Analysis of Sheet Metal Forming (Stamping Process): a Study of the Variable Friction Coefficient on 5052 Aluminum Alloy

Home , Machine press, Stamping (metalworking)

metals

Article Analysis of Sheet Metal Forming (Stamping Process): A Study of the Variable Friction Coeﬃcient on 5052 Aluminum Alloy

Shasha Dou 1,2 and Jiansheng Xia 2,* 1 College of Mechanical and Electrical Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China 2 School of Mechanical Engineering, Yancheng Institute of Technology, Yancheng 224051, China * Correspondence: [email protected]; Tel.: +86-158-6198-8970

Received: 2 July 2019; Accepted: 1 August 2019; Published: 3 August 2019

Abstract: Under a boundary lubrication regime, the effect of sliding velocity and normal loads on the friction coefficient in the sheet metal stamping process was investigated using a pin-on-disk sliding wear test. Software was used to analyze both the data generated and the friction coefficient; in addition, a variable friction model based on different velocities and normal loads was also initiated. Under different experimental conditions and numerous influences, both the analysis and microtopography examination of sheet metal helped to obtain the mechanism influence on the friction coefficient. Through further analysis of the microtopography of sheet metal, the law of the surface roughness of sheet metal after grinding with stamping die was established. The model was established to simulate the thickness distribution and spring-back of U-bend parts using ABAQUS software. The results show that the friction coefficient values between the sheet metal and the stamping die generally decrease with increasing sliding velocity and normal loads, and the decreasing tendency slows down under a higher sliding velocity and normal load. Furrow wear and abrasive wear are the main wear mechanisms, with slight sticking wear under the boundary lubrication; the surface roughness after grinding with stamping die generally increases with increasing normal loads and decreasing sliding velocity. The predicted results of thickness distribution with a constant friction coefficient of 0.1 and with the variable friction coefficient model are more consistent with the actual measured values, but the predicted accuracy of spring-back in the variable friction coefficient model is higher than that of the constant friction coefficient model.

Keywords: sheet metal forming; sliding velocity; normal loads; friction coeﬃcient; ﬁnite element simulation

1. Introduction Sheet metals are widely applied in the automotive, ship-building and aerospace industries, and have high potential for energy conservation, emission reduction, and safety improvement, but also comes with many new problems. In many cases, due to their poor plasticity at room temperature, defects are easily created in the forming process, such as wrinkling, cracking, poor forming accuracy, and spring-back [1]. At present, regarding the optimal way of forming steel plates to solve these problems, the optimization method for the forming process cannot be effective because of the different properties of the sheet metal, which lead to a longer life cycle and a higher product cost. Studies have shown that material properties, processing techniques, and friction are the main factors which affect the formability and the quality of the parts. The effect of the processing techniques on the formability of the sheet is achieved mainly through changing the friction between the sheet metal and the stamping die. Friction mainly affects the formability of the sheet by changing the stress distribution in the

Metals 2019, 9, 853; doi:10.3390/met9080853 www.mdpi.com/journal/metals Metals 2019, 9, 853 2 of 16 forming process [2]. There is the possibility of improving the formability by optimizing the processing techniques in the forming process. In addition, due to the outstanding performance of numerical simulation technology in shortening the product design cycle and saving production costs, it has been widely used in the optimization design of sheet metal forming [3]. The accuracy of the simulation results depends on the correct contact model, where the friction model occupies a decisive role. In the numerical simulation of sheet metal forming, classical Coulomb’s law is commonly used to describe the friction characteristics [4]. Coulomb’s law assumes that the friction coefficient is a constant value and that the friction force is proportional to the positive pressure [5]. Theoretically, Coulomb’s friction model is effective when the normal load is less than the yield limit of the material and the sheet metal is elastically deformed. The actual sheet metal forming process is usually accompanied by plastic deformation. Therefore, based on Coulomb’s friction model, the friction characteristics of the sheet metal forming process are inconsistent with the actual working conditions. Therefore, the accuracy of numerical simulation needs to be improved. In recent years, domestic and overseas scholars have carried out a lot of research work on the friction characteristics of the sheet metal forming process. Ramezani et al. [6] conducted an in-depth analysis of the mechanism of friction in the sheet forming process and proposed that the forming speed and normal load are the main factors affecting the friction coefficient. Figueiredo et al. [7] studied the effects of die roughness, normal load, sliding velocity, and lubrication condition on the friction coefficient between DP600 high-strength steel and 1100 aluminum alloy, and found that sliding velocity and normal load are the key factors affecting the friction coefficient. Ramezani et al. [8] studied the friction characteristics of AZ80 and ZE10 magnesium alloys under lubrication conditions using a method combining experiment and theory, and pointed out that the normal load and sliding velocity have a significant influence on the friction coefficient, and the constant friction coefficient model is not suitable for numerical simulation of sheet metal forming. Tamai et al. [9] studied the effect of normal loads, sliding velocity and punch stroke on the friction coefficient using a plate sliding friction experiment. It was found that the friction coefficient decreases with increasing normal loads and sliding velocity, and slightly increases with the increasing of the stroke. Wang et al. [10] studied the friction characteristics of an alloyed hot-dip galvanized steel plate by a plate sliding friction experiment and found that the friction coefficient decreases with increasing normal loads and sliding velocity. Wang et al. [11] studied the friction law between DP780 high-strength steel and DC53 die steel by using a pin-disc friction experiment and established a variable friction coefficient model based on different normal loads. The variable friction coefficient model and Coulomb’s friction model, which were then used to simulate the spring-back of U-shape bending, showed that the precision of the spring-back prediction using the variable friction model was greatly improved [12]. At present, sheet metals include aluminum alloys, titanium alloys, and magnesium alloys. Among them, aluminum alloys are the most widely used in the automotive, ship-building, aerospace and other mechanical industries due to their low cost and good formability [13]. However, research on the friction characteristics of the plastic forming process mainly focuses on materials such as high-strength steel and galvanized sheets. Few studies have been conducted on the friction characteristics of the aluminum alloy sheet forming process. The influence of the forming speed, normal load, and lubrication condition on the friction coefficient of the aluminum alloy sheet metal forming process is still unclear, and a friction model that can accurately describe the friction characteristics of the aluminum alloy sheet metal forming process has not yet been established [14]. Due to the slightly poor formability of aluminum alloys compared with steel plates at room temperature, research on the friction properties of aluminum alloys is mainly focused on warm forming and hot forming [15]. Studies have shown that the annealed state of 5-series aluminum alloys has good forming properties at room temperature. Therefore, it is of great significance to deeply and systematically study the influence of various process parameters on the friction coefficient and mechanism of 5-series aluminum alloys in the cold forming process. Metals 2019, 9, 853 3 of 16

In this paper, the effect of sliding velocity and normal loads on the friction coefficient between 5052 aluminum alloy and SKD11 steel under boundary lubrication was studied by using an MPX-2000 disc-pinMaterials friction 2019, 19 tester., x FOR PEER Microtopography REVIEW observations and analysis on the 5052 aluminum3 of 15 alloy specimensIn underthis paper, diff erentthe effect experimental of sliding velocity conditions and normal were loads performed on the friction to obtain coefficient the mechanism between of Materials 2019, 19, x FOR PEER REVIEW 3 of 15 the influence5052 aluminum of various alloy factorsand SKD11 on thesteel friction under boundary coefficient. lubrication Using MATLAB was studied software by using to an analyze MPX- the experimental data and obtain the law of the friction coefficient, a variable friction model based on 2000 disc-pinIn this frictionpaper, the tester. effect Mi ofcrotopography sliding velocity observations and normal loadsand analysis on the friction on the coefficient5052 aluminum between alloy differentspecimens5052 sliding aluminum under velocities differentalloy and and experimental SKD11 normal steel loads under conditions was boundary established. were lubrication performed The was modelto obtainstudied was the by then mechanismusing used an MPX- to of simulate the the thicknessinfluence2000 disc-pin distributionof various friction factors tester. and Mi spring-backoncrotopography the friction of coefficient. typicalobservations parts. Using and Atanalysis MATLAB the same on the software time,5052 aluminum the to actualanalyze alloy thickness the distributionexperimentalspecimens and under spring-backdata anddifferent obtainof experimental thethe typicallaw of conditionsthe parts friction were were coefficient, measured. performed a variableto The obtain predicted friction the mechanism model results based of obtained the on by (i) a variabledifferentinfluence frictionsliding of various velocities model factors based and on normal on the di fffriction loadserent was slidingcoefficient. established. velocities Using The MATLAB and model normal wassoftware then loads, toused andanalyze to (ii) simulate the a constant frictiontheexperimental model, thickness were distribution data compared and obtain and with spring-backthe the law result of the of offriction typica the actual lcoefficient, parts. measurement, At athe variable same time,friction which the model indicated actual based thickness the on validity distributiondifferent sliding and spring-back velocities and of normalthe typical loads parts was wereestablished. measured. The modelThe predicted was then resultsused to obtained simulate by of the variable friction coefficient model based on experimental data. (i) thea variable thickness friction distribution model basedand spring-back on different of slidingtypical velocitiesparts. At theand same normal time, loads, the actualand (ii) thickness a constant distribution and spring-back of the typical parts were measured. The predicted results obtained by 2. Materialsfriction model, and Methods were compared with the result of the actual measurement, which indicated the validity(i) a variable of the variablefriction model friction based coeffic on ientdifferent model sliding based velocities on experimental and normal data. loads, and (ii) a constant A 5052friction aluminum model, were alloy compared rod with with a diameterthe result ofof 5the mm actual was measurement, used as a friction which specimen.indicated the The yield validity of the variable friction coefficient model based on experimental data. strength2. Materials was 70 MPa,and Methods the tensile strength was 220 MPa, and the elongation was 20%. SKD11 die steel was used2. MaterialsA as 5052 a friction aluminum and pair.Methods alloy The rod chemical with a diameter composition of 5 mm is shown was used in Tableas a friction1. specimen. The yield strength was 70 MPa, the tensile strength was 220 MPa, and the elongation was 20%. SKD11 die steel A 5052 aluminum alloy rod with a diameter of 5 mm was used as a friction specimen. The yield was used as a friction pair.Table The chemical 1. Chemical composition composition is shown of SKD11 in Table (wt%). 1. strength was 70 MPa, the tensile strength was 220 MPa, and the elongation was 20%. SKD11 die steel was used as a friction pair. The chemical composition is shown in Table 1. Fe CTable 1. Chemical Si composition Mn of CrSKD11 (wt%). Mo V

