Joint estimation algorithm of vertical force and lateral force of heavy-duty tire based on internal strain analysis of tire
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摘要:
为实现对轮胎侧偏力的估计，提出一种基于胎内周向应变分析的重载轮胎垂向力与侧偏力联合估计算法。以16.00R20重载轮胎为研究对象，建立了轮胎有限元模型，并开展了垂向刚度和振动特性试验验证了模型的有效性。基于轮胎内衬层周向应变信号分析，建立了周向应变曲线峰值间距角与接地角和接地长度的关联性模型，对比了静载、滚动、侧偏等工况下的表征精度；通过胎内对称点位周向应变分析，提取侧偏力表征特征，分析了垂向力与侧偏力表征特征的线性关系；建立了基于支持向量回归机的垂向力与侧偏力联合估计模型，先以接地角和接地长度为输入识别特征实现对垂向力的估计，进而通过侧偏力表征特征结合垂向力估计对侧偏力进行估计，通过有限元试验验证了模型估计精度。结果表明：以应变曲线零阶和一阶峰值间距角均值对接地角与接地长度的表征误差在4.5%以内；所提算法适用于静载、滚动、侧偏工况，能准确估算垂向力和侧偏力，估计值与有限元仿真值误差小于3%。
Abstract:In order to estimate the lateral force of a tire, this paper proposed a joint estimation algorithm of vertical force and lateral force of a heavy-duty tire based on internal circumferential strain analysis of the tire. A 16.00R20 heavy-duty tire was taken as the research object, and the finite element model of the tire was established. The tests on vertical stiffness and vibration characteristics were carried out to verify the validity of the model. Based on the circumferential strain signal analysis of the tire liner, the correlation model of the peak spacing angle of the circumferential strain curve with the grounding angle and the grounding length was established, and the characterization accuracy under static load, rolling, and lateral force conditions was compared. Through the internal circumferential strain analysis of the symmetrical point of the tire, the characterization feature of the lateral force was extracted, and the linear relationship between the characterization feature and the vertical force was analyzed. The joint estimation model of vertical force and lateral force based on support vector regression was established, and the vertical force was estimated by using grounding angle and grounding length as input recognition features. Then, the lateral force was estimated by characterization features of lateral force combined with vertical force estimation. The estimation accuracy of the model was verified by a finite element test. The results indicate that the characterization error of grounding angle and grounding length based on zero-order and first-order peak spacing angle of the strain curve is less than 4.5%. The joint estimation algorithm of vertical force and lateral force based on internal strain analysis of the tire is suitable for static load, rolling, and lateral force conditions and can accurately estimate the vertical force and lateral force. The error between the estimated value and the finite element simulation value is less than 3%.
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图 5 基于胎内应变监测的重载轮胎滚动试验
Figure 5. Rolling test of heavy-duty tire based on internal strain monitoring of tire
图 6 重载轮胎胎面应变信号试验与仿真对比
Figure 6. Comparison of tread strain signal test and simulation for heavy-duty tire
图 7 轮胎内衬层周向应变峰值角度差与接地角对比
Figure 7. Comparison of peak angle difference of circumferential strain of tire liner and grounding angle
图 8 不同垂向力下接地参数表征效果
Figure 8. Characterization effect of grounding parameters under different loads
图 10 侧偏特性与侧偏角的关系
Figure 10. Relationship between lateral characteristics and lateral angle
图 12 侧偏角对胎侧周向应变差影响规律
Figure 12. Effect of lateral angle on lateral circumferential strain difference
图 13 应变特征与侧偏力关系
Figure 13. Relationship between strain characteristics and lateral force
图 14 不同垂向力下特征值h2归一化对比
Figure 14. Comparison of eigenvalue h2 normalization under different loads
图 17 垂向力与侧偏力联合估计流程
Figure 17. Flow of joint estimation of vertical force and lateral force
表 1 轮胎下沉量对比
Table 1. Comparison of tire subsidence
垂向力$ {F_{\text{z}}} $/ kN 下沉量仿真值$ \Delta H $/mm 下沉量试验值$ \Delta H $/mm 误差$ \delta $/% 20 8.3 8.9 7.2 30 11.8 12.1 2.5 40 14.6 15.2 4.1 50 18.4 17.5 4.9 60 21.3 22.6 6.1 
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表 2 轮胎模态特征频率
Table 2. Tire modal characteristic frequency
阶数 频率试验值/Hz 频率仿真值/Hz 振型 误差$ \delta $/% 1 59.48 58.2 错动 2.1 2 65.22 68.8 2瓣 5.5 3 80.19 82.6 3瓣 3.0 4 95.77 96.8 4瓣 1.1 5 112.1 111.4 5瓣 0.6 6 128.4 125.9 6瓣 1.9 7 144.4 139.8 7瓣 3.2 8 159.8 152.8 8瓣 4.4
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表 3 胎面中线接地角
Table 3. Tread midline grounding angle
滚速/(km·h−1) 侧偏角/(°) 仿真值$ {\phi _1} $/(°) 表征值$ {\phi _{\mathrm{c}}} $/(°) 0 0 26 25 30 1 25.5 25 2.5 25 24.75 5 25 25.25 10 25 25.25 70 1 25.5 25 2.5 25.5 24.75 5 25 25.25 10 25 25.25 100 1 25.5 25 2.5 25.5 24.75 5 25 25.25 10 25 25.25
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