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基于DEM-FEM的微粒喷丸仿真分析*

  • 张博宇1

    机 构：

    1. 重庆大学机械传动国家重点实验室 重庆 400044

    ×
  • ， 刘怀举1

    机 构：

    1. 重庆大学机械传动国家重点实验室 重庆 400044

    ×
  • ， 魏沛堂1

    机 构：

    1. 重庆大学机械传动国家重点实验室 重庆 400044

    ×
  • ， 朱加赞2

    机 构：

    2. 中国航发四川燃气涡轮研究院 成都 610500

    ×

1. 重庆大学机械传动国家重点实验室 重庆 400044；
2. 中国航发四川燃气涡轮研究院 成都 610500；

Simulation Analysis of Micro-shot Peening Based on DEM-FEM Method

  • ZHANG Boyu1

    Affiliation：

    1. State Key Laboratory of Mechanical Transmissions, Chongqing University, Chongqing 400044 , China

    ×
  • ， LIU Huaiju1

    Affiliation：

    1. State Key Laboratory of Mechanical Transmissions, Chongqing University, Chongqing 400044 , China

    ×
  • ， WEI Peitang1

    Affiliation：

    1. State Key Laboratory of Mechanical Transmissions, Chongqing University, Chongqing 400044 , China

    ×
  • ， ZHU Jiazan2

    Affiliation：

    2. Sichuan Gas Tubine Establishment, Aero Engine Corporation of China, Chengdu 610500 , China

    ×

1. State Key Laboratory of Mechanical Transmissions, Chongqing University, Chongqing 400044 , China；
2. Sichuan Gas Tubine Establishment, Aero Engine Corporation of China, Chengdu 610500 , China；

作者简介:

张博宇,女,1994年出生,博士研究生。主要研究方向为齿轮接触疲劳分析与抗疲劳设计。E-mail:407703607@qq.com;

刘怀举(通信作者),男,1986年出生,博士,副教授,博士研究生导师。主要研究方向为基础件抗疲劳制造、表面强化工艺、非金属传动件及系统等。E-mail:huaijuliu@cqu.edu.cn

中图分类号:TG17

DOI:10.11933/j.issn.1007−9289.20211126001

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目录contents

    摘要

    微粒喷丸作为一种新兴的喷丸工艺，由于工艺试验数据与仿真技术的缺失，其作用机理尚未探明。基于 ABAQUS 二次开发，采用离散元与有限元（DEM-FEM）相结合的方法，构建考虑初始残余应力与硬化层梯度的随机多弹丸微粒喷丸弹塑性模型，探究微粒喷丸的喷射速度与覆盖率对残余应力分布和表面粗糙度的影响规律。发现随着微粒喷丸喷射速度的增加， 靶体表面粗糙度的算术平均偏差 Sa 线性增加；覆盖率达到 100%后，覆盖率大小对 Sa 与残余压应力分布影响不大；喷射速度对于微粒喷丸的最大残余压应力值影响不大，但对残余应力层的厚度有显著影响。通过 DEM-FEM 耦合方法对微粒喷丸机理进行探究，为工艺参数的制定提供理论支撑。

    Abstract

    Micro-shot peening, as a special shot peening process, has the unclear mechanism due to the lack of experimental data and simulation technology. The micro-shot peening elastic-plastic model is developed by combining the discrete element method (DEM) with the finite element method (FEM) in ABAQUS. The initial residual stress and hardened layer gradient are considered to simulate the gear material state before micro-shot peening process. The effects of peening velocity and coverage rate on residual stress distribution and surface roughness are investigated. It is found that the arithmetic mean deviation Sa of the gear surface roughness increases linearly with the increase of the peening velocity. When the coverage rate reaches 100%, the coverage rate has little effect on Sa and residual compressive stress distribution. The peening velocity has little effect on the maximum value of residual compressive stress, while has significant effect on the thickness of the residual stress layer. This paper explores the mechanism of micro-shot peening by DEM-FEM method and provides theoretical support for preparation of micro-shot peening process.

