Research on friction law in deep drawing process of rectangular

Transcription

1 Vol Supp SCIENCE IN CHINA (Series A) August 001 Research on friction law in deep drawing process of rectangular parts LUO Yajun 1 HE Dannong 1 YANG Jianhua 1 ZHANG Yongqing 1 ZHANG Wei &LIJun 1 National Die & Mold CAD Engineering Research Center Shanghai Jiao Tong University Shanghai 0000 China; Shanghai Volkswagen Automotive Co Ltd Shanghai 0180 China Received July 001 Abstract Friction law is researched in rectangular parts deep drawing using simulation test machine that is used to assess lubricants performance in deep drawing process Friction coefficients in different positions on die surface in deep drawing process are measured through probe sensors Friction coefficients of flange corner near straight border and far straight border are verified and described quantitatively It plays an important role in using appropriate lubricants in auto-body panel deep drawing process Keywords: rectangular parts deep drawing auto-body panel friction coefficient Auto makers meet with keen market competitions and strict environmental protection at present What s more higher quality and performance automobiles are requisite in future So R (Reduce Cycle Reduce Cost Reduce Weight) strategy is advanced in automobile industry [1] A large proportion of automotive parts are pressing parts including auto-body panels Cost of auto-body panels is high for big size complex shape and bad forming condition Research on the grade of sheet optimum technical parameter and best lubricant for deep drawing will reduce the production cost of deep drawing parts namely reduce the cost of automobiles In this paper friction and lubrication law of rectangular parts in deep drawing process is researched with physical simulation Mathematical model of friction coefficient and drawing height friction force and friction coefficient drawing force and friction coefficient are established It is significant for producers to use lubricants to improve drawing capability of sheet and quality of products Also it s the basis of friction boundary condition in computer simulation of auto-body panel 1 Fundamental principle of deep drawing Deep drawing is a stamping and pressing method through which the plate is deformed into hollow parts with tools [] There are many kinds of deep drawing parts But each kind of drawing parts has different deforming position deforming characteristic strain and stress distribution The basal parts of deep drawing are cylinder parts and most of its deep drawing theory has been finished But theory of complex parts is still unfinished and needs more research For example metal near straight border suffers bending and that near corner deforms like cylinder parts in rectangular parts [] but de-

2 Supp FRICTION LAW IN DEEP DRAWING PROCESS OF RECTANGULAR PARTS 1 forming degree is smaller than the cylinder parts with same height Flat cup parts has two type of defects: (a) tensile rupture of critical section; (b) wrinkles happened in flange There are two parameters to describe the limited drawing ratio (LDR) in deep drawing [] : D Limited drawing ratio LDR = (1) d d Drawing coefficient m = () D One object of deep drawing technology is to avoid the limited drawing ratio So we must follow two principles in order to get bigger LDR: (1) Reduce the force P ρ in critical section; () Improve σ ρ resistant force P b in critical section σ f If P ρ P b deep drawing is success; if P ρ P b deep drawing part will break So LDR is the drawing ratio when P ρ is equal to P b The above two principles are in collection with friction In fig 1 unit drawing force P ρ in critical section can be derived as follows: P µα ρ = σ ρ + σ f + σ c ) e + ( σ () Suppose that critical section is of plane strain state P b can be written as follows: Take friction force σ f c 1 + r Pb = σ b () 1 + r into consideration the P b is: 1 + r Pb = σ b + σ f () 1 + r In eqs (1) () D d µ andα are blank diameter punch diameter friction coefficient and wrap angle respectively σ ρ σ c µ and σ f are radial tensile stress overcome bending and unbending force strength of critical section and friction force between blank holder ring and die r is coefficient of normal anisotropy Whether the parts can be drawn successfully rests with whether P ρ is smaller than P b There are many factors to influence P ρ and P b such as drawing technique determination tools design lubricant and sheet grade selection Maybe there are many ways to reduce P ρ but selecting an appropriate lubricant is a more convenient way in workshop High quality lubricant make less friction and better lubrication to reduce P ρ The problem is that there is no accurate theory so far to analyze friction and lubrication We set probe sensors in die surface to measure friction coefficient in deep drawing in our laboratory Friction conditions near straight border and corner of rectangular parts are quantitatively analyzed Fig 1 σ c P ρ µσ N µα e Critical section Stress in critical section

