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The irregular wear of carbon current collector pantograph strips increases the railway maintenance costs and introduces safety hazards in the railway operation. This paper presents a method for analyzing the irregular wear of carbon strips with numerical dynamic analyses and modal tests. The carbon strips were studied in laboratory tests, and an equivalent numerical model for the investigation of their irregular wear and performance improvement was established. The results from the computational simulations were evaluated based on the laboratory results, and the correlation between the high-frequency vibration and irregular wear of the carbon strips was studied. The irregular wear contour of the carbon strips coincides with the high-frequency mode shape according to the experimental and numerical results. Moreover, the dynamic design for carbon strips was optimized with the validated computational model. The results suggest that the optimized schemes effectively mitigate the irregular wear of carbon strips.

Electric buses in metro railway systems suffer from the irregular wear of the pantograph strips. In general, a pantograph carbon strip with irregular wear has the following two features: (1) The vertical direction of the pantograph strip has one or more grooves of different depths. (2) The slant wear of the pantograph strip (i.e., its transverse thickness) is different. Wear can mainly be classified into mechanical wear and electrical wear [

Nevertheless, with increasing train speed, dynamic parameters such as the up-and-down inertia force, gas dynamic component force, and train disturbance force generated by the pantograph movement have increasing influences on the contact state of the pantograph. For metro railway systems, when the train is moving at a high speed, the interaction between the rigid catenary and carbon strip, which leads to the high-frequency vibration of the carbon strip, indirectly causes or aggravates the irregular wear of the latter [

The high-frequency vibrations (over 100 Hz) of the bow net and friction and wear of carbon strips have not been sufficiently investigated. Nevertheless, studying and suppressing the high-frequency vibrations of carbon strips to ensure the reasonable movement and matching between pantographs and catenaries are crucial for safe operation.

In this study, a rigid catenary, nonlinear single-degree-of-freedom pantograph, and bow-net coupling models were established. The carbon strips were investigated in vertical and transverse vibration modal tests, and the pantograph model was evaluated. In addition, the vibration mode shapes were compared with the irregular wear patterns of the carbon strips to determine the high-frequency vibration range related to the irregular wear. Finally, the multiparameter method was used to optimize the design of the carbon strip structure to mitigate irregular wear. The high-frequency (over 100 Hz) vibration mode was studied to analyze the irregular wear profile of the carbon strip. According to the results, this study provides a feasible solution for the analysis of irregular wear of pantograph carbon strips.

In general, a rigid catenary comprises several successive sections. One section mainly consists of aluminum profiles that are connected by flanges. The lower part of the aluminum profile is a fixed contact wire, and the upper part is fixed to the supports. In this study, a two-dimensional model [

Finite-element model of rigid catenary.

Simulation model parameters for rigid catenary.

Component | Parameter | Value | Unit |
---|---|---|---|

General | Number of spans | 20 | |

Span length | 10 | m | |

Aluminum profile and contact wire | Section area | 25 | cm^{2} |

Inertia flexural property | 4.1 × 10^{−6} | m^{4} | |

Density | 2900 | kg/m^{3} | |

Young modulus | 6.9 × 10^{10} | N/m^{2} | |

Support | Support stiffness | 400 | kN/m |

Flange | Weight | 3 | kg |

Moment of inertia | 2.4 × 10^{−3} | kg·m^{2} |

Thus, the differential equation of motion of the rigid catenary can be expressed as follows:

The pantograph is installed on top of the train to receive current from the catenary. Pantographs can mainly be classified into two types: single- and two-arm pantographs. Owing to the structural design limit and excessive aerodynamic noise during operation, the two-arm structure has been gradually replaced with the single-arm structure. The system generally includes the following components: bottom frame, lower arm, upper arm, connecting rod, balance rod, bow head bracket, carbon strip, bow angle, and other mechanical parts. To simplify the computation, the pantograph is considered to move vertically (Figure

Simplified vertical-structure simulation model of pantograph.

Simulation model parameters for pantograph.

