李新凱，王榮，胡露瑤，任旭隆，王喜社

掃描電子束能量峰值對表面溫度場的影響規(guī)律

李新凱1，王榮1，胡露瑤2，任旭隆1，王喜社1

（1.桂林電子科技大學，廣西 桂林 541004；2.桂林旅游學院，廣西 桂林 541004）

掃描電子束；能量；溫度場；熱源；表面改性

近年來，電子束以其非接觸、可控性強、真空無污染、能量利用率高等優(yōu)點而廣泛應用于材料表面改性領域中[1-2]。常見的電子束表面處理技術包括電子束表面合金化、表面淬火、表面非晶態(tài)、表面熔凝等，以上電子束技術均是對金屬材料表層進行處理，需實現電子束大面域、均勻、穩(wěn)定下束[3-4]。

目前，國內外學者已對強流脈沖電子束與大面域輻照兩種電子束表面改性加工方法進行了深入研究，主要考察電子束類型[5]及工藝參數[6]、電子束能量分布規(guī)律[7]以及表面改性優(yōu)化方法[8]等方面。研究發(fā)現脈沖電子束能量密度較大，適用于處理高熔點、大深寬比金屬表面改性，但處理過程中表層金屬會發(fā)生濺射產生“熔坑”缺陷，同時高能作用下表層經歷驟熱急冷過程，易造成內應力與組織應力集中，產生結構裂紋缺陷[9-11]。大面積電子束輻照是通過電子束散焦的方式實現最大面積為60 mm范圍的改性，因下束面積大所以更適用于表面微熔處理，然而該方式對電子槍功率要求較高，較難實現電子束能量的均勻分布[12]。本團隊在此基礎上，針對電子束表面微熔處理能量密度均勻且穩(wěn)定分布的需求，開發(fā)了一種新型連續(xù)掃描電子束技術（Continuous Scanning Electron Beam Technique Process，CSEBP），通過聚焦線圈與偏轉線圈共同作用，實現電子束聚焦的同時以高頻率旋轉實現環(huán)狀下束效果[13-15]。研究發(fā)現環(huán)狀掃描下束下電子槍無需高功率即可實現較高能量密度的均勻分布。另外，CSEBP能量密度分布除了受到電子束束流以及加速電壓等電子槍參數影響外，還受到能量分布特征參數影。因此，有必要對電子束下束過程中能量分布規(guī)律進行探索，以指導CSEBP在表面改性領域的應用。

本文以45鋼為電子束表面改性為研究對象，通過數值求解、仿真計算與試驗驗證相結合的方式探究能量峰值系數對電子束能量分布的影響規(guī)律，詳細探討了多種峰值系數下45鋼表層溫度的變化規(guī)律，并通過電子束微熔試驗進行驗證，力圖為電子束大面域掃描提供新的方法和理論依據。

1 掃描電子束微熔處理數學物理模型的建立

1.1 CSEBP下束方式原理

本課題組自主研發(fā)的掃描電子束下束方式如圖1所示，其中，為工件移動速度，為掃描帶半徑，為掃描長度，掃描帶縱向5個均分點為后續(xù)熱循環(huán)曲線仿真取樣點。其原理是將編輯好的電子束掃描軌跡及運動方式的控制程序輸入信號發(fā)生器，用方程x+y=2來描述圓形的電子束掃描軌跡，其中方向的分量分別為cos，sin（0≤≤π），通過所產生的偏轉磁場實現電子槍內部束流沿固定角度傾斜與高頻旋轉，從而實現環(huán)狀掃描電子束軌跡。

圖1 連續(xù)掃描電子束（CSEBP）示意圖

1.2 環(huán)狀下束電子束能量分布數學模型

環(huán)狀電子束熱源與常用的高斯熱源、雙橢球熱源有較大不同，其作用形式為高斯熱源在環(huán)形區(qū)域的疊加。為此以高斯熱源為基礎搭建環(huán)狀電子束能量密度函數，如圖2和圖3所示。