  • 0 前言

  • 喷丸是一种典型的强化手段，采用高速弹丸反复撞击材料表面，使表层发生塑性变形，从而引入显著残余压应力[1-2]，增大零件表面硬度[3-5]，细化晶粒[6-9]，有利于提高材料的抗疲劳性能[10-13]。但喷丸处理也会引起零件表面形貌变化，有研究表明喷丸处理将使表面粗糙度成倍增长[14-17]。尽管可以采用二次喷丸等复合工艺改善表面粗糙度增大的问题，但其改善效果依旧依赖于最后一次喷丸所采用的丸粒尺寸。

  • 微粒喷丸作为一种特殊的喷丸工艺，改善了表面粗糙度问题，可用于航天航空、机器人、生物医疗等领域的高精密零部件表面强化，以提高零件的疲劳寿命。采用直径小于0.1mm弹丸以200m/s以上的喷射速度不断撞击零件表面。在试验方面，ITO等[18]对微粒喷丸过程中丸粒角度、速度等力学行为进行了分析；OGURI等[19]认为与传统喷丸相比，微粒喷丸可显著增强航空航天铝合金零件的疲劳性能；张继旺等[20-21]分析微粒喷丸对Al-7Si-0.3Mg铸造合金、 Cu-Ni-Si合金等试样弯曲疲劳的影响。但微粒喷丸的设备与丸粒相比于普通喷丸较为昂贵，限制了微粒喷丸的发展，也使得仿真分析成为微粒喷丸机理探究的重要途径。吕文博[22]、王超等[23]采用ANSYS有限元软件模拟TC4钛合金的微粒喷丸强化过程，但丸粒个数较少，丸粒分布也不是随机的。微粒喷丸需要大量的丸粒才能达到一定的覆盖率，用单纯的有限元分析很难快速模拟出几千次的撞击过程。

  • 本文基于离散元与有限元相结合方法 （DEM-FEM）较为真实地模拟了大量弹丸的随机撞击过程，构建了考虑初始残余应力与硬化层梯度的随机多弹丸弹塑性模型，对比分析了微粒喷丸与常规喷丸的区别，并探究了微粒喷丸的喷射速度与覆盖率对残余应力分布及表面粗糙度的影响规律。

  • 1 微粒喷丸弹塑性模型

  • 采用18CrNiMo7-6滚子试件的材料属性作为模型的输入条件，在ABAQUS中建立弹塑性靶体模型，将实测的初始残余应力和硬度梯度添加到靶体上，建立单弹丸模型计算弹坑大小及达到覆盖率100%时所需的弹丸个数；输出“inp”文件并基于PYTHON修改，添加离散单元，定义喷射速度与流量等相关参数，建立随机多弹丸微粒喷丸模型；读取“inp”文件并计算不同覆盖率与喷射速度下的应力应变结果，具体的技术路线图如图1所示。

  • 图1 技术路线图

  • Fig.1 Technology road mapping

  • 所采用的18CrNiMo7-6滚子试件材料中各元素的成分如表1所示。材料的弹性模量与泊松比分别为210GPa和0.3，试件经过渗碳、淬火、回火等处理，具体工艺如表2所示。

  • 表1 18CrNiMo7-6材料各元素成分（质量分数/wt.%）[24]

  • Table1 Elements of the material18CrNiMo7-6 (wt.%)[24]

  • 表2 滚子试件热处理工序

  • Table2 Heat treatment procedure of roller specimen

  • 1.1 硬度表征

  • 滚子试件经过渗碳处理之后，形成了从表面到芯部沿深度方向的硬度梯度。本文采用洛氏硬度计测量滚子试件的硬度梯度，该硬度计配有电动转塔和图像分析系统（HXD-1000TMC/LCD），系统允许程序控制应用、持续时间和卸载负载。探头尺寸为50um，加载力设为10N，加载时间为15s。硬度测量从表面到深度1mm，得到硬度梯度曲线。由于在模拟软件ABAQUS中无法添加硬度，可根据Pavlina-Tyne公式将硬度转化为屈服强度（YS）添加到靶材上。Pavlina-Tyne公式[25]为：