84.2 1.50TableFe 1. CChemical 0.40 Si composition 0.50Mn Cr of 12.0SKD11Mo (wt%).V 1.0 0.30 84.2Fe 1.50C 0.40Si 0.50Mn 12.0Cr Mo 1.0 V 0.30 The pin specimen and pin specimen84.2 1.50 ﬁxture0.40 are0.50 shown12.0 in 1.0 Figure 0.301 a. The principle of the disk-pin friction testThe is pin shown specimen in Figure and 1pinb. Becausespecimen thefixture hardness are shown of 5052 in Figure aluminum 1a. The alloy principle is lower of the than disk- that of pin friction test is shown in Figure 1b. Because the hardness of 5052 aluminum alloy is lower than SKD11 die steel,The pin in specimen order to and avoid pin thespecimen ploughing fixture failure are shown of thein Figure plate 1a. specimen The principle shown of the in Figuredisk- 2 and thatpin of friction SKD11 testdie steel,is shown in order in Figure to avoid 1b. Because the plough the inghardness failure of of 5052 the platealuminum specimen alloy shownis lower in than Figure the distortion of the measurement data, the pin sample was prepared with a 5052 aluminum alloy 2 andthat theof SKD11 distortion die steel, of the in ordermeasurement to avoid thedata, plough the pining failuresample of was the plateprepared specimen with shown a 5052 in aluminum Figure rod withalloy2 and low rod the hardness.with distortion low hardness. The of the sample measurement The sample was made was data, made of th SKD11e pin of SKD11sample die steeldiewas steel prepared with with higher higherwith hardnessa 5052hardness aluminum through through wire cutting.wirealloy The cutting. rod hardness with The low hardness of hardness. the disk of Thethe specimen disksample specimen was after made af heatter of SKD11heat treatment treatment die steel was withwas 62 higher62 HRC. HRC. hardness The The disk disk through andand pin face was processedfacewire was cutting. processed to accurately The hardness to accurately simulate of the disksimulate the specimen interface the inte af stateterrface heat of state thetreatment actual of the was stampingactual 62 HRC. stamping process. The disk process. Theand pin integrated The face was processed to accurately simulate the interface state of the actual stamping process. The surfaceintegrated roughness surface values roughness (Ra) of values the disc (Ra and) of the pin disc samples and pin measured samples measured by a light by microscope a light microscope were 0.2–0.5 integrated surface roughness values (Ra) of the disc and pin samples measured by a light microscope and 0.8–1.2,were 0.2–0.5 respectively. and 0.8–1.2, respectively. were 0.2–0.5 and 0.8–1.2, respectively.

(a()a )Samples Samples ( (b) Principle ofof The The Disk-Pin Disk-Pin Friction Friction test test

FigureFigureFigure 1. Experimental 1. 1.Experimental Experimental device: device: device: ( a ((a)a)) samples; samples;samples; (( (bbb)) ) principleprinciple principle of of the of the theDisk-Pin Disk-Pin Disk-Pin friction friction friction test. test. test.

Figure 2. The severe plough defect. FigureFigure 2. 2.The The severesevere plough plough defect. defect.

Metals 2019, 9, 853 4 of 16

The spindle speed of the improved MPX-2000 disk-pin friction tester (Xuanhua Kehua Test Machine Manufacturing Co., Ltd, Zhangjiakou, China) was reduced to 1/8 of the original rotational speed. According to reference [12], sliding speeds of 30.62 mm/s, 40.82 mm/s, 51.03 mm/s, 61.23 mm/s, and 71.42 mm/s, and positive pressures of 10 N, 20 N, 30 N, 40 N, and 50 N, corresponding to an interface load of 0.51 MPa–2.55 MPa at the contact interface, were individually chosen to apply on the MPX-2000 disk-pin friction tester. The disk-pin frictional diameter was 26 mm, and the experimental termination condition was set to three turns. After each experiment, the pin sample was changed. The lubricant used was oil-based stamping oil. The sample was cleaned with acetone and dried before the experiment. The lubricant was sprayed on the steel plate of the SKD11 die, according to the standard of 80–90 g/m2, by a robot nozzle. There were ﬁve groups of loads (0.510 MPa, 1.019 MPa, 1.530 MPa, 2.038 MPa and 2.550 MPa) and ﬁve groups of speeds (30.62 mm/s, 40.82 mm/s, 51.03 mm/s, 61.23 mm/s and 71.42 mm/s) tested on the MPX-2000 disk-pin friction tester. The experiment for each group was repeated three times, and the pin was replaced after each experiment.

3. Results

3.1. Friction Coefficient Measurement Taking the average value of friction test results as the effective friction coefficient, the effective friction coefficients under different loads and speeds are shown in Table2.

Table 2. Average friction coeﬃcient with diﬀerent loads and sliding velocities.

Speed (mm/s) 30.62 40.82 51.03 61.23 71.42 Load (MPa) 0.510 0.148 0.118 0.092 0.076 0.064 1.019 0.134 0.106 0.084 0.069 0.058 1.530 0.123 0.097 0.076 0.062 0.053 2.038 0.109 0.090 0.071 0.058 0.049 2.550 0.102 0.086 0.067 0.056 0.046

By analyzing the experimental data with MATLAB software (MATLAB 2018b, MathWorks, Natick, MA, USA), the quadratic polynomial fitting curve of friction coefficients with sliding speed between 5052 aluminum alloy and SKD11 die steel under constant load were drawn, as shown in Figure3. When the sliding velocity is between 30.62 mm/s and 71.42 mm/s, the friction coefficient decreases gradually with increasing sliding velocity, and the decreasing tendency slows down in the higher sliding velocity range. According to the principle of tribology, under the boundary lubrication condition, the friction coefficient is mainly composed of fluid friction coefficient, fL, and solid friction coefficient, fS [13]. As the lubricant and positive pressure remain constant, the number of Sommerfeld in the Stribeck function [14] is directly proportional to the sliding velocity. With increasing sliding velocity, the area of solid friction decreases gradually and leads to a decrease in the coefficient of solid friction, fS. The local heating effect of the friction at the peak causes the viscosity of the lubricant to decrease and leads the coefficient of fluid friction, fL, to decrease. As a result, the friction coefficient decreases with increasing sliding speed. Metals 2019, 9, 853 5 of 16 Materials 2019, 19, x FOR PEER REVIEW 5 of 15

Materials 2019, 19, x FOR PEER REVIEW 5 of 15

Figure 3. Friction coefficient curve with different sliding velocities, with five loads. Figure 3. Friction coefficient curve with different sliding velocities, with five loads. The quadratic polynomial fitting curve of the friction coefficient with constant speed conditions is shown in Figure4. Under the normal load between 0.51 MPa and 2.55 MPa, the friction coe fficient decreases with increasing normal load. The influence of normal load on the friction coefficient gradually weakened with the gradually increasing sliding speed. It is known from the tribological principle that the actual contact area of solid friction increases with increasing normal load. Since the magnitude of the increase in friction force is smaller than the increase in the normal load, the friction coefficient decreases withFigure increasing 3. Friction normal coefficient load. curve with different sliding velocities, with five loads.

Figure 4. Friction coefficient curve with different loads, with five sliding velocities.

