# 2D 3D ground surface topography modeling considering dressing and wear effects in grinding process.pdf

2D/3D ground surface topography modeling considering dressing and wear effects in grinding process J.L. Jiang a , P.Q. Ge a,b,n , W.B. Bi a , L. Zhang a , D.X. Wang a , Y. Zhang a a School of Mechanical Engineering, Shandong University, Jinan 250061, China b Key Laboratory of High-efﬁ ciency and Clean Mechanical Manufacture at Shandong University, Ministry of Education, Jinan 250061, China articleinfo Article history: Received 9 May 2013 Received in revised form 8 July 2013 Accepted 11 July 2013 Available online 26 July 2013 Keywords: Grinding Dressing Ground surface roughness Ground surface topography abstract Roughness is usually regarded as one of the most important factors to evaluate the quality of grinding process and ground surface. Many grinding parameters are affecting ground surface roughness with different extents, however, the most inﬂ uential factors are wheel dressing and wear effects which were unfortunately not get seriously attention in the previous researches. On the other hand, as a most common indicator, roughness is only a statistical evaluation which is not enough to describe the topography characteristics of a surface, especially under higher demands on grinding process and functional ground surface quality. Thus in this work, a 2D and 3D ground surface topography models wereestablishedbasedonthemicroscopicinteractionmechanism modelbetweengrainsandworkpiece in grinding contact zone. In this study, besides grinding parameters,thewheel dressingand weareffects were taken into consideration, including dressing depth, dressing lead, geometry of diamond dressing tool and wear effects of both wheel and diamond dressing tool. A dressing and wear proﬁ le line, L dw , which will describe how the grains’ shapes are changed, was established and added into a former 2D ground surface roughness prediction model. In order to obtain a better visual effect, a 3D topography modelwas established whichisbased onthe interaction situations in realgrindingprocess.Both2Dand 3D models will predict ground surface roughness more precisely and stably than traditional models by comparing with a dressing lead single-factor experiment. Results also showed that the selection of dressingparametersand dressingtoolscan refer tothe formed shape of L dw bycomparing with grinding depth, a e , and the dressing lead should be carefully chosen which will greatly inﬂ uence ground surface topography the most.otherwise the experimental workload will be greatly increased. Furthermore, the empirical models have a limit on that they will be invalidated when the grinding condition is changed. Another type of models, analytical models, is based on the people’s understanding of the grinding process. Many of these Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/ijmactool International Journal of Machine Tools however,this model includes an empirical factor and does not describe the microstructure of the grinding wheel [5]. Currently, one of the most popular formulas of maximum undeformed chip thickness and grain number per unit area were proposed by Malkin [1]: h m ¼ 4 Cr v w v sa e d e1=2 “# 1=2 ; C¼ 1 LB ð1Þ where Cisthe grainnumberperunitarea, Land Bare the lateral and longitudinal distance between two adjacent grains, respectively; r is the chip width-to-thickness ratio. However, the formulas above are obtained under these assumptions: (1) all the grains are spherical and share the same size; (2) the locations of all the grains follow uniform distribution and the protrusion heights are the same. These assumptionsdonotreﬂ ectthecharactersofstochasticnatureandthe values of L,Bandraredifﬁ culttodetermine.Hou[6]usedprobability statistics method to analyze the mechanics of the grinding process. The numbers of contacting and cutting grains are determined for a givendepthofwheelindentationandtheundeformedchipthickness was described by the minimum grain diameter. In Hou′s research, it is assumed that the diameter of grains is under normal distribution and using only one variable x to express both grain size and grain protrusion, which means that the biggest grain has the highest protrusion and vice versa. However, this assumption is not corre- sponding with the actual interacting situation very well. The grains are random located within the wheel, so the size and protrusion heightofagrainareindependentwitheachotherandtheyshouldbe represented by two variables. Younis and Alawi [7] developed an undeformed chip thickness model which is described by Rayleigh′s probability density function (p.d.f.) and this model has been used extensively in the following research papers: [8–11]. However, the Rayleigh′sp.d.f.isdeﬁ ned by only one paremeter, β, which is hard to determine and has no clear physical meanings, and this model also cannot give a clear relationship between grinding conditions and undeformed chipthickness. Jiang and Ge [12] have been developed a comprehensive model which can successfully describe the micro- interacting mechanism between workpiece material and grains with different size, location and protrude height. The model is based on a new method of calculating grain number per unit grinding wheel volume and undeformed chip thickness. Their work gives a deeper insight into contacting situation in grinding zone which is hard to achieve using experimental methods. Although these models and simulation methods mentioned above can relatively well predict ground surface roughness with different extent, unfortunately, none of them can able to take the grindingwheeldressingandweareffectsintoconsiderationwhich actually have great inﬂ uence on ground surface quality. The parameters of dressing process, such as dressing depth, dressing lead, dressing passes number and the geometry of dressing tool, Nomenclature A x,y undeformed chip cross-sectional area a d dressing depth per dressing pass a e grinding depth b w grinding width d e wheel diameter d gx grain diameter d tol total dressing depth d max maximum grain diameter d mean average grain diameter d min minimum grain diameter h cu,max maximum grain penetration depth, also undeformed chip thickness h cuz grain penetration depth h cuz,max maximum grain penetration depth l the grain location at the grinding contact length l c grinding contact length l con real contact length of a grain l cut the location when a grain starts cutting l m moving distance of grinding wheel l slid the location when a grain starts sliding l w workpiece length L A ,L A (i) ,L A n simulatedlinetodescribethegroundsurfaceproﬁ le L sd standard line to describe ideal ground surface N wheel structure number N lc number of grains in grinding contact zone N t total number of grains passing through line L A N v number of grains per unit grinding wheel volume n d dressing