  • YS=-90.7+2.876HV

  • 测得的硬度梯度曲线和计算得到的屈服强度曲线在图2中给出。将ABAQUS中的靶体沿深度方向分层，将屈服强度分别添加到该层的材料属性中。

  • 图2 硬度表征结果

  • Fig.2 Hardness measurement results

  • 1.2 残余应力表征

  • 采用商用便携式X射线衍射仪u-X360s （Pulstec u-X360s）检测滚子试件沿深度的残余应力。该设备是一种轻型无损的残余应力分析仪，能够通过2D检测器捕获完整的德拜环。电解抛光仪器采用Proto 8818V2，饱和盐水作为电解液。腐蚀深度通过螺旋测微计精确测量，分辨率为0.01mm。利用单入射角法（又称cosa法）的测量原理测量残余应力。测得的初始残余应力分为两部分，如图3所示，X 方向给出轴向残余应力（Sigma X）梯度，Y 方向给出切向残余应力（Sigma Y）梯度。在ABAQUS中靶体沿深度方向分层并在添加该深度的实测初始残余应力。

  • 图3 初始残余应力表征结果

  • Fig.3 Original residual stress measurement results

  • 1.3 微粒喷丸模型

  • 1.3.1 单弹丸模型

  • 喷丸覆盖率作为喷丸工艺中最重要的工艺参数之一，直接影响喷丸工艺的加工质量。覆盖率C表示为被喷零部件表面上的弹痕面积与零部件总面积的比值，可通过阿夫拉米公式[26]计算：

  • C=1-exp⁡-πr2N×100%

  • 式中，r 为单个弹丸撞击后留下的弹坑半径；N 为弹丸个数。由于实际加工中难测量100%的覆盖率，故采用98%作为标准的100%覆盖率[27]。为了计算在不同喷射速度下达到覆盖率100%时所需的弹丸数量，在有限元模型中建立了单弹丸模型。

  • 在有限元软件ABAQUS中建立一个3mm× 3mm×1mm（长×宽×高）的靶体，采用各向同性的随动强化本构模型。在小方块的中心位置分割一个1mm×1mm×1mm的正方体作为微粒喷丸区域，加密网格，该区域单元类型为C3D8R，网格大小为10 μm，并将前两节测量得到的初始硬度和残余应力沿深度方向分别赋予微粒喷丸区域。由于微粒弹丸的硬度与靶体硬度相差较大，将微粒弹丸设置为刚体，丸粒直径为80 μm。采用不同喷射速度（150～250mm/s）垂直入射。弹丸与靶体之间的切向摩擦设置为罚函数（penalty），摩擦因数为0.3，法向行为设置为“硬接触”。

  • 图4 为仿真得到的在喷射速度分别为150、200、 250mm/s时产生的弹坑。可以发现，当喷射速度为200mm/s时，弹坑深度约为4.4 μm，弹坑半径约为0.025mm。并且随着喷射速度的增大，弹坑深度和半径逐渐增加。图5所示为模拟不同喷射速度下产生的弹坑深度与弹坑半径，可以发现随着喷射速度的增大，弹坑深度和半径近似线性增加。

  • 图4 仿真得到的三种喷射速度下的弹坑

  • Fig.4 Crater under three peening velocity by simulation

  • 图5 仿真得到的弹坑深度与弹坑半径

  • Fig.5 Crater depth and crater radius by simulation

  • 根据图4中得出的弹坑深度和阿夫拉米公式计算达到覆盖率100%时所需的弹丸数量。表3为在不同的喷射速度下，达到覆盖率100%时所需的弹丸数量。当采用同种丸粒，喷射速度为150m/s，达到覆盖率100%时，需要弹丸数3412；而喷射速度为250m/s，达到覆盖率100%时，需要弹丸数仅1 543个。对于微粒喷丸来说，达到某一覆盖率所需要的弹丸数受喷射速度影响极大。所以当丸粒种类与流量不变时，对于一定覆盖率的不同喷射速度，应严格控制喷射的弹丸数量，以免过喷。

