represented by the coefficient of determination (R²), which serves as the evaluation criterion. The comparison showed a high degree of similarity, with the two curves nearly overlapping, thereby providing validation for the present work (Fig. 11). Moreover, given that the methodology used to derive the equations for closing and opening is identical in this study, the results for the opening process can also be considered valid.
Fig. 11.
Comparison of contact displacement during the closing process between the present work and Dong et al40., including the deviation curve (Present – Dong) and the coefficient of determination (
).
The results and discussion of this study commence in Sect. 3.1, where the motion kinematics of the mechanism’s links are analyzed using analytical equations and coded in Maple software to obtain results. Section 3.2 focuses on the role of the springs within the switch and evaluating their impact on the closing and opening times. The data and figure indicate that these times can be fine-tuned to acceptable links and adjusted to meet the intended target.
Kinematics of links
In this section, Fig. 12 illustrates the following: Part (a) shows the first three-bar sub-mechanism labeled as number 1, Part (b) displays the second three-bar sub-mechanism labeled as number 3, Part (c) presents the angular velocities of the links of these two sub-mechanisms, and Part (d) depicts their angular accelerations of the links, during the closing process. Here, the parameter 
represents the angular velocity, while the parameter 
denotes the angular acceleration in the closing process. The subscript of each parameter refers to the angular velocity of the specific.
Fig. 12.
The first and third three-bar sub-mechanisms; (a) first sub-mechanism, (b) third sub-mechanism, (c) angular velocity diagrams of the links, (d) angular acceleration diagrams of the links.
link it represents. The plot (c) depicts the angular velocity 
of selected links as a function of time, showing distinct profiles that converge at a defined closing time of t = 60.5 ms, indicated by the red dashed line. The plot (d) illustrates the angular accelerations 
of the same links, capturing their dynamic behavior during the closing operation. Peaks in acceleration correspond to critical moments in the mechanism’s motion. In Fig. 12, 
remains nearly constant, with only a slight variation. Considering the movement mechanism, it is observed that the direction of motion of the double compression springs relative to the ground remains almost unchanged. As a result, the angular velocity remains nearly constant. The angular velocities and accelerations of the links 
, 
and 
show that after approximately 30 ms, their speeds and accelerations begin to change rapidly. This is because, within the first seconds to around 30 ms, a great deal of the spring energy is spent on overcoming inertia and initiating the motion of the links from the resting position of the mechanism. As with the switch operating mechanism, this stored energy must initiate the motion of several varying links. Furthermore, the curvature of the curves of links 
and 
is also varied. The reason for this is that counterclockwise rotation is positive, whereas clockwise rotation is negative. As shown in Fig. 12a, the link 
translates in a clockwise direction and link 
translates in a counterclockwise direction, and these are expressed as rising positive and negative accelerations of the individual links.
Figure 13 illustrates a four-bar mechanism, with a focus on the kinematic analysis of its link velocities and accelerations. The upper section (a) shows the mechanism’s design and integration into the VCB, highlighting its components and geometry. The lower plots display the angular velocities (b) and accelerations (c) of selected links as functions of time during the closing operation. The velocity plot reveals dynamic behavior with curves converging at t = 60.5 ms, while the acceleration plot captures key peaks. This analysis demonstrates the mechanism’s effectiveness in achieving smooth and efficient motion. As shown in Fig. 13, in this mechanism, the motion of links is controlled by the forces transmitted from previous sub-mechanisms. At the initial stage (approximately 0–20 ms), the effective link arms of the links are relatively small. This limits the torque applied and results in low angular accelerations. As the mechanism progresses and the configuration of the links changes, the effective link arms increase in length. This produces larger torques. As a result, there is a noticeable increase in the angular velocity and acceleration of link 
. In contrast, links 
and 
move in the opposite direction. This shows the redistribution of motion within the mechanism. After about 30 ms, the arrangement improves the mechanical advantage and explains the sharp increase in acceleration seen in the curves. Although damping and friction effects partially lessen these rapid changes, they do not eliminate them.
Fig. 13.
The second sub-mechanism in the closing process; (a) schematic of the mechanism, (b) angular velocity diagrams of the links, (c) angular acceleration diagrams of the links.
