弯曲疲劳强度的工业经验

doi:10.1111/j.1460-2695.2010.01450.xIndustrial experiences of bending fatigue strength in table liner for cement millS.-H.BAEK,1S.-S.CHO 2and W.-S.JOO 31GraduateSchool of Mechanical Engineering,Dong-A University,840Hadan2-dong,Busan 604-714,Korea,2Department of Vehicle Engineering,College of Engineering,Kangwon National University,Samcheok,Gangwon-do 245-711,Korea,3Department of Mechanical Engineering,Dong-A University,840Hadan2-Dong,Busan 604-714,Korea Received in final form 17November 2009A B S T R A C T A table liner for the vertical roller mill has been used to grind natural limestone.Un-expected fatigue failure accidents have occurred during portland cement manufacturing process.The design life of a table liner is 4×107cycles,but the actual fatigue life of a table liner is 2×106to 8×106cycles.The fatigue crack of a table liner initiates from the outside edge of the grinding path of the limestone.When such a crack occurs,the table liner has to be replaced,and this requires 30%of the total maintenance cost of the vertical roller mill.Therefore,this study examines the fatigue failure of a table liner by plane-bending fatigue test,stress measurement test,finite element analysis and fatigue fracture analysis.Keywords bending fatigue strength;finite element analysis;Goodman diagram;stress-life curve;vertical roller mill.I N T R O D U C T I O NA vertical roller mill for cement production is far supe-rior than the existing tube mill with respect to energy efficiency.However,the table liner for a roller mill un-dergoes periodic repeated loading because it is a rotary machine.A fatigue function is expressed in terms of the stress ratio and mean ually,a fatigue function uses the Goodman diagram.1–3Stress ratio R in a fatigue cycle is defined as follows.4,5R =σmin σmax(1)where σmin is the minimum stress and σmax is the maximum stress in a fatigue stress cycle.Joo et al.6,7reported that the loads applied to a turbine blade are repeated bending load,torsional load and cen-trifugal load.According to X-ray fractography and the Goodman diagram,repeated bending stress is the major cause of turbine blade fatigue failure.Mandell et al.4,8,9proposed the Goodman diagram based on 13stress ratios.This method formulated the S-N behaviour considering the effect of mean stress.Correspondence :W.-S.Joo.E-mail:wsjoo@dau.ac.krFigure 1shows the photograph of the vertical roller mill analyzed in this study.The vertical roller mill consisted of two rolling tires and a table liner with eight steel plates.The table liner was made of SC450steel and had a plasma-sprayed WC-15%Co coating layer.The expected design fatigue life of the table liner was 4×107cycles,but the actual fatigue life was 2×106to 8×106cycles.The surface hardening layer of the table liner was subjected to wear and repeated bending tensile load.The prema-ture failure of the table liner can be ascertained from data on the contact fatigue.But,the surface hardening layer of the table liner was made of a big-particulate material.That is,the macrostructure of the material can relieve the stress concentration due to contact.A table liner is a rotary machine component with a very complex fail-ure pattern.Therefore,it is very difficult to simulate the in-service conditions of a table liner.In this study,the fatigue strength of a table liner is estimated by stress mea-surement,finite element analysis (FEA),bending fatigue test and the Goodman diagram.M A T E R I A L A N D E X P R I M E N T A L P R O C E D U R E SMaterial and test specimenFigure 2shows the failure pattern of the table liner exam-ined in this study.Crack initiated from the corner of the358c 2010Blackwell Publishing Ltd.Fatigue Fract Engng Mater Struct 33,358–364Fatigue & Fracture ofEngineering Materials & StructuresBENDING FATIGUE STRENGTH IN TABLE LINER FOR CEMENT MILL359Fig.1Vertical rollermill.Fig.2Sampling directions of tensile and bending specimens and fracture process of table liner.Fig.3Tensile test specimen configuration.table liner and grew in the cylindrical and axial directions.To test the mechanical properties of a table liner,the test specimen should reflect the damage pattern of the table liner.Therefore,the principal stress direction of the test specimen was made to coincide