Article. Alireza Khodaee 1, * and Arne Melander 1,2

Transcription

1 Journal Manufacturg Materials Processg Article Numerical al Analysis Size Influence on Density Variations Distortions durg Manufacturg PM s with an Innovative Powder Processg Route Incorporatg Alireza Khodaee 1, * Arne Meler 1,2 1 KTH Royal Institute Technology, Brellvägen 68, Stockholm, Sweden 2 Swerea KIMAB, Isafjordsgatan 28A, Kista, Sweden; arneme@kth.se * Correspondence: khodaee@kth.se; Tel.: Received: 3 July 2018; Accepted: 19 July 2018; Published: 23 July 2018 Abstract: paper is result research tended to develop a route for manufacturg powder metallurgical (PM) for application transmissions units for heavy duty powertra applications. ma problem PM for such applications is that generated pores that occur through conventional pressg sterg es reduce gear strength, which reduces capacity for power transmission by gear. In prior work, removg pores reachg 100% density by addg Hot Iso-static Pressg () two times pressg two times sterg steps route was suggested to solve mentioned problem. Durg vestigations this work it was revealed that gear dimensions could fluence results with respect to geometrical distortions. In this paper we have presented a fite element (FE) model based analysis on how gear geometrical parameters fluenced distortions occurrg. model is validated with experiments. Furrmore, model is used to create a prediction model for furr vestigations. research showed that PM with different sizes durg proposed route behaved differently terms distortions. This was illustrated with a series s with different gear geometries. A regression model was developed based on FE results for furr practical predictive use. distortions caused by should be considered design to prevent expensive post es wards to reach gear with accurate geometry keep costs manufacturg low. It is concluded that it is possible to use novative route cludg to reach full density close all open pores but not for all kd gear geometries. Keywords: ; powder metallurgical (PM); hot iso-static pressg (); fite element method () 1. Introduction Powder metallurgical (PM) fer a number benefits, which make m a sustaable alternative to traditional made wrought steel by conventional manufacturg es. Among all advantages for PM, lower cost production, lower amount material waste manufacturg, possibility to add new design features to shape gear are most mentioned advantages by PM researchers literature [1 4]. lower density PM manufactured by pressg-sterg routes limits ir applications for higher load transmission duties [5]. For such applications full strength steel is J. Manuf. Mater. Process. 2018, 2, 49; doi: /jmmp

2 sterg route followed by a contaer-less densification at end [9]. In this full density can be achieved [10,11]. steps are as shown 1. J. Manuf. While Mater. Process. reachg 2018, 2, x FOR full PEER density REVIEW gear Hot Iso-static Pressg () is achieved, 2 18 significant distortions occur durg operation [12 14]. distortions are caused by necessary homogeneous J. Manuf. Mater. Process. density PM 2018, 2, distribution 49 route order itial to pressg ensure steps delivery [13,14]. Existg frictional required 2forces power 18 transmission between properties. powder particles Stered PM die walls have durg lower density pressg than wrought loose powder steel, cause pores remag generation necessary a pressg neutral PM zone route middle removal order surface to ensure lubricant gear delivery face durg width, required as shown sterg power transmission step 2. In PM g pressg properties. step, is Stered where root two for PM punches lower have are density used lowerto density press traditional than powder, wrought sterg a density steel, technology. gradient pores remag is obtaed lower along density causes pressg gear problems axial direction when it removal comes with to mimum fatigue lubricant densities loadg durg located sterg durability on step middle PM PM g axial [6,7]. direction. refore, is reachg After root for first full lower sterg density step for a traditional PM PM gear gear sterg is a vital density technology. pre-request neutral lower to meet, zone density remas before causes usg at problems lowest m when for levels high performance while it comes on toapplications outer fatigue surfaces loadg [8]. two durability ends face PM width [6,7]. highest refore, densities reachgare observed full density [15]. This for abehavior PM g gearremas is aroute vital pre-request PM PM gear to meet, through this before paper usg is second based mpressg for on high a two performance times second pressg applications sterg as two [8]. well. times Fally, lower g density route neutral PM zone this will paper cause is larger baseddistortions a two times pressg densification two times step. sterg route followed by a contaer-less densification at end [9]. In this sterg distortions are route critical followed with respect by a contaer-less to complex densification geometry at. end [9]. Generated In this distortions full full density can be achieved [10,11]. steps are as shown 1. density can have beto achieved be compensated [10,11]. a fishg steps operation. are as shown 1. While reachg full density gear Hot Iso-static Pressg () is achieved, significant distortions occur durg operation [12 14]. distortions are caused by homogeneous density distribution itial pressg steps [13,14]. Existg frictional forces between powder particles die walls durg pressg loose powder cause generation a neutral zone middle surface gear face width, as shown 2. In pressg step, where two punches are used to press powder, a density gradient is obtaed along gear axial direction with mimum densities located on middle gear axial direction Process route to reach full powder metallurgical (PM) [9]. [9]. After first sterg step PM gear density neutral zone remas at lowest levels while on outer surfaces two ends face width highest densities are observed [15]. This behavior While remas reachg full PM density gear through gear second Hot Iso-static pressg Pressg second () sterg is achieved, as well. significant distortions occur durg operation [12 14]. distortions are caused by Fally, lower density neutral zone will cause larger distortions densification step. homogeneous density distribution itial pressg steps [13,14]. Existg frictional forces distortions are critical with respect to complex geometry. Generated distortions between powder particles die walls durg pressg loose powder cause generation have to a be neutral compensated zone middle a fishg surface operation. gear face width, as shown 2. In pressg step, where two punches are used to press powder, a density gradient is obtaed along gear axial direction with mimum densities located on middle gear axial direction. After first sterg step PM gear density neutral zone remas at lowest levels while on outer surfaces two ends face width highest densities are observed [15]. This 2. generation neutral zone with lower relative density (RD) at middle face width behavior remas PM gear through second pressg second sterg as well. Fally, gear. lower density neutral zone will cause larger distortions densification step. distortions are critical with respect to complex geometry. Generated distortions importance reachg right tolerances gear dimensions suggested have to be compensated 1. Process route ato fishg reach full operation. density powder metallurgical (PM) [9]. route, brgs necessity to analyze distortions PM step develop a predictg model for it. model can be used for furr developments to optimize design PM g for manufacturg route 1. In this paper, a combed numerical experimental method is used to analyze evaluations are focused on dimensional distortions caused by route shown 1. ma aim is to underst relations between gear geometrical parameters generation neutral zone consequent distortions occurrg. Validated FE results can enable us to propose a predictive model to follow component density developg durg route 1. present authors have previously evaluated effects generation generation neutral neutral zone zone with lower relative density (RD) (RD) at at middle middle face face width width gear. gear. importance reachg right right tolerances tolerances gear dimensions gear dimensions suggested suggested route, route, brgs brgs necessity necessity to analyze to analyze distortions distortions PM PM step step develop develop a a predictg model for it. model can be be used used for for furr furr developments to optimize to optimize design design PM PM g for manufacturg route route In this In this paper, paper, a a combed numerical experimental method is is used used to to analyze analyze evaluations evaluations are focused are focused on on dimensional dimensional distortions distortions caused caused by route route shown shown ma ma aim is to underst relations between gear geometrical parameters generation neutral zone consequent distortions occurrg. Validated FE results can enable us to propose a predictive model to follow component density developg durg route 1. present authors have previously evaluated effects