Subsequently, the angular velocities and accelerations of the links in sub-mechanism 4 during the closing process can be observed in Fig. 14. In the fourth sub-mechanism, at the onset of closure, the mechanical link arms are short. This results in reduced transmitted torque and negative angular velocity trends for links 
and 
. As the geometry evolves and the moment arms lengthen, the link 
maintains a steadier, positive motion. After about 30 to 40 ms, increasing the mechanical advantage accentuates the differences in motion rates. This is evident from the angular velocity curves (Fig. 14b) and angular acceleration curves (Fig. 14c).
Fig. 14.
The second four-bar sub-mechanism in the closing process; (a) schematic of the mechanism, (b) angular velocity diagrams of the links, (c) angular acceleration diagrams of the links.
The velocities and accelerations of the link motion during the opening process were also analyzed. Figure 15 illustrates the angular velocities and accelerations for the links of the first sub-mechanism, which is a four-bar linkage, in the opening process. Here, the angular velocities, angular accelerations, and parameters related to the opening mechanism are indicated with a prime superscript. The left graph highlights the velocity profiles, where 
, 
, and 
converge at t = 39.9 ms, as indicated by the red dashed line. Similarly, the right graph shows the acceleration profiles (
, 
, 
), where 
exhibits a sharp peak before stabilizing. The velocity and acceleration diagrams of the links in this mechanism can be understood by looking at the geometry, the motion of the links, and the role of the tension spring. In the initial stage, which lasts until about 30 ms, the energy stored in the tension spring is released. This energy mainly helps overcome initial inertia and starts the motion of several connected links, resulting in relatively low velocity and acceleration. As the process goes on, this stored energy gradually moves to the links, causing a growing increase in velocity. In the final stage, around 40 ms, the angle between the applied force and the link arm changes. This effectively shortens the moment arm. This geometric change improves the mechanical advantage. Even though the spring force drops, the output acceleration rises quickly. As shown in the diagrams, the terminal link, with its low moment of inertia and unique geometric shape, experiences the largest jump in velocity and acceleration. Therefore, the peaks in the late stage come from both the energy accumulated in the tension spring and the geometric features of the mechanism.
Fig. 15.
The first sub-mechanism in the opening process; (a) schematic of the mechanism, (b) angular velocity diagrams of the links, (c) angular acceleration diagrams of the links.
Figure 16 shows the angular velocities and accelerations for the second four-bar sub-mechanism during the opening process, where it can be observed that the link 
experiences a direction change at approximately 25 ms. In this sub-mechanism, the energy stored in the tension spring first goes into overcoming inertia and starting the motion of the links. This results in relatively low speeds and accelerations. As the spring keeps releasing its energy, the overall effect leads to more link motion. Around 40 ms, due to changes in angle and the effective shortening of link arms, the mechanical advantage increases significantly. As a result, the acceleration of the link 
rises quickly, while the link 
experiences more moderate changes. This behavior comes from the combined effects of the tension spring energy and the geometric arrangement of the links.
Fig. 16.
The second sub-mechanism in the opening process; (a) schematic of the mechanism, (b) angular velocity diagrams of the links, (c) angular acceleration diagrams of the links.
other studies have been conducted in this field. Yang et al.32 investigated the speed of the movable contact in a high-voltage circuit breaker through experimental and simulation methods. They reported the speed as 4.8 
during closing and 9.2 
during the opening. Zhang et al.19 reported the maximum speed of the moving core in the mechanism of a VCB as 5.39 
With an operating time of 10.8 ms. The maximum speed of the moving contact in the present study is 0.53 
during closing and 0.79 
during the opening. As observed, there is a significant difference in the speed values of the movable contact between this study and the study conducted by Zhang et al.19. This discrepancy arises because the circuit breakers analyzed by Zhang et al.19 exhibit a shorter operating time than the VCB analyzed in this study.
