行政院國家科學委員會專題研究計畫 成果報告
以工件表面磨耗建構金屬成形摩擦模式之理論推導與實驗
驗證
研究成果報告(精簡版)
計 畫 類 別 ： 個別型 計 畫 編 號 ： NSC 95-2221-E-151-012- 執 行 期 間 ： 95 年 08 月 01 日至 96 年 10 月 31 日 執 行 單 位 ： 國立高雄應用科技大學模具工程系 計 畫 主 持 人 ： 張朝誠 計畫參與人員： 碩士班研究生-兼任助理：蘇裕翔、林明宏、王騰鉸、陳建 宏、鄭元傑 處 理 方 式 ： 本計畫可公開查詢中 華 民 國 97 年 01 月 31 日
行政院國家科學委員會補助專題研究計畫
■ 成 果 報 告
□期中進度報告
以工件表面磨耗建構金屬成形摩擦模式之
理論推導與實驗驗證
計畫類別：■ 個別型計畫
□ 整合型計畫
計畫編號：NSC
95-2221-E-151-012-執行期間：
95 年 08 月 01 日 至 96 年 10 月 31 日
計畫主持人：張朝誠
共同主持人：（無）
計畫參與人員：蘇裕翔、林明宏、陳建宏、王騰鉸、鄭元傑
成果報告類型(依經費核定清單規定繳交)：■精簡報告
□完整報告
本成果報告包括以下應繳交之附件：
□赴國外出差或研習心得報告一份
□赴大陸地區出差或研習心得報告一份
□出席國際學術會議心得報告及發表之論文各一份
□國際合作研究計畫國外研究報告書一份
處理方式：除產學合作研究計畫、提升產業技術及人才培育研究計畫、
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□涉及專利或其他智慧財產權，□一年□二年後可公開查詢
執行單位：國立高雄應用科技大學 模具工程系
摘要
摩擦與磨耗交互作用於工件與模具接觸之介面，是影響金屬成形製程的重要效應。對 於摩擦效應，一般採用固定摩擦係數之模式或磨潤膜模式作為模擬依據。固定摩擦係數模 式之數學形式簡單，但未考慮接觸介面之工件表面鋒(surface asperity)隨製程變化之事實， 而磨潤膜模式雖已有考慮表面鋒變化之文獻發表，但其數學形式較複雜，仍無法廣泛應用 於一般的金屬成形模擬分析中。因此，本計畫提出一個以接觸表面之磨耗改變微結構而影 響摩擦效應之概念，以 Archard 磨耗模式為基礎，推導一個工件表面磨耗模式，經實驗方 式決定相關磨耗係數，用以預估表面粗糙度(表面鋒)之變化，並將其導入修改的崔斯卡摩擦 模式(modified Tresca friction model)，作為金屬成形工件與模具接觸介面模擬之依據，發展 一個隨金屬成形製程進行而變化的摩擦模式，並將所提出之摩擦模式植入發展中之軸對稱 有限元素分析程式，以圓環壓縮試驗(ring compression test)與雙邊反向擠出實驗(double-backward extrusion test)進行驗證。
本計畫以新的方法處理金屬成形介面摩擦之問題，並以實驗驗證所提模式之可行性， 不僅可用於一般之金屬成形模擬，且因為以微結構變化為摩擦模式推導之基礎，將有利於 微尺度成形之模擬分析。經由理論與實驗之研究，對於如何處理其他工程問題中之介面摩 擦效應也有進一步的貢獻。 關鍵詞：金屬成形、摩擦、磨耗、表面鋒 Abstract
A new method based on the wear effect of workpiece surface is proposed to modify the Tresca friction model for the use in metal forming simulation. The method is based on the consideration of the shape change of contact surface at the microscale and the incomplete filling at the contact interface due to exist of surface asperities. During metal forming process, the surface asperities are being altered and mostly flatten because of wear and fracture. The surface roughness and friction conditions are thus being changed. This change can be directly related to the wear at the contact interface. By using the stress conditions and the sliding velocities on the surface, it is possible to predict the wear depth near the contact region. The predicted wear depth is then used to describe the roughness and thus the friction conditions at the workpiece-die interface in metal forming process.
The proposed research investigates the relationship among the wear depth at the contact interface, the surface roughness and the friction effect in metal formation process. A new friction model modified from Tresca friction law is formulated with the wear depth to deal with the friction effects. To determine the relationship among wear depth, surface roughness and friction factor, special experiments is conducted. Finally, ring compression tests and double-backward extrusion tests is performed. The simulated and experimental results are analyzed to verify the proposed friction model for metal forming simulation.
