Available online at ScienceDirect. Procedia CIRP 31 (2015 ) th CIRP Conference on Modelling of Machining Operations

Transcription

1 Available online a ScienceDirec Procedia CIRP 3 (5 ) h CIRP Conference on Modelling of Machining Operaions Predicive modeling of surface roughness in grinding Sanchi Kumar Khare a, Sanja Agarwal b, * a Deparmen of Mechanical ngineering, Bundelkhand Insiue of ngineering and Technolog, Jhansi, India b Deparmen of Mechanical ngineering, Bundelkhand Insiue of ngineering and Technolog, Jhansi, India * Corresponding auhor. Tel.: ; fax: mail address: sanja7ag@rediffmail.com Absrac Surface quali of he machined componen is one of he mos imporan crieria for he assessmen of grinding process. The imporance of he surface finish of a produc depends upon is funcional requiremens. Since surface finish is governed b man facors, is experimenal deerminaion is laborious and ime consuming. So he esablishmen of a model for he reliable predicion of surface roughness is sill a ke issue for grinding. In his sud, a new analical surface roughness model is developed on he basis of sochasic naure of he grinding process, governed mainl b he random geomer and he random disribuion of cuing edges on he wheel surface having random grain prorusion heighs. A simple relaionship beween he surface roughness and he chip hickness was obained, which was validaed b he experimenal resuls of AISI 434 seel in surface grinding. 5 The Auhors. Published b lsevier B.V. This is an open access arie under he CC BY-NC-ND license (hp://creaivecommons.org/licenses/b-nc-nd/4./). Peer-review under responsibili of The Inernaional Scienific Commiee of he 5h Conference on Modelling of Machining Operaions. Peer-review under responsibili of he Inernaional Scienific Commiee of he 5h Conference on Modelling of Machining Operaions Kewords:Grinding; Surface roughness; Chip hickness. Inroducion Advanced engineering maerials have been exensivel used in indusrial applicaions during he las wo decades [, ]. However, he acual uilizaion of advanced ceramics has been quie limied mainl because of he machining difficulies and associaed high cos of machining hese maerials b grinding while ensuring he workpiece quali. A echnological basis o achieve more efficien uilizaion of he ceramic grinding process requires an undersanding of he ineracion beween he abrasive and he workpiece, which has direc bearing on he surface roughness, produced using elecron discharge machining. Alhough exensive research has been carried ou o predic he surface roughness of he ground ceramic workpiece, a complee undersanding is e o be achieved. Theoreical mehods of surface roughness evaluaion, as repored in he lieraure, can be assified ino empirical and analical mehods. In empirical mehods, he surface roughness model is developed as a funcion of kinemaic condiions [3-4]. Alhough he developmen of empirical models require minimum effors and are used in he field of grinding echnolog he have limied applicabili. Hence, he scope of hese models is limied. The analical models are alwas preferred o empirical models as hese models are deducivel derived from fundamenal principles. So, he main advanage of he analical model is ha he resuls can easil be ransferred o oher grinding condiions and oher grinding processes. Hence, hese resuls can be made applicable o a wide range of process condiions. The analical models for surface roughness have alwas been characerized b he descripion of he microsrucure of he grinding wheel, in onedimensional form, aking he grain disance, he widh of cuing edge and he grain diameer ino accoun [5-7]. However, hese models did no consider he differen heigh of cuing edges and assumed ha he disance beween he cuing edges was uniform. Tonshoff e al. [8] described he sae of ar in he modeling and simulaion of grinding processes comparing differen approaches o modeling. This work idenified one simple basic model where all he parameers such as wheel opograph, maerial properies, ec. were lumped ino he empirical consan. Several analical models, based on sochasic naure of grinding process, were proposed [9-] o simulae he surface profile generaed during grinding. Assuming a paricular The Auhors. Published b lsevier B.V. This is an open access arie under he CC BY-NC-ND license (hp://creaivecommons.org/licenses/b-nc-nd/4./). Peer-review under responsibili of he Inernaional Scienific Commiee of he 5h Conference on Modelling of Machining Operaions doi:.6/j.procir.5.4.9