Springs’ effects on VCB timing
In the closing process examined in this study, two compression springs were used to activate the mechanism and establish contact with the VI. These springs, arranged in parallel, have different free lengths. The force or energy stored in the springs is influenced by several factors, including their stiffness, free length, and the value of compression from their free state. In response to the question of whether the designer should use a single spring or double springs to supply the energy required for the mechanism’s motion, the energy variations in both scenarios were analyzed. Additionally, the effects of the spring acting as a damper were investigated, and it was observed that changes in its stiffness had a negligible impact on the operating time in both the opening and closing processes. The first scenario involves the use of a single compression spring alone, while the second scenario considers the use of double springs with different free lengths for the double springs. In the double compression spring configuration utilized in the VCB of this study, the springs are coupled in parallel, compressed equally, and exhibit different stiffness levels. In this regard, Eqs. 13 and 14 were formulated, where Eq. 13 represents the energy of the double springs in the initial state, and Eq. 14 represents their energy in the final state. By equating these values with the energy equation for a single compression spring, defined by its stiffness and compression in the initial and final states, the equivalent stiffness and free length of the single compression spring can be determined. In Scenario Two, by selecting different free lengths for each of the double compression springs, the equivalent stiffness required to satisfy the energy needs can be determined and analyzed. This allows for an investigation of the differences and effects that arise from varying the free.
lengths of the springs. By performing this procedure, it is possible to determine various combinations of stiffness and free lengths for each of the double springs and analyze the effects. Specifically, when the energy values at the beginning and end of the interval remain constant, the influence of variations in stiffness and free lengths of the double compression springs on the energy release rate can be examined.
 |
13 |
 |
14 |
where 
represents the energy stored in the double compression spring, 
and 
express the stiffness value each of the double compression springs,
and 
indicate the compression of each double spring relative to its free length at the initial moment, and 
and 
express the compression of each double spring relative to its free length in the final state. The energy values for the double springs in the initial and final states, presented in Eqs. 13 and 14, are expressed in joules. Additionally, the corresponding free lengths of the springs for these energy values are 0.1852 m and 0.1475 m, respectively.
Figure 17 illustrates the energy release rate for two scenarios: one utilizing double compression springs and the other an equivalent single compression spring. In the case of using double springs, 166 scenarios were examined, where the free length of each spring varied within a 0.090 m range from 0.100 to 0.190 m relative to each other. The equivalent stiffness was calculated based on these varying configurations. As shown in Fig. 17, the energy rate curve for the single equivalent spring overlaps with that of the double springs across all configurations of the double spring usage. This result indicates that for the energy required to move the mechanism and establish contact within the VI, there is no difference in the energy release rate between using single or double spring and it can be stated that, in this context, only the amount of energy stored in the springs in the initial and final states is significant, while the manner in which the stored energy is released from the springs is of little importance. In VCBs, compression double springs and tension springs are crucial for regulating the closing and opening times. Optimizing and right selecting these springs can help minimize losses in the VCB’s operational mechanism and prevent damage.
Fig. 17.
The energy release rate for double compression springs with 166 different free length configurations and their equivalent single compression spring.
In another analysis presented in Fig. 18, the relationship between the energy of compression double springs and the tension spring over closing and opening time is studied. This allows the designer to select springs based on the energy needed for the switch mechanism’s operation. This provides an advantage compared to the previous version. Constants can reduce mechanical losses and wear on VCBs. Such as, a closing time of 40 ms requires 391 joules of energy in the compression double springs and 54 joules of energy in the tension spring, while a closing time of 21 ms requires 1089 joules of energy in the compression double springs and 82 joules in the tension spring. Figure 19 presents the required energy values for the double compression springs and the tension spring at several operating times during the closing process, which can be considered as data points derived from multiple cases shown in Fig. 18.
Fig. 18.
The relationship between the variations in the energy of the double compression springs and the tension spring with the operational time during the closing process.
Fig. 19.
The relationship between the stiffness of double compression springs and tension springs with the operational time during the closing process.
Figure 20 examines the impact of tension and compression springs on the operating time of the mechanism under two scenarios. In scenario (a), the stiffness of the tension spring is fixed at three constant values, while the stiffness of the equivalent compression spring varies. In scenario (b), the stiffness of the equivalent compression spring is fixed at three constant values, while the stiffness of the tension spring varies. Here, the free length of the equivalent compression spring is set to 0.1633 m, and the free length of the tension spring is set to 0.0875 m. For instance, to achieve a closing time of 60 ms with three fixed stiffness values, 3000, 6500, and 10,000 
for the tension spring, the corresponding effective stiffness values 31,237, 47,372, and 61,663 
for the equivalent compression spring are required accordingly. Conversely, in case b, the equivalent compression spring stiffness is held constant, and the tension spring stiffness is adjusted. The presented charts depict three scenarios where both the tension and compression spring stiffness remain fixed. Based on Fig. 20 (b), it can be observed that since the slope of the red curve (
=60000 
) has nearly stabilized, the tension spring can ultimately have a maximum stiffness of 10,585 
. Any stiffness beyond this value would indicate that the equivalent compression spring is unable to overcome the tension spring.