3 J. Manuf. Mater. Process. 2018, 2, aim is to underst relations between gear geometrical parameters generation neutral zone consequent distortions occurrg. Validated FE results can enable us to propose a predictive model to follow component density developg durg route 1. present authors have previously evaluated effects gear geometry on pressg PM y have shown that different gear parameters could result different density gradients PM gear [15]. In present paper, fluence two parameters, which are defg gear size, are considered for analysis. first parameter is outside diameter gear (d a ) second parameter is face width gear. outside diameter is a function gear normal module (m n ) number teeth (Z), as shown Equation (1): d a = f (m n, Z), (1) refore, ma dependent variables analysis to develop predictive model are normal module (m n ), number teeth (Z), face width gear. next section will expla conducted experiments, which were used to verify model. details tested sample gear geometries were given. n, next section, numerical steps is presented by explag material model, material parameters for s, boundary conditions, frictional model used s. After explag experimental numerical procedures research, experimental results numerical results are presented toger results section to validate model. relations between gear geometrical parameters distortions caused PM are studied a subsequent separate section. verified model is used to predict different effects geometrical parameters followg section. A discussion section toger with fal concludg remarks are presented last two sections to deliver ma fdgs contributions research work. 2. al Procedure In this chapter paper, details about experimental tests performed research to manufacture two different gear geometries based on proposed route is explaed. function requires case hardeng high core toughness. For such requirement PM require to have high compressibility homogenous microstructure sterg. For this purpose, water atomized steel powder manufactured by Höganäs AB Sweden is used for vestigations this work. This powder has a good compressibility as well as hardenability. powder is pre-alloyed with 1.5 wt. % Mo (Astaloy Mo). powder has stard powder size fractions with range 20 to 180 µm. For experimental tests, powder is admixed with 0.6% LubeE for lubrication 0.2 wt. % graphite to add carbon to mixture [16]. As mentioned troduction, g route for production metal powder consists five es (see 1). first step (P1) is to press loose powder to so called green component. This is performed by mechanically pressg powder. For this two punches press powder to near net shape gear. second step (S1) is to ster green component. This step is a rmal to remove lubricant powder. Naturally this, removal lubricant will create pores component, which could be source furr problems g PM. To crease shape accuracy reach higher levels density, one more cycle pressg sterg is considered g route. Second pressg (P2) is also performed usg a mechanical press. ma difference between first pressg second pressg is amount deformation, which is limited second pressg. Durg P2 subsequent sterg, S2, a furr reduction porosity will occur pores will become rounder shape. shape component will become closer to tended shape before. After second sterg gear should reach a relative density some 90% or higher everywhere gear order to avoid open porosity [17,18]. Such an open porosity must be avoided durg fal stage sce no densification can occur if