2 376 Sanchi Kumar Khare and Sanja Agarwal / Procedia CIRP 3 ( 5 ) probabili disribuion of hese random cuing poins, oupu surface profiles were generaed for known inpu surface profile and inpu grinding condiions. xperimens conduced b Lal and Shaw [] wih single abrasive grain under fine grinding condiions indicaed ha he grain ip could be beer approximaed b circular arc. Therefore, i is eviden ha he groove produced b an individual grain can be beer approximaed b an arc of a cire. Based on his concep, Agarwal and Rao [3-5] developed an analical model for he predicion of surface roughness in ceramic grinding. A probabilisic approach, for geomeric analsis of he grooves generaed, was used o describe he surface roughness, in which, he random variable had been defined b undeformed chip hickness probabili densi funcion. A simple relaionship beween he surface roughness and he undeformed chip hickness was found. In his paper, an analical model has been envisaged o evaluae surface roughness from he chip hickness probabili densi funcion. A simple relaionship beween surface roughness and he chip hickness has been esablished wih he chip hickness as random variable. The model is hen verified using experimenal daa from he surface grinding of AISI 434 seel wih aluminum oxide abrasive.. Model developmen A schemaic diagram showing he ransformaion of he grain ip o he work piece is given in Fig.. A an ransverse secion, he profile of groove generaed b an grain is as shown in Fig.. Since an individual grain has man in cuing poins on is surface and he speed raio is high, he groove produced b an individual grain can be assumed o be an arc of a cire. I can be furher assumed ha he maerial is eiher plowed wih lile side pile-up or removed in he form of chips whenever grain-work piece inerference occurs. Since he posiion of grain ip will be random due o random occurrence of grains on he wheel surface, a probabili densi funcion is required o describe he surface roughness for all he grains engaged. Thus, he undeformed chip hickness can be beer described b Raleigh s probabili densi funcion f () [8] as; f exp for () = for < where β is a parameer ha compleel defines he probabili densi funcion and i depends upon he cuing condiions, he direcion of grinding wheel and he properies of work piece maerials. The expeced value and he variance of he above funcion will be given as where β is a parameer ha compleel defines he probabili densi funcion and i depends upon he cuing condiions, he direcion of grinding wheel and he properies of work piece maerials. The expeced value and he variance of he above funcion will be work surface given as () = / and sd () = ( ) The surface roughness R a which is defined as he arihmeic average of he absolue values of he deviaions of he surface profile heigh from he mean line wihin he sampling lengh l. Ra can be expressed as l R a = l dl where denoes he cener line drawn in such a wa ha he areas above and below i are equal. I can also be expressed saisicall as R a = l max p( ) d min where max and min are he lowes and highes peak heigh of he surface profile and p() is he probabili ha heigh of grain has a paricular value and ma be expressed as p Y Fig. Schemaic view of he workpiece in caresian coordinae ssem z lim V m z probabili{ / / m profile of groove groove raced b grain x x profile of groove Fig. Secional view showing he shape of groove generaed () }

3 Sanchi Kumar Khare and Sanja Agarwal / Procedia CIRP 3 ( 5 ) The surface roughness R a can be calculaed using probabili densi funcion defined in eq. (). The complee descripion of surface generaed is ver difficul due o he complex behavior of differen grains producing grooves because of he random grain-work ineracion. Thus, cerain assumpions have o be made while predicing he surface roughness. The assumpions are as: () The profile of he grooves generaed is same and compleel defined b he deph of engagemen or undeformed chip hickness () There is no groove overlapping (3) An individual grain has man in cuing poins in is surface, herefore, for simplici, he grains are approximaed as uniform spheres of diameer d g (=), randoml disribued hroughou he wheel volume. On he average, he expeced value of an inerference area hrough a sphere is abou half of he area of a cire. As per definiion of surface roughness, he area above and below he cenre line mus be equal i.e. he oal expeced area can be wrien as A (3) The above expression can be represened in erms of he probabili densi funcion f () as. f. d A (4) There are wo pes of grooves generaed depending upon heir deph of engagemen is eiher less or greaer han cenre line. For he case when he deph of engagemen is less han can be expressed as A A. f d., (4a) Similarl, for he groove wih deph of engagemen is greaer han can be expressed as A A. f d. (4b) Subsiuing he values from eq. (4a) and (4b), in eq. (3), equaion becomes A f upper lower d A A f d upper lower or, A p A A p (6) (5) where p and p are he probabiliies defined in erms of he chip hickness probabili densi funcion f() as p f p d for f d for (8) The expeced area value, for he groove wih deph less han cenre line conribuing o surface roughness R a can be calculaed as A (7) (9) and he expeced value of area, for he groove wih deph greaer han he cenre line conribuing o surface roughness R a will be given as upper k A sin k k () lower k A k sin k lower upper where A and A () are he areas below and above he cenre line as shown in Fig. 3. Rewriing he eq.(6) afer subsiuing he expeced values from eq. (9), (), () as p p p p () To calculae he expeced values in he above equaion requires anoher probabili densi funcion for he cases where he chip hickness is smaller and greaer han he cenre line. Thus, he condiional probabili densi funcion f () and f () defined for each region as f f f f d (3) for chip hickness smaller han and for res of he chip hickness f f f f d (4) Subsiuing he eq. (7), (8), (3) and (4) in eq. (6) o find.