圖2 電子束能量密度分布圖

設表面中心處的熱流密度()為：

式中：為任意一點的熱流密度（W）；m為最大熱流密度（W/m2）；為任意一點到加熱中心的距離（m）；為熱源集中系數。

掃描電子束微熔處理時在掃描面的功率為：

由式（2）得：

將式（3）代入（1）得：

通常情況下掃描電子束處理時，一般取95%的有效能量范圍[18]。

由此可得：

因電子束作用過程中，束斑內能量峰值可調，為此引入能量峰值位置參數，綜合以上計算可將掃描電子束能量分布數學模型表征為：

式中：Rx為電子束下束環(huán)外徑（mm）；Rp為電子束能量峰值位置距離z軸的距離（mm）；rx為圓環(huán)內徑（mm）；為束流偏轉角（°）；為能量峰位置系數，；z為離焦量（mm），R0為束斑寬度（mm）。

1.3 能量峰值對電子束熱源模型的影響

圖4 不同入射角度和能量峰值系數下的電子束能量分布模擬圖

上述所建立的電子束熱源數學模型中引入能量峰位置系數，可對環(huán)形區(qū)域內的電子束能量分布狀態(tài)作更加詳細的定義，該系數對平衡環(huán)形束斑內外側溫度補償與中心熱傳導有重要意義。

2 建立掃描電子束有限元模型

2.1 模型假設

電子束表面處理過程是一個驟熱急冷的非穩(wěn)態(tài)過程，表層的金屬的熔融與凝固均在極短時間內完成，為簡化模型、減少運算量，對模型作出以下假設：45鋼的熱物性參數為溫度的函數；電子束掃描過程中熱傳導處于穩(wěn)態(tài)；樣為各向同性的均勻介質；試樣被處理前的溫度和所處的工作室溫度均為300 K；不考慮熱對流；忽略組織相變引起的塑性變形[19-20]。

2.2 幾何建模與網格劃分

采用COMSOL軟件對45鋼掃描電子束微熔過程進行模擬，模型尺寸與實際試樣尺寸一致，為50 mm× 50 mm×50 mm，在工作面選取50 mm×8 mm區(qū)域作為電子束加工區(qū)域，并進行網格加密處理，電子束掃描區(qū)域采用六面體的單元類型進行較細的網格劃分，其他區(qū)域采用四面體的單元類型進行智能網格劃分，網格劃分模型如圖5所示[21-22]。模型內部為均勻介質，所以將試樣中某處定義為微元控制體積ddd。

電子束掃描試樣表面時，熱傳導會通過控制體積的各個面發(fā)生。利用泰勒公式展開控制表面的導熱速度，直角坐標系中的熱擴散方程為：

式中：為密度（kg/m3）；為定壓比熱容（J·kg/K）；k為導熱系數（W/(m·K)）。

2.3 電子束熱源模型及邊界條件

掃描電子束是以高能電子束轟擊金屬表面產生的高溫為熱源，并以指定速度平移實現大面域掃描，由上述搭建能量分布數學模型，其移動熱源與時間的函數表達式為：

掃描電子束微熔處理是在真空環(huán)境中進行，真空度為10?2Pa，故可忽略空氣熱對流造成的熱量損失，而熱輻射的傳遞不需借助任何介質[23]。因此可認為基體的導熱與表面的熱輻射是工件主要散熱方式，電子束熱源作用區(qū)域的傳熱方程為：

熱輻射滿足第三類邊界條件，可由斯蒂芬–波爾茲曼方程來計算：

3 掃描電子束微熔處理溫度場仿真分析

根據前期研究結果[24-25]，溫度場仿真工藝參數為：=60 kV，=5 mA，=3 mm/s，=230 mm，R+0/2=2 mm，=5°，=400 Hz，整個電子束加熱時間為16.7 s。

3.1 電子束能量峰值對熱循環(huán)過程的影響

圖6 掃描帶上不同點熱循環(huán)曲線

3.2 電子束能量峰值對溫度場的影響

圖7 掃描區(qū)溫度云圖

4 掃描電子束微熔處理試驗

試驗選用45鋼作為實驗用原材料，使用銑床將原材料加工成50 mm×50 mm×50 mm的立方體，加工過程中通過控制進刀量、銑削速度、主軸轉速等參數恒定，將試樣表面粗糙度控制在1.9～2.0 μm內，電子束加工前使用酒精擦拭表面并風干，去除表面油污。使用HDZ–6F型高壓數控真空電子束機進行表面處理試驗，實驗參數與數值模擬參數一致。采用光學顯微鏡對熔融層進行觀測，采用OLS4100激光顯微鏡測試處理后表面粗糙度。每個待測面均勻測量5次粗糙度，取其均值作為該面粗糙度值。

