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摘要: 针对跨坐式单轨车辆抗倾覆性能影响因素繁多且复杂的特点, 利用降维思想提出一种综合评价车辆抗倾覆性能的方法, 并分析其影响参数敏感性; 基于浮心高度、柔性系数和临界侧滚角的定义, 推导了针对跨坐式单轨车辆的3个指标计算方法, 讨论了3个指标的区别, 综合提出13个可量化的抗倾覆影响因子; 基于测试和仿真数据建立了跨坐式单轨车辆的抗倾覆影响因子模型, 计算得到5个主因子和各参数的影响权重; 提出以抗倾系数来综合评价跨坐式单轨车辆的抗倾覆性能, 并得到其便捷计算方法; 利用多体动力学软件Universal Mechanism建立车辆-轨道参数化动力学模型, 验证了所得到的参数权重与评价指标的准确性。分析结果表明: 跨坐式单轨车辆的浮心高度、柔性系数和临界侧滚角均能不同程度地反映车辆抗倾覆性, 但不能体现参数敏感性; 跨坐式单轨车辆的抗倾覆性能受稳定轮与轨道梁表面接触状态的影响明显, 当稳定轮一侧脱离轨面时, 车辆的抗倾覆性能下降约50%;影响车辆抗倾覆性能的5个主因子分别是稳定轮、二系悬挂、横向跨距、一系悬挂和车体; 适当降低稳定轮垂向位置和车体质心位置, 增大水平轮预压力和走行轮横向跨距可有效提高跨坐式单轨车辆的抗倾覆性能。Abstract: Aiming at the characteristic that factors affecting the anti-overturning capacity of straddling monorail vehicle are numerous and complicated, a comprehensive evaluation method of vehicle anti-overturning capacity was proposed, and the sensitivities of influencing parameters were analysed based on the thought of dimensionality reduction. From the definitions of height of buoyancy center, flexibility coefficient and critical roll angle, the calculation methods for the three indexes of straddling monorail vehicle were deduced, and the differences of three indexes were discussed. Thirteen quantifiable anti-overturning factors were comprehensively proposed. Based on the test and simulation data, the anti-overturning factor model of straddling monorail vehicle was built, and the five main factors and influence weights of parameters were calculated. The anti-overturning coefficient was proposed to comprehensively evaluate the anti-overturning capacity of straddling monorail vehicle, and its convenient calculation method was obtained. The vehicle-track parameterized dynamics model was established based on the multibody dynamics software Universal Mechanism to verify the accuracies of parameter weights and evaluation indexes. Research result indicates that the height of buoyancy center, flexibility coefficient and critical roll angle of straddling monorail vehicle can reflect the anti-overturning capacity of vehicle to some extent, but they cannot reflect the parameter sensitivity. The contact state between the stabilizing wheel and the track beam surface significantly affects the anti-overturning capacity of straddling monorail vehicle. When one side of the stabilizing wheel departs from the track surface, the anti-overturning capacity of vehicle decreases by about 50%. The five main factors affecting the anti-overturning capacity of vehicle are the stabilizing wheel, the second suspension, the lateral span, the first suspension and the car body. Reducing the vertical position of stabilizing wheel and the centroid position of car body and increasing the pre-load of horizontal wheel and the lateral span of running wheel, can effectively improve the anti-overturning capacity of straddling monorail vehicle.
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图 4 临界侧滚角、临界超高率与预压力的关系
Figure 4. Relationships between critical roll angle, critical super-elevation ratio and pre-load
表 1 车辆参数与限值
Table 1. Vehicle parameters and limits
参数 方案1 方案2 方案3 下限 上限 车体重力G1/kN 210 210 210 转向架重力G2/kN 24 24 24 一系悬挂垂向刚度Kpz/(MN·m-1) 1.40 1.21 1.58 1.10 1.58 二系悬挂垂向刚度Ksz/(MN·m-1) 0.43 0.50 0.68 0.30 0.68 二系悬挂横向(y)刚度Ksy/(MN·m-1) 0.086 0.090 0.091 0.085 0.130 转向架一侧导向轮径向刚度Kgt/(MN·m-1) 1.25 1.42 1.35 1.00 2.00 转向架一侧稳定轮径向刚度Kst/(MN·m-1) 0.625 0.680 0.680 0.500 1.000 车体重心高度h2/m 0.563 0.563 0.591 0.50 1.20 二系悬挂上支撑面高度h3/m 0.110 0.110 0.100 -0.005 0.180 转向架重心高度h4/m 0.00 0.02 0.01 -0.05 0.45 导向轮中心高度h5/m 0.14 0.12 0.11 0.10 0.40 稳定轮中心高度h6/m 0.82 0.88 0.96 0.75 1.60 走行轮1/2横向跨距b1/m 0.11 0.13 0.11 0.08 0.16 二系悬挂1/2横向跨距b2/m 1.0 1.25 1.12 0.83 1.20 走行轮滚动半径r/m 0.445 0.445 0.445 预压力Fp/kN 5.0 4.8 5.5 4.5 13.0 