4 378 Sanchi Kumar Khare and Sanja Agarwal / Procedia CIRP 3 ( 5 ) Afer simplificaion he expression for cenre line can be expressed as 4 d (5) subsiuing he expeced values in he above equaion, and afer mahemaical simplificaion, he value of he cenre line will be. (6) For he calculaion of he surface roughness, boh pes of grooves are required. Since he conribuion of wo pes of grooves is differen, hus, he oal expeced value of surface roughness can be calculaed as; R p R p R a (7) a a Where and R a R a are he expeced value of he surface roughness for deph of engagemen smaller or greaer han. Thus, he values of he expeced values can be calculaed b he definiion of he surface roughness according o which he surface roughness can be calculaed b adding he area beween he profile and he cenre line and divide i b he oal profile lengh. Hence from Fig. 3, he values can be wrien as A a (8) R upper lower A A a (9) R Rewriing he eq. (8) & (9) afer subsiuing he upper expressions of A, A & A lower from eq. (9), () and () as Ra () 4 R a RSin () 4 Subsiuing he expeced values of ( ), ( ) R sin and from eq. (8), (), (3) and (6) in eq. (), () and hen from eq. (7), he expeced value of surface roughness can be expressed as.59 () R a I can also expressed also in erms of he chip hickness expeced value () b replacing in erms of (), as R.47 a (3) q.(3) shows a proporional relaionship beween he surface roughness and he chip hickness expeced values under he assumpion ha he profile of grove generaed b an individual grain o be a semicircular in shape and he phenomena like back ransferring of maerial, grain overlapping are absen. 3. Predicion of surface roughness The model has o be evaluaed o deermine is validi and versaili. The validi of he model is assessed hrough a comparison beween he prediced value and measured value of he surface roughness wihin he predefined range of parameers. The versaili is based upon he usefulness of he model in predicing he kinemaic condiions which would be required in order o produce specified surface finish. In order o compare he heoreical resuls obained b making use of he model developed, experimens has been conduced in he horizonal surface grinding configuraion. The work maerial aken was AISI 434 seel wih hardness 65HRC. The amoun of maerial removed was he same for each experimen o mainain a consisen sae of he wheel surface. The oher condiions aken for experimen purpose are as follows; wheel speed 36.6 m/sec, wheel diameer 5 mm, wheel widh 9 mm. The kinemaic parameers for each experimen are deph of cu (a e ) and he speed raio (v s /v w ) where v w (5, and 5 m/min) is he feed rae and v s is he wheel speed, as shown in able. xp.no a e (μm) v s /v w R a (μm) Table xperimenal Condiions Surface roughness measuremens were made using Talsurf-VI (cu-off lengh was.8mm) a five differen places on he 5mm cross-secion of he workpiece afer grinding and he arihmeic mean of he values of he measuremens has been repored in he experimenal resuls as shown in Table. The experimens are replicaed five imes (as shown in Table ) o mask he variabili of he process. B making use of he model of chip hickness developed in [6], he chip hickness expeced value was calculaed for each experimen. To validae he model, he cenre line average of surface roughness of all ground work pieces of he each se of experimen afer a single pass was obained using Talsurf-6 surface roughness measuring insrumen. The resuls are