Comparing Figures 3 and 4, the sliding speed increased by 2.33 times from 30.62 mm/s to 71.42 mm/s with constant load, so the coefficient of friction decreased by a maximum of 0.084; the normal loads increased by five times from 0.51 MPa to 2.55 MPa with constant speed, so the coefficient of friction decreased by a maximum of 0.046. It can be seen that when the sliding speed is between 30.62 mm/s and 71.42 mm/s, the normal load is between 0.51 MPa and 2.55 MPa, the maximum average decrease in the friction coefficient is 0.036 with a doubling of the sliding speed, and the maximum FigureFigure 4. 4. FrictionFriction coefficient coefficient curve curve with with different different loads, loads, with with five five sliding sliding velocities. velocities. average decrease in the friction coefficient is 0.0092 with a doubling of the normal load. That is to say, the ComparingfrictionComparing coefficient Figures Figures between33 andand 4,4, the5052 the sliding slidingaluminum speed speed alincreasedloy increased and bySKD11 by 2.33 2.33 timesdie times steel from fromis 30.62 affected 30.62 mm/s mmby to sliding 71.42/s to mm/s71.42velocity with mm nearly/ sconstant with four constant load,times so as load, the much coefficient so theas it coeis affected ffiofcient friction ofby friction decreasednormal decreasedload. by a maximum by a maximum of 0.084; ofthe 0.084; normal the loadsnormal increased loads increased by five bytimes five from times 0.51 from MPa 0.51 to MPa 2.55 to MPa 2.55 MPawith withconstant constant speed, speed, so the so thecoefficient coefficient of 3.2. Surface Morphology of the 5052 Aluminum Alloy frictionof friction decreased decreased by a by ma aximum maximum of 0.046. of 0.046. It can It be can seen be seenthat when that when the sliding the sliding speed speedis between is between 30.62 mm/s30.62Under mmand/ s71.42 andthe boundary 71.42mm/s, mm the/ s,lubrication normal the normal load condition, load is between is between the surface0.51 0.51 MPa MPamorphology and and 2.55 2.55 MPa, of MPa, 5052 the the aluminum maximum maximum alloy average average after decreasedecreasegrinding in inwith the the SKD11friction friction die coefficient coe steel,fficient at isa is sliding0.036 0.036 wi with speedth a a doubling doublingof 40.82 mm/sof of the the and sliding sliding normal speed, speed, loads and and of the the0.51 maximum maximum MPa and averageaverage2.55 MPa, decrease decrease is shown in in the thein frictionFigure friction 5.coefficient coe Thefficient maximum is is 0.0092 0.0092 valley with with deptha a doubling doubling of the of of 5052 the the normal normalaluminum load. load. alloy That That surfaceis is to to say, say, is thethe3.547 friction µm, the coecoefficient maximumfficient between between peak 5052height 5052 aluminum isaluminum 5.839 µm, alloy al andloy and theand SKD11 height SKD11 die of steel dieall points issteel affected isaround affected by sliding 5.0 byµm. velocitysliding When velocitynearlythe surface four nearly timesis foursmooth, as times much a assmall as much it is number a ffasected it is ofaffected by scratches normal by load.normal appear, load. and a large number of fine abrasive particles as well as slight abrasions can be observed. It is shown that the friction mechanism is mainly 3.2.ploughing Surface Morphologywear and abrasive of the 5052 wear, Aluminum under lower Alloy normal load. The maximum valley depth of the 5052 aluminumUnder thealloy boundary surface islubrication 1.795 µm, condition, the maximum the surface peak of morphology height is 4.650 of 5052 µm, aluminum and the height alloy afterof all grindingpoints around with SKD11 3.338 µm, die as steel, shown at a in sliding Figure speed 5b. There of 40.82 is a marked mm/s and increase normal in scratchesloads of 0.51on the MPa surface, and 2.55 MPa, is shown in Figure 5. The maximum valley depth of the 5052 aluminum alloy surface is 3.547 µm, the maximum peak height is 5.839 µm, and the height of all points around 5.0 µm. When the surface is smooth, a small number of scratches appear, and a large number of fine abrasive particles as well as slight abrasions can be observed. It is shown that the friction mechanism is mainly ploughing wear and abrasive wear, under lower normal load. The maximum valley depth of the 5052 aluminum alloy surface is 1.795 µm, the maximum peak of height is 4.650 µm, and the height of all points around 3.338 µm, as shown in Figure 5b. There is a marked increase in scratches on the surface,

Metals 2019, 9, 853 6 of 16

3.2. Surface Morphology of the 5052 Aluminum Alloy Under the boundary lubrication condition, the surface morphology of 5052 aluminum alloy after grinding with SKD11 die steel, at a sliding speed of 40.82 mm/s and normal loads of 0.51 MPa and 2.55 MPa, is shown in Figure5. The maximum valley depth of the 5052 aluminum alloy surface is 3.547 µm, the maximum peak height is 5.839 µm, and the height of all points around 5.0 µm. When the surface is smooth, a small number of scratches appear, and a large number of fine abrasive particles as well as slight abrasions can be observed. It is shown that the friction mechanism is mainly ploughing wearMaterials and 2019 abrasive, 19, x FOR wear, PEER under REVIEW lower normal load. The maximum valley depth of the 5052 aluminum6 of 15 alloy surface is 1.795 µm, the maximum peak of height is 4.650 µm, and the height of all points around 3.338markedµm, adhesion as shown marks, in Figure and 5anb. increase There is in a the marked depth increase of the ploughing. in scratches It onis shown the surface, that the marked friction adhesionmechanism marks, is mainly and an increaseploughing in thewear depth with of slight the ploughing. adhesive It wear, is shown under that higher the friction normal mechanism load. In issummary, mainly ploughing with constant wear speed with slightconditions, adhesive the wear,scratches under on higherthe surface normal of the load. 5052 In aluminum summary, withalloy constantgradually speed increase; conditions, the depth the scratches of the furrow on the gradua surfacelly of increases the 5052 aluminum with increasing alloy gradually normal load. increase; The theactual depth contact of the area furrow between gradually the 5052 increases aluminum with alloy increasing and SKD11 normal gradually load. increases. The actual The contact lubrication area betweenoil flowing the into 5052 the aluminum groove enhances alloy and the SKD11 lubrication gradually effect, increases. making The the lubricationincreasing oiltrend flowing of the into friction the grooveforce slow enhances down. the The lubrication increase rate effect, of makingfriction is the le increasingss than the trendincrease of the rate friction of normal force load, slow and down. the Thefriction increase coefficient rate of gradually friction is decreases, less than thewhich increase is consistent rate of normalwith the load, above and conclusion the friction of coethe ffifrictioncient graduallycharacteristic decreases, study. which is consistent with the above conclusion of the friction characteristic study.

(a) (b)

FigureFigure 5.5. Surface morphology morphology with with different diﬀerent loads: loads: (a ()a 40.82) 40.82 mm/s, mm /0.51s, 0.51 MPa; MPa; and and (b) 40.82 (b) 40.82 mm/s, mm 2.55/s, 2.55MPa. MPa.

TheThe surfacesurface morphology morphology of of the the 5052 5052 aluminum aluminum alloy alloy after after grinding grinding with with SKD11 SKD11 at at a a normalnormal loadload ofof 1.021.02 MPa,MPa, withwith speedsspeeds ofof 30.6230.62 mmmm/s/s andand 71.4271.42 mmmm/s,/s, is is shown shown in in Figure Figure6 .6. The The maximum maximum valley valley isis 2.7732.773 µµm,m, thethe maximummaximum peakpeak heightheight isis 5.0265.026 µµm,m, andand thethe heightheight ofof allall pointspoints isis aroundaround 4.04.0 µµm.m. ThereThere areare aa lot lot of of deep deep scratches scratches on on the the surface. surface. TheThe frictionfriction mechanismmechanism isis mainlymainly ploughingploughing wearwear andand abrasiveabrasive wear, under lower sliding sliding speed. speed. As As sh shownown in inFigure Figure 6b,6b, the the surface surface morphology morphology of two of twosliding sliding speeds, speeds, the themaximum maximum valley valley depth depth of ofthe the 5052 5052 aluminum aluminum alloy alloy surface surface is is 1.631 µµm,m, thethe maximummaximum peakpeak heightheight isis 3.6273.627µ µm,m, and and the the height height of of all all points points is is about about 3.0 3.0µ µm.m. TheThe scratchesscratches onon thethe surfacesurface are are significantly significantly reduced reduced and and smooth, smooth, and aand small a amountsmall amount of adhesion of adhesion marks can marks be observed. can be Inobserved. summary, In if summary, the load conditions if the load are conditions constant, theare scratches constant, on the the scratches surface ofon the the 5052 surface aluminum of the alloy5052 graduallyaluminum decrease, alloy gradually and the furrowdecrease, depth and gradually the furrow becomes depth shallower gradually with becomes increasing shallower speed. with The actualincreasing contact speed. areas The between actual the contact 5052aluminum areas between alloy the and 5052 the SKD11aluminum die steel alloy gradually and the SKD11 decrease. die With steel increasinggradually speed,decrease. the temperatureWith increasing between speed, the frictionthe temperature contact points between increases the gradually,friction contact which causespoints theincreases viscosity gradually, of the lubricant which tocauses decrease the viscosity and leads of the the coe lubricantfficient of to friction decrease to decreaseand leads noticeably. the coefficient The frictionof friction coe ffitocient decrease decreases noticeably. gradually The withfriction increasing coefficient speed; decreases the velocity graduall decreases,y with withincreasing the increase speed; inthe velocity velocity being decreases, larger thanwith thethe increaseincrease inin load.velocity being larger than the increase in load.

