Mathematical Modeling and Sensitivity Analysis of Mounting Forces in Quick Connectors Thierry Bénard Hutchinson, Montargis, France September 2024 Abstract This study investigates the mounting force dynamics of quick connectors used in automotive engine pipe connections. The research focuses on the two primary contributors to mounting force: the rubber O-ring and the metal locking spring. Using beam theory and Lindley’s formula as a foundation, we develop a comprehensive mathematical model to quantify the mounting force generated by the locking spring and the O-ring, respectively. We employ variance-based sensitivity analysis, specifically the Sobol method, to evaluate the relative influence of various properties and characteristics on the overall mounting force. The results are based on the coding of a model using the Python language. Our findings reveal that the second- order Sobol indices are very low. Each variable influences the output independently. These insights provide a deeper understanding of quick connector mechanics and offer a quantitative basis for improving connector design. Keywords— Quick connector, O-ring, locking spring, sensitivity analysis, Sobol indices, beam theory 1 INTRODUCTION 1.1 Background on quick connectors in automotive applications Quick connectors (see Figure 1) play a crucial role in modern automotive engines by providing rapid, secure, and leak-free connections for fluid and gas lines [7]. They are essential for efficient assembly in production lines, reducing manufacturing time and labor costs compared to traditional fastening methods. Quick connectors ensure reliable sealing under various operating conditions, including high temperatures, vibrations, and pressure fluctuations typical in engine environments [13] [8]. These connectors allow for easy maintenance and replacement of components, improving serviceability and reducing downtime during repairs. Quick connectors enhance safety by minimizing the risk of improper connections, which could lead to fluid leaks or system failures. Unlike clamps, which require tools and more time to install or remove, quick connectors can be engaged or disengaged by hand, often with a simple push-to-connect mechanism. While clamps can accommodate a wider range of tube sizes and materials with a single design, quick connectors often require specific matching components but offer superior reliability and ease of use in automotive applications. Figure 1: View of a quick connector 1.2 Research objectives For manual assembly, a well-designed mounting force balances the need for a secure connection with the ergonomic considerations for assembly line workers, reducing the risk of repetitive strain injuries. Understanding and controlling mounting force is thus critical for ensuring the reliability, safety, and efficiency of automotive assembly processes, as well as the long-term performance of the vehicle. The research focuses on the development of a mathematical model of assembly effort, taking material characteristics and part geometry as parameters. We will then apply a sensitivity analysis to understand the contribution importance of each parameter. 2 THEORETICAL FRAMEWORK 2.1 Integrated mounting force model Understanding the total mounting force for a quick connector requires considering both the O-ring contribution and the locking spring force. The figure 2 below shows the main 3 components of a quick connector in an exploded view. Figure 2: Exploded view of quick connector (Body, O-ring and locking spring) International Journal of Engineering Research & Technology (IJERT) ISSN: 2278-0181 http://www.ijert.org IJERTV13IS090076 (This work is licensed under a Creative Commons Attribution 4.0 International License.) Published by : Vol. 13 Issue 9, September 2024