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Calculation of brake disk life based on unsteady discontinuous brake
ZHOU Bin, LI Shulin , CHANG Fei, SHI Xiaopeng, YIN Junjie
Aeronautics and Astronautics Engineering College, Airforce Engineering University, Xi'an 710038, China
Abstract:Focus on the problem that the actual service life of brake disks is always shorter than the calculated data underground test, made use of the friction coefficient curves and took the actual statistic using boundary of carbon brake disk to fit a friction coefficient curve of unsteady discontinuous brake. The wear distance of one and several brakes to stop is calculated by using dynamic theory, and the wear rate of the two different braking is 1:1.899 7-1:2.036 3 using the formula of abrasive wear, which is exact compared with the statistic result 1:1.88-1:2.09 in the airfield. The wear condition becoming worse in unsteady discontinuous brake is the main reason leading to the wear speeding up of carbon brake disks fitting on the airplane. The important role of friction layer to reduce wear is proven and a calculation method is established to improve brake disks life test and estimate actual service lives of different-material brake disks by this study.
Key words: unsteady discontinuous brake     carbon brake disk     service life     friction coefficient     wear

《GJB 1184航空机轮和刹车装置通用规范》和《HB 5434.4—2004航空机轮摩擦材料试验方法第4部分动力试验台刹车性能试验方法》明确规定,刹车盘寿命试验总次数应根据GJB 1184—1991中表 2的循环规律达到订货方规定的起落次数.但刹车盘在地面台架的寿命试验是根据能量来设计,按单次计算,即给定要求的能量,在实验室模拟机轮连续刹车,当刹车装置吸收足够的能量后就退出试验.而在外场起飞，着陆的过程中,飞行员一般都要进行4～6次滑行刹车,直到飞机速度降为零[1],造成外场刹车盘实际使用寿命低于实验室台架给定的寿命[2, 3].因此要较为精确地预测刹车盘外场实际使用寿命,就必须在单次连续刹车试验数据的基础上,引入非稳态间断刹车因素的修正.

1 理论分析 1.1 基于能量磨损理论的磨损差异性分析

 图 1 典型摩擦副磨损曲线Fig. 1 Representative wear curve of friction pairs

 图 2 磨损量变化直观图Fig. 2 Direct-viewing chart of wear change

 图 3 非稳态间断刹车磨损增量示意图Fig. 3 Wear increment diagrammatic drawing of unsteady discontinuous brake

 图 4 刹车试验数据Fig. 4 Brake test data

 图 5 典型全过程碳盘摩擦系数曲线Fig. 5 Representative overall friction coefficient curve of carbon brake disks

Ⅰ阶段为原始膜破坏阶段,经历了压力响应、孔隙水分润滑、孔隙水分蒸发等过程[10].Ⅱ阶段为新摩擦膜形成阶段.其对应时间与刹车压力、速度有关.在该过程中,摩擦面温度进一步升高,不仅增加了磨屑层的变形能力,还可以引起碳结构的削弱,产生并细化更多的磨屑起润滑作用[9].这些磨屑一部分在刹车压力和剪切力的作用下形成新的连续均匀摩擦膜,另一部分剥落造成质量损失[13].Ⅲ阶段为稳定摩擦阶段,产生的磨屑与剥落的磨屑达到动平衡.一方面,摩擦面的微凸体不断在剪切力的作用下脱离碳盘滚动,另一方面,部分磨屑不断填补犁沟效应产生的凹痕,从而保证了摩擦膜持续工作,减少磨损.Ⅳ阶段为摩擦膜再破损阶段,主要受温度影响[10].

1) 单次连续刹车模型(刹车速度25→0 m/s).

 参数 惯量/(kg·m2) 刹车压力/MPa 刹车速度/(m·s-1) 刹车转速/(r·min-1) 数值 0.3 1.0 25 7 463
 图 6 简化后单次刹停摩擦系数曲线Fig. 6 Simplified friction coefficient curve of one brake to stop

2) 非稳态间断刹车模型.

 刹车速度/(m·s-1) 刹车转速/(r·min-1) 角速度/(rad·s-1) 25 7 463 781.52 20 5 970 625.18 15 4 478 468.94 10 2 985 312.59 5 1 493 156.35

5次刹车过程中,因存在刹车间隙,摩擦膜会在离心力的作用下剥落,造成不均匀,且后期摩擦膜在高温下直接暴露在空气中,发生氧化反应,所以上次刹车形成的摩擦膜很难保持到下次刹车中,因而摩擦膜对下次刹车造成的影响可忽略不计.由文献[9]测得的不同刹车速度(由各个速度分别刹停)下摩擦系数曲线,近似得到非稳态间断刹车时的摩擦系数曲线,如图 7所示.