4 J. Manuf. Mater. Process. 2018, 2, gas chamber can penetrate to side material through open pore passages. gas is only allowed on outside component durg step. This is a very critical requirement present route where no contaer is used outside each gear wheel. An dividual contaer could prevent gas penetratg to gear, however, such a J. Manuf. Mater. Process. 2018, 2, x FOR PEER REVIEW 4 18 contaer is much too expensive to be acceptable present route. For vestigations presented presented here, here, all all mentioned mentioned steps steps are performed are performed experimentally experimentally to manufacture to manufacture two different two different as a reference as a reference for for development development verification verification numerical numerical model. model. first second pressg steps are performed at 800 MPa press. first sterg is performed at 800 first second pressg steps are performed at 800 MPa press. first C N2 atmosphere for 1 h second sterg is performed at 1300 sterg is performed at 800 C N2 atmosphere C for 1 h vacuum. is performed at 1150 for 1 h second sterg is performed at 1300 C for 1 h vacuum. is performed at 1150 C for C 2 h for 2 h by applyg by applyg 100 MPa 100 MPa pressure pressure usg usg Argon Argon gas. gas. Two types Two types,, I I II, II, are are manufactured manufactured usg usg explaed explaed route route above. above. have have different different design design parameters parameters ir ir specifications specifications are are given given 3a. 3a. experimental experimental results results obtaed obtaed manufacturg manufacturg se se will be will used be used next section next section to to compare compare validate validate numerical numerical model. model. As As focus focus vestigation vestigation is on is on gear gear size fluence size fluence on on geometrical geometrical distortions distortions manufacture manufacture PM PM by by proposed proposed route, route, it it is necessary is necessary to defe to defe measurg measurg references references to measure to measure fluence fluence gear size gear parameters size parameters on on results results PM g PM g route route under under discussion discussion this work. this work. For this For purpose, this purpose, two dimensions two dimensions are selected are selected to be to followed, be followed, as shown as shown 3b. 3b. first dimension first dimension is is gear outside gear outside diameter, diameter, which which is also is referred also referred to as to as addendum addendum diameter diameter (d a ). (da). second second dimension dimension gear gear is is its height, its height, which which is referred is referred to as to as face-width face-width gear. gear. se se two two dimensional dimensional parameters parameters are are measured measured experiments experiments each each step. step. measurements measurements were were all done all done usg usg a digital a digital micrometer micrometer that presents that presents a value a value with with 1 µm. 1 In µm. addition, In addition, component component average average density density is measured is measured usg usg Archimedes Archimedes prciple prciple all steps. all steps. For measurg For measurg density density P1 to P1 avoid to avoid penetration penetration water water to to open open pores pores component component surfaces surfaces are sealed are sealed density density is measured. is measured. density density measurement measurement accuracy accuracy is around is around 0.03 g/cm g/cm. All 3. All measurements measurements are performed are performed on three on three samples samples I I II. II. averaged averaged values values are reported are reported used used paper. paper. (a) 3. (a) gear specification for experiments; Major dimensions gear considered 3. (a) gear specification for experiments; Major dimensions gear considered analysis. analysis. To improve material modellg accuracy, one experiment is performed to compress powder To behavior improve durg material compaction. modellg rg accuracy, shape one component experiment with is performed dimensions to compress given powder 4a, is used behavior for this durg experiment. compaction. n powder rg shape is compressed component usg with dimensions mechanical given press with two punches 4a, is used for this force-displacement experiment. n curve powder for test is compressed is recorded. To usg calibrate mechanical material press model with parameters, two punches same force-displacement is simulated numerically curve for as test shown is recorded. To 4b calibrate optimized material until a model good fit for parameters, material same hardeng curve is simulated between numerically experiments as shown 4b is achieved, optimized as until shown a good fit for 4c. Later material on, hardeng s curve between PM g experiments for with same is hardeng achieved, curve as shown for powder 4c. Later on, s first pressg are used PM g numerical for model. with same hardeng curve for powder first pressg are used numerical model.

5 J. Manuf. Mater. Process. 2018, 2, J. Manuf. Mater. Process. 2018, 2, x FOR PEER REVIEW 5 18 (a) (c) Pressure on Punch (MPa) Exp_Höganäs _KTH Punch Displacement (mm) (d) 4. (a) rg specimen dimensions used for compaction test; model 4. (a) rg specimen dimensions used for compaction test; model for for compaction test; (c) powder deformation compacted rg compaction test; (c) powder deformation compacted rg loose loose powder; (d) fitted hardeng curve for displacement-force powder. powder; (d) fitted hardeng curve for displacement-force powder. 3. Numerical Simulation 3. Numerical Simulation In this chapter, numerical model is described with respect to material modellg, friction In this chapter, numerical model is described with respect to material modellg, modellg, boundary conditions model, geometrical modellg to simulate friction modellg, boundary conditions model, geometrical modellg to simulate experiments order to develop a validated model for furr analysis. experiments order to develop a validated model for furr analysis Material Material Models Models first first is is to to press press loose loose powder powder to to green green component component (P1). (P1). For For this this step step modified modified Drucker Drucker Prager Prager model model (CAP) (CAP) has been has used been [19,20]. used [19,20]. To defe To defe CAP model, CAP CAP parameters are taken [21] are given Table 1. Also, to describe powder model, CAP parameters are taken [21] are given Table 1. Also, to describe hardeng curve CAP model, fitted model that was created results rg powder hardeng curve CAP model, fitted model that was created results rg compaction explaed experiments is used as put for numerical model compaction explaed experiments is used as put for numerical model (see 4c). (see 4c). results experiments showed very small deviation geometry average density Table component 1. Modified Drucker both Prager sterg model CAP plasticity steps (S1 parameters S2). refore, ABAQUS for effect sterg es P1. are just taken to account by a lear modification factor applied over Relative Density (RD) distribution numerical models. This is performed by applyg experimental Material factor on output P1 for RD distributed Initial Yield on mesh Transition nodes, usg it as Angle Cap Flow Stress put for Cohesion P2. same Friction procedure [ is repeated aga by applyg experimental factor for S2 on [MPa] Surface Surface ] Eccentricity [-] Ratio [-] Position [MPa] Radius [-] output P2 for RD distribution on mesh nodes usg it as RD put for After first sterg (S1), powder particles are bonded due to high temperature sterg furnace. refore, CAP model for loose powder could not be used anymore second pressg (P2) neir for. Hence material model needs to be

