To master the basic characteristics of steady-state cornering for a semitrailer, this paper summarises the current modelling methods for handling and stability and discusses their limitations. The classical linear mathematical model for a two-degree-of-freedom (DOF) handling and stability system is used to develop a new model. Analysis methods are proposed to introduce the influence of the camber angle and body roll into the model parameters. Thus, a mathematical model for the lateral stability of semitrailer with five DOFs is established. At the same time, a modified formula to calculate the stability factor of the semitrailer is developed with a MATLAB model to solve the dynamic state equation. The mathematical model, which considers the body roll and the changes in the camber angle caused by roll, compares the turning radius ratio and yaw rate as the evaluation index with the classical linear mathematical model of a two-DOF system. The vehicle parameters for three different types of semi-tractor trailers are used to calculate and compare two mathematical models for handling and stability using real vehicle test data. The results show that the new modelling and analysis method proposed in this paper has a high calculation accuracy and fast calculation speed, is clear and concise, and is consistent with the real vehicle test data. In addition, the accuracy of the new mathematical model for handling and stability and the improved stability factor are verified.

中文翻译：

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基于弯度参数变化的半挂车数学模型的稳态转向特性

为了掌握半挂车稳态转弯的基本特征，本文总结了当前的操纵性和稳定性建模方法，并讨论了它们的局限性。针对两自由度（DOF）处理和稳定性系统的经典线性数学模型用于开发新模型。提出了将弯度角和车身侧倾的影响引入模型参数的分析方法。因此，建立了具有五个自由度的半挂车横向稳定性的数学模型。同时，用MATLAB模型开发了计算半挂车稳定性系数的修正公式，以求解动态状态方程。该数学模型考虑了车身侧倾以及侧倾引起的外倾角变化，将转弯半径比和偏航率作为评估指标与两自由度系统的经典线性数学模型进行比较。三种不同类型的半挂车拖车的车辆参数用于使用真实的车辆测试数据来计算和比较两个数学模型，以处理和提高稳定性。结果表明，本文提出的新的建模与分析方法具有较高的计算精度和较快的计算速度，简洁明了，与真实的车辆测试数据相吻合。此外，验证了用于处理和稳定性的新数学模型的准确性以及改进的稳定性因子。三种不同类型的半挂车拖车的车辆参数用于使用真实的车辆测试数据来计算和比较两个用于操纵和稳定性的数学模型。结果表明，本文提出的新的建模与分析方法具有较高的计算精度和较快的计算速度，简洁明了，与真实的车辆测试数据相吻合。此外，验证了用于处理和稳定性的新数学模型的准确性以及改进的稳定性因子。三种不同类型的半挂车拖车的车辆参数用于使用真实的车辆测试数据来计算和比较两个用于操纵和稳定性的数学模型。结果表明，本文提出的新的建模与分析方法具有较高的计算精度和较快的计算速度，简洁明了，与真实的车辆测试数据相吻合。此外，验证了用于处理和稳定性的新数学模型的准确性以及改进的稳定性因子。