  • 表3 仿真得到不同喷射速度下达到覆盖率100%时所需的弹丸数量

  • Table3 Number of particles required to achieve100%coverage at different injection speeds by simulation

  • 1.3.2 离散元与有限元相结合的微粒喷丸模型

  • 在单弹丸模型的基础上，靶体保持不变。在微粒喷丸区域上方2mm处建立一个1mm×1mm的正方形模拟喷枪。输出“inp”文件并基于PYTHON编程语言修改，使喷枪可以喷射出离散元丸粒，微粒为刚体，弹性模量与泊松比分别为210GPa和0.3；不考虑丸粒之间的相互作用，丸粒直径均为80 μm，入射角度90°，流量为0.05kg/s，分布喷射速度150～250m/s。弹丸与靶体之间的接触属性不变。模型建立好之后，选用ABAQUS/Explicit求解器的显示时间积分算法进行求解，建立的随机多弹丸有限元模型如图6所示。

  • 图6 微粒喷丸随机多弹丸模型

  • Fig.6 Micro-shot peening random multiple particles model

  • 2 随机多弹丸结果讨论

  • 2.1 常规喷丸与微粒喷丸

  • 为了对比常规喷丸与微粒喷丸的效果，取某一典型常规喷丸结果与微粒喷丸结果相比较，考虑到丸粒大小与喷射速度均不同，这里只做定性分析。常规喷丸模型中，采用丸粒直径0.6mm的铸钢丸对18CrNiMo7-6靶体进行常规喷丸处理，其喷射速度为56m/s，达到覆盖率100%时，常规喷丸仅需125个丸粒；选取典型的微粒喷丸参数与其对比，丸粒直径0.08mm，喷射速度为200m/s，达到覆盖率100%时，微粒喷丸需要2 040个丸粒。常规喷丸后产生的表面形貌与微粒喷丸的形貌对比如图7。可以发现，常规喷丸产生的表面形貌波动剧烈，算术平均偏差 Sa 达到3.06 μm；而微粒喷丸后的表面形貌质量较好，Sa 达到1.33 μm，数值大小与试验结果[19]中的近似。

  • 图7 仿真得到的常规喷丸与微粒喷丸的表面形貌对比

  • Fig.7 Comparison of surface morphology after shot peening and micro-shot peening by simulation

  • 图8 为覆盖率100%下常规喷丸与微粒喷丸的残余应力S11对比图。可以发现，相比于未喷丸情况，常规喷丸与微粒喷丸的残余应力S11均有显著增大。两者产生的最大残余应力相差不大，但最大残余应力的深度和残余应力层的厚度有着明显的差距。常规喷丸的最大残余压应力出现的深度位置约为0.11mm，微粒喷丸的最大残余压应力出现的深度位置为0.035mm，相差3～4倍。常规喷丸后产生的残余应力层深度可达0.2mm，而微粒喷丸产生的残余应力层深仅为0.1mm，相差2倍。由于微粒喷丸产生的表面粗糙度较小，残余应力层深较浅，更适用于精密零件。

  • 图8 仿真得到的常规喷丸与微粒喷丸的残余应力对比

  • Fig.8 Comparison of residual stress after shot peening and micro-shot peening by simulation

  • 2.2 微粒喷丸对表面形貌的影响

  • 图9 为不同喷射速度与不同覆盖率下的中心区形貌云图。可以发现，喷丸后的表面形貌呈现各向同性。随着覆盖率的增加，表面波动越来越剧烈，算术平均偏差 Sa 逐渐增大。随着喷射速度的增加，表面波动越来越剧烈， Sa 与表面粗糙度均方根值 Sq 均逐渐增大。

  • 图9 不同喷射速度与不同覆盖率下的中心区形貌云图

  • Fig.9 Morphology of central area under different peening velocity and different coverage rate

