電風扇旋鈕注塑模具設計
電風扇旋鈕注塑模具設計,電風扇,旋鈕,注塑,模具設計
基于注塑模具鋼研磨和拋光工序的自動化表面處理
摘要
本文研究了注塑模具鋼自動研磨與球面拋光加工工序的可能性，這種注塑模具鋼PDS5的塑性曲面是在數控加工中心完成的。這項研究已經完成了磨削刀架的設計與制造。 最佳表面研磨參數是在鋼鐵PDS5 的加工中心測定的。對于PDS5注塑模具鋼的最佳球面研磨參數是以下一系列的組合：研磨材料的磨料為粉紅氧化鋁，進給量500毫米/分鐘，磨削深度20微米，磨削轉速為18000RPM。用優(yōu)化的參數進行表面研磨，表面粗糙度Ra值可由大約1.60微米改善至0.35微米。 用球拋光工藝和參數優(yōu)化拋光，可以進一步改善表面粗糙度Ra值從0.343微米至0.06微米左右。在模具內部曲面的測試部分，用最佳參數的表面研磨、拋光，曲面表面粗糙度就可以提高約2.15微米到0 0.07微米。
關鍵詞: 自動化表面處理 拋光 磨削加工 表面粗糙度 田口方法
一、引言
塑膠工程材料由于其重要特點,如耐化學腐蝕性、低密度、易于制造,并已日漸取代金屬部件在工業(yè)中廣泛應用。 注塑成型對于塑料制品是一個重要工藝。注塑模具的表面質量是設計的本質要求,因為它直接影響了塑膠產品的外觀和性能。 加工工藝如球面研磨、拋光常用于改善表面光潔度。
研磨工具(輪子)的安裝已廣泛用于傳統(tǒng)模具的制造產業(yè)。自動化表面研磨加工工具的幾何模型將介紹。自動化表面處理的球磨研磨工具將得到示范和開發(fā)。 磨削速度, 磨削深度，進給速率和砂輪尺寸、研磨材料特性（如磨料粒度大?。┦乔蛐窝心スに囍兄饕膮担鐖D1（球面研磨過程示意圖）所示。注塑模具鋼的球面研磨最優(yōu)化參數目前尚未在文獻得到確切的依據。
步距
研磨高度
球磨研磨
進給速度
工作臺
圖1 球面研磨過程示意圖
進給
研磨球
工作臺
研磨深度
研磨表面
近年來 ，已經進行了一些研究，確定了球面拋光工藝的最優(yōu)參數(圖2) （球面拋光過程示意圖）。 比如，人們發(fā)現(xiàn), 用碳化鎢球滾壓的方法可以使工件表面的塑性變形減少,從而改善表面粗糙度、表面硬度、抗疲勞強度。 拋光的工藝的過程是由加工中心和車床共同完成的。對表面粗糙度有重大影響的拋光工藝主要參數，主要是球或滾子材料，拋光力， 進給速率,拋光速度,潤滑、拋光率及其他因素等。注塑模具鋼PDS5的表面拋光的參數優(yōu)化，分別結合了油脂潤滑劑，碳化鎢球,拋光速度200毫米/分鐘,拋光力300牛，40微米的進給量。采用最佳參數進行表面研磨和球面拋光的深度為2.5微米。 通過拋光工藝，表面粗糙度可以改善大致為40％至90％。
圖2 球面拋光過程示意圖
此項目研究的目的是，發(fā)展注塑模具鋼的球形研磨和球面拋光工序，這種注塑模具鋼的曲面實在加工中心完成的。表面光潔度的球研磨與球拋光的自動化流程工序，如圖3所示。 我們開始自行設計和制造的球面研磨工具及加工中心的對刀裝置。利用田口正交法，確定了表面球研磨最佳參數。選擇為田口L18型矩陣實驗相應的四個因素和三個層次。 用最佳參數進行表面球研磨則適用于一個曲面表面光潔度要求較高的注塑模具。 為了改善表面粗糙, 利用最佳球面拋光工藝參數，再進行對表層打磨。
PDS試樣的設計與制造
選擇最佳矩陣實驗因子
確定最佳參數
實施實驗
分析并確定最佳因子
進行表面拋光
應用最佳參數加工曲面
測量試樣的表面粗糙度
球研磨和拋光裝置的設計與制造
圖3自動球面研磨與拋光工序的流程圖
二、球研磨的設計和對準裝置
實施過程中可能出現(xiàn)的曲面的球研磨,研磨球的中心應和加工中心的Z軸相一致。 球面研磨工具的安裝及調整裝置的設計，如圖4（球面研磨工具及其調整裝置）所示。電動磨床展開了兩個具有可調支撐螺絲的刀架。磨床中心正好與具有輔助作用的圓錐槽線配合。 擁有磨床的球接軌,當兩個可調支撐螺絲被收緊時，其后的對準部件就可以拆除。研磨球中心坐標偏差約為5微米, 這是衡量一個數控坐標測量機性能的重要標準。 機床的機械振動力是被螺旋彈簧所吸收。球形研磨球和拋光工具的安裝，如圖5（a. 球面研磨工具的圖片. b.球拋光工具的圖片）所示。為使球面磨削加工和拋光加工的進行，主軸通過球鎖機制而被鎖定。
模柄
彈簧
工具可調支撐
緊固螺釘
磨球
自動研磨
磨球組件
圖4 球面研磨工具及其調整裝置
圖5 a. 球面研磨工具的圖片. b.球拋光工具的圖片
三、矩陣實驗的規(guī)劃
3.1田口正交表
利用矩陣實驗田口正交法，可以確定參數的有影響程度。 為了配合上述球面研磨參數，該材料磨料的研磨球(直徑10毫米),進給速率，研磨深度,在次研究中電氣磨床被假定為四個因素，指定為從A到D（見表1實驗因素和水平）。三個層次的因素涵蓋了不同的范圍特征,并用了數字1、2、3標明。挑選三類磨料,即碳化硅,白色氧化鋁,粉紅氧化鋁來研究. 這三個數值的大小取決于每個因素實驗結果。選定L18型正交矩陣進行實驗，進而研究四——三級因素的球形研磨過程。
表1實驗因素和水平
因素
水平
1
2
3
A.
碳化硅
白色氧化鋁
粉紅氧化鋁
B.
50
100
200
C.研磨深度（μm）
20
50
80
D.
12000
18000
24000
3.2數據分析的界定
工程設計問題,可以分為較小而好的類型,象征性最好類型,大而好類型，目標取向類型等。 信噪比(S/N)的比值，常作為目標函數來優(yōu)化產品或者工藝設計。 被加工面的表面粗糙度值經過適當地組合磨削參數，應小于原來的未加工表面。 因此,球面研磨過程屬于工程問題中的小而好類型。這里的信噪比（S/N）,η,按下列公式定義:
η =?10 log 平方等于質量特性
=?10 log （1）
這里，
y——不同噪聲條件下所觀察的質量特性
