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Developing an Analytical Model and Computing Tool for Optimizing Lapping Operations of Flat Objects Made of Alloyed Steels

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Developing an Analytical Model and Computing Tool for Optimizing Lapping Operations of Flat Objects Made of Alloyed Steels materials Article Developing an Analytical Model and Computing Tool for Optimizing Lapping Operations of Flat Objects Made of Alloyed Steels Tudor Deaconescu * and Andrea Deaconescu Department of Industrial Engineering and Management, Transilvania University of Brasov, 500036 Brasov, Romania; [email protected] * Correspondence: [email protected]; Tel.: +40-268-477113 Received: 22 February 2020; Accepted: 13 March 2020; Published: 16 March 2020 Abstract: Lapping is a finishing process where loose abrasive grains contained in a slurry are pressed against a workpiece to reduce its surface roughness. To perform a lapping operation, the user needs to set the values of the respective lapping conditions (e.g., pressure, depth of cut, the rotational speed of the pressing lap plate, and alike) based on some material properties of the workpiece, abrasive grains, and slurry, as well as on the desired surface roughness. Therefore, a mathematical model is needed that establishes the relationships among the abovementioned parameters. The mathematical model can be used to develop a lapping operation optimization system, as well. Tothis date, such a model and system are not available mainly because the relationships among lapping conditions, material properties of abrasive grains and slurry, and surface roughness are difficult to establish. This study solves this problem. It presents a mathematical model establishing the required relationships. It also presents a system developed based on the mathematical model. In addition, the efficacy of the system is also shown using a case study. This study thus helps systematize lapping operations in regard to real-world applications. Keywords: lapping; spherical abrasive grain model; material removal rate; software tool 1. Introduction Surface lapping has been known for thousands of years as a procedure used for the manual finishing of stone objects [1]. For a long period of time, lapping remained a manual process and was considered an art, a craft rather than a science, due to the stochastic, often unpredictable nature of the results [2]. Generally, surfaces were lapped without applying certain rules, merely by combining work parameters based on the operator’s experience. At present manual lapping is rare and has been replaced by mechanized and automated processes. There are some components (mechanical seals, components of pacemakers, measuring instruments, and surgical devices, cutting tools, hard disk drive heads, guiding surfaces of machine tools, and pistons of pumps) which are frequently used in automotive, aircraft, manufacturing, computer, and electronic industries. In most cases, the performances of these components depend on both form accuracy and surface finish. Therefore, if the form accuracy and surface finish of the abovementioned components do not meet the desired level after machining (e.g., turning, grinding, and alike), lapping (and in some cases followed by polishing) is performed. Therefore, how the form accuracy and surface finish of a workpiece change due to lapping is an important issue of research and implementation. In lapping, loose abrasive grains mixed with slurry are pressed against a workpiece to reduce its surface roughness as well as its form accuracy (e.g., flatness). To perform a lapping operation, the user needs to set the values of the respective lapping conditions (e.g., pressure, depth of cut, the rotational Materials 2020, 13, 1343; doi:10.3390/ma13061343 www.mdpi.com/journal/materials Materials 2020, 13, x FOR PEER REVIEW 2 of 15 Materialsrotational2020 speed, 13, 1343 of the pressing lap plate, and alike) based on some material properties of2 ofthe 15 workpiece, abrasive grains, and slurry, as well as on the desired surface roughness. Therefore, a speedmathematical of the pressingmodel is lap needed plate, andthat alike)establishes based onthe somerelationships material am propertiesong the ofabovementioned the workpiece, abrasiveparameters. grains, and slurry, as well as on the desired surface roughness. Therefore, a mathematical modelA isrelatively needed that reduced establishes amount the of relationships specialist study among has the been abovementioned dedicated to parameters.surface lapping. The literatureA relatively features no reduced general amount computational of specialist relationships study linking has been the dedicatedvarious parameters to surface that lapping. impact Thethe outcome literature of features lapping. no The general values computationalof the output quantities relationships like roughness, linking the superficial various parameters layer hardness that, impactor material the outcome removal of rate lapping. are Thepresented values strictly of the output for concrete quantities cases like, roughness,and the results superficial cannot layer be hardness,generalized. or materialAt present removal, lapping rate is are a process presented that strictly lacks fordigital concrete support cases,, including and the resultsa database cannot of bepractice generalized.