Fig. 20.
Relation between: (a) the equivalent compression spring (
) and closing time (
) for 3 stiffness of the tension spring, (b) the stiffness of the tension spring (
) and closing time (
) for 3 equivalent compression spring stiffness (
).
In another analysis of the obtained results, aimed at assisting designers in selecting and designing a suitable spring to achieve the desired closing and opening times, a table entitled ‘Parameter Selection’ is provided in Fig. 21. In this table, 
the closing operating time, 
the opening operating time, 
the stiffness of the double compression springs, and 
the stiffness of the tension spring in the operating mechanism is presented. The free lengths are considered as 0.1852 m and 0.1475 m for the double compression springs, and 0.0875 m for the tension spring. This table assists designers in selecting suitable springs that match the operating mechanism, whether in VCBs or other circuit breakers. On one hand, the spring specifications can be directly selected from this table; on the other hand, by knowing the free length and displacement of each spring, where the compression of each double compression spring at the moment of energy release is 0.0388 m and the extension of the tension spring is 0.0622 m, the energy stored in each spring can be calculated. With the required energy for operating the mechanism known, a balance between the free length and stiffness of the springs can be achieved, allowing the free length to be determined once the stiffness is chosen, and vice versa.
Fig. 21.
Design parameter selection table for VCB spring stiffnesses.
Figure 22 illustrates the relationship between tension spring stiffness (
) in 
and the operation time in milliseconds by keeping the free length and the amount of elongation constant, during the VCB opening process. The red region indicates values of 
that fall outside the effective range for optimal operation. As 
increases, the operation time decreases significantly, emphasizing the tension spring’s key role in contact separation and current interruption. Proper selection and optimization of 
are crucial for reducing operation time and improving VCB performance.
Fig. 22.
Tension spring stiffness versus opening time.
Conclusions
In summary, this paper investigated the time response of a VCB case study using an analytical multi-body dynamics approach. Moreover, an analysis of the springs and damper in the mechanism showed that the damper does not significantly affect the timing or motion. In contrast, the tension and compression springs are key in determining how the mechanism operates. Therefore, a sensitivity analysis focused specifically on the main springs, including the tension spring and the compression springs, was conducted under both opening and closing conditions. In this study, by applying kinematic equations to the sub-mechanisms within the main mechanism, the angular relationships between different links were determined. Subsequently, the angular and linear velocities were calculated by differentiating the angular relations. Finally, with the velocity and displacement variations of all mechanism links determined, the operating time was obtained using a fully analytical approach. The key findings of this study will be detailed as follows:
• The operating times of a 12 kV VCB mechanism were analytically determined as 39.9 ms for opening and 60.5 ms for closing. These values align with previous findings, which generally report closing times under 100 ms and opening times under 60 ms.
• With free lengths fixed at 0.1633 m (compression) and 0.0875 m (tension), and displacements of 0.0388 m and 0.0622 m, achieving a 60 ms closing time requires matched stiffness values. For tension springs of 3000, 6500, and 10,000 
, the equivalent compression spring must be 31,237, 47,372, and 61,663 
, respectively. If the compression spring is 60,000 N/m, the tension spring should not exceed 10,585 
.
• The energy release rate remains virtually identical when using double compression springs- tested over 166 configurations with free lengths ranging from 0.100 to 0.190 m- or an equivalent single spring. This shows that, for achieving the required motion and contact in the VI, the decisive factor is the total stored energy in the springs, not the way it is released.
• A parameter selection framework was established to assist designers in selecting springs that meet the desired closing and opening times. By considering the specified free lengths - 0.1852 m and 0.1475 m for the double compression springs, and 0.0875 m for the tension spring- along with their corresponding displacements at energy release (0.0388 m compression and 0.0622 m extension), the energy stored in each spring can be calculated. This approach allows for the direct determination of appropriate stiffness values or enables adjustment of the free length and stiffness to achieve the required operating energy.