圖8 不同峰值系數下的表面形貌

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The Influence of the Peak Energy of Scanning Electron Beam on the Surface Temperature Field

1,1,2,1,1

(1. Guilin University of Electronic Technology, Guangxi Guilin 541004, China; 2. Guilin Tourism University, Guangxi Guilin 541004, China)

The mathematical model of energy distribution in the circular downward beam mode of scanning electron beams is clearly defined. Obtain the influence law of energy crest factor on the surface temperature field of 45 steel. Based on the Gaussian heat source model, the energy peak position parameter is introduced to calculate the mathematical model of the energy distribution in the scanning electron beam downward beam mode. The COMSOL software was used to simulate the thermal cycle curve and temperature field of the scanning zone. Revised the electron beam heat source model in the ring-shaped downward beam mode. The results show that the electron beam energy distribution was symmetrically distributed along the center line. The surface energy distribution was related to the deflection angle and the energy peak parameter. When the energy peak parameter was within 0 to 1, the value becomes higher and higher, the larger the first and second energy peaks at point, the larger the difference between the two. When the parameter was 0, the maximum temperature difference at the sampling point was 1 065 K. The smaller the temperature difference between the longitudinal points of the scanning belt, the smaller the distance between the thermal cycle curves. At the same time, it can be seen from the heat source model that the energy peak has a greater impact on the beam diameter of the ring electron beam, and the maximum ring diameter can be up to 8 mm under the selected basic parameters. When the parameter was 1, the temperature curves of the sampling points are the closest, which indicates that the surface heat distribution under this parameter was uniform. It can be seen from the temperature field simulation diagram that the beam spot temperature varies greatly during the down and converging phases of the electron beam, while the temperature in the middle of the scan was relatively stable, and the temperature difference was basically stable within 20 K. The larger the energy peak parameter, the larger the radius of the high temperature area on the surface of 45 steel, and the maximum temperature will increase accordingly. After 45 steel was subjected to different energy peak coefficients, the width of the scanning zone and the sub-high temperature zone were different. Finally, based on the simulation parameters, the scanning electron beam micro-melting polishing experiment was carried out. It was found that the surface roughness of 45 steel was reduced under this scanning mode, and the surface showed a bright white scanning area relative to the substrate. The scanning area width increased with the increase of the energy peak parameter. This was in full agreement with the simulation results. The surface roughness after scanning electron beam treatment was as low as 0.36 μm relative to the substrate. In the end, the following conclusion can be drawn that the energy peak parameter has a great influence on the energy distribution of the ring electron beam. When= 1, the energy gradient of each position on the surface of the scanning area was the smallest, which was beneficial to the uniform energy distribution under the surface modification of the large area electron beam.

scanning electron beams; energy; temperature field; heat source; surface modification

V261.6

A

1001-3660(2022)07-0306-08

10.16490/j.cnki.issn.1001-3660.2022.07.030

2021–04–02；

2021–11–20

2021-04-02；

2021-11-20

廣西自然科學基金項目（2020GXNSFBA297079，2022GXNSFAA035585）；國家自然科學基金資助項目（52165057，51665009）；桂林市重點研發(fā)計劃（20211B032068）

Guangxi Natural Science Foundation Project (2020GXNSFBA297079, 2022GXNSFAA035585); National Natural Science Foundation of China (52165057, 51665009); Guilin City Key Research and Development Plan (20211B032068)

李新凱（1993—），男，博士研究生，主要研究方向為電子束表面改性。

LI Xin-kai (1993-), Male, Ph. D. candidate, Research focus: electron beam surface modification.

王喜社（1966—），女，高級實驗師，主要研究方向為數控加工與工藝優(yōu)化。

WANG Xi-she (1966-), Female, Senior experimenter, Research focus: CNC machining and process optimization.

李新凱, 王榮, 胡露瑤, 等. 掃描電子束能量峰值對表面溫度場的影響規(guī)律[J]. 表面技術, 2022, 51(7): 306-313.

LI Xin-kai, WANG Rong, HU Lu-yao, et al. The Influence of the Peak Energy of Scanning Electron Beam on the Surface Temperature Field[J]. Surface Technology, 2022, 51(7): 306-313.

責任編輯：萬長清