n——實驗次數
從每個L18型正交實驗得到的信噪比（S/N）數據，經計算后，運用差異分析技術(變異)和殲比檢驗來測定每一個主要的因素。 優(yōu)化小而好類型的工程問題問題更是盡量使η最大而定。各級η選擇的最大化將對最終的η因素有重大影響。 最優(yōu)條件可視研磨球而待定。
四、實驗工作和結果
這項研究使用的材料是PDS5工具鋼(相當于艾西塑膠模具)， 它常用于大型注塑模具產品在國內汽車零件領域和國內設備。 該材料的硬度約HRC33(HS46)。 具體好處之一是, 由于其特殊的熱處理前處理，模具可直接用于未經進一步加工工序而對這一材料進行加工。式樣的設計和制造,應使它們可以安裝在底盤，來測量相應的反力。 PDS5試樣的加工完畢后，裝在大底盤上在三坐標加工中心進行了銑削，這種加工中心是由鋼鐵公司所生產(中壓型三號),配備了FANUC-18M公司的數控控制器(0.99型)。用hommelwerket4000設備來測量前機加工前表面的粗糙度,使其可達到1.6微米。 圖6試驗顯示了球面磨削加工工藝的設置。 一個由Renishaw公司生產的視頻觸摸觸發(fā)探頭，安裝在加工中心上，來測量和確定和原始式樣的協(xié)調。 數控代碼所需要的磨球路徑由PowerMILL軟件產。這些代碼經過RS232串口界面，可以傳送到裝有控制器的數控加工中心上。
加工中心
數控機床
電腦
圖6
完成了L18型矩陣實驗后，表2 （PDS5試樣光滑表層的粗糙度）總結了光滑表面的粗糙度RA值，計算了每一個L18型矩陣實驗的信噪比（S/N）,從而用于方程（1）。通過表2提供的各個數值，可以得到四種不同程度因素的平均信噪比（S/N），在圖7中已用圖表顯示。
表2 PDS5試樣光滑表層的粗糙度
實驗
序號
A
B
C
D
S/N(η(dB))
Mean
1
1
1
1
1
0.35
0.35
0.35
9.119
0.350
2
1
2
2
2
0.37
0.36
0.38
8.634
0.370
3
1
3
3
3
0.41
0.44
0.40
7.597
0.417
4
2
1
2
3
0.63
0.65
0.64
3.876
0.640
5
2
2
3
1
0.73
0.77
0.78
2.380
0.760
6
2
3
1
2
0.45
0.42
0.39
7.530
0.420
7
3
1
3
2
0.34
0.31
0.32
9.801
0.323
8
3
2
1
3
0.27
0.25
0.28
11.471
0.267
9
3
3
2
1
0.32
0.32
0.32
9.897
0.320
10
1
1
2
2
0.35
0.39
0.40
8.390
0.380
11
1
2
3
3
0.41
0.50
0.43
6.968
0.447
12
1
3
1
1
0.40
0.39
0.42
7.883
0.403
13
2
1
1
3
0.33
0.34
0.31
9.712
0.327
14
2
2
2
1
0.48
0.50
0.47
6.312
0.483
15
2
3
3
2
0.57
0.61
0.53
4.868
0.570
16
3
1
3
1
0.59
0.55
0.54
5.030
0.560
17
3
2
1
2
0.36
0.36
0.35
8.954
0.357
18
3
3
2
3
0.57
0.53
0.53
5.293
0.543
控制因素
信噪比
圖7 控制影響因素
球面研磨工藝的目標，就是通過確定每一種因子的最佳優(yōu)化程度值，來使試樣光滑表層的表面粗糙度值達到最小。因為? log是一個減函數，我們應當使信噪比（S/N）達到最大。因此，我們能夠確定每一種因子的最優(yōu)程度使得η的值達到最大。因此基于這個點陣式實驗的最優(yōu)轉速應該是18000RPM，如表3（優(yōu)化組合球面研磨參數）所示。
表3 優(yōu)化組合球面研磨參數
因素
水平
白色氧化鋁
50mm/min
20μm
18000rpm
從田口矩陣實驗獲得的球面研磨優(yōu)化參數，適用于曲面光滑的模具，從而改善表面的粗糙度。選擇香水瓶為一個測試載體。對于被測物體的模具數控加工中心，由PowerMILL軟件來模擬測試。經過精銑，通過使用從田口矩陣實驗獲得的球面研磨優(yōu)化參數，模具表面進一步光滑。緊接著,使用打磨拋光的最佳參數，來對光滑曲面進行拋光工藝，進一步改善了被測物體的表面粗糙度。(見圖 9)。模具內部的表面粗糙度用hommelwerket4000設備來測量。模具內部的表面粗糙度RA的平均值為2.15微米，光滑表面粗糙度RA的平均值為0.45微米，拋光表面粗糙度RA的平均值為0.07微米。被測物體的光滑表面的粗糙度改善了：(2.15-0.45)/2.15=79.1％，拋光表面的粗糙度改善了：(2.15-0.07)/2.15=96.7％。
拋光表面
Ra=0.07μm
內部表面
Ra=2.15μm
光滑表面
Ra=0.45μm
圖8 被測物體表面粗糙度
五、結論
在這項工作中,對注塑模具的曲面進行了自動球面研磨與球面拋光加工，并將其工藝最佳參數成功地運用到加工中心上。 設計和制造了球面研磨裝置(及其對準組件)。通過實施田口L18型矩陣進行實驗，確定了球面研磨的最佳參數。對于PDS5注塑模具鋼的最佳球面研磨參數是以下一系列的組合：材料的磨料為粉紅氧化鋁，進給量料500毫米/分鐘，磨削深度20微米，轉速為18000RPM。通過使用最佳球面研磨參數，試樣的表面粗糙度Ra值從約1.6微米提高到0.35微米。應用最優(yōu)化表面磨削參數和最佳拋光參數，來加工模具的內部光滑曲面，可使模具內部的光滑表面改善79.1％，拋光表面改善96.7％。
鳴謝