with the radial direction of the table liner.Six tensile test specimens and 18fatigue test specimens were prepared.Figure 3shows a tensile test specimen made according to ASTM E8M-94a.10An electro-mechanical system of 98kN capacity (Instron,model 1337,USA)was used to carry out the tensile tests.An extensometer was calibrated to an accuracy of under 2μm.It had a standard deviation of 2.5μm.11Poisson’s ratio was measured by a strain gauge of 5mm in length (Kyowa,KFC-5-D16-23,Japan)and a strain measurement device (Kyowa,UCOM-93,Japan).Table 1Mechanical properties of SC450steel PropertiesUnused Used Yield strength (MPa)238.2241.6Ultimate tensile strength (MPa)480474Poisson’s ratio 0.30.306Elongation (%)2422.7Young’s modulus (GPa)203206The test specimens were made of materials taken from an unused table liner and a fractured table liner,respec-tively.Table 1shows the results of the tensile test.The mechanical properties of the fractured table liner showed hardly any difference from those of the unused table liner.We could expect the table liner to be in an elastic state.Plane bending fatigue testFigure 4shows theSchenck-type bending fatigue test-ing machine (Mori testing machine,model 5171,Japan)and a fatigue test specimen.The configuration of the fa-tigue test specimen was determined,considering Peter-son’s stress concentration factor and the grip size of theFig.4Configuration of test specimen used in Schenck-type bending fatigue tests.c 2010Blackwell Publishing Ltd.Fatigue Fract Engng Mater Struct 33,358–364360S.-H.BAEK etal.Fig.5Fracture aspect of table liner for vertical mill.testing machine.12The stress concentration factor and curvature radius of the fatigue testing specimen were 1.05and 39mm,respectively.The maximum bending mo-ment,the loading speed and the test temperature were 20N m,1500rpm and room temperature,respectively.F A T IG U E S T R E N G TH A N A L Y SI S O F T H E T A B L E L I N E RFailure accident of the table linerThe diameter of the vertical roller mill was 6240mm,and the radius of the table liner was 2390mm.The driv-ing power and grinding volume of the limestone were 4250kW and 5.5MN/hr,respectively.Figure 5shows the failure pattern of the vertical roller mill.A table liner is used to prevent the mill table from being worn by lime-stone.The top of the table liner were made from SC450steel and the bottom of the table liner had a built-up welding layer.Figure 6shows the hardening layer crack that formed after the built-up welding.The average diameter of the cracks was 6.5mm.These cracks occurred during the welding process but not when the table liner was in service.Also,particulate cracks minimized the welding residual stress anddelamination.Fig.6Macrostructure of hardfacing layer in table liner.The surface hardening layer of the table liner had a life of less than 4×107cycles.If the life of the table liner exceeds 4×107cycles,the surface hardening layer would reach its wear limit.But,more than 80%of table liners are replaced by fatigue fracture and not by wear.Fatigue crack was initiated at the interface between the surface hardening layer and the base metal of the ta-ble liner.Also,the fatigue crack grew in the radial and the thickness direction from the edge of the table liner.Ahmed et al.13proposed that the rolling contact fatigue crack in a WC-15%Co sprayed material initiates due to the shear stress in the base metal as well as the difference in the mechanical properties between the coating layer and the base metal.Static structural analysisFigure 7shows the results of the plane bending fatigue test for stress ratio –1.Unfractured test conditions appear104105106107160180200220240260280300320S t r e s s a m p l i t u d e σ (M P a )Cycles to failure N (cycle)Fig.7S-N curve of SC450steel.c 2010Blackwell Publishing Ltd.Fatigue Fract Engng Mater Struct 33,358–364BENDING FATIGUE STRENGTH IN TABLE LINER FOR CEMENT MILL361Fig.8Finite element model of vertical rollermill.Fig.9Von-Mises stress distribution of table liner for vertical roller mill.upon more than 1×107cycles.The endurance limit obtained from the staircase test method was 185MPa.FEA of the vertical style roller mill was performed with ANSYS R8.0.14An 8-node hexahedron element was used.The numbers of elements and nodes