passes in a dressing process Q w ′ speciﬁ c remove rate R a roughness, R a t total the time of L A changing into L A n V cut,xy removed workpiece material volume by grain G x,y v s wheel speed v w work speed x variable x expressing grain diameter x p the x-coordinate value of the intersecting point of line y¼y max and line y¼g(x) y protrude height of a grain y′ comp compensation amount y′ drw,min lowest point location of L dw Y′ CL center line of L A Δ t time interval of two adjacent grains δ coefﬁ cient, equals to d maxd min s standard deviation of normal distribution φ volume percentage of grains J.L. Jiang et al. / International Journal of Machine Tools ﬁ ner dressings (ﬁ ne truing lead, slow dressing feed and small truing/dressing depth) will produce higher densities of cutting asperities [22] and experiments in [23] showed that smaller dressing depth, dressing speed ratio and dressing cross-feed rate will produce smoother ground surface. At the same time, the wheel wear will also affect grinding process. Although the ground surface roughness will be reduced when the cutting edges are worn ﬂ at, however their ability of removing material is weakened, thus in grinding contact zone, sliding and plowing between grains and workpiece material are mainly occurred. Here much energy of heat will be generated and majoring of the heat will transferred into workpiece material and cause thermal damage and other unexpected defects. Additionally, the roughness parameter cannot fully express the characteristics of surface topography. Roughness is essentially a statistical indicator of peaks and valleys on the surface, so the surfaces with different topographies may have the same rough- ness values. Therefore, when higher requirements on surface quality is put forward, for example some surfaces of optical elements or precision bearing raceways, the roughness indicator is not enough for expressing the topography of the surfaces. Towards to this problem, many researchers have established 2D/3D ground surface topography models which have better visual effects. Chen and Rowe [16–18] have discussed comprehen- sively the impact of single-point dressing on grinding process. Simulated grinding wheel topography was established taking account of the motion of the dressing tool, grain size, grain spacing, grain fracture and break-out. Then a 2D ground surface topography was obtained and contains features which bear a resemblance to the experimental surface. However, the method of calculating undeformed chip thickness has not given, and the inﬂ uences of wear effect of grinding wheel and dressing tools was nottakenintoconsideration.IntheresearchofGongetal.[24],the virtual reality technology was applied to simulate ground surface, a virtual grinding wheel has been created and a 3D images were obtained and the dressing and wear effects were considered. However, in this model, only one parameter (maximal remaining height) was used to describe dressing effect and several coefﬁ - cients were introduced to describe grain diameter changing, grain geometrical shape, grain roughness and grain wear which value are lacking of theoretical basis. Aurich et al. [25] have developed a kinematic simulation of the grinding process model (KSIM). Rely on KSIM, a series of important terms in grinding process can be obtained such as undeformed chip thickness and cross sectional area, grinding forces and ground surface topography. KSIM also consideredthedressingeffectshoweverinaquitesimplewaythat was just simply realized by cutting down the grain protrusion height of every single grain to a speciﬁ ed limit (dressing height) which leads toa larger numberof grains with the same maximum grain protrusion height. Actually, this approach is more like a grinding wheel wear process. In the work of this paper, the interaction mechanism between grainsandworkpiecematerialareﬁ rstlymodeledanddiscussedin Section 2, which give a basis of the following simulations. In Section 3, a ground surface topography model considering dressing and wear effects was established which is a modiﬁ ed model fromthe author′s former research which already tookall of the grinding parameters included. In Section 4, additionally, a 3D model of ground surface topography, which is more close to the grinding process, also considering dressing and wear and has bettervisualeffects,hasbeendeveloped.The3Dsimulatedsurface was compared and in good accordance with the measured work- piece surface under the same grinding conditions. It is found that both analytically and experimentally, the value of dressing leads has a greater impact compared with the other dressing parameters. 2. Interaction mechanisms between grains and workpiece material in grinding contact zone The detailed introduction of microscopic interaction mechan- ism was published in the author′s former paper [12], and the following are some basic principles. In grinding contact zone, a large amount of grains with random geometry and random distributed location contact with workpiece material with differ- ent microscopic interacting types, which will affect both grain number and single grain force calculation. Generally, it is believed that a grain will experience three stages when it goes through grinding contact zone: sliding, plowing and cutting. But for different grains, the starting points of plowing and cutting stages are different for the reason that the critical conditions of plowing and cutting are related with grain sizes and penetration depths. Basedonthispoint,itisreasonabletosupposethatwhenagrainis at the end of grinding contact length, it may not enter the cutting stage and still in sliding or plowing stage, or even cannot contact with workpiece material in the whole contact length, so that different grains will experience different interacting situations which means that the starting points and the lengths of sliding, plowing and cutting stages are different between grains within grinding contact zone. Furthermore, these three types of grains may exist at the same location of the grinding contact zone. As shown in Fig. 1, there are nine grains in grinding contact zone. Because of the different sizes and protrusion heights, these grains contacting with workpiece material in different situation. Fig. 1 shows that: (1) only Grain No. 7 contacts with workpiece material from the beginning of the grinding contact zone and the others do not; (2) Grains No. 1 and No. 3 share the same ‘grain′s realcontactlength ,butthelengthsofsliding,plowingandcutting stagesaredifferentbetweenthetwo;(3)GrainNo.4andNo.9are end at plowing stage and Grain No. 2 is end at sliding stage; (4) Grain No. 5–No. 8 experience three stages, but their ‘grain′s real contact lengths′ and the starting points & lengths of three J.L. Jiang et al. / International Journal of Machine Tools & Manufacture 74 (2013) 29–40 31