報告內容
1. Introduction
Friction at the workpiece-die interface is one of important factors in a system of metal forming. It not only increases the energy consumed in the forming process, but also causes the wear on the surface of the workpiece and die. The wear thus influences the surface quality of the product and probably results in further damages in both workpiece and die. As the size of the workpiece decreases, especially in micro metal forming processes, the size effects become significant and the ratio of the surface increases. This situation could enlarge the effects of friction in metal forming [1]. Thus, to understand the friction phenomena at the workpiece-die interface and to construct a model for modeling its effects in the metal forming process are highly attracted research topics.
The friction and wear effects at the workpiece-die interface depend on many parameters including the roughness, the contact pressure and the sliding speed. Due to strong interactions between the parameters, a model considering friction and wear has not been developed for modeling the contact behavior in the metal forming process. Many researchers, such as, Lee and Altan [2], Kobayashi et al. [3], Ramaekers and Kals [4], Sahi [5] and Chenot et al. [6], use the Coulomb friction model or the Tresca friction model to simulate the friction effects at the workpiece-die contact interface in the metal forming process. The factors for the two friction models can be obtained by the calibration curves form the simulated and experimental results of the ring compression tests or the double-backward extrusion tests. The form of the Coulomb friction model and the Tresca friction model are simple and thus commonly used to noodle metal forming problems. Nevertheless, the friction factors for the two model are constant values, and the changes of the roughness of the contact surface and the conditions of lubrication are not taken into account. Wilson [7] proposed a model for describing the types of lubrication by considerations of the lubricant thickness and the surface roughness at the contact interface in metal forming operations. Wilson and Sheu [8] proposed a model based on the change of the surface asperity due to the plastic deformation in order to predict the contact ratio in the cold rolling process. The effective surface hardness was also considered in the model. Sutcliffe and Montmitonnet [9] applied the Tresca friction model and the method (Sutcliffe and Le[10]) for estimating the change of the surface asperity to model the rolling of lubricated thin aluminum foils.Hsu and Huang [11]proposed a“realisticfriction model”to dealwith thefriction problem in the metal extrusion process. Although, the above models based on thin-film lubrication conditions were successfully used to simulate the some forming problems with relatively simple shapes, there are still obstacles to the metal forming processes, such as forging and backward extrusion, with transient conditions and relative complex shape of the products. Recently, Yang [12] tried to apply a thin-film lubrication model for three dimensional forming problems but more experimental verifications are needed. Lo and Tai [13] preformed some experiments for the deformation of the surface asperity and found that the elastic microwedges on the tools surface plays an important role on the variation of the contact ratio which influences the friction effects
significantly. In addition, Stupkiew and Mroz [14] proposed an asperity flattening model based on bulk plastic straining but its relations with friction has not been established. The above literature reviews show that the surface asperities of the workpiece are flattened, thus the contact ratio increases and the surface roughness decreases at the workpiece-die interface during metal forming process. The change of the asperities also affects lubrication regime.
In 1953, Archard proposed the wear volume W is proportional to the contact force P and the sliding length L and inversely proportional to the hardness of the material H.The model is given as follows:
H PL k W
where k is the coefficient of wear measured from the experiments.
The Archard’s model was modified and applied in the modeling of die wear in the metal forming process. Hambli [18] proposed a coefficient of wear based on cone-shaped asperity on the surface to predict the wear of the die by using the finite element method. The study shows that the predicted wear is close to the experimental one. Lee and Im [19] modified and implemented the Archard’s model into the a finite element analysis using a constant coefficient of wear and a constant hardness of material to predict die wear. However, there is no experimental data for comparison. Behrens and Schaefer [20] and Kang et al [21] considered the hardness of the die material as a function of temperature in the finite element simulation of the hot forging process. Some predicted results are different from the experimental ones. Lee and Jou [22] not only model the hardness of die material as a function of temperature, but also considered that the coefficient of wear k varies with the temperature after some wearing tests were conducted at high temperature. The proposed idea was used to predict the wear of die and is thus able to estimate the life of die. Moreover, Gierzynska-Dolna and Lacki [23] proposed a model based on the strain energy to predict the wear volume. They used simple upsetting tests to obtain critical wear volume. Masen and Rooji [24] considered the contact behavior at the micro scale and estimated the wear according to the fact of deformed asperities caused by the applied force in the deep drawing process. Experimental work is still needed to evaluate the accuracy of the prediction.