6 J. Manuf. Mater. Process. 2018, 2, results experiments showed very small deviation geometry average density component both sterg steps (S1 S2). refore, effect sterg es are just taken to account by a lear modification factor applied over Relative Density (RD) distribution numerical models. This is performed by applyg experimental factor on output P1 for RD distributed on mesh nodes, usg it as put for P2. same procedure is repeated aga by applyg experimental factor for S2 on output P2 for RD distribution on mesh nodes usg it as RD put for. After first sterg (S1), powder particles are bonded due to high temperature sterg furnace. refore, CAP model for loose powder could not be used anymore second pressg (P2) neir for. Hence material model needs to be changed to a model for modellg porous metals. In this work Gurson model is used for P2 [22]. In that model all pores are considered to be spherical [22 24]. Material Model Parameters Table 1 presents parameters used s P1 for CAP plasticity Table 2 presents Gurson parameters for P2. Table 3 presents modification factors applied on RD distribution P1 P2 to consider sterg effects, which are recorded experimental data S1 S2 are considered as a constant change factor for s rest this work. Table 2. Gurson plasticity parameters ABAQUS for P2 Hot Iso-static Pressg (). q1 [-] q2 [-] q3 [-] Table 3. Lear modification factors for S1 S2. Process Modification Factor [%] S S Geometrical Modellg 3D geometrical models dies punches for es are created by usg dimensions dies punches experiments for two types gear used: I II. models for P1, P2, are shown 5. details geometrical models are exactly same as experiments to ensure validity model with respect to dimensions tolerances. In first pressg (P1), a displacement controlled compaction powder is defed. amount displacements are controlled based on itial powder density required height green component P1. For second pressg (P2), a displacement controlled motion dies is also applied. For densification material strength high temperature is considered while a uniform normal pressure has been applied on all gear surfaces to simulate conditions.

7 7, P1 predicted density is very close to 7.3 g/cc. This means average relative density is higher than 90%. But results, it is observed that it does not mean that 90% is reached everywhere gear wheels. Actually, close to neutral zone gear, relative density is slightly lower than 90% for both, as shown s 8 9. This shows importance J. Manuf. Mater. Process. model, 2018, 2, where 49 it is possible to see density distribution component but 7 not 18 just average density, which is possible to be measured experiments. (a) (c) (a) (a) First First pressg pressg model; model; second Second pressg pressg model; model; (c) (c) Boundary Boundary conditions conditions for for model. model. For second pressg (P2) as it is illustrated s 6 7, average density measured 3.3. Friction experiment is very close to average density calculated model. Here, average Columb density friction 95% model is achieved is usedfor for both considerg geometries friction experiment between dies. punches Aga powder results particles P1 also could give stered better component sight to surfaces, density punches, distribution dies as shown P2. s friction 10 coefficient 11. for Columb terestg model observation was same is that for rgtwo specimen different compaction geometries experiment lowest achieved all density or s. neutral zone Columb coefficient gear is different. friction was refore, set to 0.2. even though same material temperatures are used for P1, P2 S1 S2, results for density distribution 4. Results different geometries varies. This observation will be discussed later. Lookg In this section, at results, it is observed experiments that both s it is possible are presented to reach toger full to density check 7.89 accuracy g/cc. same is recorded model. experiments Subsequently while results for model II will shows be used slightly to predict higher average distortions densities, for a range which gear could geometries be caused also next section. gear size results effects are sce based all on or variants measurements two experiments are similar. also results models for same are also twoshown s FE Average Density Results 6 shows results experiments s average density for I. re is a good agreement between experiments s. same applies to 7, which shows average densities for II.

8 J. Manuf. Mater. Process. 2018, 2, J. Manuf. Mater. Process. 2018, 2, x FOR PEER REVIEW J. Manuf. Mater. Process. 2018, 2, x FOR PEER REVIEW ρave ρave (g/cc) (g/cc) J. Manuf. Mater. Process. 2018, 2, x FOR PEER REVIEW ρave ρave (g/cc) (g/cc)ρave (g/cc) P1 S1 P2 S2 8 P1 S1 P2 S I: average density growth (ρ ave). 7.8 ) I:I: average average density density growth growth (ρ (ρave ave) P1 S1 P2 S2 6. I: average density growth (ρave). P1 S1 P2 S2 P1 S1 P2 S2 ρave (g/cc) 8 7. II: average density growth (ρave) II: II: average average density density growth growth (ρ (ρave).). 7. ave density prediction 7.5accuracy is important sce it could be a sign for correct characterization material response7.4 different steps route. For both, as shown 7.3 s 6 7, P17.2 predicted density is very close to 7.3 g/cc. This means average relative density is higher7.1 than 90%. But results, it is observed that it does not 7 mean that 90% is reached6.9 everywhere gear wheels. Actually, close to neutral zone gear, relative density is slightly, as shown s 8 9. P1lower than S1 90% for P2both S2 This shows importance model, where it is possible to see density distribution 8. I, relative density (RD) P1. II: density, average density (ρave ). component but not just 7.average which is possible be measured experiments. 8. I, relative density (RD)growth top1. 9. II, relative density (RD) P1. 9. II, relative density (RD) P1. density(rd) (RD) 8.8. I,I,relative relative density P1.P1. For second pressg (P2) as it is illustrated s 6 7, average density measured experiment is very close to average density calculated model. Here, average density 95% is achieved for both geometries experiment. Aga results could give better sight to density distribution as shown s terestg observation is that for two different geometries lowest achieved density neutral zone gear is different. refore, even though same 10. I, relative density (RD) P I, relative density (RD) P2. 9. II, relative density (RD) P1.

9 J. Manuf. Mater. Process. 2018, 2, material temperatures are used for P1, P2 S1 S2, results for density distribution 8. I, relative (RD) P1. different geometries varies. This observation will bedensity discussed later. density(rd) (RD) 9.9. II, II,relative relative density P1.P1. J. Manuf. Mater. Process. 2018, 2, x FOR PEER10. REVIEW 10. I,I,relative relative density P2.P2. density(rd) (RD) 9 18 J. Manuf. Mater. Process. 2018, 2, x FOR PEER REVIEW II, II,relative relative density P2.P2. density(rd) (RD) Lookg at results, it is observed that both it is possible to reach full density 7.89 g/cc. same is recorded experiments while results for II shows slightly higher average densities, which could be caused also gear size effects sce all or variants relative density P2. s two are similar. results11. II, for (RD) are also shown 12. I, relative density (RD) density(rd) (RD). I,I,relative relative density. 13. II, relative density (RD). 9 18