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表 2 因子相关系数
Table 2. Correlation coefficients of factors
因子 Kpz Ksz Ksy Kgt Kst h2 h3 h4 h5 h6 b1 b2 Fp Kpz 1.000 0.376 0.471 0.429 0.183 0.359 0.223 0.135 0.122 0.185 0.268 0.195 0.220 Ksz 0.376 1.000 0.186 0.054 0.387 0.118 0.001 0.000 0.418 0.000 0.311 0.008 0.000 Ksy 0.471 0.186 1.000 0.463 0.423 0.480 0.321 0.148 0.289 0.396 0.128 0.388 0.327 Kgt 0.429 0.054 0.463 1.000 0.458 0.277 0.245 0.031 0.077 0.013 0.417 0.137 0.016 Kst 0.183 0.387 0.423 0.458 1.000 0.166 0.392 0.138 0.052 0.134 0.438 0.312 0.216 h2 0.359 0.118 0.480 0.277 0.166 1.000 0.370 0.055 0.081 0.004 0.454 0.006 0.004 h3 0.223 0.001 0.321 0.245 0.392 0.370 1.000 0.005 0.472 0.101 0.094 0.023 0.148 h4 0.135 0.000 0.148 0.031 0.138 0.055 0.005 1.000 0.250 0.000 0.340 0.000 0.002 h5 0.122 0.418 0.289 0.077 0.052 0.081 0.472 0.250 1.000 0.476 0.188 0.266 0.482 h6 0.185 0.000 0.396 0.013 0.134 0.004 0.101 0.000 0.476 1.000 0.086 0.031 0.000 b1 0.268 0.311 0.128 0.417 0.438 0.454 0.094 0.340 0.188 0.086 1.000 0.158 0.081 b2 0.195 0.008 0.388 0.137 0.312 0.006 0.023 0.000 0.266 0.031 0.158 1.000 0.044 Fp 0.220 0.000 0.327 0.016 0.216 0.004 0.148 0.002 0.482 0.000 0.081 0.044 1.000
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表 3 因子特征值和累积方差
Table 3. Eigenvalues and cumulative variances of factors
主因子 初始特征值 提取平方和载入 旋转平方和载入 特征值 方差贡献率/% 累积方差贡献率/% 特征值 方差贡献率/% 累积方差贡献率/% 特征值 方差贡献率/% 累积方差贡献率/% 1 3.412 26.245 26.245 3.412 26.245 26.245 2.377 18.284 18.284 2 1.564 12.031 38.276 1.564 12.031 38.276 2.149 16.534 34.818 3 1.404 10.801 49.077 1.404 10.801 49.077 1.518 11.677 46.495 4 1.187 9.129 58.205 1.187 9.129 58.205 1.398 10.753 57.247 5 1.051 8.087 66.292 1.051 8.087 66.292 1.176 9.045 66.292
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表 4 旋转前后因子载荷
Table 4. Factor loads before and after rotation
因子 旋转前因子载荷 旋转后因子载荷 M1 M2 M3 M4 M5 M1 M2 M3 M4 M5 h6 0.831 0.421 -0.149 -0.073 0.184 0.932 -0.144 -0.149 0.098 -0.009 Fp 0.800 0.448 -0.182 -0.080 0.202 0.923 -0.189 -0.169 0.118 0.005 h4 0.766 -0.290 0.175 -0.014 -0.141 -0.413 0.231 0.079 0.301 0.068 Ksz -0.721 0.230 -0.199 0.198 -0.126 0.040 -0.777 0.173 0.020 -0.076 h3 -0.582 0.370 -0.045 -0.249 0.324 -0.391 0.706 0.071 -0.034 -0.102 Kgt -0.414 0.068 0.297 0.193 -0.153 0.280 -0.688 -0.377 0.094 0.138 b1 0.023 0.656 0.089 -0.438 -0.238 0.268 0.091 -0.799 0.026 -0.002 b2 0.411 -0.487 0.336 -0.149 0.318 -0.036 0.512 0.611 -0.082 -0.016 h5 -0.076 0.347 0.716 0.096 0.189 -0.017 -0.015 0.402 0.711 0.125 Kpz 0.201 0.172 0.432 0.242 -0.044 -0.051 -0.054 0.273 -0.676 0.167 Kst -0.184 -0.269 -0.316 -0.595 0.073 0.056 -0.123 -0.060 0.539 0.063 Ksy -0.067 0.064 -0.371 0.515 0.617 0.167 0.191 0.075 0.013 -0.850 h2 0.458 0.118 -0.363 0.367 -0.480 0.382 0.372 0.162 0.105 0.605
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表 5 因子得分系数
Table 5. Factor score coefficients
因子 M1 M2 M3 M4 M5 Kpz -0.035 -0.040 -0.033 0.386 0.024 Ksz -0.093 0.324 -0.107 0.018 -0.058 Ksy 0.165 0.100 0.109 0.045 -0.744 Kgt -0.193 0.070 -0.052 0.246 0.064 Kst 0.049 -0.085 0.216 -0.506 0.166 h2 0.010 0.199 -0.595 0.018 0.031 h3 -0.045 -0.445 0.259 -0.002 -0.092 h4 -0.021 -0.282 -0.158 0.037 0.110 h5 0.006 -0.053 0.295 0.507 0.048 h6 0.414 0.039 0.051 0.026 -0.042 b1 0.233 0.240 0.102 0.024 0.494 b2 0.157 0.185 0.402 -0.058 -0.034 Fp 0.430 0.061 0.063 0.012 -0.054
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表 6 抗倾覆性能评价指标
Table 6. Evaluation indexes of anti-overturning capacity
方案编号 浮心高度/m 柔性系数 临界超高率/% 抗倾系数 1 4.08 0.57 4.22 5.1 2 6.27 0.38 5.36 5.6 3 7.03 0.31 6.65 10.2
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