The reviewed research works do not consider the interaction between the friction and the wear at the workpiece-die interface during the metal forming process. However, the deformation of surface asperity may cause the contact ratio increase and influence the lubrication. Moreover, the roughness and asperity vary with the plastic deformation of the workpiece. The experimental works conducted by Lee et al. [26], Kato [27] and Lovell and Deng [28]show that the friction is affected by the roughness, the sliding speed and the contact length at the contact interface. The parameters also are the main factors for inducing the wear [29]. Therefore, this study proposed a new friction model, based on the change in the wear and roughness on the workpiece surface, for the simulation of the metal forming process. The study modified the Archard’s model and formulated a new wear model based on the roughness to predict the deformation of the asperities on the workpiece surface. The model was then implanted into an in-house plane strain finite element program for the simulation of metal forming process. Experiments including ring
compression tests and double backward extrusion tests were carried out to studies the relationship between roughness and friction, and also to assess the usability of the proposed friction model.
2. Wear and friction model
The microscale of the workpiece-die contact interface is shown in Fig. 1. The die and the workpiece are considered as rigid and deformable bodies, respectively. During the deformation, the surface asperities of the workpiece are compressed by the dies. Fracture could also exist at the contact interface and induce wear. These phenomena cause the change of the porosity and thus the contact and friction conditions which affect metal forming processes significantly.
The Archard’s model considers the wear volume,W, as
H PL k W ,
where Pis the contact force, Lis the sliding length, His the hardness of the material and associated with the yield stress, and k is the coefficient of wear measured from the experiments. The model may be written in terms of the normal stress , the contact arean A, the sliding speed
v and the contact time t as
H t v A k W n.
If a tiny area A and a small timet, the small amount of volume wearW can be expressed as
H t v A k W n ,
and the depth of the wear h is
H t v k A W h n .
The depth of the wearhcan be accumulated by a finite element analysis and written as ) ( ) ( ) 1 (i i i h h h . Wear height, h
Fig. 1. Change in surface asperity and porosity due to pressure and wear in metal forming process
(a) Before deformation (b) Worn and Deformed Die surface
Workpiece surface Force, P
Sliding length, L Worn debits
Sliding direction
During the metal forming process, the wear on the workpiece surface causes the change in asperities and thus the roughness. The surface roughness of the workpiece,R , therefore can bew
treated as a function of the depth of the wear,h, and expressed as )
(h
f
Rw .
There are many formulas can be established forR . This study proposew R asw
h R R R R R w t w t w ,
whereR is the roughness of the die surface andis a measured coefficient. The proposed modelt implies that the roughness of the workpiece surface is close to the roughness of the die surface,
i.e. R is close tow R , as the wear is significant.t
After the roughness of the workpiece surface has been estimated, it is possible to use the Wilson’smodel[7]to describe the tribological effects. In this study, the Tresca friction model, which is common used in the metal forming process, is studied for the dray condition. The model is expressed as
k
,
where is estimated shear stress, is the shear strength and is the friction factor. Byk considering the depth of the wearhand the roughness of the workpiece surfaceR , the Trescaw
model can be written as
s s k w v v h R , , ) ( ,
where v is the sliding speed at the contact interface, ands is a function ofh,R andw R and cant
be determined by a data fitting technique. The proposed friction model not only takes the sliding speed at the contact interface into account, but also considers the effects of the roughness on the friction in the metal forming process.
3. Modeling of metal forming
The material flow of the workpiece is described by a purely viscoplastic behaviour with the neglect of the elastic effects, i.e. the workpiece is a rigid-viscoplastic material. The flow behaviour can be expressed by the Norton-Hoff viscoplastic potential law,(),
1 ) 3 ( 1 ) ( m m K
to form the following constitutive equation:
1 ) 3 ( 2 m K s
where s is the deviatoric stress tensor, K is the material consistency, m is the strain rate
sensitivity index and is the effective strain rate with 2 / 1 2 3 2
ij .The material consistency can be a function of strain hardening, e.g. n
K
K 0(0 )
whereK material constant,0 is the effective strain, n is strain hardening index, and is a0
small positive constant to avoid the numerical problems.
For the special case withm0, the rigid-viscoplastic potential tends to the von Mises flow rule 0 3 2 s
with K 0 3, where is the yield stress. The flow rule can be applied to cold metal0 forming processes in which the strain rate sensitivity may be not sensitive. It is clear that the deviatoric stress tensor s takes zero-over-zero indeterminate form if the effective strain rate
trends to zero. The problem is treated by introducing a small constant 0 and the deviatoric stress tensor is expressed as
2 0 2 0 3 2 s .
The workpiece is assumed as the incompressibility during the forming process. In terms of the velocity field, the incompressibility condition can be written as
0 ) (v div
where v is the velocity filed. This constraint can be achieved by the Lagrange multiplier method
or the penalty method. In this study, the penalty method is used.
