# A Study on the Pantograph Slide Wear Model Based on Energy Dissipation
## 7 Conclusions  
From the perspective of system work, this study investigates the relationship between the wear of the pantograph slide and the current-carrying frictional energy dissipation in the pantograph-catenary system. A mathematical wear model for the pantograph slide based on energy dissipation is established and validated. Within the parameter ranges considered in this study, the main conclusions are as follows. 1. A method is proposed to quantitatively characterize the wear of the pantograph slide using the current-carrying frictional energy dissipation in the pantograph-catenary system. The study demonstrates a significant linear relationship between pantograph slide wear and current-carrying frictional energy dissipation. 2. A mathematical wear model for the pantograph slide based on energy dissipation was developed. The predicted results from the proposed model show good agreement with the experimental measurements, with a maximum relative error of 12.776% and an average relative error of only 4.611%, demonstrating its applicability in engineering practice. 3. When the sliding speed and contact pressure are constant, the pantograph slide wear shows a negative correlation with the frictional force as the contact current increases; the energy generated by frictional work decreases, while the energy generated by electrical work increases. When the contact current and sliding speed are constant, an increase in contact pressure leads to an increase in the energy generated by frictional work and a decrease in the energy generated by electrical work, with the rate of decrease gradually slowing. When the contact current and contact pressure are constant, both the energy generated by frictional work and that generated by electrical work increase with rising sliding speeds. The pantograph slide wear prediction model established in this study, as a foundational exploration, currently does not account for key uncertainty factors such as arcing energy during off-contact and environmental temperature-humidity fluctuations. Recognizing this limitation, future research will focus on the following directions to enhance the model's prediction accuracy and applicability: (1) incorporation of uncertainty factors--based on the existing model framework, probabilistic characterization parameters for arcing energy and correction factors for environmental influences are planned to be introduced, aiming to construct a wear prediction model that more comprehensively reflects the complexity of the actual operating conditions; (2) deepening of physical model foundations--the simplifying conditions (e.g., linear assumptions) relied upon by the current model may become invalid beyond the specific operating conditions defined in this study. Thus, future work will explore modeling approaches for nonlinear effects and wear threshold behaviors to enhance the model's physical rigor and broaden its applicability. It is important to emphasize that, despite the aforementioned limitations--including the exclusion of arcing and environmental uncertainties--the model proposed herein, as a novel research methodology, offers significant exploratory value in revealing the fundamental mechanisms of current-carrying tribo-wear in pantograph-catenary systems. This study lays the foundation for the development of more refined models in subsequent research. Conceptualization, B.L. ; Methodology, Z.C. ; Software, Y.D. ; Formal analysis, H.W. ; Investigation, H.W. ; Resources, Z.C. ; Data curation, Y.D. ; Visualization, H.Z. All authors have read and agreed to the published version of the manuscript. This research received no external funding. Not applicable. The data presented in this study are available on request from the corresponding author. The data are not publicly available due to the data in this study were obtained through dynamic loading tests and other measurements using a self-developed sliding electrical contact testing machine. These data involve the core technical details of our laboratory.