Component | Material | Elastic modulus (GPa) | Poisson’s ratio | Density (kg·m^{−3}) | Cross-sectional area (mm^{2}) |
---|---|---|---|---|---|

Bow head bracket | Aluminum alloy | 72 | 0.33 | 2800 | 300 |

Bow head strip | Carbon | 12.4 | 0.35 | 2000 | 300 |

Upper frame | Steel | 210 | 0.3 | 7850 | 600 |

Balance bar | Steel | 210 | 0.3 | 7850 | 7800 |

Putter | Steel | 210 | 0.3 | 7850 | 1250 |

As depicted in Figure

Equations (

The parameters

Equation (

Based on the presented theory, the motion differential equation of the pantograph head is written as follows:

Based on [

By considering the vibration characteristics of the pantograph strip, the modal analysis was conducted based on the numerical model presented in Section

Mode shapes and modal frequencies of the first six vertical modes. (a) Mode 1,65.86 Hz. (b) Mode 2,139.81 Hz. (c) Mode 3,241.57 Hz. (d) Mode 4,389.10 Hz. (e) Mode 5,588.94 Hz. (f) Mode 6,810.66 Hz.

The vibrations in the vertical and transverse directions are most relevant to pantograph strips [

A real carbon strip was selected for the experimental modal analysis, and the modal parameters of the carbon strip were identified in a frequency domain analysis. The experiment was conducted through multi-input multi-output channels [

Arrangement of measuring points and acceleration sensors on the carbon strip.

Modal test flow of carbon strip.

According to the correlation curve of the excitations and responses, the coherence coefficients of the vertical and transverse modal frequencies are close to 1.0 in the 0–1000 Hz frequency band. Thus, the measured data of the experiment are effective, the external noise is low, and the vibration characteristics of the carbon strip can reliably be reflected. Figure

Frequency response functions of modal tests on carbon strip: (a) vertical and (b) transverse modal frequencies.

Modal frequency: (a) vertical and (b) transverse.

Figure

Test modal shapes of carbon strip: (a) vertical and (b) transverse.

Modal parameters of vertical and transverse modes.

Mode | Frequency (Hz)/vertical | Damping ratio (%)/vertical | Frequency (Hz)/transverse | Damping ratio (%)/transverse |
---|---|---|---|---|

First | 63.7 | 1.426 | 120.2 | 1.127 |

Second | 137.5 | 0.532 | 152.6 | 0.332 |

Third | 236.5 | 0.782 | 399.9 | 0.519 |

Fourth | 386.7 | 1.652 | 706.8 | 1.074 |

Fifth | 582.9 | 1.571 | 783.5 | 1.253 |

Sixth | 807.3 | 0.580 | 1145.5 | 0.462 |

Table

Comparison of experimental and simulated vertical modal frequencies.

Mode | Simulation (Hz) | Laboratory test (Hz) | Discrepancy (%) |
---|---|---|---|

First | 65.9 | 63.7 | 3.4 |

Second | 139.8 | 137.5 | 1.7 |

Third | 241.6 | 236.5 | 2.1 |

Fourth | 389.1 | 386.7 | 0.6 |

Fifth | 588.9 | 582.9 | 1.0 |

Sixth | 810.7 | 807.3 | 0.4 |

The formation mechanism of irregular wear was mainly predicted based on the kinetic characteristics of the carbon strip and then simulated with the numerical method. Figure

Comparison of carbon strip wear traces. (a) New carbon strip. (b) Carbon strip after abrasion (ideal case). (c) Carbon strip after abrasion (reality).

The interaction and contact between the carbon strip in service and catenary generate an unsteady dynamic force

Interaction between carbon strip and catenary. (a) Vertical model. (b) Transverse model.

In addition to the vertical vibrations, which change the friction force and contact state caused by friction wear, the transverse and vertical sliding of the carbon strip and catenary is inevitable owing to the sliding and swinging movements during operation. At constant vehicle speed, the transverse vibration and vertical component of the carbon strip cause contact pressure fluctuations and transverse alternating sliding [

By comparing the vertical mode shapes in Figure

Comparison of irregular abrasion profiles and vertical modal shapes.

Limited by space, the mechanism of two grooves and high-frequency vibration is mainly validated. Based on the numerical model in Section

Time-domain diagram and spectrum of contact force between carbon strip and catenary.

Time-domain diagram and spectrum of vertical acceleration of carbon strip.