  • 常用的表面形貌参数有算术平均偏差 Sa，表面粗糙度均方根值 Sq，偏度 Ssk，峰度 Sku 等，分别表示为：

  • Sa=1n∑i=1n ZiSq=1n∑i=1n Zi212

  • Ssk=1nSq3∑i=1n Zi3Sku=1nSq4∑i=1n Zi4

  • 式中，n 表示数据点个数，Zi 表示 z 轴方向上数据点的高度（mm）。

  • 为了进一步探究喷射速度对表面形貌的影响，提取了图9中的表面形貌参数，绘制了覆盖率为100%时，喷射速度与形貌参数散点图，如图10所示。可以发现，随着喷射速度的增加，形貌参数Sa从1.07 μm（150m/s）线性增大至1.58 μm（250m/s），线性拟合后得到微粒喷丸的公式v-Sa：

  • Sa=4.87e-6×v+0.0003459,R2=0.9929

  • 图10 喷射速度对表面形貌参数的影响

  • Fig.10 Influence of particle speed on surface morphology parameters

  • 虽然表面粗糙度均方根值 Sq 随着喷射速度的增加，整体呈现增加的趋势，但并不稳定。这也是大多数喷丸文献采用算术平均偏差 Sa 评价表面形貌的原因。不管喷射速度的值为多少，偏度 Ssk 均小于0，说明表面形貌谷多于峰；峰度 Sku 基本小于3，说明喷丸后表面呈现为低峰态。

  • 为了进一步探究覆盖率对表面形貌的影响，提取了图9中的表面形貌参数，绘制了三种喷射速度下的 Sa-覆盖率散点图，如图11所示。覆盖率低于100%时，表面 Sa 迅速增大，当覆盖率高于100%时， Sa 变化较为平缓。

  • 图11 仿真得到的覆盖率对 Sa 的影响

  • Fig.11 Influence of coverage rate on Sa by simulation

  • 2.3 微粒喷丸对残余应力的影响

  • 当喷射速度分别为150、200、250m/s，覆盖率为200%时，部分中心区的残余应力云图如图12所示。可以发现，S11（X 方向）与S22（Y 方向） 在数值上相差不大，残余应力呈现为近似各向同性，该趋势与参考文献[28]中类似。最大残余拉应力S11与S22均出现在表面，并且随着喷射速度的增加，表面呈现为残余拉应力的区域逐渐增多，最大残余拉应力也逐渐增大。从截面可以看出，残余压应力最大值出现的深度位置约为0.03～0.04mm，这与常规喷丸的0.05～0.1mm[29]有明显差异。

  • 图12 仿真得到的残余应力云图

  • Fig.12 Residual stress results by simulation

  • 当喷射速度分别为200mm/s，覆盖率分别为100%、200%、300%时，残余应力S11散点图如图13所示。曲线表示残余应力平均值。由于S11与S22差别不大，故只给出了S11散点图。从残余应力散点中可以发现，近表面处残余应力的波动程度较为剧烈，同时存在残余拉应力与残余压应力； 随着深度的增加，只有残余压应力存在；当深度增加至芯部时，残余应力波动范围不大。随着覆盖率的增加，表面处的残余应力散点逐渐离散，但平均残余应力的结果差异不大，这个结论与常规喷丸结果[30]类似。表面处残余压应力均近似为500MPa，最大残余压应力均约为1 130MPa，深度均约为0.035mm。

  • 图13 仿真得到的三种覆盖率下残余应力 S11沿深度方向的变化情况

  • Fig.13 Variation of residual stress S11along the depth direction under the three coverage rates by simulation