作者感謝中國國家科學理事會對本次研究的支持, NSC 89-2212-E-011-059。
Automated surface finishing of plastic injection mold steel with spherical grinding and ball burnishing processes
Abstract
This study investigates the possibilities of automated spherical grinding and ball burnishing surface finishing processes in a freeform surface plastic injection mold steel PDS5 on a CNC machining center. The design and manufacture of a grinding tool holder has been accomplished in this study. The optimal surface grinding parameters were determined using Taguchi’s orthogonal array method for plastic injection molding steel PDS5 on a machining center. The optimal surface grinding parameters for the plastic injection mold steel PDS5 were the combination of an abrasive material of PA Al2O3, a grinding speed of 18 000 rpm, a grinding depth of 20 μm, and a feed of 50 mm/min. The surface roughness Ra of the specimen can be improved from about 1.60 μm to 0.35 μm by using the optimal parameters for surface grinding. Surface roughness Ra can be further improved from about 0.343 μm to 0.06 μm by using the ball burnishing process with the optimal burnishing parameters. Applying the optimal surface grinding and burnishing parameters sequentially to a fine-milled freeform surface mold insert, the surface roughness Ra of freeform surface region on the tested part can be improved from about 2.15 μm to 0.07 μm.
Keywords Automated surface finishing · Ball burnishing process · Grinding process · Surface roughness · Taguchi’s method
1 Introduction
Plastics are important engineering materials due to their specific characteristics, such as corrosion resistance, resistance to chemicals, low density, and ease of manufacture, and have increasingly replaced metallic components in industrial applications. Injection molding is one of the important forming processes for plastic products. The surface finish quality of the plastic injection mold is an essential requirement due to its direct effects on the appearance of the plastic product. Finishing processes such as grinding, polishing and lapping are commonly used to improve the surface finish.
The mounted grinding tools (wheels) have been widely used in conventional mold and die finishing industries. The geometric model of mounted grinding tools for automated surface finishing processes was introduced in. A finishing process mode of spherical grinding tools for automated surface finishing systems was developed in. Grinding speed, depth of cut, feed rate, and wheel properties such as abrasive material and abrasive grain size, are the dominant parameters for the spherical grinding process, as shown in Fig. 1. The optimal spherical grinding parameters for the injection mold steel have not yet been investigated based in the literature.