At the contact interface between the workpiece and the die, the stress and the externals traction T can be expressed as follows:
T n
where n is the vector of the normal direction of the contact surface. The relative velocity s
v between the workpiece and the die is calculated by d
s v v
v
v
Ω
Fig. 2. System of metal forming
Workpiece
Top die
Ωc
where v is the velocity of the die. On the contact interfaced , the material point to slide on thec
die surface can be written as 0
n
vs .
This constraint is imposed by the penalty method in this study.
The proposed friction model, , was applied to the modeling of the large deformation of metal forming with isothermal condition. With the penalty method for dealing with impressibility, the energy of a metal forming system, , can be expressed by the following equation
div v
dV vdS T vdS dV m K v s m c
1 2 ) ( ) 3 ( 1 ) ( where V and S are the volume and the sliding contact interface, respectively. is an assigned value for dealing with the incompressible or near incompressible material flows. By applying the finite element method and minimizing the energy with and the Newton-Raphson method, the nodal velocity field Vt ban be solved. The newly updated nodal position vector
t t
X can also be obtained by after a small increment of timet by
t V X
Xtt t t.
The strain rate tensor at the end of the increment can be calculated by
T t t t t t t t t t t x v x v 2 1
t t t t
t t t t V V X , The stress tensor can be expressed by means of the strain rate tensor as tt
tt , and the incremental displacement vector Ut is expressed byUt Vtt. Finally, the strain increment
can also be calculated.
4. Results and discussion
The rings with the outer diameter/inner diameter/thickness equal to 3/1.5/1 mm are compressed by a screw press at a constant speed at the die speed of 0.01 0.1 and 1 mm per second without lubrication. With the comparison with a set of calibration curves constructed by a commercial software, the friction factor of the Tresca model is in a range between 0.15 to 0.25 for different roughness of the surface at the die speed of 0.01 mm per second (see Fig. 3). The scattering effect on the measured friction factors gradually increases as the height of ring reduces. In addition, the reduction in the surface roughness described by the arithmetic mean value (Ra) in the range from 0.2 to 0.05 μm does not show the decrease in the friction factor. This might be caused by the present of stronger adhesion friction than abrasive friction. The other reason could be the insensitivity of the ring compression test to local friction effects. It can be seen in Fig. 5 that the measured friction factors slightly increase as the die speed increase to 1 mm per second. The scattering effect on the measured data becomes larger, especially for higher reduction in the height of the ring.
-60 -40 -20 0 20 40 60 0 10 20 30 40 50 60 70 Reduction in height (%) D e c re a s e in in te rn a l d ia m e te r (% ) Ra=0.5 Ra=0.2 Ra=0.05 a=0 a=0.1 a=0.2 a=0.3 a=0.4 a=0.5
Fig. 3. The calibration curves and measured friction factors for different surface roughness at the die speed of 0.01 mm per second
-60 -40 -20 0 20 40 60 0 10 20 30 40 50 60 70 Reduction in height (%) D e c re a s e in in te rn a l d ia m e te r (% ) Ra=0.5 Ra=0.2 Ra=0.05 a=0 a=0.1 a=0.2 a=0.3 a=0.4 a=0.5
Fig. 4. The calibration curves and measured friction factors for different surface roughness at the die speed of 0.1 mm per second
-60 -40 -20 0 20 40 60 0 10 20 30 40 50 60 70 Reduction in height (%) D e c re a s e in in te rn a l d ia m e te r (% ) Ra=0.5 Ra=0.2 Ra=0.05 a=0 a=0.1 a=0.2 a=0.3 a=0.4 a=0.5
Fig. 5. The calibration curves and measured friction factors for different surface roughness at the die speed of 1 mm per second
5. Conclusions
A new method based on the wear effect of workpiece surface is proposed to modify the Tresca friction model for the use in metal forming simulation. The method is based on the consideration of the shape change of contact surface at the microscale and the incomplete filling at the contact interface due to exist of surface asperities. During metal forming process, the surface asperities are being altered and mostly flatten because of wear and fracture. The surface roughness and friction conditions are thus being changed. This change can be directly related to the wear at the contact interface. By using the stress conditions and the sliding velocities on the surface, it is possible to predict the wear depth near the contact region. The predicted wear depth is then used to describe the roughness and thus the friction conditions at the workpiece-die interface in metal forming process. The proposed research investigates the relationship among the wear depth at the contact interface, the surface roughness and the friction effect in metal formation process. A new friction model modified from Tresca friction law is formulated with the wear depth to deal with the friction effects. To determine the relationship among wear depth, surface roughness and friction factor, special experiments is conducted. Finally, ring compression tests and double-backward extrusion tests is performed. The simulated and experimental results are analyzed to verify the proposed friction model for metal forming simulation.