-based information At present, that lapping would is aenable process machining that lacks proc digitaless planning support, and including optimization. a database of practice-basedWithin this information context, the that paper would addresses enable this machining gap in knowledge process planning by putting and forward optimization. an algorithm for theWithin modeling this context, of the lapping the paper process addresses of flat this surfaces gap in knowledgeand a software by putting tool developed forward anas algorithma support forfor thespecialists. modeling The of main the lapping objective process of the of paper flat surfaces is to make and available a software to industrial tool developed specialists as a support concerned for specialists.with lapping The technologies main objective, a of working the paper instrument is to make availablethat simplifies to industrial and specialistssignificantly concerned reduces with the lappingduration technologies, for calculating a working output instrumentquantities thatthat simplifiesare the optimized and significantly machining reduces parameters the duration for flat for calculatinglapping. Chapter output 2 quantities presents the that principle are the optimized of processing machining and data parameters on the state for- flatof-art lapping. in this Chapterfield. The 2 presentsnext chapter the principle discusses of the processing computational and data methodology on the state-of-art of the in main this field. output The quantities next chapter of a discusses lapping thesystem computational based on the methodology spherical model of the considered main output for the quantities abrasive of grains. a lapping Further system, in this based chapter on the, a sphericalsoftware modelapplication considered is described for the developed abrasive grains. for the Further, planning in this and chapter, optimization a software of the application process by is describedmeans that developed, the operator for thecan planningset the optimum and optimization work parameters of the process swiftly by. The means paper that, ends the with operator a chapter can setof conclusions. the optimum work parameters swiftly. The paper ends with a chapter of conclusions. 2.2. Principle of Lapping and Related Works InIn lapping,lapping, thethe machiningmachining allowance allowance is is small small (< (<50 50µ m),μm), hence hence the the similarity similarity of of such such machining machining to theto the phenomenon phenomenon of of wear wear by by abrasion abrasion [3 ].[3]. It It is is not not abrasion abrasion only only that that removes removes thethe surplussurplus materialmaterial layer,layer, butbut toto a a smaller smaller extent, extent, also also the the corrosion corrosion caused caused by by the the working working medium medium and and the the occurrence occurrence of fatigueof fatigue [4]. The[4]. coexistenceThe coexistence of all theseof all processes these processes needs detailed needs study detailed and a thoroughstudy and understanding a thorough ofun thederstanding numerous of factors the numerous that contribute factors tothat the contribu removalte of to material. the removal of material. TheThe lappinglapping systemsystem cancan bebe assimilatedassimilated toto aa tribosystemtribosystem consistingconsisting ofof thethe elementselements shownshown inin FigureFigure1 1:: FigureFigure 1.1. Principle of lapping.lapping. TheThe tribosystemtribosystem consists consists of theof lapthe plate, lap oneplate, or more one workpiecesor more thatworkpieces are machined that simultaneously,are machined andsimultaneously the semi-liquid, and the medium semi-liquid known medium as slurry. known Each as ofslurry. these Each elements of these cumulates elements a cumulate numbers of a characteristicsnumber of characteristics like hardness, like surface hardness, roughness, surface type roughness, of material, type stateof material, of the surface state of layer, the s graining,urface layer, etc. Allgraining, these characteristicsetc. All these arecharacteristics completed byare parameters completed pertaining by parameters to the pertaining kinematics to of the the kinematics machine-tool of (machining speed, lap plate pressure, eccentricity between the lap plate axis and the axis of rotation of the workpiece support, etc.). Materials 2020, 13, 1343 3 of 15 Lapping entails the use of a semi-liquid working medium (lapping paste or slurry) consisting of a carrier fluid that holds the abrasive grains in free distribution. The lapping system does not use a
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