were 88149and 100638,respectively.The finite element model exam-ined a quarter of the mill.The boundary condition for the mill was set to the axisymmetric condition.The ap-plied load was determined by using the static equilibrium relation between the rolling tire and the table liner (See Fig.8).Based on this assumption,the applied force on the inner and outer contact region is 1.1MN and 2.9MN,respectively.15,16Figure 9shows the FEA of the table liner.The maximum principal stress of 222.3MPa was obtained at the loading point.The minimum principal stress of 28.94MPa was obtained at 90◦from the loading point.To examine the FEA results,static stress measurement tests were performed by using a hydraulic pressurepistonFig.10Location of strain gauge used at static stress measurement.Photography of strain gauge attached to table liner.2400210018001500120090060030006080100120140160180200220240260280V o n -M i s e s s t r e s s (M P a )Radius from center of table (mm)Fig.11Radial stress distribution of the table liner.(RG 400/180-550).The strain gauge used in the stress measurement test was the delta rosette gauge (Kyowa-KFG-5-120-D17-11).The length of the strain gauge was set to 5mm considering the area of the table liner.Figure 10shows the attachment locations of the strain gauges.These locations were the “most dangerous”areas according to the FEA result and were most likely to cause failure accidents of the table liner.Strain gauges were attached at 15◦intervals from location A.Experimental principal stresses were obtained from the strain gauges.Figure 11shows the radial direction stress distribution in the table liner.A sine stress waveform was obtained in the radial direction.In the grinding path,the outside stress distribution was 1.3times higher than the inner stress distribution.Therefore,the stress concentrated on the outer grinding path.Stresses at 45◦and 90◦from location A appeared to be lower than the stresses at 0◦c 2010Blackwell Publishing Ltd.Fatigue Fract Engng Mater Struct 33,358–364362S.-H.BAEK et al.360330300270240210180150120906030P r i n c i p a l s t r e s s (M P a )Circumferential angle (degree)Fig.12Comparison of principal stress distribution of circumferential direction.from location A.From the above results,the maximum stress in the table liner was produced at location A on the outside grinding path.Figure 12shows the cylindrical directional stress distri-bution at intervals of 15◦around the maximum principle stress.The solid line is the maximum principal stress re-gression curve,which was generated from measurements given by the strain gauges,and the dotted line is the maxi-mum principal stress regression curve obtained from FEA.The difference between the FEA and strain gauge meth-ods themselves generated an error of 12%of the maxi-mum principal stress values.But,the distribution of the principal stress obtained from the FEA was similar with that obtained from the strain gauge.Therefore,the stress waveform of the table linerwas similar to that of the rotary machine such as a pump and gear.17The stress pattern of the table liner indicated a symmetric structure with re-spect to 180◦.The table liner was subjected to two repeat bending stress per one revolution.Figure 13shows the location of the maximum principal stress and the location of actual failure from the centre of the outside grinding path of the table liner.The maximum principal stress was measured experimentally at 10locations in the high stressC e n t e r o f v e r t i c a l r ol l e r m i l lFig.13Fracture position at the outside grinding path by visual examination and FEA.S t r e s s a m p l i t u d e σa (M P a )Mean stress σm (MPa)Fig.14Goodman diagram for table liner.Note that the Goodman line endpoint is the UTS from an axial tensile test.distribution area.The experimental maximum principal stress was located between 118mm and 358mm from the centre of the outside table liner.The analytic maximum principal stress was located 257mm from the centre of the outside table liner.Therefore,the maximum princi-pal stress region was found to be the area that fractured most frequently in the table liner.Fatigue strength estimationThe Goodman diagram 1–3,18is used to evaluate fatigue failure of parts under repeated load.Figure 14shows the operation condition of the table liner in the Goodman diagram.A safe domain was bounded by a limit line in the form of a straight line through two limit points taken from the ultimate tensile strength of 474MPa and the fatigue limit of 185MPa.The line was a solid line.Stress ratio in table liner is 0.5.The endurance limit line given above doesn’t consider the mean stress effect.Therefore,the effect of the mean stress on life can be estimated by ap-plying the modified Goodman expression to an equivalent reversed value for the stress at the notch.