For further investigation, the equations and methods developed in this study can be used to calculate the forces on each link of the mechanism and to evaluate the resulting stresses on its components. In addition, energy losses in different parts can be identified. The effects of damping, friction, and spring fatigue life on operating time can also be examined to expand the applicability of the current findings.
Acknowledgements
This work was funded by Kerman Tablo Corporation, and the authors gratefully acknowledge their support and assistance. Special thanks are extended to the technical staff and management for their invaluable contributions and insights throughout the research process.
Author contributions
Amir Arsalan Baniasadi, Hossein Darijani, and Mahmood Matin report financial support was provided by Kerman Tablo Corporation. Amir Arsalan Baniasadi, Hossein Darijani, and Mahmood Matin report a relationship with Kerman Tablo Corporation that includes: employment. If there are other authors, they declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Data availability
All data generated or analyzed during this study are included in this published article.
Declarations
Competing interests
The authors declare no competing interests.
Footnotes
Publisher’s note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
References
- 1.Matin, M., Dehghanian, A., Dastranj, M. & Darijani, H. Explainable artificial intelligence modeling of internal Arc in a medium voltage switchgear based on different CFD simulations. Heliyon10 (8), 29594 (2024). [DOI] [PMC free article] [PubMed] [Google Scholar]
- 2.Alsumaidaee, Y. A. M. et al. Detecting arcing faults in switchgear by using deep learning techniques. Appl. Sci.13 (7), 4617 (2023). [Google Scholar]
- 3.Zhou, N., Xu, Y., Cho, S. & Wee, C. T. A systematic review for switchgear asset management in power grids: condition monitoring, health assessment, and maintenance strategy. IEEE Trans. Power Delivery. 38 (5), 3296–3311 (2023). [Google Scholar]
- 4.Matin, M., Dehghanian, A., Zeinaddini, A. H. & Darijani, H. Interpretable machine learning modeling of temperature rise in a medium voltage switchgear using multiphysics CFD analysis. Case Stud. Therm. Eng.65, 105585 (2025). [Google Scholar]
- 5.Karunakaran, P., Lee, M. D., Ting, K. H., Osman, M. S. & John, A. A high voltage switchgear switching system. 2020 IEEE Int. Conf. Innov. Technol. (INOCON). 10.1109/INOCON50539.2020.9298368 (2020). [Google Scholar]
- 6.Sołtysek, Ł., Szczepanik, J., Dudzik, R., Sułowicz, M. & Schwung, A. Protection and control standards with auto diagnosis for the motor in Low-Voltage switchgear according to industry 4.0. Electronics10 (23), 2993 (2021). [Google Scholar]
- 7.Dong, E. et al. Analysis of capacitive closing pre-breakdown arcing ignition characteristics of vacuum circuit breaker. Vacuum239, 114374 (2025). [Google Scholar]
- 8.Wang, Y., Xu, J., Li, W. & Liu, J. Research on dynamic modeling and control strategy of motor driven operating mechanism for 126 kV high voltage vacuum circuit breaker. Sci. Rep.15, 17039 (2025). [DOI] [PMC free article] [PubMed] [Google Scholar]
- 9.Yu, L., Geng, Y., Liu, Z., Sun, L. & Yao, J. Relationship between displacement characteristics of a 126kV vacuum circuit breaker and spring type operating mechanism. 23rd Int. Symp. Discharges Electr. Insul. Vacuum10.1109/DEIV.2008.4676738 (2008). [Google Scholar]
- 10.Geng, Y. et al. Prestrike characteristics of non-synchronous closing of double-break vacuum circuit breakers under DC voltages. Electr. Power Syst. Res.248, 111891 (2025). [Google Scholar]
- 11.Liu, T., Ding, J., Xu, J., Zhao, D. & Qiu, X. Design and dynamics analysis of three-degree-of-freedom kinematic mechanism for helicopter attitude simulation. Sci. Rep.15 (1), 7463 (2025). [DOI] [PMC free article] [PubMed] [Google Scholar]
- 12.Mohan, H. S. et al. Raja. Design, dynamics and development of upgraded tiltable wing associated quadcopter through advanced computational simulations incorporated Bottom-Up approach. Sci. Rep.15 (1), 12055 (2025). [DOI] [PMC free article] [PubMed] [Google Scholar]
- 13.Sun, T., Yang, L. & Shu, P. A study of dynamics of marine circuit breakers based on vibration. J. Phys: Conf. Ser.2206 (1), 012010 (2022). [Google Scholar]
- 14.Li, X. et al. Simulation on failure analysis of vacuum circuit breaker permanent magnet operating mechanism based on three-parameter method. 2016 IEEE Int. Conf. Power Syst. Technol. (POWERCON). 10.1109/POWERCON.2016.7754078 (2016). [Google Scholar]
- 15.Choi, G. et al. Performance improvement of a gas-insulated circuit breaker using multibody dynamic simulations and experiments. J. Mech. Sci. Technol.27 (11), 3223–3229 (2013). [Google Scholar]
- 16.Ma, Y. et al. W.Lei. Load Analysis of Motor-driven Vacuum Circuit Breakers. 2024 6th Asia Energy and Electrical Engineering Symposium (AEEES). 10.1109/AEEES61147.2024.105445352024.
