Prediction model for TBM disc cutter wear based on dense core theory
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摘要: CCS（Constant Cross Section）盘形滚刀磨损是影响硬岩隧道掘进工作效率和成本预算的关键问题。根据CCS型滚刀的工作特点和岩石切割破碎原理，分析研究滚刀破碎岩石的复杂应力状态，建立了考虑密实核效应的滚刀破岩机理。通过推导密实核长度的理论解析式，获得了基于塑性去除磨粒磨损机制的滚刀磨损量与法向荷载之间的数学关系式，进而提出了滚刀磨损速率及切削寿命预测模型。基于此，分析计算了深圳地铁12号线某区间共757环的正面滚刀实测磨损数据，发现预测值与实测值的相对差异率值均小于10%，验证了预测模型的有效性。此外，通过与现有滚刀磨损预测模型对比分析，结果表明本文提出的预测模型计算结果更接近于现场实测值，说明了滚刀磨损速率和切削寿命指标可作为评价滚刀磨损特性的可靠指标，为TBM工程现场刀具更换方案设计提供更为合理可行的理论依据。Abstract: The CCS (constant cross section) type disc cutter wear is an inevitably crucial puzzle that affects the construction efficiency and cost budgeting of hard rock excavation. In this paper, according to the working characteristics of the CCS type disc cutter and the theory of rock squeezing and cutting, the complex stress state of rock-breaking by the cutter is analyzed and the mechanism of disc cutter rock-breaking considering the dense core effect is established. By deducing theoretical analytical expressions of dense core length, the mathematical relationship between cutter wear amount and normal force based on the principle of plastic removal abrasiveness is obtained, then the prediction models for wear rate and the cutting life of a disc cutter are proposed. Based on this context, by analyzing and calculating the measured wear data of the front disc cutter of a total of 757 rings in a section of Metro Line 12 in Shenzhen, China, it is found that the relative difference rate between the predicted value and the measured value is less than 10%, which validates the reliability and accuracy of the prediction model. In addition, by comparing with an existing typical prediction model of the CCS type disc wear, the results show that the calculation results of the prediction model proposed in this paper are more consistent with the field measured values, indicating that the disc cutter wear rate and cutting life can be regarded as reliable indexes to evaluate the cutter wear characteristics, which provides a more reasonable and feasible theoretical basis for the design of tool replacement scheme in TBM engineering.
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图 2 基于塑性去除机制的磨粒磨损示意图
Figure 2. Schematic diagram of abrasiveness based on plastic removal mechanism
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图 4 刀盘布置和刀盘区域划分示意图
Figure 4. Schematic diagram of cutterhead layout and cutterhead area division
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图 7 滚刀磨损速率预测模型验证及对比
Figure 7. Validation and comparison of prediction models for cutter wear rate
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图 8 滚刀切削寿命预测模型验证及对比
Figure 8. Validation and comparison of prediction models for cutter cutting life
表 1 国内外现有典型的盘形滚刀磨损预测模型
Table 1 Existing domestic and foreign typical disc cutter wear prediction models
预测模型 原理或方法 公式 数据范围 应用情况 CSM[6] 岩石挤压与剪切破坏理论、LCM试验 FV=8.76T0.797R0.788φ0.602S0.28σ0.629cσ0.195t — 完整性较好的玄武岩、石灰岩、花岗岩 NTNU[7] 挪威磨蚀性试验(SJ、AVS) Hf=π D2⋅H0⋅ki⋅PR4N 超过250 km隧道 花岗岩、凝灰岩 魏南珍等[8] 现场磨损数据拟合 M=0.0229R2i+2431Ri−3.2245 约3.7 km秦岭隧道 混合花岗岩和混合片麻岩 张照煌等[9] 岩石挤压、剪切及张拉破坏理论 FV=KAP2f⋅P 约5.6 km秦岭隧道 完整性较好的混合花岗岩 Frenzel等[10] Cerchar磨蚀性试验(CAI) Hf=π D24⋅n⋅P1000⋅2SD⋅1000 超过127 km隧道 微风化花岗岩 Hassanpour等[11] 岩石硬度试验(VHNR) Hf=−2.669VHNR−7.891UCS+3430.955 约30 km长Karaj输水隧洞 弱风化火山岩 李刚等[12] CSM模型 Ft=TRϕPr1 + ψ, Pr=C⋅(Sσ2cσtφ√RT)1/3 约18.5 km秦岭隧道 完整较好的玄武岩、石灰岩、花岗岩 杨延栋等[13] Rabinowicz微切削原理 ω=0.16KsS13RiσcD0T16h16σs 约2 km狮子洋隧道和531 m广州地铁隧道 微风化混合花岗岩 注：Fv为滚刀法向垂直力（N），Hf为滚刀基本寿命（m3/cutter），M为滚刀径向磨损量（mm），Ft为滚刀法向和切向合力（N）。 
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表 2 复合式土压平衡盾构机技术参数
Table 2 Technical parameters of composite EPB shield machine
参数 整机功率/kW 刀盘转速/(r·min-1) 扭矩/(kN·m) 推力/kN 推进速度/(mm·min-1) 刀盘开口率/% 滚刀数量/把 计算值 1668.05 1.8 2300 10000 15 35 41 参数 中心滚刀数量/把 正面滚刀数量/把 边滚刀数量/把 滚刀直径/mm 刀刃宽度/mm 刀刃角/(°) 刀圈硬度/HRC 计算值 6 23 12 457 19 20 60
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表 3 微风化花岗岩力学性质及计算参数
Table 3 Mechanical properties and calculation parameters of slightly weathered granulated granite
参数 密度/(kg·m-3) 抗压强度/MPa 抗拉强度/MPa 黏聚力/MPa 内摩擦角/(°) 弹性模量/GPa 泊松比 完整性系Kv 滚压系Kn 计算值 2700 90 6.89 20.8 42.5 26.7 0.22 0.55 0.7
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