10 J. Manuf. Mater. Process. 2018, 2, I, relative density (RD) II, II, relative density (RD) (RD) Geometrical 4.2. Geometrical Results Results Addendum Diameter Variations Addendum Diameter Variations s show variations addendum diameter (d a ) for I II, s respectively. 14 In both 15 s show 14 variations 15, measurements addendum diameter experiments (da) for also predicted I II, respectively. values In both s FE 14 are15, shown. measurements Similar to density experiments results, here we observe also good predicted values prediction accuracy FE for are shown. models Similar for all to steps density results, route. here we crease observe good addendum diameter observed second pressg (P2) is due to expansion stered prediction accuracy for models for all steps route. crease component die. This expansion is possible sce re is a gap that exists between die wall addendum diameter observed second pressg (P2) is due to expansion stered outer surface stered component P2. This is to ensure reachg net shape component is a die. This design expansion technique, is which possible is not sce partre ouris vestigation. a gap that exists reduction between observed die wall outer both s surface stered durg component step is distortion P2. This is caused to ensure by reachg on outer net diameter. shape This is a a drawback design technique, suggestedwhich is route. not part refore, our vestigation. aim here is to bereduction able to follow observed both this s sort 14 distortion 15 durg our furr analysis step is gear distortion size fluence caused on by geometrical on distortions. outer diameter. This is Ita can drawback also be observed suggested that variations route. gear diameter refore, are small aim durg here S1is to be S2, able as shown to follow this s sort J. distortion Manuf. Mater. 14 Process. 15. our 2018, furr 2, x FOR analysis PEER REVIEW gear size fluence on geometrical distortions It J. Manuf. Mater. Process. 2018, 2, x FOR PEER REVIEW can also be observed that variations gear diameter are small durg S1 S2, as shown 32 s d a d (mm) a P1 S1 P2 S2 P1 S1 P2 S2 14. addendum diameter P1, P2, experiments s. 14. addendum diameter P1, P2, I experiments s. d a d (mm) a P1 S1 P2 S2 P1 S1 P2 S2 15. addendum diameter P1, P2, II experiments s addendum addendum diameter diameter P1, P1, P2, P2, II II experiments experiments s. s Face Width Variations Face Width Variations s show variations face width I II, respectively. s show variations face width I II, respectively. numerical model as well as experimental tests for both pressg steps numerical model as well as experimental tests for both pressg steps powder (P1 P2) are displacement controlled. Sce startg height powder both powder (P1 P2) are displacement controlled. Sce startg height powder both is same as startg height powder, as experiments, it is expected that accurate

11 J. Manuf. Mater. Process. 2018, 2, Face Width Variations s show variations face width I II, respectively. numerical model as well as experimental tests for both pressg steps powder (P1 P2) are displacement controlled. Sce startg height powder both is same as startg height powder, as experiments, it is expected that accurate results on face-width P1 P2 both s will be achieved. This is confirmed by lookg at results shown s As explaed earlier, model for S1 S2 considers density changes but neglects dimensional variations. This assumption is confirmed with experimental results S1 S2 on face-width variations. It is shown that changes face-width are very small durg sterg es refore suggested lear modification to apply on density distribution can be a reasonable approximation. last pot to discuss results face-width variation is distortion caused by. As it is illustrated by both s 16 17, similar to addendum diameter, face-width will experience some distortions durg, which should be considered design. Comparg results experiment both confirms that model can predict face-width variation with a good approximation. refore, it is possible to use model for later prediction geometrical distortion caused by for different gear sizes J. Manuf. Mater. make Process. some 2018, predictions 2, x FOR PEER based REVIEW on model presented here J. Manuf. Mater. Process. 2018, 2, x FOR PEER REVIEW b (mm) b P1 S1 P2 S2 P1 S1 P2 S Face Face width width P1, P1, P2, P2, experiments experiments s. s. 16. Face width P1, P2, I experiments s. b (mm) b P1 S1 P2 S2 P1 S1 P2 S2 17. Face width P1, P2, II experiments s Face Face width width P1, P1, P2, P2, II II experiments experiments s. s. In 18, average density prediction results show high accuracy for prediction In 18, average density prediction results show high accuracy for prediction 4.3. densities Validation with error Numerical order Simulation 1%. This amount error validates material model parameters densities with error order 1%. This amount error validates material model parameters s as well as fitted hardeng curve used s present work s comparison as well experimental as fitted results hardeng numerical curve used results is s performed for present predictions work based on experiments. This means model could be good tool to analyze on based on addendum experiments. diameter This (d a ), means face width, average model density could be (ρ ave a good ) tool two to experiments analyze vestigate furr geometries without performg experiments necessarily. vestigate ir respective furr geometries without models usg performg mean experiments squared necessarily. errors (MSE) percentage. MSE important aspect models presented here is to build tool for prediction results forimportant I aspect II are shown models 18. presented here is to build a tool for prediction distortions caused by PM g steps route under study research. For this distortions caused by PM g steps route under study research. For this purpose, 18 results deviation for addendum diameter (da) between purpose, 18 results deviation for addendum diameter (da) between experiment toger with results for face-width deviations between experiment toger with results for face-width deviations between experiments are given. As explaed earlier, trends behavior is well predicted for both experiments are given. As explaed earlier, trends behavior is well predicted for both parameters all steps. parameters all steps. MSE prediction is very low for face-width order 1%, as shown MSE prediction is very low for face-width order 1%, as shown 18, which is very good. MSE value for prediction addendum diameter (da) is 18, which is very good. MSE value for prediction addendum diameter (da) is higher order 10%. This is still acceptable considerg expected errors nature higher order 10%. This is still acceptable considerg expected errors nature