Fig.1. Schematic diagram of the spherical grinding process
In recent years, some research has been carried out in determining the optimal parameters of the ball burnishing process (Fig. 2). For instance, it has been found that plastic deformation on the workpiece surface can be reduced by using a tungsten carbide ball or a roller, thus improving the surface roughness, surface hardness, and fatigue resistance. The burnishing process is accomplished by machining centers and lathes. The main burnishing parameters having significant effects on the surface roughness are ball or roller material, burnishing force, feed rate, burnishing speed, lubrication, and number of burnishing passes, among others. The optimal surface burnishing parameters for the plastic injection mold steel PDS5 were a combination of grease lubricant, the tungsten carbide ball, a burnishing speed of 200 mm/min, a burnishing force of 300 N, and a feed of 40 μm. The depth of penetration of the burnished surface using the optimal ball burnishing parameters was about 2.5 microns. The improvement of the surface roughness through burnishing process generally ranged between 40% and 90%.
Fig. 2. Schematic diagram of the ball-burnishing process
The aim of this study was to develop spherical grinding and ball burnishing surface finish processes of a freeform surface plastic injection mold on a machining center. The flowchart of automated surface finish using spherical grinding and ball burnishing processes is shown in Fig. 3. We began by designing and manufacturing the spherical grinding tool and its alignment device for use on a machining center. The optimal surface spherical grinding parameters were determined by utilizing a Taguchi’s orthogonal array method. Four factors and three corresponding levels were then chosen for the Taguchi’s L18 matrix experiment. The optimal mounted spherical grinding parameters for surface grinding were then applied to the surface finish of a freeform surface carrier. To improve the surface roughness, the ground surface was further burnished, using the optimal ball burnishing parameters.