Acknowledgement
The author wishes to thank the National Kaohsiung University of Applied Sciences for the use of its facilities. The support from the National Science Council under grant NSC 95-2221-E-151-012- is also gratefully acknowledged.
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29. Burakowski,T.and Wierzchon,T.,“Surfaceengineering ofmetal”,CRC Press,New York, 1999, Chapter 5.
計畫成果自評
研究內容與原計畫相符程度 研究內容與原計畫所提大致相符，唯需要更多時間建構軸對稱問題之有限元素分析程 式，因此由原訂針對軸對稱問題更改為平面應變問題之電腦程式寫作。 達成預期目標情況 本計畫完成之工作項目為下列四項： 1. 推導計畫主持人所提出的以磨耗效應為考慮的摩擦模式。 2. 執行磨耗係數試驗、表面粗糙度與摩擦係數關係試驗與實驗驗證工作。 3. 建立金屬成形平面應變問題之有限元素分析電腦程式。 4. 執行實驗驗證工作：(1)材料壓縮試驗量測應力應變曲線; (2)環形壓縮試驗量測摩擦係數; (3)雙邊反向擠出試驗檢測提出之摩擦模式。 5. 比較與分析所提摩擦模式與其他模式及實驗數據之差異。 其中第 1、3 與 4 項均達成預期目標。唯需要更多時間處理軸對稱問題之有限元素分 析程式寫作，因此第 2 項由原訂針對軸對稱問題更改為平面應變問題之電腦程式建構，另 外也增加平面應變壓縮實驗之工作，以驗證所提之摩擦模式。 研究成果之學術或應用價值 本計畫所提之摩擦模式以反應接觸之微結構變化為出發點，考慮金屬成形過程工件表 面磨耗效應對表面鋒造成改變，也使得接觸介面之表面粗糙度發生變化，並將此變化，作 為摩擦模式之參數，將可以改善傳統模擬方法以固定摩擦係數值無法反應接觸狀態改變之 問題，亦可以解決磨潤模式不易處理動態問題之缺點。此外基於摩擦模式考量微結構之變 化，將可有效反應微金屬成形之介面摩擦問題，並可以運用於其他工程問題中，對摩擦效 應做更精確之模擬分析。研究成果適合在學術期刊發表。 主要發現或其他有關價值 本研究利用磨耗效應處理摩擦問題，不僅考慮變接觸介面磨耗之事實件，並考慮工件 表面鋒之微結構變化，以更直接的方式將磨耗、表面鋒與粗糙度之變化導入摩擦模式，除 應用於一般金屬成形之模擬外，將提供處理微成形摩擦問題的新研究方向。是一個處理摩 擦問題之新技術，且可廣泛應用於存在摩擦效應之成形問題。可供推廣之研發成果資料表
□ 可申請專利 ■ 可技術移轉 日期：97 年 1 月 26 日國科會補助計畫
計畫名稱：以工件表面磨耗建構金屬成形摩擦模式之理論推導與實 驗驗證 計畫主持人：張朝誠 計畫編號：NSC 95-2221-E-151-012-學門領域：機械固力技術/創作名稱
接觸介面表面磨耗之金屬成形摩擦模式發明人/創作人
張朝誠 本技術利用接觸表面之磨耗改變微結構而影響摩擦效應之概 念，以 Archard 磨耗模式為基礎，建立一個工件表面磨耗模式，經 實驗方式決定相關磨耗係數，用以預估表面粗糙度之變化，並將其 導入修改的崔斯卡摩擦模式(modified Tresca friction model)，作為金 屬成形工件與模具接觸介面模擬之依據。提出之摩擦模式乃以工件 微結構變化為考量，計算表面粗糙度因磨耗效應隨金屬成形製程之 塑性變形而發生變化之現象，並將此變化摩擦模式，用於金屬成形 模擬。技術說明
A new method based on the wear effect of workpiece surface is proposed to modify the Tresca friction model for the use in metal forming simulation. The method is based on the consideration of the shape change of contact surface at the microscale and the incomplete filling at the contact interface due to exist of surface asperities. During metal forming process, the surface asperities are being altered and mostly flatten because of wear and fracture. The surface roughness and friction conditions are thus being changed. This change can be directly related to the wear at the contact interface. By using the stress conditions and the sliding velocities on the surface, it is possible to predict the wear depth near the contact region. The predicted wear depth is then used to describe the roughness and thus the friction conditions at the workpiece-die interface in metal forming process.
