硬质路面条件下履带车辆转向模型分析及验证

doi:10.12382/bgxb.2021.0849

摘要/Abstract

摘要：

履带车辆与地面之间的作用关系复杂,基于地面剪切位移的方法通常会用到对时间和位置的积分,模型较为复杂,无法直接应用到车辆的实时控制算法中。通常情况下,履带车辆转向分析会将接地压力看作连续线性分布或者多矩形分布,但是试验和计算结果均表明硬质土壤条件下,履带接地压力为多峰值分布,前述两种分布均不能体现接地压力的真实状态。本文针对上述问题,在前人研究的基础上,对履带接地压力分布进行求解,提出了履带车辆接地压力简化模型。该简化模型更符合硬质路面履带接地压力的真实状态,并被应用于履带车辆转向动力学分析与验证。利用J.Y.Wong提出的垂向负载-剪切位移变化关系解决了垂向压力变化的同时剪切位移计算的问题,提出了履带车辆转向分析模型(以下简称分析模型),试验结果表明该模型有较高的精度。但是其复杂度仍然较高,为了进一步简化模型,借鉴轮式车辆轮胎侧偏角和滑转率的概念,利用履带车辆履带-地面剪切位移关系推导了简化履带车辆动力学模型(以下简称简化模型)。该模型避免了复杂的积分或者求和,显著降低了履带车辆动力学模型的复杂度,能够应用于基于模型的无人驾驶履带车辆轨迹控制方法中,且模型精度接近前述履带车辆转向分析模型。

关键词: 履带装甲车辆, 转向特性, 非均布载荷, 模型验证

Abstract:

The interaction between tracked vehicles and the ground is complex. In general, methods based on shear stress-shear displacement theory require the integration of time and position, which is complicated and rarely applied to real-time vehicle control algorithms. Turning analysis of tracked vehicles typically assumes that grounding pressure is uniformly or concentratedly distributed.However, the calculations and test results show that the track-ground pressure forms multiple peaks on hard ground. In view of the above problems, based on previous studies, this paper proposes a simplified model of track-ground pressure, which has good consistency with the actual track-ground pressure on hard road surfaces. The model is then applied to the dynamic analysis of tracked vehicle turning. The vertical pressure-shear displacement relationship proposed by J.Y.Wong is employed to calculate the shear displacement when the track-grounding pressure keeps changing. A steering discretized model for tracked vehicles is proposed, and the test results show that the model has high accuracy yet still high complexity. To further simplify the model, the concepts of wheeled vehicle tire slip angle and slip rate are used.Then, a simplified tracked vehicle dynamics model is derived by using the shear stress-shear displacement theory. It avoids complex integration or summation, and can be applied to model-based motion control methods. Besides, it is almost as accurate as the complex steering analysis model.

Key words: tracked vehicle, steering characteristics, non-uniformly distributed load, model verification

中图分类号:

U469.6⁺94

张瑞增, 龚建伟, 陈慧岩, 刘海鸥, 卢佳兴. 硬质路面条件下履带车辆转向模型分析及验证[J]. 兵工学报, 2023, 44(1): 233-246.

ZHANG Ruizeng, GONG Jianwei, CHEN Huiyan, LIU Haiou, LU Jiaxing. Turning Model for Tracked Vehicles on Hard Ground: Analysis and Verification[J]. Acta Armamentarii, 2023, 44(1): 233-246.

图/表 20

图1 履带土壤接触变形简图

Fig.1 Track-ground contact deformation

图2 余弦曲线拟合内侧负重轮接地压力效果

Fig.2 Curve fitting of track-ground pressure on the middle road wheel

图3 余弦曲线拟合两侧负重轮接地压力效果

Fig.3 Curve fitting of track-ground pressure on the outer road wheels on both sides

图4 集中载荷作用下的履带接地压力

Fig.4 Track-ground pressure under concentrated load

图5 车辆转向过程分析

Fig.5 Analysis of racked vehicle turning

图6 垂向负载-剪切位移变化关系

Fig.6 Relationship between vertical load and shear displacement

图7 履带微元划分

Fig.7 Infinitesimal analysis of a track

图8 单个负重轮下履带接地状态分析

Fig.8 Track-groundcontactanalysis for a single road wheel

图9 试验采集

Fig.9 Test conditions

表1 试验相关参数

Table 1 Test parameters

参数	数值
总质量m/t	9.66
履带中心距B/m	2.464
履带接地长L/m	3.095
履带接地宽度b/m	0.365
主动轮半径r/m	0.2654
负重轮数量n	4
单侧驱动电机额定功率/kW	75
单侧驱动电机峰值功率/kW	110
转矩误差反馈/(N·m)	≤10
组合导航系统差分定位误差/cm	≤15
一挡传动效率/%	92
Z轴转动惯量(估计)J/(kg·m²)	15800
一挡质量增加系数δ	1.446
沙石/硬土/水泥路面摩擦因数μ	0.99/0.95/0.55
沙石/硬土/水泥路面抗剪模量K/m	0.008/0.0025/0.0018
沙石/硬土/水泥路面行驶阻力系数f	0.065~0.076/0.076/0.063