12 4.4. Analysis on Size Influences Usg validated model last chapter paper, next step is to use model to predict distortion gear geometry step. present authors have shown an earlier work that density distribution density growth pressg is fluenced by gear parameters [15]. It has been shown that a different density distribution is achieved, where J. Manuf. Mater. Process. 2018, 2, mimum relative density (RDm) could be different neutral zone [15] Mean squared error (%) Mean squared error (%) Average density (%) Face width (%) da (%) GEAR I GEAR II GEAR I GEAR II GEAR I GEAR II (a) (c) Mean squared error (%) Mean squared errors (MSE) percentage as comparison experimental 18. Mean squared errors (MSE) percentage as comparison experimental results for I & II; (a) MSE for average density; MSE for face width; (c) MSE for addendum results for I & II; (a) MSE for average density; MSE for face width; (c) MSE for diameter. addendum diameter. In this section, authors provide an analysis on fluence gear size parameters on In PM g 18, route average under density discussion prediction paper. results show research highaims accuracy to answer fortwo goals. prediction densities first is with to reveal error potential orderrelation 1%. This between amount gear geometrical error validates parameters material distortions model parameters that occurred s durg as. well assecond fitted goal hardeng is to provide curve a simple usedpredictive s model that could predict present work distortion levels based on gear geometrical parameters. Such a model would be used under based on experiments. This means model could be a good tool to analyze assumption that it is just for specific powder material this research is valid for vestigate furr geometries without performg experiments necessarily. route studied this work. refore, it could be used as an estimator for vestigatg important aspect models presented here is to build a tool for prediction possibilities manufacturg PM with full density low distortion. distortions It is known causedthat by PMdriver g steps distortions is route density under gradients studycaused by research. pressg For this purpose, powder. 18 results Also, closure deviation pores for usg addendum is dependent diameter on (d a ) between density level experiment component before toger. with It is assumed resultsa for mimum face-width relative density deviations 90% should between reached before experiments through are given. pressg/sterg As explaed earlier, steps, to be trends able to close behavior all pores is well predicted reach a fully for both dense parameters component all [17]. steps. hyposis is that critical criterion is mimum relative density (RDm) MSE before. prediction With this ishyposis very low bigger for face-width ranges relative density order gradients 1%, caused as shown P1 respectively 18, whichkept is very at P2 good. will cause larger MSEdistortions value fordurg prediction. refore, addendum diameter predictions (d a ) is should give an estimation values for RDm P1 P2. higher order 10%. This is still acceptable considerg expected errors nature parameters for used for s are presented 19. selected numerical s. In models this work a mesh density 1 element per are based on realistic dimensions dustrial application. Such a selection is made with 1 mm face-width direction is used, while on cross-section direction mesh density is lower, at purpose implementg results this research as a guidele for dustrial application 1 element per 2route mm. difference future. is to control model size computational cost keep model convergg, but one way to reduce amount MSE for predictions addendum diameter (d a ) is to crease mesh density on cross-sectional area especially on teeth so contact condition can be modelled more accurately. This is a normal route based models where fer mesh can result a more accurate result. However, sce this work distortion trends fluence geometrical parameters on this trend is under focus, presented model could be a valid model sce certaly it is predictg distortion trends with enough accuracy. To sum up this section, it is concluded that is modelled with good accuracy so it can be used as a tool for furr analysis without performg experiments. This tool could help to simulate predict results manufacturg PM with route presented this paper follow trends effects gear size fluence on distortions density distribution.

13 J. Manuf. Mater. Process. 2018, 2, Analysis on Size Influences Usg validated model last chapter paper, next step is to use model to predict distortion gear geometry step. present authors have shown an earlier work that density distribution density growth pressg is fluenced by gear parameters [15]. It has been shown that a different density distribution is achieved, where mimum relative density (RD m ) could be different neutral zone [15]. In this section, authors provide an analysis on fluence gear size parameters on PM g route under discussion paper. research aims to answer two goals. first is to reveal potential relation between gear geometrical parameters distortions that occurred durg. second goal is to provide a simple predictive model that could predict distortion levels based on gear geometrical parameters. Such a model would be used under assumption that it is just for specific powder material this research is valid for route studied this work. refore, it could be used as an estimator for vestigatg possibilities manufacturg PM with full density low distortion. It is known that driver distortions is density gradients caused by pressg powder. Also, closure pores usg is dependent on density level component before. It is assumed a mimum relative density 90% should be reached before through pressg/sterg steps, to be able to close all pores reach a fully dense component J. Manuf. Mater. Process. [17]. 2018, 2, x FOR hyposis PEER REVIEW is that critical criterion is mimum relative 13 density 18 (RD m ) before. With this hyposis bigger ranges relative density gradients caused P1 respectively kept effects at P2se will cause geometrical larger size distortions parameters durg on. results are refore, simulated here. predictions should s give an are estimation performed values to predict for RD distortions m P1 P2. addendum diameter (da) face width gear for each eight samples 19. parameters for used for s are presented 19. selected In 19, Samples #1, #2, #3, #4 have equal addendum diameters. design are based on realistic dimensions dustrial application. Such a selection is made with samples for numerical is order to underst effect module number purpose implementg results this research as a guidele for dustrial application teeth on results. As it is presented Equation (1), addendum diameter is a function normal route module (mn) future. number teeth (Z). 35 b mn Z 30 b (mm), mn (mm), Z(-) Sample # 19. Eight selected gear parameters for furr analysis on fluence gear size on PM 19. Eight selected gear parameters for furr analysis on fluence gear size on g. PM g. mimum relative densities (RDm) are recorded for both P1 P2 results are presented 20. re is clearly a difference amount predictions for RDm between samples s. In 20, results #1 #2 show fluence face width on RDm values. While normal module number teeth are kept constant both, it is observed that lower face-width will result higher RDm values compared with creased face-width sample #2.