σar =σa1−σmσu (2)where σar is the equivalent completely reversed stress am-plitude,σm is the mean stress (=125MPa),σa is the stress amplitude (=125MPa)and σu is the ultimate strength (=480MPa).Fatigue notch factor k f =1is employed in this study because notch has a large radius and SC450steel is ductile material.The dotted line represents the endurance limit line in the form of a straight line through two limit points taken from the ultimate tensile strength of 474MPa and the equivalent completely reversed stress amplitude of 169MPa.c 2010Blackwell Publishing Ltd.Fatigue Fract Engng Mater Struct 33,358–364BENDING FATIGUE STRENGTH IN TABLE LINER FOR CEMENT MILL363The dash dotted line marked the region where the mean stress was equal to the stress amplitude;that is,this line means the region where stress ratio equals0.The mean stress and stress amplitude of the table liner were deter-mined from the maximum and minimum stress obtained by FEA.The table liner can move to the structurally dan-gerous area easily due to the in-service conditions because the stress condition of the table liner existed on the bound-ary of the Goodman diagram.The fatigue limit used in the Goodman diagram was measured in the controlled test conditions.The fatigue limit of a machine part depends strongly on its various conditions(surface roughness,material struc-ture,residual stress,and processing method).The cor-relation of the fatigue limit and some of the factors can be expressed by the empirical equation.To account for the important of these conditions,we employ a variety of modifying factors,each of which is intended to account for a single ing this idea,we may writeSe=C load C size C surf C temp C residual C reliab S e(3) where S e is fatigue limit of the table liner and S e is fatigue limit of SC450steel(R=−1).Cho et al.16proposed some strength reduction factors in the table liner.These are as follows.C load=1,C size=0.6,C surf0.814,C temp=1,C reliab=0.897(4)Residual stress in the surface layer of table liner plays an important role in the overall fatigue properties of the part.In this study,we may consider the induced residual stress at table liner surface as tensile stress.Grover et al.19 proposed that the residual stress factor C residual had0.52 for the worst welded test condition.We obtain C residual= 0.52.If we substitute above factors into Eq.(3),we obtainmodified fatigue limit38.5MPa.When all the modifying factors are considered,fatigue limit dropped by77.2%. From the above test result,the fatigue limit in the stress amplitude axis was set to38.5MPa.The fatigue limit line was represented with a dotted line in Fig.14.The results from FEA and strain gauge analysis exist in the dangerous area of the Goodman diagram.Therefore, the fatigue limit of the table liner should be determined by considering the fatigue strength reduction factors of the table liner.C O N C L U S I O N SThis study investigated the fatigue strength estimation of a table liner for a vertical roller mill by using the plane-bending fatigue test,stress measurement,FEA and the Goodman diagram.1Fatigue crack was initiated at the interface between the surface hardening layer and the base metal of the table liner.Also,the fatigue crack grew in the radial and the thickness direction from the edge of the table liner.2The table liner was subjected to two repeat bending stress per one revolution.3The table liner exists in the structurally“dangerous”area because the stress condition of the table liner exists out of the boundary of the Goodman diagram.4Fatigue strength reduction factors are useful in explaining the premature failure of the table liner. 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