(a) (b)

Figure 6. Surface morphology with different velocities: (a) 1.02 MPa, 30.62 mm/s; and (b) 1.02 MPa, 71.42 mm/s.

Materials 2019, 19, x FOR PEER REVIEW 6 of 15 marked adhesion marks, and an increase in the depth of the ploughing. It is shown that the friction mechanism is mainly ploughing wear with slight adhesive wear, under higher normal load. In summary, with constant speed conditions, the scratches on the surface of the 5052 aluminum alloy gradually increase; the depth of the furrow gradually increases with increasing normal load. The actual contact area between the 5052 aluminum alloy and SKD11 gradually increases. The lubrication oil flowing into the groove enhances the lubrication effect, making the increasing trend of the friction force slow down. The increase rate of friction is less than the increase rate of normal load, and the friction coefficient gradually decreases, which is consistent with the above conclusion of the friction characteristic study.

(a) (b)

Figure 5. Surface morphology with different loads: (a) 40.82 mm/s, 0.51 MPa; and (b) 40.82 mm/s, 2.55 MPa.

The surface morphology of the 5052 aluminum alloy after grinding with SKD11 at a normal load of 1.02 MPa, with speeds of 30.62 mm/s and 71.42 mm/s, is shown in Figure 6. The maximum valley is 2.773 µm, the maximum peak height is 5.026 µm, and the height of all points is around 4.0 µm. There are a lot of deep scratches on the surface. The friction mechanism is mainly ploughing wear and abrasive wear, under lower sliding speed. As shown in Figure 6b, the surface morphology of two sliding speeds, the maximum valley depth of the 5052 aluminum alloy surface is 1.631 µm, the maximum peak height is 3.627 µm, and the height of all points is about 3.0 µm. The scratches on the surface are significantly reduced and smooth, and a small amount of adhesion marks can be observed. In summary, if the load conditions are constant, the scratches on the surface of the 5052 aluminum alloy gradually decrease, and the furrow depth gradually becomes shallower with increasing speed. The actual contact areas between the 5052 aluminum alloy and the SKD11 die steel gradually decrease. With increasing speed, the temperature between the friction contact points increases gradually, which causes the viscosity of the lubricant to decrease and leads the coefficient ofMetals friction2019, 9to, 853 decrease noticeably. The friction coefficient decreases gradually with increasing speed;7 of 16 the velocity decreases, with the increase in velocity being larger than the increase in load.

(a) (b)

Figure 6. SurfaceSurface morphology morphology with with different diﬀerent velocities: velocities: ( (aa)) 1.02 1.02 MPa, MPa, 30.62 30.62 mm/s; mm/s; and and ( (bb)) 1.02 1.02 MPa, MPa, 71.4271.42 mm/s. mm/s.

As can be seen from Figures5 and6, the surface morphology of the 5052 aluminum alloy after grinding with the SKD11 mold steel greatly varies with different process parameters. The process parameters must have a significant influence on the surface roughness of the 5052 aluminum alloy. Six roughness parameters, namely Ra, Rp, Rv, Rz, Rc and Rq, as shown in Table3, are used to illustrate the boundary lubrication condition.

Table 3. Summary of surface ﬁnish parameters Ra, Rp, Rv, Rz, Rc and Rq, data from [15].

Parameter Description Calculation Formula

Average roughness = area between surface trace and average. L 1 R Ra Measured by adding or integrating absolute values of height, z Ra = L r(x) dx (see Figure1). 0 s L 1 R Rq Root-Mean-Square roughness 1.1 Ra. R = r2(x) dx × q L 0 Peak roughness = amplitude of the highest peak within the R R = max[r(x)] p scan length. p Valley roughness = amplitude of the deepest valley within the R R = min[r(x)] v scan length. v Total roughness = height diﬀerence between the highest peak R R = R + R z and lowest valley within the scan length. z p v

The surface roughness values of 5052 aluminum alloy after grinding with SKD11 die steel under four diﬀerent process parameters, with a sliding stroke of 245 mm, are shown in Table4. With the constant speed condition and the increase of normal loads from 0.51 to 2.55 MPa, all six surface roughness values increased. The contour arithmetic mean deviation Ra increased from 0.148 µm to 0.241 µm. With the increase in sliding speed from 30.62 to 71.42 mm/s, all six surface roughness values decreased. The contour arithmetic mean deviation Ra decreased from 0.229 to 0.125 µm. This is consistent with the conclusion that the friction coeﬃcient decreases with increasing sliding speed.

Table 4. Surface roughness value under boundary lubrication with diﬀerent parameters.

Surface Roughness Parameters, µm Process Parameters Ra Rp Rv Rz Rc Rq 40.82 mm/s, 0.51 MPa 0.148 0.904 1.388 2.292 1.349 0.223 40.82 mm/s, 2.55 MPa 0.241 1.183 1.672 2.855 1.504 0.342 1.02 MPa, 30.62 mm/s 0.229 1.060 1.193 2.253 1.600 0.310 1.02 MPa, 71.42 mm/s 0.125 0.826 1.170 1.996 1.201 0.201

3.3. Variable Friction Modeling As can be seen from Figures3 and4, the friction behavior between 5052 aluminum alloy and SKD11 die steel is obviously aﬀected by sliding speed and normal load. Therefore, the simulation analysis Metals 2019, 9, 853 8 of 16

of 5052 aluminum alloy sheet forming with the constant friction coefficient model is not consistent with the actual working condition, and the prediction error is large. To accurately describe the friction characteristics in the forming process of 5052 aluminum alloy, and to improve the precision of the forming simulation and roughcast outline of complex sheet metal parts, it is particularly important to establish a variable friction coefficient model that comprehensively considers the sliding speed and the normal load. To quickly establish a real friction model that can accurately describe the friction characteristics between 5052 aluminum alloy and SKD11 die steel, with the fitting function of MATLAB software, the friction coefficient and sliding speed under five normal loads were, respectively, fitted by an inverse function curve. The inverse function fitting curve between friction coefficient and sliding Materials 2019, 19, x FOR PEER REVIEW 8 of 15 velocity is shown in Figure7.

FigureFigure 7. 7. InverseInverse function function fitting ﬁtting curve. curve.

AsAs shown shown in in Figure Figure 77,, the variation law of the friction coecoefficientfficient with with the the sliding sliding speed speed and and the the fivefive kinds kinds of of normal normal load load conditions conditions is is in in accordance accordance with the inverse function, which is as follows: m µ = m , (1) μ =v + n + (1) v n , where m and n are constants related to normal loads, v is the sliding speed, and µ is the friction coefficient. whereThe m experimentaland n are constants data to fitrelated the values to normal of m and loads,n with v is the the five sliding normal speed, load and conditions µ is the are friction shown coefficient.in Table5, based on the analysis of MATLAB software. The experimental data to fit the values of m and n with the five normal load conditions are shown in Table 5, based on theTable analysis 5. Results of MATLAB for m, n and software. goodness of fit with different loads.