5 Sanchi Kumar Khare and Sanja Agarwal / Procedia CIRP 3 ( 5 ) ploed along wih he experimen values of he surface roughness as shown in Fig. 3. I can be easil observed ha he prediced value of he surface roughness shows a good agreemen wih he experimenal daa obained from he differen kinemaic condiions in horizonal surface grinding. 4. Resuls and discussion The number of variables ha influence he surface roughness of ground surfaces are numerous. These inude he wheel, work and machine characerisics and he operaing characerisics. Since he surface roughness model developed above is based on he chip hickness model which inudes man parameers such as kinemaic condiions, maerial properies ec. Therefore, his model can be used o calculae he surface roughness under differen condiions of hese parameers. The mos common kinemaic parameers are deph of cu and he speed raio. Furher he deviaion of he surface roughness of he new models from he acual values, for various feeds and deph of cu is shown in Fig. 4. Tpical resuls showing he effec of he grinding condiions on he surface roughness. I is seen ha wih increase in he values of feeds and deph of cu, surface-finish deoriaes. This is probabl due o he forces generaed a higher feeds and deph Surface roughness(um) xperimenal Simulaed xperimen No. No. Fig. 3 R a experimenal and simulaed values of surface roughness for surface grinding of cu ha resuls in higher deflecions. Also, he value of surface roughness is slighl higher han he measured value for various values of feeds and deph of cu. The probable reason for his is he assumpion ha he profile of grooves generaed is perfe semi-cire which is no alwas he case. I can be observed from he Fig. 4 ha he maximum deviaion in he predicion of surface roughness wih chip hickness model is abou.5 imes from he acual value. Anoher imporan parameer ha will have significan effec on he surface roughness is he undeformed chip hickness. Wih increasing chip hickness, surface roughness will increase. Thus i appears ha he chip hickness has pronounced effec causing a deoriaion of surface finish. This Ra (μm) Ra (μm) Ra Ra (μm) (μm) aspec is indicaed b boh heoreical and experimenal resuls as shown in Fig. 3. Furher, here appears o be reasonabl ose agreemen beween he experimenal and simulaed resuls. 5. Conusion a e=5m calculaed measured feed (m/min) feed(m/min) a e=m calculaed.5.4 measured a e=5m calculaed feed(m/min) measured feed feed(m/min) Fig. 4 Surface roughness presened agains feed a various dephs of cu In his paper, a simplified model is proposed for predicing he surface roughness of he work piece during he grinding process, aking ino consideraion he random disribuion of he grain prorusion heighs and assuming he profile of groove generaed b an individual grain o be an arc of a cire. The model is based on he relaionship beween he variables of he surface roughness and he undeformed chip hickness. The variables like kinemaic condiions, maerial

6 38 Sanchi Kumar Khare and Sanja Agarwal / Procedia CIRP 3 ( 5 ) properies ec. are aken ino consideraions. The prediced surface roughness appears o ield resuls which agree reasonabl well wih he experimenal values for differen kinemaic condiions in he horizonal surface grinding of AISI 434 seel. Thus, he analical model developed above proves o be a powerful and useful ime efficien soluion for he predicion of surface roughness. References [] Agarwal Sanja, Rao PV. Grinding characerisics, maerial removal and damage formaion mechanisms in high removal rae grinding of Silicon Carbide. Inernaional Journal of Machine Tools and Manufacure ; 77 87:5-, [] Agarwal Sanja, Rao P V. xperimenal Invesigaion of Surface/Subsurface Damage Formaion and Maerial Removal Mechanisms in SiC Grinding. Inernaional Journal of Machine Tools and Manufacure 8; 698-7:48-6. [3] Malkin, S. Grinding Technolog: Theor and Applicaions of Machining wih Abrasives, 989 (llis Horwood, Chicheser, Wes Sussex). [4] Suo, T, Saa, T. Simulaion of grinding process based on wheel surface characerisics. Bull. Jap. Soc. Prec. ngng, 98; 7-33: 5-. [5] Sao, K. On he surface roughness in grinding echnolog. Repors of Tokohu Universi, 955; 59-7: -. [6] Orioka, T. Probabilisic reamen on he grinding geomer. Bull. Japan Soc. Grinding ngrs, 96; 7-9. [7] Lal, GK, Shaw, MC. The role of grain ip radius in fine grinding. Trans. ASM, J. ngng for Indusr. 975; 9-5. [8] Tonshoff, H, Peers, J, Inasaki, I, Paul, T. Modeling and simulaion of grinding processes. Ann. CIRP. 99; : 4-. [9] Zhou, X, Xi, F. Modeling and predicing surface roughness of he grinding process. In. J. Mach. Tools Mf. ; :4. [] Law, SS, Wu, SM. Simulaion sud of he grinding process. Trans. ASM, J. ngng for Indusr. 973; :95. [] Hecker, RL, Liang, S. Predicive modeling of surface roughness in grinding. In. J. Mach. Tools Mf. 3; : 43. [] Lal, GK, Shaw, MC. Wear of single abrasive grain in fine grinding. Proc. In. Grindng Conf., Carnegie-Mellon Universi, Pisburgh, USA. 97; 7. [3] Agarwal, S, Rao, PV. A probabilisic approach o predic surface roughness in ceramic grinding. In. J. Mach. Tools Mf. 5; 69-66: [4] Agarwal, S, Rao, PV. A new surface roughness predicion model for ceramic grinding. Proc. of IMech, Par B, Journal of ngineering Manufacure. 5; 8-8: 9. [5] Agarwal, S, Rao, PV. Modeling and predicion of surface roughness in Ceramic Grinding. Inernaional Journal of Machine Tools and Manufacure. ; 65 76: 5-. [6] Agarwal, S, Rao, PV. Predicive modeling of undeformed chip-hickness in ceramic grinding. Inernaional Journal of Machine Tools and Manufacure. ; 59-68: 56.