  • 当覆盖率为200%，喷射速度分别为150、200、 250m/s时，残余应力S11散点图如图14所示。对比图14a～14c三图可以发现，三种喷射速度下的残余压应力最大值相差不大，大约在1 100MPa左右。这可能是因为残余应力不能无限增加，存在一定极限0.5～0.6倍的抗拉极限[31-32]，当微粒喷丸的速度达到一定程度时，残余压应力最大值就不再增加了。但当喷射速度为150m/s时，残余压应力最大值出现在约0.032mm深度位置；而200m/s时约为0.036mm深度位置；250m/s时在深度为0.04～0.055mm位置处，残余压应力均可达到1 000MPa。尽管最大残余压应力的值不再随着喷射速度的增加而增加，但最大残余应力出现的深度逐渐增加，LIN等[33]在研究常规喷丸机理时也得出过类似结论。除此之外，随着喷射速度的增大，近表面处散点的离散程度逐渐增加，残余压应力层厚度逐渐加深（从0.075mm到0.09mm，再到0.1mm），这个趋势也与LIN等[33]的结论一致。

  • 图14 仿真得到的三种喷射速度下残余应力 S11沿深度方向的变化情况

  • Fig.14 Variation of residual stress S11along the depth direction under the three peening velocity by simulation

  • 3 结论

  • 基于ABAQUS二次开发，采用离散元与有限元（DEM-FEM）相结合的方法，构建了考虑初始残余应力与硬化层梯度的随机多弹丸微粒喷丸弹塑性模型，探究了微粒喷丸的喷射速度与覆盖率对残余应力分布和表面粗糙度的影响规律。

  • （1）相比于普通喷丸，微粒喷丸后形成的表面粗糙度更小，形成的残余压应力层更薄，最大残余压应力相差不大。微粒喷丸更适用于表面形貌和残余应力需要兼顾的精密零件。

  • （2）微粒喷丸达到某一覆盖率所需要的弹丸数受喷射速度影响极大，相差甚至超过一倍。所以当丸粒种类与流量不变时，对于一定的覆盖率不同喷射速度，应严格控制喷射的弹丸数量，以免过喷。

  • （3）随着微粒喷丸喷射速度的增加，形貌参数算术平均偏差 Sa 线性增加；喷射速度对于微粒喷丸的最大残余压应力值影响不大，但对残余应力层的厚度有显著影响。

  • （4）当微粒喷丸覆盖率达到100%以上后，覆盖率大小对 Sa 与残余压应力分布影响不大，硬度680HV表面处残余压应力均近似为500MPa，最大残余压应力的大小均约为1 130MPa，深度均约为0.035mm。

  • 参考文献

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    • [4] HASSAN A M,MOMANI A M S.Further improvements in some properties of shot peened components using the burnishing process[J].International Journal of Machine Tools & Manufacture,2000,40(12):1775-1786.

    • [5] CHILD D J,WEST G D,THOMSON R C.Assessment of surface hardening effects from shot peening on a Ni-based alloy using electron backscatter diffraction techniques[J].Acta Materialia,2011,59(12):4825-4834.

    • [6] KARAOGLANLI A C,DOLEKER K M,DEMIREL B,et al.Effect of shot peening on the oxidation behavior of thermal barrier coatings[J].Applied Surface Science,2015,354:314-322.

    • [7] LIU G,LU J,LU K.Surface nanocrystallization of 316L stainless steel induced by ultrasonic shot peening[J].Materials Science and Engineering:A,2000,286(1):91-95.

    • [8] LUO K,LU J,ZHANG Y,et al.Effects of laser shock processing on mechanical properties and micro-structure of ANSI 304 austenitic stainless steel[J].Materials Science and Engineering:A,2011,528(13-14):4783-4788.

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  • 基本信息

    中图分类号: TG17
    DOI: 10.11933/j.issn.1007−9289.20211126001

    基金信息

    中央高校基本科研业务费资助项目(2021CDJCGJ003)；
    Supported by Fundamental Research Funds for the Central Universities of China (2021CDJCGJ003).；

    引用信息

    稿件历史

    收稿日期: 2021-11-26

  • 参考文献

    • [1] AL-OBAID Y F.Shot peening mechanics:experimental and theoretical analysis[J].Mechanics of Materials,1995,19(2-3):251-260.