Normal Load Table 5. Results for mm, n and goodness of nfit with differentGoodness loads. of Fit (MPa) 0.510Normal Load (MPa) 4.811 m n 1.97Goodness of Fit 0.9772 1.0190.510 4.4054.811 1.97 2.383 0.9772 0.9752 1.5301.019 4.0324.405 2.383 2.802 0.9752 0.9658 2.038 3.807 3.413 0.9575 1.530 4.032 2.802 0.9658 2.550 3.611 3.799 0.9503 2.038 3.807 3.413 0.9575 2.550 3.611 3.799 0.9503 As shown in Table5, the goodness of fit between the inverse function and the real value is more thanAs 0.95, shown so it in can Table be concluded5, the goodness that theof fit fitted between values the of inversem and functionn are eff andective. the Forreal verificationvalue is more of thanthe correlation 0.95, so it can between be concluded normal loadthat the and fittedm and valuesn, the of first m and column n are values effective. of m Forand verificationn were analyzed of the correlationseparately. between From Table normal5, it can load be seenand m that andm ndecreases, the firstwith column increasing values normalof m and load, n were but n analyzedincreases separately.with increasing From normalTable 5,load. it can Tobe findseen athat functional m decreases relationship with increasing between normalm, n and load, normal but n increases load, the with increasing normal load. To find a functional relationship between m, n and normal load, the relationship curve between the normal load and m and n was obtained by fitting, as shown in Figure 8. According to the fitting results, the relationship between the normal load and m is as follows: a ⋅ P + b m = , (2) P + c where a, b and c are constants, the values of a, b and c are 1.849, 13.3 and 2.446, respectively, and the goodness of fit is 0.9974. It can be seen that the goodness of fit between the function and the actual value is better, and the values of a, b and c obtained by fitting are valid. The functional relationship between m and the normal load is as follows: 1.849 ⋅ P +13.3 m = . (3) P + 2.446

Metals 2019, 9, 853 9 of 16 relationship curve between the normal load and m and n was obtained by fitting, as shown in Figure8. According to the fitting results, the relationship between the normal load and m is as follows: Materials 2019, 19, x FOR PEER REVIEW 9 of 15 a P + b The relationship between the normalm load= and· n was, in accordance with the following functional (2) P + c relationship: where a, b and c are constants, the values of a, b and c are 1.849, 13.3 and 2.446, respectively, and the n = a ⋅ P + b , (4) goodness of fit is 0.9974. It can be seen that the goodness of fit between the function and the actual valuewhere is better,a and andb are the constants, values of anda, b theand valuesc obtained of a and by fittingb, obtained are valid. from The the functionalfitting results, relationship are 0.9193 betweenand 1.467,m and respectively. the normal The load goodness is as follows: of fit was 0.9927. It can be seen that the goodness of fit between the function and the actual value is better, and the values of a and b obtained by fitting are valid. The 1.849 P + 13.3 functional relationship between n andm the= normal· load is as. follows: (3) P + 2.446 n = 0.9193⋅ P +1.467 . (5)

(a) (b)

FigureFigure 8. 8.Fitting Fitting curves curves between betweenm mand andn andn and the the normal normal load: load: (a )(a ﬁtting) fitting curve curve between betweenm andm and the the normalnormal load; load; and and (b )(b Fitting) Fitting curve curve between betweenn and n and the the normal normal load. load.

TheThe relationship functional relationship between the of normalfriction coefficient, load and nslidingwas inspeed accordance and normal with load the was following obtained functionalby combining relationship: Equations (1), (3) and (5): n = a P + b, (4) 1·.849P +13.3 μ = , (6) where a and b are constants, and the values(P + of2.446a and)(0b,.9193 obtainedP +1 from.467 the+ v fitting) results, are 0.9193 and 1.467, respectively. The goodness of fit was 0.9927. It can be seen that the goodness of fit between the functionwhere P and is the the normal actual valueload, v is is better, the sliding and the speed, values and of µ aisand the bfrictionobtained coefficient. by fitting are valid. The functional relationship between n and the normal load is as follows: 3.4. Verification Parameters of the Variable Friction Model n = 0.9193 P + 1.467. (5) To verify the validity of the above variable ·friction model based on different sliding speeds and normal loads, five groups of normal loads and sliding speed values were substituted, respectively, The functional relationship of friction coefficient, sliding speed and normal load was obtained by and the ratios of the predicted values to the actual measured values are shown in Table 6. The error combining Equations (1), (3) and (5): between the prediction results of the variable friction model and the actual measured values was less than 7%, which preliminarily verified the validity1.849P +of 13.3the model. µ = , (6) (P + 2.446)(0.9193P + 1.467 + v) Table 6. Ratio and error between function prediction and measured value. where P is the normal load, v is the sliding speed, and µ is the friction coefficient. Speed 30.62 40.82 51.03 61.23 71.42 (mm/s) 3.4. Verification ParametersRatio ofError the VariableRatio Friction Error Model Ratio Error Ratio Error Ratio Error Load (MPa) Value (%) Value (%) Value (%) value (%) Value (%) To0.510 verify the1.0000 validity of0.00 the above0.9550 variable −4.50 friction 0.9888 model based−1.12 on1.0037 different 0.37sliding speeds 1.0198 and 1.98 1.019 0.9903 −0.97 0.9563 −4.37 0.9763 −2.37 0.9980 −0.20 1.0235 2.35 normal loads, five groups of normal loads and sliding speed values were substituted, respectively, 1.530 0.9847 −1.53 0.9571 −4.29 0.9902 −0.98 1.0207 2.07 1.0302 3.02 and the2.038 ratios of the1.0283 predicted 2.83 values0.9577 to the actual−4.23 measured0.9861 values−1.39 are1.0164 shown in 1.64 Table 6. 1.0391 The error 3.91 2.550 1.0267 2.67 0.9394 −6.06 0.9814 −1.86 1.0387 3.87 1.0420 4.20

To further verify the accuracy of the variable friction model based on the different sliding speeds and normal loads established in this paper, under the condition of a constant load of 1.28 MPa, five groups of speeds, namely 30.62 mm/s, 40.82 mm/s, 51.03 mm/s, 61.23 mm/s and 71.42 mm/s, were individually chosen to be applied on the MPX-2000 disk-pin friction tester, and the obtained friction coefficients were 0.128, 0.098, 0.0787, 0.0645 and 0.0552, respectively. With the condition of a constant

Metals 2019, 9, 853 10 of 16 between the prediction results of the variable friction model and the actual measured values was less than 7%, which preliminarily veriﬁed the validity of the model.

Table 6. Ratio and error between function prediction and measured value.

Speed (mm/s) 30.62 40.82 51.03 61.23 71.42 Ratio Error Ratio Error Ratio Error Ratio Error Ratio Error Load (MPa) Value (%) Value (%) Value (%) value (%) Value (%) 0.510 1.0000 0.00 0.9550 4.50 0.9888 1.12 1.0037 0.37 1.0198 1.98 − − 1.019 0.9903 0.97 0.9563 4.37 0.9763 2.37 0.9980 0.20 1.0235 2.35 − − − − 1.530 0.9847 1.53 0.9571 4.29 0.9902 0.98 1.0207 2.07 1.0302 3.02 − − − 2.038 1.0283 2.83 0.9577 4.23 0.9861 1.39 1.0164 1.64 1.0391 3.91 − − 2.550 1.0267 2.67 0.9394 6.06 0.9814 1.86 1.0387 3.87 1.0420 4.20 − −

To further verify the accuracy of the variable friction model based on the different sliding speeds and normal loads established in this paper, under the condition of a constant load of 1.28 MPa, five groupsMaterials 2019 of speeds,, 19, x FOR namely PEER REVIEW 30.62 mm/s, 40.82 mm/s, 51.03 mm/s, 61.23 mm/s and 71.42 mm/s,10 were of 15 individually chosen to be applied on the MPX-2000 disk-pin friction tester, and the obtained friction coespeedfficients of 44.22 were mm/s, 0.128, five 0.098, groups 0.0787, of 0.0645loads (0.510 and 0.0552, MPa, respectively.1.019 MPa, 1.530 With MPa, the condition 2.038 MPa of aand constant 2.550 speedMPa) ofwere 44.22 individually mm/s, five groupschosen of to loads be applied (0.510 MPa, on the 1.019 MPX-2000 MPa, 1.530 disk-pin MPa, 2.038 friction MPa andtester, 2.550 and MPa) the wereobtained individually friction coefficients chosen to bewere applied 0.106, on 0.095, the MPX-20000.086, 0.0799 disk-pin and 0.07386. friction The tester, measured and the values obtained and frictionthe predicted coefficients results were are 0.106, shown 0.095, in 0.086,Figure 0.0799 9 and and Tables 0.07386. 7 and The 8. measuredThe error values between and the the predicted resultsresults areand shown the measured in Figure values9 and is Tables less than7 and 5%,8. The which error verifies between the thevalidity predicted of the results variable and friction the measuredmodel established values is in less this than paper 5%, whichto describe verifies the the fric validitytion characteristics of the variable in frictionsheet metal model forming established with in5052 this aluminum paper to describealloy. the friction characteristics in sheet metal forming with 5052 aluminum alloy.

(a) (b)

FigureFigure 9.9. Experimental values and predicted values with ( a) a constant load of 1.28 MPaMPa andand ((b)) aa constantconstant speedspeed ofof 44.2244.22 mmmm/s./s.

Table 7.7. RatioRatio betweenbetween functionfunction predictionprediction andand measuredmeasured value,value, whenwhen loadingloading ((PP))= = 1.281.28 MPa.MPa. Friction Coeﬃcient Friction Coeﬃcient VelocityVelocity (mmFriction/s) Coefficient (Measured Friction Coefficient (FunctionError (%) Error (mm/s) (MeasuredValue) Value) (Function Prediction)Prediction) (%) 30.62 0.1280 0.1264 1.25 30.62 0.1280 0.1264 − −1.25 40.82 0.0980 0.0967 1.33 40.82 0.0980 0.0967 − −1.33 51.03 0.0787 0.0783 0.51 − 51.03 61.230.0787 0.0645 0.06580.0783 2.20 −0.51 61.23 71.420.0645 0.0552 0.05680.0658 2.90 2.20 71.42 0.0552 0.0568 2.90

Table 8. Ratio between function prediction and measured value, when velocity (v) = 44.22 mm/s.