 图 7 非稳态间断刹车摩擦系数近似曲线Fig. 7 Approximate friction coefficient curve of unsteady discontinuous brake
2.2 磨损行程计算

1) 单次连续刹车模型.

2) 非稳态间断刹车模型.

 阶段 刹车时间/s Δθ/rad A 1.53 1 070.41 B 1.80 980.74 C 1.66 648.42 D 1.47 344.80 E 4.42 345.27 累计 10.88 3 389.64
2.3 无能量修正下的磨损比

 刹车速度/(m·s-1) 刹停转角/rad 线性磨损/(μm·面-1·次-1) 25 3 589.31 0.30 20 2 424.20 0.26 15 1 165.12 0.23 10 460.17 0.33 5 345.27

 阶段 A B C D E Z/10-5 8.358 10.725 19.740 71.713 0

ΔH1=0.569 9 μm/(面·次)

ξ1H1h25=1.899 7

2.4 能量修正下的磨损比 2.4.1 能量修正的必要性

tb=600℃,对应的碳盘比热c=1 348 J/(kg·℃)[14],代入式(11)可得刹车速度为25 m/s时,刹车盘的平均工作温度tb=600.25℃.同理,其余各个速度刹停的碳盘的平均工作温度如表 6所示.

 刹车速度/(m·s-1) 刹车材料单位面积吸收能量AS/(J·cm-2) 整盘刹车能量 A/J 碳盘比热c/(J·kg-1·℃-1) 平均工作温度/℃ 25 4 108 90 855.86 1 348 600.25 20 2 728 60 334.66 1 227 456.91 15 1 510 33 396.39 1 101 308.63 10 685 15 150.02 1 017 187.19 5 179 3 958.91 1 000 101.15

 阶段 起始速度/(m·s-1) 刹车能量增量ΔAi/(J·cm-2) 累计刹车能量/(J·cm-2) 整盘能量/J 碳盘比热/(J·kg-1· ℃-1) 平均工作温度/ ℃ A 25 1 491.55 1 491.55 32 988.31 1 101 305.72 B 20 1 159.37 2 650.92 58 629.87 1 227 445.92 C 15 828.72 3 479.64 76 958.50 1 308 532.88 D 10 496.91 3 976.55 87 948.56 1 348 583.28 E 5 165.80 4 142.35 91 615.53 1 348 604.68

 图 8 线性磨损与能量的关系Fig. 8 Relationship between linear wear and energy
2.4.2 磨损比计算

 图 9高能阶段线性拟合结果Fig. 9 Linear fitting result at high energy phase

 阶段 A B C D E Δh′ 0.023 0.013 0.005

ξ2H2h25=2.036 3(有能量修正) 2.5 计算结果分析

 图 10 Z随刹车次数的变化趋势Fig. 10 Curve of Z at different number of brake

Z的上升说明在摩擦膜不能发挥作用的多次刹车情况下,磨损的工况状态随速度的减小急剧恶化,但这一点在力矩和摩擦系数曲线上反映不明显,导致在刹车后期的低速时,减速率虽然变化不大,但磨损急剧增大,而这种磨损是在单次刹车中摩擦膜保护下可以完全避免的,这正是造成预测寿命与实际寿命差异的主要原因. 3 结 论

1) 非稳态间断刹车通过松刹增加了磨屑损耗,造成刹车后期磨损加剧,基于能量磨损理论可知,相同刹车距离下,这种刹车方式以牺牲磨损量提高了刹车效能；

2) 根据不同刹车速度的摩擦系数曲线,拟合了非稳态间断刹车的摩擦系数曲线,再结合连续刹车的摩擦系数曲线,计算了两种刹车方式下的磨损比为1∶1.899 7～1∶2.036 3,与统计结果相比,较为精确,计算方法可以应用到不同材料刹车盘的外场寿命预测中；

3) 理论上分析了非稳态间断刹车后期,磨损工况条件系数急剧升高是造成该刹车方式下磨损增大的重要原因,而在连续刹车中形成稳定的摩擦膜作用下,变化不大,利用摩擦学原理定量地分析了摩擦膜的重要影响,从而验证了外场非稳态间断刹车是造成刹车盘寿命缩短的重要因素.

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#### 文章信息

ZHOU Bin, LI Shulin, CHANG Fei, SHI Xiaopeng, YIN Junjie

Calculation of brake disk life based on unsteady discontinuous brake

Journal of Beijing University of Aeronautics and Astronsutics, 2015, 41(3): 538-544.
http://dx.doi.org/10.13700/j.bh.1001-5965.2014.0184