图10 履带接地压力定性测试结果

Fig.10 Qualitative test results of track-ground pressure

图11 砂石路面3km/h计算结果与试验采集结果对比

Fig.11 Comparison of calculation and test results on sand-gravel road at 3km/h

图12 砂石路面10km/h计算结果与试验采集结果对比

Fig.12 Comparison of calculation and test results on sand-gravel road at 10km/h

图13 砂石路面15km/h计算结果与试验采集结果对比

Fig.13 Comparison of calculation and test results on sand-gravel road at 15km/h

图14 硬质土路2.5~10.5km/h计算结果与试验采集结果对比

Fig.14 Comparison of calculation and test results on hard dirt road at 2.5~10.5km/h

图15 水泥路面3~8km/h计算结果与试验采集结果对比

Fig.15 Comparison of calculation and test results on cement road at 3~8km/h

图16 简化转向动力学模型砂石路面15km/h计算结果与试验采集结果对比

Fig.16 Comparison of calculation and test results on sand-gravel road at 15km/h using the simplified model

图17 简化转向动力学模型砂石路面10km/h计算结果与试验采集结果对比

Fig.17 Comparison of calculation and test results on sand-gravel road at 10km/h using the simplified model

图18 简化转向动力学模型砂石路面3km/h计算结果与试验采集结果对比

Fig.18 Comparison of calculation and test results on sand-gravel road at 3km/h using the simplified model