Loading Friction Coefficient (Measured Friction Coefficient (Function Error (MPa) Value) Prediction) (%) 0.510 0.1060 0.1044 −1.51 1.019 0.095 0.0940 −1.05 1.530 0.0860 0.0861 0.12 2.038 0.0799 0.0800 0.13 2.550 0.0739 0.0751 1.62

4. Discussion

4.1. Simulation of Sheet Metal Forming To test the effectiveness of the variable friction model, based on different normal loads and sliding speeds, in predicting the numerical simulation of sheet metal forming, the model established in this paper was used to simulate the thickness distribution and spring-back of U-bend parts, based on ABAQUS software. The three-dimensional models, including punch, die, binder and blank, were modeled using NX software, and then exported in IGS format (General conversion format of three-dimensional software) to ABAQUS software. The punch, die and binder were defined as discrete rigid bodies, and the blank

Metals 2019, 9, 853 11 of 16

Table 8. Ratio between function prediction and measured value, when velocity (v) = 44.22 mm/s.

Friction Coeﬃcient Friction Coeﬃcient Loading (MPa) Error (%) (Measured Value) (Function Prediction) 0.510 0.1060 0.1044 1.51 − 1.019 0.095 0.0940 1.05 − 1.530 0.0860 0.0861 0.12 2.038 0.0799 0.0800 0.13 2.550 0.0739 0.0751 1.62

4. Discussion

4.1. Simulation of Sheet Metal Forming To test the effectiveness of the variable friction model, based on different normal loads and sliding Materials 2019, 19, x FOR PEER REVIEW 11 of 15 speeds, in predicting the numerical simulation of sheet metal forming, the model established in this waspaper defined was used as a deformable to simulate body. the thickness The material distribution of the blank and spring-backwas 5052 aluminum of U-bend alloy, parts, of which based the on physicalABAQUS parameters software. are shown in Table 9. The three-dimensional models, including punch, die, binder and blank, were modeled using NX software, and then exported in IGSTable format 9. Physical (General properties conversion of materials. format of three-dimensional software) to ABAQUS software. The punch, die and binder were defined as discrete rigid bodies, and the blank 3 was defined as a deformableDensity (g/cm body.) The Young's material Modulus of the blank (GPa) was Poisson5052 aluminum Ratio alloy, of which the physical parameters are shown2.72 in Table9. E = 69.9 v = 0.33 To make the simulation structure more consistent with the actual working conditions, the punch, Table 9. Physical properties of materials. die and holder were defined as non-deformable solid structures, and the sheet was defined as a deformable shellDensity structure. (g/cm 3The) numericalYoung’s model Modulus of ABAQUS (GPa) U-bend parts Poisson forming Ratio the simulation is shown in Figure 10.2.72 E = 69.9 v = 0.33 In mesh generation, the blank element type was explicit and shell element SR4, and the punch, die and binder were explicit and discrete rigid body element R3D4. FromTo make the thecomparison simulation of structurethe predicted more results, consistent we drew with the following actual working conclusions: conditions, (i) the the variable punch, frictiondie and model holder based were on defined different as sliding non-deformable velocities and solid normal structures, loads; andand (ii) the three sheet groups was defined of constant as a frictiondeformable coefficients, shell structure. and the The measured numerical value model of the of ABAQUSactual parts U-bend to verify parts the forming validity the of simulationthe variable is frictionshown inmodel Figure established 10. in this paper.

Figure 10. Numerical modeling of stamping. Figure 10. Numerical modeling of stamping. In mesh generation, the blank element type was explicit and shell element SR4, and the punch, 4.2.die Thickness and binder Distribution were explicit Result and discrete rigid body element R3D4. ABAQUS/ExplicitFrom the comparison was of used the predictedto simulate results, the thickne we drewss thedistribution following of conclusions: U-bend parts. (i) the To variableensure thefriction effectiveness model based of the on comparison diﬀerent sliding between velocities the resu andlts normal of the loads;thickness and distribution (ii) three groups simulation of constant and thefriction actual coe measuredﬃcients, values, and the the measured constant value friction of coefficient the actual partsmodel to and verify the variable the validity friction of the coefficient variable modelfriction established model established in this paper in this were paper. used to simulate the thickness distribution of the Box-shape parts. The lubrication conditions of the sliding friction in the forming process were divided into dry friction (µ > 0.3), boundary lubrication (0.1 < µ < 0.3), mixed lubrication (0.03 < µ < 0.1) and hydrodynamic lubrication (µ ≤ 0.03), according to the friction coefficient [16]. Dry friction usually occurs when the area between the sliding surfaces has a complete absence of lubricant. As the friction test and sheet metal stamping were carried out under lubricant conditions, the lubrication condition of sheet metal forming cannot be classified as dry friction. Generally, hydrodynamic lubrication does not occur in the sheet metal forming process. After analysis of the friction test data in Table 2, the friction condition was either boundary lubrication or mixed lubrication condition. Therefore, the three groups of constant friction coefficients selected to simulate the thickness distribution of the Box-shape parts were 0.05, 0.1 and 0.15. The comparison of the predicted results involved: (i) the variable friction model based on different sliding velocities and normal loads; and (ii) three groups of constant friction coefficient, and the measured values of the actual parts. In the simulation, the size of the numerical model of the mold was consistent with the actual size. The model of the sheet material was selected as Young's modulus E = 69.9 GPa, the Poisson's ratio v = 0.33, and the stress-strain curve according to reference [17]. The sheet thickness (STH) of constant friction coefficients and the variable friction model are shown in Figure 11 [18,19]. It can be seen from the STH distribution prediction results that the most severe thinning occurred in the vicinity of the punch fillet. Therefore, the deep drawing forming process had the highest risk

Metals 2019, 9, 853 12 of 16

4.2. Thickness Distribution Result ABAQUS/Explicit was used to simulate the thickness distribution of U-bend parts. To ensure the effectiveness of the comparison between the results of the thickness distribution simulation and theMaterials actual 2019 measured, 19, x FOR PEER values, REVIEW the constant friction coefficient model and the variable friction coe12ffi cientof 15 model established in this paper were used to simulate the thickness distribution of the Box-shape parts. Theof crack lubrication failure near conditions the punch of the fillet. sliding Although friction the in thickness the forming distribution process were prediction divided simulations into dry friction were (conductedµ > 0.3), boundary under the lubrication same forming (0.1 speed< µ < and0.3), blank mixed holder lubrication pressure (0.03 conditions,< µ < 0.1) the and predicted hydrodynamic results lubricationof thickness ( µdistribution0.03), according for the friction to the frictioncoefficients coeffi 0.05,cient 0.1 [16 and]. Dry 0.15 friction were obviously usually occurs different. when It can the ≤ areabe seen between that the the thinning sliding surfaceswas more has serious a complete with absencethe increasing of lubricant. of the Asfriction the friction coefficient. test andThis sheet was metalmainly stamping due to a larger were carried friction out coefficient under lubricant resulting conditions, in greater friction the lubrication between condition the sheet ofand sheet the mold; metal formingthus, there cannot was a be greater classified force as to dry prevent friction. the Generally, sheet me hydrodynamictal flowing into lubrication the cavity of does the not die. occur Under in the sheetsame metalforming forming speed process.conditions, After it was analysis necessary of the to friction apply testa greater data in force Table to2 ,the the punch friction to condition bring the wassheet either material boundary to flow lubrication into the cavity or mixed of the lubricationdie to complete condition. the forming of the sheet metal, which then producedTherefore, more thenormal three load groups and friction of constant force friction at the corner coeffi cientsof the selectedpunch and to the simulate dies. Therefore, the thickness the distributionsheet flowing of became the Box-shape increasingly parts were difficult, 0.05, 0.1and and the 0.15. thinning The comparison of the sheet of metal the predicted was not results fully involved:supplemented. (i) the Eventually, variable friction with increasing model based friction on di coefficient,fferent sliding the velocitiesthinning of and sheet normal metal loads; becomes and (ii)increasingly three groups serious. of constant At the same friction time, coe itffi cancient, be seen and thethat measured the friction values conditions of the and actual normal parts. loads In the of simulation,the sheet metal the size forming of the numerical process were model relatively of the mold complicated. was consistent Therefore, with the actualthe constant size. The friction model ofcoefficient the sheet model material was was not selectedsuitable for as Young’sa numerical modulus simulationE = 69.9 of sheet GPa, metal the Poisson’s forming. ratio The vvariable= 0.33, andfriction the model stress-strain based curveon sliding according speed to and reference normal [ 17load]. The was sheet more thickness suitable for (STH) describing of constant the friction coecharacteristicsfficients and of the the variable sheet metal friction forming model process. are shown in Figure 11[18,19].