As shown in Figure

Based on the results in Section

Based on the optimization model and laboratory conditions, the optimization design is divided into different sections of carbon strip and different damping parameters for experimental comparative analysis [

Location distribution of excitation and response points.

The same experimental principle and environment as in Section

Modal frequencies and damping ratios of trapezoidal carbon strips with different damping parameters.

Mode | Scheme 1 | Scheme 2 | Scheme 3 | |||
---|---|---|---|---|---|---|

Frequency (Hz) | Damping ratio | Frequency (Hz) | Damping ratio | Frequency (Hz) | Damping ratio | |

First | 63.4 | 1.466 | 56.4 | 1.810 | 51.4 | 2.155 |

Second | 141.9 | 0.523 | 122.6 | 1.233 | 112.9 | 1.654 |

Third | 242.6 | 0.862 | 212.8 | 1.680 | 194.2 | 1.379 |

Fourth | 396.3 | 1.652 | 349.7 | 1.785 | 320.9 | 2.511 |

Fifth | 595.3 | 1.471 | 514.0 | 1.602 | 482.9 | 1.661 |

Sixth | 827.4 | 0.580 | 714.5 | 1.225 | 661.8 | 1.559 |

Frequency response functions at different damping parameters in trapezoidal cross section: excitation response at points (a) (2, 7), (b) (3, 7), and (c) (5, 10).

As shown in Figure

In addition to the damping parameters, the cross-sectional shape of the carbon strip may affect its modal response. Therefore, carbon strips with two different cross-sectional shapes were investigated; the optimal damping scheme in Section

Trapezoidal and rectangular cross sections of carbon strips.

Comparison of frequency response curves and amplitude reductions of rectangular and trapezoidal cross sections before and after optimization.

The original frequency response functions of the trapezoidal and rectangular cross sections are illustrated in Figure

According to the results in Sections

Parameter calculation of the optimization model for schemes 2 and 3 for different cross sections.

Model parameters (incentive response point) | Trapezoidal cross section | Rectangular cross section | ||
---|---|---|---|---|

Scheme 2 | Scheme 3 | Scheme 2 | Scheme 3 | |

0.901 | 0.887 | 0.889 | 0.868 | |

49.483 | 73.800 | 56.352 | 81.625 | |

0.926 | 0.899 | 0.885 | 0.736 | |

48.384 | 72.951 | 56.241 | 82.176 | |

0.925 | 0.899 | 0.886 | 0.855 | |

49.862 | 74.870 | 57.368 | 81.979 |

In this paper, a numerical model for analyzing the irregular wear of carbon strips based on the vibration mode is proposed; the model is based on a rigid catenary and pantograph with a single degree of freedom. First, the vibration characteristics of the carbon strip were analyzed with the numerical model and then validated in experiments. The modal analysis results show that the mode shapes are significantly correlated with the irregular wear profile of the carbon strip; in addition, the wear profile of the two-groove carbon strip is consistent with the third mode shape, which was confirmed with the numerical model. On this basis, the carbon strip structure and cross section were optimized, and the mechanism of irregular wear on the carbon strip was discussed based on the modal analysis. The main conclusions are as follows:

The vertical vibration of the carbon strip is the main factor of irregular wear with two and three grooves, and transverse vibration causes partial wear and edge drops on the carbon strip.

The abnormal-wear profiles of the two and three grooves in the carbon strip are consistent with the third and fifth mode shapes in the modal test. When the pantograph runs at 60 km/h, the carbon strip resonates with the catenary at approximately 230 Hz. Thus, the modal frequency of approximately 230 Hz is the main vibration frequency that causes the two grooves.

The optimization schemes can avoid the harmful vibration frequency and reduce the response peaks. Scheme 3 has the most significant reduction effect on the modal frequency and response peak, and the decreased response peak of the rectangular cross-section results in a better performance than that of the trapezoidal cross section of the carbon strip.

The raw/processed data required to reproduce these findings cannot be shared at this time as the data also form part of an ongoing study.

The authors declare that there are no conflicts of interest regarding the publication of this paper.

This work was supported by the Natural National Science Foundation of China (NSFC) (no. U1834201).