图19 砂石路面下存在纵向加速度时模型验证效果

Fig.19 Model verification effect during acceleration on sand-gravel road

参考文献 24

[1]	SEBASTIAN B, BEN-TZVI P. Physics based path planning for autonomous tracked vehicle in challenging terrain[J]. Journal of Intelligent & Robotic Systems, 2018, 95(1):1-16.
[2]	NIKITIN A O, SERGEYEV L V. Teoriya tanka[M]. Moscow, Russia: Izdaniye Akademii Bro-netankovykh Voysk Publ, 1962.
[3]	诺维科夫. 坦克理论[M]. 北京: 国防工业出版社, 1956.
	Novikov. Tank theory[M]. Beijing: National Defense Industry Press, 1956. (in Chinese)
[4]	WONG J Y, CHIANG C F. A general theory for skid steering of tracked vehicles on firm ground[J]. Proceedings of the Institution of Mechanical Engineers Part D Journal of Automobile Engineering, 2001, 215(3):343-355. doi: 10.1243/0954407011525683 URL
[5]	BEKKER M G, MIECZYSLAW G. Theory of land locomotion[M]. Ann Arbor, MI, US: University of Michigan Press, 1956.
[6]	BEKKER M G. Russian approach to terrain-vehicle systems(an exercise in pragmatism and continuity)[R]. General Motors Corp Goleta CA Delco Electronics DIV. 1971.
[7]	王红岩, 王钦龙, 芮强, 等. 高速履带车辆转向过程分析与试验验证[J]. 机械工程学报, 2014, 50(16):162-172.
	WANG H Y, WANG Q L, RUI Q, et al. Analyzing and testing verification the performance about high-speed tracked vehicles in steering process[J]. Journal of Mechanical Engineering, 2014, 50(16):162-172. (in Chinese)
[8]	魏宸官. 履带车辆转向问题的研究[J]. 拖拉机, 1980(1):17-35.
	WEI C G. Research on the steering problem of tracked vehicles[J]. Tractor & Farm Transporter, 1980(1):17-35. (in Chinese)
[9]	余群. 地面机器系统的研究现状及展望[J]. 农业机械学报, 2000, 31(2):1-3,26.
	YU Q. Review and development on terrain machine systems in China[J]. Transactions of the Chinese Society for Agricultural Machinery, 2000, 31(2):1-3,26. (in Chinese)
[10]	芮强, 王红岩, 王钦龙, 等. 基于剪应力模型的履带车辆转向力矩分析与试验[J]. 兵工学报, 2015, 36(6):968-977. doi: 10.3969/j.issn.1000-1093.2015.06.002
	RUI Q, WANG H Y, WANG Q L, et al. Analysis and experiment of tracked vehicle steering torque based on shear stress model[J]. Acta Armamentarii, 2015, 36(6):968-977. (in Chinese) doi: 10.3969/j.issn.1000-1093.2015.06.002
[11]	王红岩, 陈冰, 芮强, 等. 集中载荷作用下的履带车辆稳态转向分析与试验[J]. 兵工学报, 2016, 37(12):2196-2204. doi: 10.3969/j.issn.1000-1093.2016.12.003
	WANG H Y, CHEN B, RUI Q, et al. Analysis and experiment of steady-state steering of tracked vehicle under concentrated load[J]. Acta Armamentarii, 2016, 37(12):2196-2204. (in Chinese)
[12]	芮强, 王红岩, 王钦龙, 等. 履带车辆转向性能参数分析与试验研究[J]. 机械工程学报, 2015, 51(12):127-136. doi: 10.3901/JME.2015.12.127
	RUI Q, WANG H Y, WANG Q L, et al. Research on the acquisition of steering performance parameters of armored vehicle based on experiments[J]. Journal of Mechanical Engineering, 2015, 51(12):127-136. (in Chinese) doi: 10.3901/JME.2015.12.127
[13]	ZHAO Z Y, LIU H O, CHEN H Y, et al. Kinematics-aware model predictive control for autonomous high-speed tracked vehicles under the off-road conditions[J]. Mechanical Systems and Signal Processing, 2019, 123: 333-350. doi: 10.1016/j.ymssp.2019.01.005 URL
[14]	LU H, XIONG G M, GUO K H. Motion predicting of autonomous tracked vehicles with online slip model identification[J]. Mathematical Problems in Engineering, 2016, 2016.
[15]	熊光明, 鲁浩, 郭孔辉, 等. 基于滑动参数实时估计的履带车辆运行轨迹预测方法研究[J]. 兵工学报, 2017, 38(3):600-607. doi: 10.3969/j.issn.1000-1093.2017.03.025
	XIONG G M, LU H, GUO K H, et al. Research on trajectory prediction of tracked vehicles based on real time slip estimation[J]. Acta Armamentarii, 2017, 38(3):600-607. (in Chinese)
[16]	梁文利, 陈慧岩, 王博洋. 基于独立电驱动履带车辆的地面参量估计方法研究[J]. 兵工学报, 2019, 40(6):1146-1153. doi: 10.3969/j.issn.1000-1093.2019.06.004
	LIANG W L, CHEN H Y, WANG B Y. A ground parameter estimation method for independent electric tracked vehicle[J]. Acta Armamentarii, 2019, 40(6):1146-1153. (in Chinese) doi: 10.3969/j.issn.1000-1093.2019.06.004
[17]	陈冰, 王红岩, 芮强, 等. 考虑履带张力作用的稳态转向性能[J]. 装甲兵工程学院学报, 2016, 30(3):36-40.
	CHEN B, WANG H Y, RUI Q, et al. Steady-state steering performances under the action of track tension[J]. Journal of Academy of Armored Force Engineering, 2016, 30(3):36-40. (in Chinese)
[18]	张滔, 戴瑜, 刘少军, 等. 深海履带式集矿机多体动力学建模与行走性能仿真分析[J]. 机械工程学报, 2015, 51(6):173-180. doi: 10.3901/JME.2015.06.173
	ZHANG T, DAI Y, LIU S J, et al. Multi-body dynamic modeling and mobility simulation analysis of deep ocean tracked miner[J]. Journal of Mechanical Engineering, 2015, 51(6):173-180. (in Chinese) doi: 10.3901/JME.2015.06.173
[19]	DONG C, CHENG K, HU W Q, et al. Dynamic modelling of the steering performance of an articulated tracked vehicle using shear stress analysis of the soil[J]. Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering, 2017, 231(5): 653-683. doi: 10.1177/0954407016660268 URL
[20]	ÖZDEMIR M N, KILIC V, ÜNLÜSOY Y S. A new contact & slip model for tracked vehicle transient dynamics on hard ground[J]. Journal of Terramechanics, 2017, 73:3-23. doi: 10.1016/j.jterra.2017.07.001 URL
[21]	MAHALINGAM I, PADMANABHAN C. A novel alternate multibody model for the longitudinal and ride dynamics of a tracked vehicle[J]. Vehicle System Dynamics, 2019, 59(2):1-25. doi: 10.1080/00423114.2019.1656812 URL
[22]	GARBER M, WONG J Y. Prediction of ground pressure distribution under tracked vehicles-Ⅰ. an analytical method for predicting ground pressure distribution[J]. Journal of Terramechanics, 1981, 18(1):1-23. doi: 10.1016/0022-4898(81)90015-X URL
[23]	WONG J Y. Terramechanics and off-road vehicle engineering: terrain behaviour, off-road vehicle performance and design[M]. Oxford, UK: Butterworth-Heinemann, 2009.
[24]	BAKKER E, NYBORG L, PACEJKA H B. Tyre modeling for use in vehicle dynamics studies[J]. SAE Transactions, 1987:190-204.