    • [2] 高玉魁.残余应力基础理论及应用[M].上海：上海科学技术出版社，2019.GAO Yukui.Theory and application of residual stresses [M].Shanghai:Shanghai Science and Technology Press,2019.(in Chinese)

    • [3] SEKI M,SOMEYA H,FUJII M,et al.Rolling contact fatigue life of cavitation-peened steel gear[J].Tribology Online,2008,3(2):116-121.

    • [4] HASSAN A M,MOMANI A M S.Further improvements in some properties of shot peened components using the burnishing process[J].International Journal of Machine Tools & Manufacture,2000,40(12):1775-1786.

    • [5] CHILD D J,WEST G D,THOMSON R C.Assessment of surface hardening effects from shot peening on a Ni-based alloy using electron backscatter diffraction techniques[J].Acta Materialia,2011,59(12):4825-4834.

    • [6] KARAOGLANLI A C,DOLEKER K M,DEMIREL B,et al.Effect of shot peening on the oxidation behavior of thermal barrier coatings[J].Applied Surface Science,2015,354:314-322.

    • [7] LIU G,LU J,LU K.Surface nanocrystallization of 316L stainless steel induced by ultrasonic shot peening[J].Materials Science and Engineering:A,2000,286(1):91-95.

    • [8] LUO K,LU J,ZHANG Y,et al.Effects of laser shock processing on mechanical properties and micro-structure of ANSI 304 austenitic stainless steel[J].Materials Science and Engineering:A,2011,528(13-14):4783-4788.

    • [9] 何浩然，刘峰，李恒智，等.喷丸处理Q235钢中晶粒尺寸与残余应力的关系预测[J].中国表面工程，2021，34(2)：49-58 HE Haoran,LIU Feng,LI Hengzhi,et al.Prediction of relationship between grain size and residual stress in shot peening Q235 steel[J].China Surface Engineering,2021,34(2):49-58(in Chinese).

    • [10] LI W,LIU B.Experimental investigation on the effect of shot peening on contact fatigue strength for carburized and quenched gears[J].International Journal of Fatigue,2017,106:103-113.

    • [11] 谢俊峰，何声馨，李纪强，等.喷丸强化对 18CrNiMo7-6 渗碳齿轮表面性能的影响[J].热加工工艺，2017(18)：179-181.XIE Junfeng,HE Shengxin,LI Jiqiang,et al.Effect of shot peening on surface properties of 18CrNiMo7-6 carburized gear[J].Hot Working Technology,2017(18):179-181.(in Chinese)

    • [12] MO S,ZHANG T,JIN G,et al.Elastohydrodynamic lubrication characteristics of spiral bevel gear subjected to shot peening treatment[J].Mathematical Problems in Engineering,2018:3043712.

    • [13] 高玉魁.表面完整性理论与应用[M].北京：化学工业出版社，2014.GAO Yukui.Theory and application of surface integrity [M].Beijing:Chemical Industry Press,2014(in Chinese).

    • [14] BAGHERIFARD S,GUAGLIANO M.Fatigue behavior of a low-alloy steel with nanostructured surface obtained by severe shot peening[J].Engineering Fracture Mechanics,2012,81:56-68.

    • [15] VRBKA M,KŘUPKA I,SVOBODA P,et al.Effect of shot peening on rolling contact fatigue and lubricant film thickness within mixed lubricated non-conformal rolling/sliding contacts[J].Tribology International,2011,44(12):1726-1735.

    • [16] SEKI M,SOYAMA H,KOBAYASHI Y,et al.Rolling contact fatigue life of steel rollers treated by cavitation peening and shot peening[J].Journal of Solid Mechanics and Materials Engineering,2012,6(6):478-486.

    • [17] WIDMARK M,MELANDER A.Effect of material,heat treatment,grinding and shot peening on contact fatigue life of carburized steels[J].International Journal of Fatigue,1999,21(4):309-327.

    • [18] ITO T,KIKUCHI S,HIROTA Y,et al.Analysis of pneumatic fine particle peening process by using a high-speed-camera[J].International Journal of Modern Physics B,2010,24(15-16):3047-3052.

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