(a) Friction coefficient of 0.05 (b) Friction coefficient of 0.1

Figure 11. SheetSheet thickness thickness (STH) (STH) under under different different friction friction coefficients: coefficients: (a) (frictiona) friction coefficient coefficient of 0.05, of 0.05, (b) (frictionb) friction coefficient coefficient of 0.1, of 0.1, (c) friction (c) friction coefficient coefficient of 0.15 of 0.15 and and (d) (variabled) variable friction friction model. model.

ItThe can thickness be seen frommeasuring the STH point distribution is shown predictionin Figure 11a. results The that thickness the most value severe was thinning measured occurred by the inultrasonic the vicinity thickness of the punchmeasuring fillet. Therefore,instrument, the and deep the drawing thickness forming simulation process prediction had the highest result risk was of crackmeasured failure at the near red the node punch using fillet. software, Although as shown the thickness in Figure distribution 12. The thickness prediction comparison simulations between were conductedthe numerical under result the and same actual forming measurements speed and is blank shown holder in Figure pressure 11b. conditions, From the thickness the predicted distribution results ofcomparison thickness distributionchart, it can be for seen the frictionthat the coe actualfficients measured 0.05, 0.1 thickness and 0.15 and were simulated obviously prediction different. values It can were most severely thinned at measurement point 9. The maximum thinning rate of the measured values, for a constant friction coefficient of 0.1 and for the variable friction model, was about 15%. The maximum thinning rate with a constant friction coefficient of 0.05 was about 7%, and with a constant friction coefficient of 0.15 it was about 35%. Therefore, it can be preliminarily considered that the variable friction model and the constant friction coefficient of 0.1 were more suitable for describing the friction characteristics of the sheet metal forming process.

Metals 2019, 9, 853 13 of 16 be seen that the thinning was more serious with the increasing of the friction coefficient. This was mainly due to a larger friction coefficient resulting in greater friction between the sheet and the mold; thus, there was a greater force to prevent the sheet metal flowing into the cavity of the die. Under the same forming speed conditions, it was necessary to apply a greater force to the punch to bring the sheet material to flow into the cavity of the die to complete the forming of the sheet metal, which then produced more normal load and friction force at the corner of the punch and the dies. Therefore, the sheet flowing became increasingly difficult, and the thinning of the sheet metal was not fully supplemented. Eventually, with increasing friction coefficient, the thinning of sheet metal becomes increasingly serious. At the same time, it can be seen that the friction conditions and normal loads of the sheet metal forming process were relatively complicated. Therefore, the constant friction coefficient model was not suitable for a numerical simulation of sheet metal forming. The variable friction model based on sliding speed and normal load was more suitable for describing the friction characteristics of the sheet metal forming process. The thickness measuring point is shown in Figure 11a. The thickness value was measured by the ultrasonic thickness measuring instrument, and the thickness simulation prediction result was measured at the red node using software, as shown in Figure 12. The thickness comparison between the numerical result and actual measurements is shown in Figure 11b. From the thickness distribution comparison chart, it can be seen that the actual measured thickness and simulated prediction values were most severely thinned at measurement point 9. The maximum thinning rate of the measured values, for a constant friction coefficient of 0.1 and for the variable friction model, was about 15%. The maximum thinning rate with a constant friction coefficient of 0.05 was about 7%, and with a constant friction coefficient of 0.15 it was about 35%. Therefore, it can be preliminarily considered that the variable friction model and the constant friction coefficient of 0.1 were more suitable for describing the frictionMaterials characteristics2019, 19, x FOR PEER of the REVIEW sheet metal forming process. 13 of 15

(a) (b)

FigureFigure 12.12. ThicknessThickness measuringmeasuring pointspoints andand comparison:comparison: ((aa)) thicknessthickness measuringmeasuring points;points; ((bb)) thicknessthickness comparisoncomparison betweenbetween numerical numerical result result and and actual actual measurements. measurements.

4.3.4.3. Spring-BackSpring-Back DistributionDistribution AccordingAccording toto thethe simulationsimulation resultsresults ofof thicknessthickness distribution,distribution, thisthis sectionsection selectsselects aa fixedfixed frictionfriction coecoefficientfficient ofof 0.10.1 andand thethe modified modified friction friction model model to to predict predict spring-back spring-back in in sheet sheet metal metal forming. forming. TheThe averageaverage valuesvalues ofof thethe twotwo stamping stamping tests tests were werea a= =11.2 11.2and andb b= = 7.8.7.8. TheThe spring-backspring-back angleangle representsrepresents thethe amountamount ofof spring-back.spring-back. ToTo ensureensure thethe accuracyaccuracy ofof spring-backspring-back predictionprediction results,results, anan analyticalanalytical stepstep waswas setset toto removeremove punches,punches, concaveconcave diesdies andand blankblank holderholder ringsrings afterafter thethe simulationsimulation ofof formingforming withwith twotwo frictionfriction coecoefficients.fficients. This This step step was was taken taken in inorder order to avoid to avoid the effect the e ffofect force of forceupon uponsheet metal sheet affecting metal aff spring-ecting spring-backback prediction prediction accuracy. accuracy. Figure Figure 13 shows 13 shows a comparison a comparison of the of spring-back the spring-back prediction prediction results results from fromthe two the friction two friction coefficient coefficient models. models. The Thespring-back spring-back angles angles a1 = 8.4a1 = and8.4 b and1 = 6.3,b1 = obtained6.3, obtained by the by fixed the fixed friction coefficient model, are 25% and 19.2%, respectively, compared with the spring-back friction coefficient model, are −25%− and −19.2%,− respectively, compared with the spring-back values valuesof the actual of the actualstamping stamping tests. The tests. spring-back The spring-back angles a angles2 = 12.1a 2and= 12.1 b2 = and8.3, obtainedb2 = 8.3, obtainedby the modified by the friction model, are 8% and 6.4%, respectively, compared with the actual spring-back of the stamping test. The comparison results of spring-back are shown in Table 10.

(a) (b)

Figure 13. Comparison of spring-back with variable friction and the fixed friction model. (a) Finite Element Analysis measurement of parts; (b) measuring angle.

Table 10. Comparison of experimental and simulated results.

Spring-Back Value a (mm) b (mm) Experimental data 11.2 7.8 Fixed friction model data（0.1） 8.4 6.3 Variable friction model 12.1 8.3

The experimental results show that the spring-back error of the model with variable friction coefficient is smaller than that of the model with constant friction coefficient, which improves the simulation accuracy. The experimental verification results are shown in Figure 14.

Materials 2019, 19, x FOR PEER REVIEW 13 of 15

(a) (b)

Figure 12. Thickness measuring points and comparison: (a) thickness measuring points; (b) thickness comparison between numerical result and actual measurements.

4.3. Spring-Back Distribution According to the simulation results of thickness distribution, this section selects a fixed friction coefficient of 0.1 and the modified friction model to predict spring-back in sheet metal forming. The average values of the two stamping tests were a = 11.2 and b = 7.8. The spring-back angle represents the amount of spring-back. To ensure the accuracy of spring-back prediction results, an analytical step was set to remove punches, concave dies and blank holder rings after the simulation of forming with two friction coefficients. This step was taken in order to avoid the effect of force upon sheet metal affecting spring- Metalsback 2019 prediction, 9, 853 accuracy. Figure 13 shows a comparison of the spring-back prediction results14 of 16 from the two friction modiﬁed friction model, are 8% and 6.4%, respectively, compared with the actual spring-back of the stamping test. The comparison results of spring-back are shown in Table 10.

(a) (b)

FigureFigure 13.13. ComparisonComparison of spring-backspring-back withwith variablevariable frictionfriction andand thethe ﬁxedfixed frictionfriction model.model. ((aa)) FiniteFinite ElementElement AnalysisAnalysis measurementmeasurement ofof parts;parts; ((bb)) measuringmeasuring angle.angle.

Table 10. Table 10. ComparisonComparison ofof experimentalexperimental andand simulatedsimulated results.results.

Spring-Back ValueSpring-Back Valuea (mm) a (mm) b (mm)b (mm) Experimental dataExperimental data 11.2 11.2 7.8 7.8 Fixed friction modelFixed datafriction (0.1) model data（ 8.40.1） 8.4 6.3 6.3 Variable friction model 12.1 8.3 Variable friction model 12.1 8.3

TheThe experimentalexperimental resultsresults showshow thatthat thethe spring-backspring-back errorerror ofof thethe modelmodel withwith variablevariable frictionfriction coecoefficientfficient isis smallersmaller thanthan thatthat ofof thethe modelmodel withwith constantconstant frictionfriction coecoefficient,fficient, whichwhich improvesimproves thethe simulation accuracy. The experimental verification results are shown in Figure 14. Materialssimulation 2019,accuracy. 19, x FOR PEER The REVIEW experimental verification results are shown in Figure 14. 14 of 15

(a) (b)

Figure 14. ComparisonComparison of of roughcast roughcast outline: ( (aa)) actual actual bending bending parts; parts; ( (bb)) part part measurement. measurement.