14 J. Manuf. Mater. Process. 2018, 2, 49 x FOR PEER REVIEW Samples #7 #8 are designed with even smaller addendum diameters. In se two s, effects as is shown se by geometrical 20, size resulted parameters on results are simulated here. RDm is lower than samples #5 #6. This set s results are performed also suggests to predict hyposis distortions that at a addendum constant module diameter (d a face-width, ) width a larger addendum gear for diameter, each which eight is due samples to more number 19. teeth, could have an fluence on RDm values. In This could 19, Samples be observed #1, #2, #3, a pairwise #4 have comparison equal addendum samples diameters. #5 #7, as well design as pairwise samples comparison for numerical samples #6 #8. is order to underst effect module number teeth on results results. distortions As it presented gear Equation with respect (1), to addendum gear addendum diameter diameter is a function its face normal width are module presented (m n ) number 21. From teeth results (Z). presented 20, to confirm hyposis presented mimum earlier, it relative is expected densities that (RD samples m ) are #1 recorded #3 show for both lowest P1 distortions P2 caused by results sce are y presented have higher RDm 20. values re is clearly P2. As well, a difference it is expected amount highest predictions amount distortions for RD m between will observed samples samples s. #6 #8. RD m [%] P1- RDm P2- RDm Sample # 20. RDm for s eight samples s # RD m for s eight samples s #1 8. diametral distortion face width distortion In 20, results #1 #2 show fluence face width on RD m values. While normal module number 0 teeth are kept constant both, it is observed that lower face-width will result higher -0.5RD m values compared with creased face-width sample #2. same trend is observed -1 comparg results sample #3 #4. difference is that sample #3 #4, normal module is creased number teeth is decreased to keep addendum diameter equal to -1.5 addendum diameter samples #1 #2. This geometrical change shows a slight improvement -2RD m, specifically if we compare results case #2 #4 toger this effect is very clear. In samples -2.5 #2 #4, addendum diameter face-width is equal but re is a noticeable difference RD m generated P1 P2. This observation could support ory that for larger face-widths, -3 it is more favorable to design with larger normal modules to crease RD m values Samples #5 #6 are designed1based2on smaller 3 4 addendum 5 6 diameter 7 8 compared to samples #1 #4. In se samples results suggest that with a constant Sample # normal module number teeth it is expected to reach higher 21. Maximum RD m values distortions when form face-width shrkage is lower as it s is shown # Comparg results all sample #1 to #6 supports hyposis that havg a larger diameter Distortions at constant are face-width defed here as gear changes geometry could gear fluence addendum diameter todurg reach higher RD m values. changes This could gear be face seen width by comparg durg #1,. #3, values #5 separately distortions as well are asmeasured comparg #2, #4, results #6 with each numerical or, as s shown by for all 20. eight sample gear geometries are visualized 21. Samples results #7 shown #8 are designed 21 with confirm eventhat smaller re addendum should be a diameters. strong relation In se between two s, RDm as value is shown created by pressg 20, resulted caused RD m distortions lowerby than. samples For #5 #6. with This highest set RDm, as results samples also #1 suggests #3, predicted hyposis distortions that at aare constant lowest. module At same face-width, time, it ais larger predicted addendum by diameter, numerical which is duemodel to more that number teeth, that have could lowest haverdm an fluence values will on experience RD m values. largest This distortions durg among simulated samples this study. trends results that are illustrated 21 confirm that geometrical parameters, which defe gear Distortion [%]

15 J. Manuf. Mater. Process. 2018, 2, could be observed a pairwise 82 comparison samples #5 #7, as well as pairwise comparison samples #6 #8. 81 results distortions80 gear with respect to gear addendum diameter its face width are presented From results presented 20, to confirm hyposis presented earlier, it is expected that 1samples 2 #1 3 4 #35show 6 7lowest 8 distortions caused by sce y have higher RD m values P2. As well, Sample it is # expected highest amount distortions will be observed samples 20. #6 #8. RDm for s eight samples s #1 8. RD m [%] Distortion [%] diametral distortion face width distortion Sample # Maximum Maximum distortions distortions form form shrkage shrkage s s #1 8. #1 8. Distortions are defed here as changes gear addendum diameter durg Distortions are defed here as changes gear addendum diameter durg changes gear face width durg. values distortions are measured results changes gear face width durg. values distortions are measured results numerical s for all eight sample gear geometries are visualized 21. numerical s for all eight sample gear geometries are visualized 21. results shown 21 confirm that re should be a strong relation between RDm results shown 21 confirm that re should be a strong relation between RD value created pressg caused distortions by. For with highest RDm, as m value created pressg caused distortions by. For with highest RD samples #1 #3, predicted distortions are lowest. At same time, it is predicted m, as by samples #1 #3, predicted distortions are lowest. At same time, it is predicted by numerical model that that have lowest RDm values will experience largest numerical model that that have lowest RD distortions durg among simulated samples this study. m values will experience largest trends results that are distortions durg among simulated samples this study. trends results that illustrated 21 confirm that geometrical parameters, which defe gear are illustrated 21 confirm that geometrical parameters, which defe gear dimensions, are effective when it comes to manufacturg gear usg vestigated PM g route this work. This fact dictates that for reachg full density usg two times pressg two times sterg stages, it is necessary to reach some critical RD m to ensure that distortions caused by, due to un-avoidable density gradient PM components, are not out design limits for post g. post g gear could become very expensive if large distortions occur PM g, which will crease material waste as well as cost manufacturg. 5. Discussion Let us take results previous section discuss a prediction model to estimate RD m based on gear parameters. Such a model could be used practice for selection most suited gear geometries for present PM route. This should be combed with expertise knowledge on gear post g to defe acceptable levels distortion, which could be compensated post g but is not scope this work. For our purpose a correlation analysis is performed to confirm connection between distortions for samples ir RD m values P2. Pearson correlation coefficient 0.84 is calculated for correlation between distortions addendum diameter RD m. Also, a Pearson

