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Static and Dynamic Analysis of Nonlinear Valve Springs Based on Finite Element Analysis and Machine Learning Algorithm

Research output: ThesisDoctoral Thesis

Publication date2022
Number of pages201
Awarding Institution
  • Lancaster University
<mark>Original language</mark>English


The valve spring is a fundamental type of helical spring which is essential for enabling the opening and closure of a valve in a car engine. Nowadays, it is increasingly common to use valve springs of nonlinear geometry in high-speed car engines for better dynamic performance. However, practical issues such as malfunction and pre-failure are also raised by spring researchers and manufacturers using and analysing these nonlinear springs. It is commonly stated that existing spring models and empirical formula do not allow for the analysis of these nonlinear springs. To tackle such difficulties, it is imperative that all the varied geometric parameters of a nonlinear spring be clarified in order to facilitate efficient and generalizable analysis. Past research efforts have mainly emphasized the analysis of standard valve springs of constant geometric parameters and the development of spring models for low-speed static conditions. However, these models do not take into account the full breadth of conditions and consequently are considered to be insufficient and compromised in accuracy. Therefore, it remains a challenge to effectively leverage such models in the analysis and design of nonlinear valve springs.
This thesis aims to address the existing gaps and present a comprehensive study on the analysis of nonlinear valve springs and their dynamic response in high-speed engines. An advanced spring formula is developed based on simplified curved beam theory to formulate the relationships between the nonlinear spring geometry (varied coil diameter, varied pitch and coil clash) and the mechanical properties of a beehive valve spring. These nonlinear considerations deliver a higher predictive accuracy than the existing spring formulas by comparing FE and experimental results. The new spring formula is coupled with the distributed parameter model to simulate the dynamic spring responses. However, whilst it accurately simulates the dynamic responses at lower engine speeds (lower 5000-rpm), it fails to simulate the significant abnormal spring forces at high engine speeds (over 8000-rpm). On the contrary, the FE springs model is developed, of which static and dynamic simulation results fit well with the experimental data at both low and high engine speeds. More importantly, analysis of the dynamic FE results explains how the violent coil clash leads to significant abnormal spring forces. In the last part, a machine learning model, based on genetic programming techniques and the FE results, is developed to aid the design of nonlinear helical springs. The model enables researchers to analyse nonlinear helical spring properties directly using information extracted from FE results data, bypassing the necessity to unravel the complex inner relationships between the nonlinear spring parameters.