5. Conclusions Conclusions InIn this paper, the eeffectsffects of the slidingsliding velocity and normal loads on the friction characteristics between sheet metal and stamping die under the bo boundaryundary lubrication condition were were studied by using an MPX-2000 disc-pin friction tester. Then, the results of the friction test were used to simulate thethe thickness distribution distribution and and spring-back of of U-be U-bendnd parts. Using Using MATLAB MATLAB software to analyze the experimental data, data, a a variable friction model based on different different sliding velocities and normal loads was established, which was more suitable for describing the friction characteristics of the sheet metal forming process. Then, Then, the the model model established established in in th thisis paper paper and and three three groups groups of of constant friction coefficientcoefficient were used to simulate the thicknessthickness andand spring-backspring-back distributiondistribution of U-bendU-bend parts.parts. The results allow us to draw the following conclusions: (1) Under the boundary lubrication condition, when the sliding velocity is between 30.62 mm/s and 71.42 mm/s, the friction coefficient decreases gradually with increasing sliding velocity, and the decreasing tendency slows down in the higher sliding velocity range. When the normal load is between 0.51 MPa and 2.55 MPa, the friction coefficient decreases with an increase in the normal load. The influence of normal load on the friction coefficient gradually weakened with a gradual increase in the sliding speed. (2) Under the boundary lubrication condition, the friction mechanism between sheet metal and stamping die is mainly ploughing wear and abrasive wear, with slight adhesive wear. The surface roughness of the sheet metal after grinding with stamping die generally increases with increasing normal load and decreasing sliding velocity. (3) The thickness distribution and spring-back of U-bend parts, with the variable friction model and three groups of constant friction coefficient, were simulated by using ABAQUS. The thickness distribution prediction results showed the most severe thinning in the vicinity of the punch fillet. With an increasing friction coefficient, the thinning of sheet metal in the vicinity of the punch fillet becomes increasingly serious. When the thinning of the sheet metal was not fully supplemented, there was the highest risk of crack failure near the punch fillet. The thickness distribution predicted results with a constant friction coefficient of 0.1 and with the variable friction model results were more consistent with the measured values. The spring-back predicted result from the variable friction model was more accurate than that obtained when using a constant friction coefficient of 0.1. The effectiveness of the variable friction model based on sliding speed and normal load was verified.

Funding: This research was funded by the National Natural Science Foundation of China, grant number 51505408.

Conflicts of Interest: The authors declare no conflict of interest.

Metals 2019, 9, 853 15 of 16

(1) Under the boundary lubrication condition, when the sliding velocity is between 30.62 mm/s and 71.42 mm/s, the friction coefficient decreases gradually with increasing sliding velocity, and the decreasing tendency slows down in the higher sliding velocity range. When the normal load is between 0.51 MPa and 2.55 MPa, the friction coefficient decreases with an increase in the normal load. The influence of normal load on the friction coefficient gradually weakened with a gradual increase in the sliding speed. (2) Under the boundary lubrication condition, the friction mechanism between sheet metal and stamping die is mainly ploughing wear and abrasive wear, with slight adhesive wear. The surface roughness of the sheet metal after grinding with stamping die generally increases with increasing normal load and decreasing sliding velocity. (3) The thickness distribution and spring-back of U-bend parts, with the variable friction model and three groups of constant friction coefficient, were simulated by using ABAQUS. The thickness distribution prediction results showed the most severe thinning in the vicinity of the punch fillet. With an increasing friction coefficient, the thinning of sheet metal in the vicinity of the punch fillet becomes increasingly serious. When the thinning of the sheet metal was not fully supplemented, there was the highest risk of crack failure near the punch fillet. The thickness distribution predicted results with a constant friction coefficient of 0.1 and with the variable friction model results were more consistent with the measured values. The spring-back predicted result from the variable friction model was more accurate than that obtained when using a constant friction coefficient of 0.1. The effectiveness of the variable friction model based on sliding speed and normal load was verified.

Author Contributions: Conceptualization, J.X. and S.D.; methodology, S.D.; software, S.D.; formal analysis, J.X.; Data curation, S.D.; writing—original draft preparation, S.D.; writing—review and editing, S.D.; funding acquisition, J.X. Funding: This research was funded by the National Natural Science Foundation of China, grant number 51505408. Conﬂicts of Interest: The authors declare no conﬂict of interest.

References

1. Isik, K.; Silva, M.B.; Tekkaya, A.E.; Martins, P. Formability limits by fracture in sheet metal forming. J. Mater. Process. Technol. 2014, 214, 1557–1565. [CrossRef] 2. Ramezani, M.; Ripin, Z.M. Analysis of deep drawing of sheet metal using the Marform process. Int. J. Adv. Manuf. Technol. 2012, 59, 491–505. [CrossRef] 3. Klocke, F.; Trauth, D.; Shirobokov, A.; Mattfeld, P. FE-analysis and in situ visualization of pressure slip rate and temperature dependent coeﬃcient of friction for advanced sheet metal forming: development of a novel coupled user subroutine for shell and continuum discretization. Int. J. Adv. Manuf. Technol. 2015, 81, 397–410. [CrossRef] 4. Hol, J.; Cid Alfaro, M.V.; De Rooij, M.B.; Meinders, T. Advanced friction modeling for sheet metal forming. Wear 2012, 286, 66–78. [CrossRef] 5. Zhao, Y.Z.; Wang, K.; Wang, W.R. A variable friction model in sheet metal forming with advanced high strength steels DP780. J. Shanghai Jiaotong Univ. 2015, 10, 1446–1451. 6. Ramezani, M.; Ripin, Z.M.; Ahmad, R. Modelling of kinetic friction in V-bending of ultra high strength steel sheets. Int. J. Adv. Manuf. Technol. 2010, 46, 101–111. [CrossRef] 7. Figueiredo, L.; Ramalho, A.; Oliveira, M.C.; Menezes, L.F. Experimental study of friction in sheet metal forming. Wear 2011, 271, 1651–1657. [CrossRef] 8. Ramezani, M.; Thomas, N.; Pasang, T.; Selles, M.A. Characterization of friction behaviour of AZ80 and ZE10 magnesium alloys under lubricated contact condition by strip draw and bend test. Int. J. Mach. Tools Manuf. 2014, 85, 70–78. [CrossRef] 9. Tamai, Y.; Inazumi, T.; Manabe, K. FE forming analysis with nonlinear friction coeﬃcient model considering contact pressure, sliding velocity and sliding length. J. Mater. Process. Technol. 2016, 227, 161–168. [CrossRef] 10. Wang, L.G.; Zhou, J.F.; Xu, Y.T. Study on friction characteristics of galvanized sheet by strip drawing test. J. Plast. Eng. 2016, 2, 87–91. Metals 2019, 9, 853 16 of 16

11. Wang, W.; Zhao, Y.Z.; Wang, Z. A study on variable friction model in sheet metal forming with advanced high strength steels. Tribol. Int. 2016, 93, 17–28. [CrossRef] 12. Wang, P.J.; Cheng, H. Handbook of Stamping Die Designers; China Machine Press: Beijing, China, 2008; pp. 120–189. 13. Wen, S.Z.; Huang, P. Tribology Principle; Tsinghua University Press: Beijing, China, 2002; pp. 35–67. 14. Akbarzadeh, S.; Khonsari, M.M. Study on friction characteristics of galvanized sheet by strip drawing test. Tribol. Lett. 2010, 37, 477–486. [CrossRef] 15. Varun Kumar. Summary of Surface Finish Parameters. Available online: https://www.scribd.com/document/ 255993260/Summary-of-Surface-Finish-Parameters (accessed on 8 May 2019). 16. Gerke, S.; Zistl, M.; Bhardwaj, A.; Brünig, M. Experiments with the X0-specimen on the eﬀect of non-proportional loading paths on damage and fracture mechanisms in aluminum alloys. Int. J. Solids Struct. 2019, 163, 157–169. [CrossRef] 17. Boyer, H.E. Atlas of Stress-Strain Curves; ASM International: Metal Park, OH, USA, 2002; pp. 235–270. 18. Schey, J. Tribology in Metalworking: Lubrication, Friction and Wear; American Society for Metal: Metal Park, OH, USA, 1983; pp. 125–150. 19. ISO 12004-2:2008. Metallic Materials—Sheet and Strip—Determination of Forming-Limit Curves—Part 2: Determination of Forming-Limit Curves in the Laboratory; ICS: Geneva, Switzerland, 2008.

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).