- 17.Chen, H. et al. Analysis of dynamic Arc parameters for vacuum circuit breaker under Short-Circuit current breaking. IEEE Trans. Appl. Supercond.29 (2), 1–5 (2019). [Google Scholar]
- 18.Kang, Y. H., Huang, H. C. & Yang, B. Y. Optimal design and dynamic analysis of a Spring-Actuated Cam-Linkage mechanism in a vacuum circuit breaker. Machines11 (2), 150 (2023). [Google Scholar]
- 19.Zhang, Y. et al. Dynamic fault analysis model development for vacuum circuit breaker action. J. Power Electron.24 (12), 1966–1978 (2024). [Google Scholar]
- 20.Cao, C. & Lin, X. Dynamic simulation and closing bouncing analysis on the 12 kV vacuum circuit breaker with permanent magnetic actuator. 2013 2nd Int. Conf. Electr. Power Equip. - Switching Technol. (ICEPE-ST). 10.1109/ICEPE-ST.2013.6804392 (2013). [Google Scholar]
- 21.Yao, X., Wang, J., Geng, Y., Liu, Z. & Zhai, X. X. Determination of opening velocities for vacuum circuit breakers at transmission voltage. 2016 27th International Symposium on Discharges and Electrical Insulation in Vacuum (ISDEIV). 10.1109/DEIV.2016.7748703(2016).
- 22.Kim, Y. S., Ryu, B. J. & Ahn, K. Y. Development of a molded case circuit breaker with a spring-actuated linkage based on multi-body dynamics analysis. Adv. Mater. Res.711, 299–304 (2013). [Google Scholar]
- 23.Matin, M., Fatahi, E., Darijani, H. & Arjmand, A. Theoretical and numerical stress analysis in the cam of a medium voltage switchgear vacuum circuit breaker supported by image processing of deformation. Forces Mech.17, 100298 (2024). [Google Scholar]
- 24.Coneo, R. J. C., de Araujo, W. L., Garcia, A. P., de Paula, M. V. & Santos, A. A. Rubber-tracked crawler undercarriage multibody dynamic simulation for agriculture operation. Sci. Rep.15, 24829 (2025). [DOI] [PMC free article] [PubMed] [Google Scholar]
- 25.Liu, S., Cui, Y., Xing, M., Gao, L. & Zhu, F. A general tribo-dynamic model for lubricated clearance joints in Spatial multibody systems. Sci. Rep.15 (1), 8438 (2025). [DOI] [PMC free article] [PubMed] [Google Scholar]
- 26.Soodmand, I. et al. Kebbach. Multibody kinematics optimization for motion reconstruction of the human upper extremity using potential field method. Sci. Rep.15, 10411 (2025). [DOI] [PMC free article] [PubMed] [Google Scholar]
- 27.Shafei, A. M. & Yousefzadeh, M. E. Dynamics of omni-directional multi-rotor aerial vehicles, hexacopter as a case study. Propuls. Power Res.14, 14–34 (2025). [Google Scholar]
- 28.Shafei, A. M. & Mirzaeinejad, H. Kinetic formulation and path tracking control of wheeled collaborative robots using Gibbs-Appell and optimal predictive control methods. Asian. J. Control.2025, 10.1002/asjc.3731. [Google Scholar]
- 29.Yang, J. et al. High voltage circuit breaker dynamics simulation and mechanical state recognition. 2017 1st Int. Conf. Electr. Mater. Power Equip. (ICEMPE). 10.1109/ICEMPE.2017.7982114 (2017). [Google Scholar]