Fig. 3. Flow chart of automated surface finish using spherical grinding and ball burnishing processes
2 Design of the spherical grinding tool and its alignment device
To carry out the possible spherical grinding process of a freeform surface, the center of the ball grinder should coincide with the z-axis of the machining center. The mounted spherical grinding tool and its adjustment device was designed, as shown in Fig. 4. The electric grinder was mounted in a tool holder with two adjustable pivot screws. The center of the grinder ball was well aligned with the help of the conic groove of the alignment components. Having aligned the grinder ball, two adjustable pivot screws were tightened; after which, the alignment components could be removed. The deviation between the center coordinates of the ball grinder and that of the shank was about 5 μm, which was measured by a CNC coordinate measuring machine. The force induced by the vibration of the machine bed is absorbed by a helical spring. The manufactured spherical grinding tool and ball-burnishing tool were mounted, as shown in Fig. 5. The spindle was locked for both the spherical grinding process and the ball burnishing process by a spindle-locking mechanism.
Fig.4. Schematic illustration of the spherical grinding tool and its adjustment device
Fig.5. (a) Photo of the spherical grinding tool (b) Photo of the ball burnishing tool
3 Planning of the matrix experiment
3.1 Configuration of Taguchi’s orthogonal array
The effects of several parameters can be determined efficiently by conducting matrix experiments using Taguchi’s orthogonal array. To match the aforementioned spherical grinding parameters, the abrasive material of the grinder ball (with the diameter of 10 mm), the feed rate, the depth of grinding, and the revolution of the electric grinder were selected as the four experimental factors (parameters) and designated as factor A to D (see Table 1) in this research. Three levels (settings) for each factor were configured to cover the range of interest, and were identified by the digits 1, 2, and 3. Three types of abrasive materials, namely silicon carbide (SiC), white aluminum oxide (Al2O3, WA), and pink aluminum oxide (Al2O3, PA), were selected and studied. Three numerical values of each factor were determined based on the pre-study results. The L18 orthogonal array was selected to conduct the matrix experiment for four 3-level factors of the spherical grinding process.
Table1. The experimental factors and their levels
3.2 Definition of the data analysis
Engineering design problems can be divided into smaller-the better types, nominal-the-best types, larger-the-better types, signed-target types, among others [8]. The signal-to-noise (S/N) ratio is used as the objective function for optimizing a product or process design. The surface roughness value of the ground surface via an adequate combination of grinding parameters should be smaller than that of the original surface. Consequently, the spherical grinding process is an example of a smaller-the-better type problem. The S/N ratio, η, is defined by the following equation:
η =?10 log10(mean square quality characteristic)
=?10 log10
where:
yi : observations of the quality characteristic under different noise conditions
n: number of experiment
After the S/N ratio from the experimental data of each L18 orthogonal array is calculated, the main effect of each factor was determined by using an analysis of variance (ANOVA) technique and an F-ratio test. The optimization strategy of the smaller-the better problem is to maximize η, as defined by Eq. 1. Levels that maximize η will be selected for the factors that have a significant effect on η. The optimal conditions for spherical grinding can then be determined.
4 Experimental work and results
The material used in this study was PDS5 tool steel (equivalent to AISI P20), which is commonly used for the molds of large plastic injection products in the field of automobile components and domestic appliances. The hardness of this material is about HRC33 (HS46). One specific advantage of this material is that after machining, the mold can be directly used for further finishing processes without heat treatment due to its special pre-treatment. The specimens were designed and manufactured so that they could be mounted on a dynamometer to measure the reaction force. The PDS5 specimen was roughly machined and then mounted on the dynamometer to carry out the fine milling on a three-axis machining center made by Yang-Iron Company (type MV-3A), equipped with a FUNUC Company NC-controller (type 0M). The pre-machined surface roughness was measured, using Hommelwerke T4000 equipment, to be about 1.6 μm. Figure 6 shows the experimental set-up of the spherical grinding process. A MP10 touch-trigger probe made by the Renishaw Company was also integrated with the machining center tool magazine to measure and determine the coordinated origin of the specimen to be ground. The NC codes needed for the ball-burnishing path were generated by PowerMILL CAM software. These codes can be transmitted to the CNC controller of the machining center via RS232 serial interface.
Fig.6. Experimental set-up to determine the optimal spherical grinding parameters
Table 2 summarizes the measured ground surface roughness alue Ra and the calculated S/N ratio of each L18 orthogonal array sing Eq. 1, after having executed the 18 matrix experiments. The average S/N ratio for each level of the four actors is shown graphically in Fig. 7.
