基于拉格朗日法的悬臂输送槽阻尼摆模型构建与验证

为准确分析联合收割机输送槽在作业时产生的不平衡摆动现象，该研究建立了基于液压缸支撑的联合收割机悬臂输送槽阻尼摆模型。首先对悬臂输送槽系统进行受力分析，并基于拉格朗日法建立其动力学微分方程。为进一步确定动力学微分方程中的参数，利用有限元法和模态分析法对液压缸刚度和阻尼进行参数标定；并进行田间试验获取输送槽所受外界激励。利用二次积分与快速傅里叶变换（fast fourier transform，FFT）处理田间试验采集到的加速度信号，得到悬臂输送槽振幅及振动的主频成分，为动力学微分方程的验证提供依据。最后求得悬臂输送槽角速度和摆角的表达式，将理论得到的初始状态下悬臂输送槽摆幅与田间试验实际摆幅进行对比。结果表明：稳定状态下，理论求解得到的同一水平位置两测点对应的摆幅分别约为0.0979、0.0957mm，与试验实际摆幅误差约为1.11%和4.30%，验证了该联合收割机悬臂输送槽阻尼摆模型的准确性。研究结果可为长江中下游地区水稻联合收割机悬臂输送槽结构优化提供理论依据。

Development and validation of the damped pendulum model for cantilever conveyor trough using Lagrangian method

Cantilever conveying trough has often caused the unbalanced swing in the rice combine harvester, leading to the high failure rate with the low operation efficiency. The purpose of this study is to establish a damped pendulum model for the cantilever conveyor trough of the combine harvester in the support of the hydraulic cylinder, in order to accurately analyze the unbalanced pendulum during operation. Taking the rice combine harvester as the research object, the force and dynamic models were established for the cantilever conveying trough using Lagrange equation. The hydraulic cylinder stiffness, damping and the total excitation were also determined in the damped pendulum model of the cantilever conveyor trough. Firstly, a static analysis of hydraulic cylinder was carried out using Workbench software. The hydraulic cylinder stiffness was solved to be 1.0236×10⁸ N/m. Then, the modal analysis was performed on the hydraulic cylinder, where the main vibration mode was corresponded to the intrinsic frequency of 60.604 Hz. The vibration acquisition test was also carried out, where the measurement points were set up at the front end and the rear end of the hydraulic cylinder. The hydraulic cylinder amplitude was obtained to integrate the acceleration signal. The logarithmic attenuation rate of amplitude was ln2. The intrinsic frequency and logarithmic attenuation rate of amplitude were then substituted into the damping formula to calculate the damping c of the hydraulic cylinder, which was 228.58 N·s/m. Finally, the half- and full-width field harvesting tests were implemented for the external excitation of conveyor trough. Four points were measured at the connection between the cutting platform and the conveyor trough. The acceleration signals were collected during the field tests. The quadratic integration and the Fast Fourier Transform (FFT) were utilized to obtain the amplitude of cantilevered conveyor trough and the main frequency components of vibration. The excitation characteristics of cantilever conveyor trough were obtained to verify the subsequent differential equations of dynamics. All parameters were verified in the damped pendulum model of the cantilever conveyor trough. The ODE45 function in MATLAB was used to solve the equations of angular velocity and pendulum angle of damped pendulum model. The amplitudes of pendulums were compared between the theoretical solution and field test at the measurement points 3 and 4 in the initial and steady state, indicating the excellent performance. It was found that the theoretically solved pendulum amplitudes of measurement points 3 and 4 were very close to the test under stable conditions, with the errors of about 1.11% and 4.30%, respectively. Therefore, the accuracy and feasibility of damped pendulum model can be expected to serve as the cantilever conveyor trough.