- 30.Jo, J., Yang, H., Ahn, K., Park, Y. & Kim, Y. A study on the dynamic behavior of multibody dynamics model on vacuum circuit breaker: operating characteritics improvement of the VCB using Taguchi method. 2015 3rd Int. Conf. Electr. Power Equip. – Switching Technol. (ICEPE-ST). 10.1109/ICEPE-ST.2015.7368409 (2015). [Google Scholar]
- 31.Anjaneyulu, J., Rao, G. K. M. & Rao, G. Stress Analysis of a Circuit Breaker Switchgear Mechanism by Using Multi Body Dynamics. CAD/CAM, Robotics and Factories of the Future: Proceedings of the 28th International Conference on CARs & FoF 2016. 10.1007/978-81-322-2740-3_19(2016).
- 32.Yang, J. G., Zhao, K., Pan, Y., Liu, X. D. & on Mechanical Characteristic of Vacuum Circuit Breaker. Research on the Simulation Method of Dynamic Response of High Voltage Circuit Breaker During Operation.ASME 2016 International Mechanical Engineering Congress and Exposition. 2016.10.1115/IMECE2016-66357.
- 33. X. Duan, T. Wang, H. Ye, D. Feng, M. Fan, S. Xiu. Experiment and Simulation Research. 2016 27th International Symposium on Discharges and Electrical Insulation in Vacuum (ISDEIV). (2016). 10.1109/DEIV.2016.7763978
- 34.Ahn, K. Y. & Kim, S. H. Modelling and analysis of a high-speed circuit breaker mechanism with a spring-actuated cam. Proc. Institution Mech. Eng. Part. C: J. Mech. Eng. Sci.215 (6), 663–672 (2001). [Google Scholar]
- 35.Cao, C. & Lin, X. Dynamic simulation and closing bouncing analysis on the 12 kV vacuum circuit breaker with permanent magnetic actuator. 2013 2nd Int. Conf. Electr. Power Equipment-Switching Technol. (ICEPE-ST). 10.1109/ICEPE-ST.2013.6804392 (2013). [Google Scholar]
- 36.Fei, M. et al. Mechanical Parameters On-line Monitoring Method for High Voltage Vacuum Circuit Breaker Using Fiber Optic Displacement Sensors. 23rd International Conference on Mechatronics and Machine Vision in Practice (M2VIP). https://doi.org/10.1109/DEIV.2016.7763978 (2016).
- 37.S. Xiu. Experiment and Simulation Research on Mechanical Characteristic of Vacuum Circuit Breaker. 2016 27th International Symposium on Discharges and Electrical Insulation in Vacuum (ISDEIV). 2016. (2016). 10.1109/DEIV.2016.7763978
- 38.Kang, J. H., Kwak, S. Y., Kim, R. E. & Jung, H. The optimal design and dynamic characteristics analysis of electric actuator (EMFA) for 170 kV/50kA VCB based on Three-link structure. 2008 23rd Int. Symp. Discharges Electr. Insul. Vacuum. 10.1109/DEIV.2008.4676748 (2008). [Google Scholar]
- 39.Tang, J., Lu, S., Xie, J. & Cheng, Z. Contact force monitoring and its application in vacuum circuit breakers. IEEE Trans. Power Delivery. 32 (5), 2154–2161 (2015). [Google Scholar]
- 40.Dong, E., Qin, T., Wang, Y., Duan, X. & Zou, J. Experimental research on speed control of vacuum breaker. IEEE Trans. Power Delivery. 28 (4), 2594–2601 (2013). [Google Scholar]
Associated Data
This section collects any data citations, data availability statements, or supplementary materials included in this article.
Data Availability Statement
All data generated or analyzed during this study are included in this published article.