基于最优分布拟合的拖拉机三点悬挂牵引力载荷谱编制与台架试验

拖拉机三点悬挂装置作业载荷特性与分布研究对于预测零件寿命、产品可靠性分析等具有重要意义。针对传统参数外推编制方法对于多峰及概率分布不明确的作业载荷存在验证不通过或拟合效果差等问题，该研究提出基于最优分布拟合的载荷谱编制方法，建立了均值服从混合高斯、幅值服从混合威布尔的混合分布模型，采用AIC准则（Akaike Information Criterion）与BIC准则（Bayesian Information Criterion）相结合确定混合分布最优基函数个数，并利用EM（Expectation-Maximization）算法进行混合分布最优参数估计。以拖拉机三点悬挂牵引力实测载荷为对象进行最优分布拟合求解，与单分布相比，混合高斯分布与混合威布尔决定系数分别提高3.45%和6.02%，相关系数分别提高1.73%和4.87%，均方根误差分别降低31.38%和40%，残差平方和分别降低52.92%和64.01%。利用最优分布拟合进行极值和频次外推，并对外推一倍载荷谱与原始载荷进行统计特性与雨流计数对比分析，结果表明：外推载荷极值范围得到扩充，载荷分布规律一致，能够在保留原始载荷特性的前提下实现均幅值的双向外推。将外推牵引力载荷谱应用于拖拉机三点悬挂牵引力室内台架加载系统，并基于PID控制实现悬挂牵引力的反馈调节。加载试验结果表明：系统最大超调量为5.19%，最大稳定时间为0.2 s，最大延时为0.4 s，系统响应特性较好，室内台架系统能够满足拖拉机三点悬挂牵引力的加载与复现，并对外推牵引力载荷谱与反馈牵引力载荷谱进行雨流计数分析，均值、幅值频次保持一致，两者疲劳损伤等效，研究结果可为基于载荷谱的拖拉机室内台架试验提供理论依据和参考。

Compilation and bench test of traction force load spectrum of tractor three-point hitch based on optimal distribution fitting

Abstract: This study aims to clarify the working load characteristics and distribution of tractor three-point suspension devices, further to predict the life of parts and product reliability analysis. A load spectrum preparation was also proposed using optimal distribution fitting, in order to verify the multi-peak and uncertain probability distribution of the operating load. A mixed distribution model was established with the mean value following the Gaussian mixture and the amplitude following the Weibull mixture. The number of optimal basis functions in the mixed distribution was determined to combine the Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC). Furthermore, the Expectation-Maximization algorithm was selected to estimate the optimal parameters of the mixed distribution, particularly on the optimal solution and curve fitting. Taking the measured load of tractor three-point suspension traction as the research object, the optimal distribution fitting was carried out to determine the estimation parameters of the mixed distribution. Specifically, the determination coefficients of mixed Gaussian and Weibull distribution increased by 3.45% and 6.02%, respectively, the correlation coefficients increased by 1.73% and 4.87%, respectively, the root mean square errors decreased by 31.38% and 40%, respectively, and the residual sum of squares decreased by 52.92% and 64.01%, respectively, compared with the single distribution fitting. The extreme value and frequency were extrapolated using the optimal distribution fitting, thereby preparing the two-dimensional program load spectrum. The damage of the two-dimensional load spectrum was equivalently converted into the one-dimensional load spectrum, according to the Miner fatigue cumulative damage theory and S-N curve. A comparison was made on the statistical characteristics and rain flow counting of the extrapolated double load spectrum and the original load. The results show that the range of the extrapolated extreme value was expanded for the load, indicating the consistent load distribution. The bidirectional extrapolation of the average amplitude was realized under the premise of retaining the original load characteristics. The extrapolated traction load spectrum was then applied to the indoor bench loading system of tractor three-point suspension traction. The feedback regulation and the loading of suspension traction were realized using a PID control. A loading test of the three-point suspension frame was also performed on the bench loading system. The loading test results show that the maximum overshoot of the system was 5.19%, the maximum stability time was 0.2 s, and the maximum delay was 0.4 s, indicating an excellent response characteristic of the system. Correspondingly, the indoor bench system can fully meet the loading and reproduction of the three-point suspension traction in the tractor. The rain flow counting analysis was also made on the external traction load spectrum, further to acquire the feedback traction load spectrum. Anyway, there were consistent mean and amplitude frequency of the rain flow counting, indicating the consistent fatigue damage caused by the two parts. The finding can also provide a theoretical reference for the tractor indoor bench test using the load spectrum.