16 J. Manuf. Mater. Process. 2018, 2, correlation value 0.87 is calculated for correlation between distortions face-width RD m. se two coefficient values, supports assumption that RD m value gear achieved durg two times pressg two times sterg steps route could be a proper dicator for prediction distortions caused by as last step route. This has led us to construct predictive models for RD m as a tool for estimatg fluence gear parameters that defe size geometrical distortions caused durg. This is performed usg a simple lear regression analysis with three dependent variables (m n, b, Z) one dependent variable (RD m ) for P2. resultg p-values for Z is 0.551, which suggests that Z is not statistically significant on RD m P2. refore, second analysis is performed results are shown Table 4 for P2. Table 4. Results ANOVA [25] for eight different samples results P2 without considerg Z as a parameter. Coefficients Stard Error t Stat p-value Lower 95% Upper 95% Intercept b m n An examation Table 4 makes it clear that both two geometrical parameters (m n, b) stard model are significantly predictive RD m accordg to ANOVA statistics [F (2, 5) = , p < 0.004]. Followg stard regression analysis, model s degree predictg dependent variable is R = model s degree explag variance dependent variable is R 2 = With se coefficients, it may be said that model predicts RD m P2 well. Based on regression analysis results, regression equation for prediction RD m P2 is as Equation (2): 6. Conclusions RD m, P2 = m n b (2) In this paper, we have considered a powder g route consistg five steps to manufacture a metal powder. powder is ed through two times pressg two times sterg to fally reach full density, where a hot iso-static pressg component is done. paper aim was to answer two ma research questions. first is to fd out potential relation between distortions caused by lowest relative density gear neutral zone (RD m ). hyposis was that distortion driver is density gradient caused pressg amount distortion could be different for different RD m values. This was validated by results presented this work. This fdg brought us to second research question on how RD m could be affected by gear dimensions. hyposis was that with a similar condition a certa material, geometry gear could be decisive RD m values generated by pressg es, which consequently could affect distortions. This hyposis is also accepted shown to be true by results presented our s experiments. Answerg research questions enabled us to present a predictive model for RD m based on geometrical parameters pressg steps PM route. This was delivered usg data an experimentally validated numerical es volved PM route. predictive model is created by usg lear regression analysis. Such a predictive model for RD m could be useful to have an estimation about outcome before gog to costly experiences. For this purpose, a lear regression analysis has been performed usg data results eight samples to create a predictive model for RD m P2. To implement fdgs to practice for gear manufacturg usg PM, fdgs this paper imply that for a specific group gear geometries (with a certa combation gear parameters)

17 J. Manuf. Mater. Process. 2018, 2, it is easier to manufacture PM gear with lower distortions. This means such geometries will require less post g (a fishg application such as grdg) to reach fal gear geometry. At same time re is a group that might show larger distortions durg because geometrical parameter fluence. This means y will require higher amounts fishg post es, which is expensive should be avoided to keep manufacturg economically comparable with traditional methods. reason is that case a larger distortion, it would be necessary to add more stock on component design so it might be possible to reach accurate tolerances fishg. This fdg will allow us to wisely choose which geometries are proper for beg considered to be manufactured usg PM route vestigated this work. regression model predicts that general, larger normal modules lower face widths are more suitable to reach higher levels RD m neutral zone PM gear, which could cause less distortions. Considerg application for manufacturg, results are very dependent on gear parameters. For with larger normal modules (4 6 mm), which are common for heavy vehicles, we can recommend presented route to be used when gear face-width is not higher than 20 mm. Author Contributions: Conceptualization, A.K.; Methodology, A.K.; Stware, A.K.; Validation, A.K. A.M.; Formal Analysis, A.K.; Investigation, A.K.; Resources, A.M.; Data Curation, A.K.; Writg Origal Draft Preparation, A.K.; Writg Review & Editg, A.M.; Visualization, A.K.; Supervision, A.M.; Project Admistration, A.M.; Fundg Acquisition, A.M. Fundg: This research was funded by Swedish Governmental National Fundg Agency VINNOVA grant number [ ]. Acknowledgments: authors would like to express ir gratitude to Michael Andersson, Höganäs AB for his collaboration runng experimental test material verifications as well as his contued support durg research by providg sightful comments feedback on results. Also, we would like to thank Maheswaran Vattur Chalmers University technology for performg experimental measurements his time for fruitful discussions durg project. Conflicts Interest: authors declare no conflict terest. funders had no role design study; collection, analyses, or terpretation data; writg manuscript, decision to publish results. References 1. Flod, A.; Karlsson, P. Automotive transmission design usg full potential powder metal. In Proceedgs PM2012, Yokohama, Japan, October 2012; pp Capus, J. Industry Roadmap update MPIF. Met. Powder Rep. 2012, 67, [CrossRef] 3. Capus, J.M. Surface-densified PM : New hope new transmissions. Met. Powder Rep. 2006, 61, [CrossRef] 4. Cedergren, J.; Mel, S.; Lidström, P. Numerical vestigation Powder Metallurgy manufactured gear wheels subjected to fatigue loadg. Powder Technol. 2005, 160, [CrossRef] 5. Glodež, S.; Šori, M. Bendg Fatigue Analysis PM s. Key Eng. Mater. 2017, 754, [CrossRef] 6. Klocke, F.; Gorgels, C.; Kauffmann, P. Challenges Surface Densification PM s by Rollg. In Advances Powder Metallurgy Particulate Materials, Proceedgs 2008 World Congress on Powder Metallurgy & Particulate Materials, Washgton, DC, USA, 8 12 June 2008; Metal Powder Industries Federation: Prceton, NJ, USA, Klocke, F.; Gorgels, C.; Kauffmann, P.; Gräser, E. Influencg Densification PM s. In Future Trends Production Engeerg; Sprger: Berl/Heidelberg, Germany, Klocke, F.; Schröder, T.; Kauffmann, P. Fundamental study surface densification PM by rollg usg FE analysis. Prod. Eng. 2007, 1, [CrossRef]

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