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1、Mechanics of ShapeIntroductionObjective of the Session - What do you want?What is Shape / Flatness?What are the different types of off-Flatness?Why do we require Flatness?How is Flatness measured / quantified?What are the various factors that effect Flatness?How is Flatness Controlled at the Mills?O

2、ff-line Flatness / Shape errorsWhat is Shape / Flatness?Shape or Flatness is defines as the strain profile or strain differential across the width of the strip.In simple languages, it is the ability of all portions of the strip, sheet or foil to touch the base when rested on a flat base.In the proce

3、ss of Rolling, the large forces imposed on the rolls causes them to bend or flatten. Also a lot of heat is generated in the Rolling Process. This and other factors can create a non-parallel roll gap This causes uneven reduction across the width of the strip. What is Shape / Flatness? (cont.)This lea

4、ds to non-uniform elongation such that the emerging strip is longer in certain portions. For example, the emerging strip may be longer at the middle than at the edges. The middle portion will therefore become wavy to accommodate the extra length and the strip will not lie flat when relaxedStrip Leng

5、ths across the widthLaHOW DO THE DEFECTS LOOK LIKE?Full Center BuckleEdge PocketsEdge PocketsEdge Wave / RippleEdge RippleEdgeRipple(plant light)EdgeRipple(office light)WAVY EDGESCENTRE BUCKLESQUARTER POCKETSBBAABBAABBAALateral CurvatureCoil-setCross-bowDefinitions: Lateral Curvature, Cross-bow and

6、Coil-setDefinition: Anticlastic CurvatureAnticlastic CurvatureAnticlastic curvature is a curvature which is induced when a sheet that is curved in one plane is elastically flattenedTensileCompressiveForces at the Upper and Lower Surfaces of a Strip being bent around a Radius of CurvatureSources of F

7、latness Variation: Bending of sheetr = the radius at which the outer portion of the sheet will deform under applied stress aProductivity Acceleration & deceleration Higher top speedsRecovery Threading Strip breaks Weaving Coil Build-UpQuality Customer and Process demandsWhy do we need good shape / f

8、lat strip?Litho ClosureFoilstockAnodising Quality SheetPre-painted StockSheets for Panellingetc.Which Products need good shape?Measurement of ShapeThe I Unit is the standard Engineering unit for the measurement of Shape throughout the Rolling Industry.The I Unit is defined as the Shape error resulti

9、ng from a strain differential between adjacent elements of a strip of 0.001% or one part in 100,000. That is, if a 1000 mm long strip is rolled with an edge that is 1000.01 mm long when relaxed, then the shape error between the centre and the edge would be 1 I Unit.LaDefinitions: Flatness IndexIU =

10、105* L/LaldLDefinitions for a Sinusoidal BuckleOn-line measurement of ShapeWhen the strip is under high tensions and the waviness is less apparent, the elongation differences are converted into strain variations, which in turn give rise to a uneven stress profile across the width of the strip.These

11、stress variations represent the latent shape of the relaxed material and can be measured by means of a tension monitoring device such as the Vidimon Shapemeter RollWhat are the factors that affect the Shape of the Outgoing Strip?Factors that affect the on-line ShapeFactors that affect the off-line S

12、hapeLonger middleIncoming SheetUniform ThicknessRoll gapNarrower at centreSources of Flatness Variation: Roll Gap GeometryFull CentreEdge WaveQuarter BuckleTensionDistributionOn MillRollBiteStripAppearanceOn-line Shape is affected by the roll gap geometryFactors that Effect Shape / FlatnessProcess (

13、Method)Pass ScheduleMill SchedulingOptimum Ground Camber on the RollsCoil TemperatureWarm-Up PracticeMill Zeroing PracticesVidimon Zeroing PracticeCoiling TensionsRolling oil temperaturesFactors that Effect Shape / Flatness (cont.)MachineResponse of the Shape Control Systems viz. Bending, Steer / ti

14、lt, Spray nozzles etc. by a leak proof systemsTouch Roll alignmentsRegular Calibration of the ShapemeterFactors that Effect Shape / Flatness (cont.)ManStrip Centering while feedingProper Tail-out in Previous PassesRolling on FoldsRegular Roll CoolingMinimize Turn Around TimeFactors that Effect Shape

15、 / Flatness (cont.)MaterialGood ShapeGood ProfileQuality of SpoolOptimization of Strip width - so that the rotor coverage area is more than 50%Difference in Online and Offline ShapeCan be caused by inaccuracy in the measurement, or ifsomething happens to the strip between the time it is measured on

16、the mill and when it is processed downstreamBad Input Coil ProfileImproper Coil Centering at the MillIncorrect Coil WidthsHigh Rewind StressHigher Entry Temperature of the CoilsWide Differential temperature across the width of the coilHigher Absolute Coil temperatureHigher Roll Coolant temperatureRe

17、duction ScheduleUsage of Bad SpoolsFactors that cause difference in On-line and Off-line ShapeProfile - Flatness RelationshipWith No Lateral Flow - Off-Flat- Length change in fibre lengths across strip- Edges longer than middleOver-roll EdgesWith Lateral Flow- Profile is changed- Flatness is not cha

18、nged“Hot mill” “Cold mill” Relationship between profile and flatnessFlatness ChangesDuring Hot Strip RollingOn latercold Rolling or RecoilingProfile ChangesfromtoororororChanges Between Profile and FlatnessSources of Flatness Variation: Thermal EffectsNon-uniform heating or cooling = relative strain

19、 in sheetThe Coefficient of Linear Thermal Expansion is defined as: where t is temperature. For Aluminium a temperature difference of 4C between one section and another produces about 10 I-units of strain. This will not cause permanent off-flatness unless the total stress takes the material beyond i

20、ts yield point. Long-middleWavy EdgesSources of Flatness Variation: CoilingCoiling EffectsCoiling a sheet under tension can create flatness variations.When coiling, a sheet under tension is wrapped around a spool/core and the internal stresses generated are redistributed as each new lap affects the

21、ones under it.These stresses are affected by The compliance of the wraps The effect of the mandrel The profile of the strip Subsequent temperature changes of the coil The bending of the sheet to conform to the sheet under itCoiling EffectsThe general effect is to concentrate the forces in the areas

22、where the sheet is thick. On most mills the sheet is thickest in the center. The concentration of forces can lead to a plastic change in the coils length. Thus creating a center pocket or belly. The effect is “additive” in that the center pocket will slowly disappear as the coil is unwound. The shee

23、t next to the core is likely to have an edge wave.The cooling of a hot/warm coil will greatly increase the effect as will coiling under higher tensions.Flatness Control Flatness control is simple. There is only one rule:“The % reduction must be the same at every point across the sheets width”Tilt /

24、Steer The Tilt loop of the control system is typically the fastest control loop as it uses the Automatic Gauge Control (AGC) cylinders to tilt the mill.The amount of correction needed is usually determined by a linear regression (best fit) approach. However, many different methods have been used. A

25、comparison of the sum of the outer 2 edge zones An independent linear fit A polynomial fit with the linear term used for tilt A linear term plus a 7th order term BendingThe bending loop of the control system is typically the “middle” control loop and it uses the bending jacks to open or close the ends of the work rollsThe amount of correction needed is usually determined by a using best fit approach to a curve. However, many different methods have been used. A comparison of the outer 2 edges to the center zone. An independent polynomial (X2) fit A polynomial fit

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