3 SCIENCE IN CHINA (Series A) Vol Measuring system and test principle 1 Measuring system Drawing parts are formed with high pressure and new surface appearing [] We should learn the difference between drawing parts and other mechanical ones when we research the friction in deep drawing It is also different from the friction in other plastic deformation [] So we use simulation test machine which is coincident with the real drawing process to measure friction coefficient Simulation test machine system includes experiment tools sensors automatic strain gage and computer aided measuring system (CAMS) It s shown in fig Circumferential sensors 1 Normal sensors 1 Drawing force sensor Extensometer Displacement sensor Manual control Signal standardization A/D card Data show save CAMS Adjust mold Stroke control Hydraulic press Data processing Friction coefficient analysis Printer BHF control Load strain foil BHD sensor Fig Scheme of test machine system Test principle Simulation test machine system measures friction coefficient in deep drawing using probe sensors in die surface Its advantage is that it can measure friction force (circumferential force) and normal force and friction coefficient can be computed from them from eqs (6) It is also convenient to use # CAMS 1 # Fig # Distribution of probes on die surface µ = F C / F N (6) In rectangular parts deep drawing deformations near corner and straight border are different [7] So we set three probe sensors near corner and straight border whose locations are shown in fig Test process: Firstly determine drawing speed blank holder force tools and blank Secondly clear

4 Supp FRICTION LAW IN DEEP DRAWING PROCESS OF RECTANGULAR PARTS blank and tools and standardize sensors with CAMS Thirdly run hydraulic press and measure friction force and vertical force Lastly process data using computer-processing system and get the result Fig Normal and circumferential force curve in deep drawing process Testandresults Drawing speed is 0mm/s Lubricants are m and Diameter of blank is Φ88 mm Φ96 mm Repeat the test 8 times under the same condition Measure and process data using computer aided measuring and processing system We can get the total drawing force circumferential and normal force of each probe sensor Therefore friction coefficient can be computed as eqs (6) The system can also get Fig Friction coefficient curve of lubricant the average of total drawing force normal force circumferential force and friction coefficient Fig (a) and (b) show trends of normal force and friction force of one probe sensor in deep drawing Units of x-coordinate and y-coordinate in fig are voltage and time Fig shows the average result of friction coefficients of lubricant m We can get the mathematical model between friction coefficients and drawing heights total drawing force and friction coefficient in different position of die surface of square parts from the test data The mathematical models of friction coefficient of lubricant in position 1 # ( µ 1) # ( µ )and # ( µ ) are as follows: Cubic and quintic regression equation of friction coefficient µ 1:( x 18 ) µ 1 = x 0008x x µ 1 = 00070x + 000x 00161x + 000x + 069x (7) (8)

5 SCIENCE IN CHINA (Series A) Vol Cubic and quintic regression equation of friction coefficient µ :( x 1 ) µ = x 001x + 07x µ = 00009x 00071x + 008x 0069x + 067x Cubic and quintic regression equation of friction coefficient µ :( x 18 ) (9) (10) µ = 00010x + 066x (11) µ = 00008x x 0088x x x (1) Conclusion It can be seen from fig andeqs(7) (1) that friction force and normal force can be measured using probe sensor and friction coefficient can be computed from them as shown in fig Because metal flowing near straight border and corner of square parts is different friction states in those positions are different Varying trends of friction coefficient µ 1 µ andµ measuredby three probe sensors can be seen from fig Judging from the numerical values friction coefficient of # (far from straight border) is bigger than that of 1 # (near straight border) and the friction coefficient of # (near corner) is the biggest among three ones Varying trends of friction force normal force and friction coefficient in square cup parts deep drawing can be analyzed quantitatively from fig and eqs (7) (1) which is consistent with the facts that forming conditions near corner is severe and defects are easy to occur near corner Aside from that forming conditions far from straight border is severer than that near border Therefore lubricants are used near corner and draw beads are introduced near straight border in production of bigger and more complex stamping parts Taking these measures is in favor of deep drawing prolonging molds life span improving products quality At the same time this is a scientific test method to determine the boundary condition of friction coefficient in computer simulation of rectangular parts deep drawing Through researches on three different lubricants it is found that under the same conditions the higher the viscidity value of the lubricant the lower the friction coefficient References 1 Xu Weili Lin Zhongqin Liu Gang et al State and trends of auto-body panel stamping simulation Chinese Journal of Mechanical Engineering 000 6(7): 1 Li Shuoben Stamping technic Beijing: China Machine Press 198 Nakagawa T Abe K Yutaka HAYASHI Sheet metal stamping Tianjin Science & Technology Press 198 Chang Rongfu Friction analysis in stamping Beijing: China Aerospace Press 1989 He Dannong Tao Hongzhi Bao Xiangjun et al Research on the relationship between the friction coefficients of lubricants for drawing and blank holder force Tribology 000 0(): 6 He D N Yin X F Tao H Z etc Research on the evaluation method of friction and lubrication in deep drawing Acta Metallurgica Sinica (English Letters) 000 1(): 9 7 Mizuno K ER Daixin Experiment on rectangular cup drawing of sheet metal Journal of JSTP (): 7