Table2. Ground surface roughness of PDS5 specimen
Exp.
Inner array
(control factors)
Measured surface
roughness value (Ra)
Response
no
A
B
C
D
S/N(η(dB))
Mean
1
1
1
1
1
0.35
0.35
0.35
9.119
0.350
2
1
2
2
2
0.37
0.36
0.38
8.634
0.370
3
1
3
3
3
0.41
0.44
0.40
7.597
0.417
4
2
1
2
3
0.63
0.65
0.64
3.876
0.640
5
2
2
3
1
0.73
0.77
0.78
2.380
0.760
6
2
3
1
2
0.45
0.42
0.39
7.530
0.420
7
3
1
3
2
0.34
0.31
0.32
9.801
0.323
8
3
2
1
3
0.27
0.25
0.28
11.471
0.267
9
3
3
2
1
0.32
0.32
0.32
9.897
0.320
10
1
1
2
2
0.35
0.39
0.40
8.390
0.380
11
1
2
3
3
0.41
0.50
0.43
6.968
0.447
12
1
3
1
1
0.40
0.39
0.42
7.883
0.403
13
2
1
1
3
0.33
0.34
0.31
9.712
0.327
14
2
2
2
1
0.48
0.50
0.47
6.312
0.483
15
2
3
3
2
0.57
0.61
0.53
4.868
0.570
16
3
1
3
1
0.59
0.55
0.54
5.030
0.560
17
3
2
1
2
0.36
0.36
0.35
8.954
0.357
18
3
3
2
3
0.57
0.53
0.53
5.293
0.543
Fig.7. Plots of control factor effects
The goal in the spherical grinding process is to minimize the surface roughness value of the ground specimen by determining the optimal level of each factor. Since ?log is a monotone decreasing function, we should maximize the S/N ratio. Consequently, we can determine the optimal level for each factor as being the level that has the highest value of η. Therefore, based on the matrix experiment, the optimal abrasive material was pink aluminum oxide; the optimal feed was 50 mm/min; the optimal depth of grinding was 20 μm; and the optimal revolution was 18 000 rpm, as shown in Table 3.
The optimal parameters for surface spherical grinding obtained from the Taguchi’s matrix experiments were applied to the surface finish of the freeform surface mold insert to evaluate the surface roughness improvement. A perfume bottle was selected as the tested carrier. The CNC machining of the mold insert for the tested object was simulated with Power MILL CAM software. After fine milling, the mold insert was further ground with the optimal spherical grinding parameters obtained from the Taguchi’s matrix experiment. Shortly afterwards, the ground surface was burnished with the optimal ball burnishing parameters to further improve the surface roughness of the tested object (see Fig. 8). The surface roughness of the mold insert was measured with Hommelwerke T4000 equipment. The average surface roughness value Ra on a fine-milled surface of the mold insert was 2.15 μm on average; that on the ground surface was 0.45 μm on average; and that on burnished surface was 0.07 μm on average. The surface roughness improvement of the tested object on ground surface was about (2.15?0.45)/2.15 = 79.1%, and that on the burnished surface was about (2.15?0.07)/2.15 = 96.7%.
Fig.8. Fine-milled, ground and burnished mold insert of a perfume bottle
5 Conclusion
In this work, the optimal parameters of automated spherical grinding and ball-burnishing surface finishing processes in a freeform surface plastic injection mold were developed successfully on a machining center. The mounted spherical grinding tool (and its alignment components) was designed and manufactured. The optimal spherical grinding parameters for surface grinding were determined by conducting a Taguchi L18 matrix experiments. The optimal spherical grinding parameters for the plastic injection mold steel PDS5 were the combination of the abrasive material of pink aluminum oxide (Al2O3, PA), a feed of 50 mm/min, a depth of grinding 20 μm, and a revolution of 18 000 rpm. The surface roughness Ra of the specimen can be improved from about 1.6 μm to 0.35 μm by using the optimal spherical grinding conditions for surface grinding. By applying the optimal surface grinding and burnishing parameters to the surface finish of the freeform surface mold insert, the surface roughness improvements were measured to be ground surface was about 79.1% in terms of ground surfaces, and about 96.7% in terms of burnished surfaces.
Acknowledgement
The authors are grateful to the National Science Council of the Republic of China for supporting this research with grant NSC 89-2212-E-011-059.
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