Potentials of Vitrified and Elastic Bonded Fine Grinding

Journal of Manufacturing and Materials Processing

Article Potentials of Vitriﬁed and Elastic Bonded Fine Grinding Worms in Continuous Generating Gear Grinding

Maximilian Schrank 1,* , Jens Brimmers 1 and Thomas Bergs 1,2

1 Laboratory of Machine Tools and Production Engineering (WZL), RWTH Aachen University, Campus Boulevard 30, 52074 Aachen, Germany; [email protected] (J.B.); [email protected] (T.B.) 2 Fraunhofer Institute for Production Technology (IPT), Steinbachstraße 17, 52074 Aachen, Germany * Correspondence: [email protected]

Abstract: Continuous generating gear grinding with vitrified grinding worms is an established process for the hard finishing of gears for high-performance transmissions. Due to the increasing requirements for gears in terms of power density, the required surface roughness is continuously decreasing. In order to meet the required tooth flank roughness, common manufacturing processes are polish grinding with elastic bonded grinding tools and fine grinding with vitrified grinding tools. The process behavior and potential of the different bonds for producing super fine surfaces in generating gear grinding have not been sufficiently scientifically investigated yet. Therefore, the objective of this report is to evaluate these potentials. Part of the investigations are the generating gear grinding process with elastic bonded, as well as vitrified grinding worms with comparable grit sizes. The potential of the different tool specifications is empirically investigated independent of the grain size, focusing on the influence of the bond. One result of the investigations was that the tooth flank roughness could be reduced to nearly the same values with the polish and the fine grinding tool. Furthermore, a dependence of the roughness on the selected grinding parameters could not be determined. However, it was found out that the profile line after polish grinding is significantly dependent on the process strategy used. Citation: Schrank, M.; Brimmers, J.; Bergs, T. Potentials of Vitrified and Keywords: grinding tool; polishing; generating gear grinding Elastic Bonded Fine Grinding Worms in Continuous Generating Gear Grinding. J. Manuf. Mater. Process. 2021, 5, 4. https://doi.org/10.3390/ 1. Introduction jmmp5010004 Due to the continuous increase in required power density, hard fine machining of gears Received: 10 December 2020 is mandatory in many cases in order to correct deviations from soft machining and heat Accepted: 24 December 2020 treatment [1,2]. Furthermore, hard fine machining can improve the running characteristics Published: 5 January 2021 of gears in terms of noise behavior and load-carrying capacity [3,4]. Hard fine machining with undefined cutting edge is an established type of process for achieving high and Publisher’s Note: MDPI stays neu- repeatable gear qualities [5]. Because of its high productivity, continuous generating gear tral with regard to jurisdictional clai- grinding is the process that is preferably used in series production, as in the automotive ms in published maps and institutio- industry [2]. Continuous generating gear grinding is the dominant process for hard fine nal affiliations. machining, particularly for gears with a normal module of up to mn ≤ 8 mm and a number of teeth of z > 20 [5–7]. For gear grinding, vitrified bonding systems are widely used, due to their good profileability and high dimensional stability. Furthermore, vitrified grinding tools have a Copyright: © 2021 by the authors. Li- censee MDPI, Basel, Switzerland. high hardness, which is defined as the strength with which the abrasive grain is held by This article is an open access article the bond [8]. The hardness prevents the early breakout of the grain from the bond and distributed under the terms and con- it holds the abrasive grain in place during the engagement with the workpiece. Besides ditions of the Creative Commons At- vitrified bonds, metal bonds are available, which are characterized by a particularly high tribution (CC BY) license (https:// hardness [9]. However, the disadvantage of metal bonds is the lack of profileability. With creativecommons.org/licenses/by/ elastic bonds, including synthetic resin and polyurethane bonds, produce low roughness 4.0/). depths on the workpiece surface. However, elastic bonds only have low dimensional

J. Manuf. Mater. Process. 2021, 5, 4. https://doi.org/10.3390/jmmp5010004 https://www.mdpi.com/journal/jmmp J. Manuf. Mater. Process. 2021, 5, x FOR PEER REVIEW 2 of 15 J. Manuf. Mater. Process. 2021, 5, 4 2 of 15

depthsstability, on which the workpiece can have surface. a negative However, effect elas on thetic bonds geometry only duringhave low the dimensional process [10 ].stabil- The ity,reduction which can of toothhave a flank negative roughness effect on by the means geometry of grinding during the is particularlyprocess [10]. The beneficial reduction for ofincreasing tooth flank the roughness tooth flank by load-carrying means of grinding capacity is [ 11particularly]. Furthermore, beneficial with afor reduction increasing of the tooth flank flank load-carrying roughness, the capacity efficiency [11]. of Furthe gearboxesrmore, could with be a increasedreduction [of12 ].the The tooth required flank roughness,roughness the in the efficiency range ofof Rzgearboxes < 1 µm could cannot be beincreased achieved [12]. with The conventional required roughness grinding in thetools range that of are Rz made < 1 μ ofm vitrifiedcannot be corundum achieved with in many conventional cases. Gears grinding are post-processed tools that are made after ofhard vitrified finishing corundum in order in to many achieve cases. the Gears required are post-processed roughness. Chemically after hard assisted finishing vibratory in order togrinding, achieve asthe well required as polish roughness. grinding Chemically with elastic assisted bonded vibratory grinding grinding, tools, as are well commonly as polish grindingused for superwith elastic finishing. bonded For chemically grinding tool assisteds, are vibratorycommonly grinding, used for a super significant finishing. potential For chemicallyfor increasing assisted the load-carrying vibratory grinding, capacity a signific was identified.ant potential From for theincreasing results ofthe the load-carry- running ingtests, capacity a new was factor identified. for calculating From the the results maximum of the stressrunning of tests, the flank a new in factor accordance for calculating to DIN the3990 maximum was derived stress [11 of,13 the]. The flank roughness in accordan factorce to Z DINR can 3990 be extended was derived to the [11,13]. roughness The rough- factor nessZR,VG factor. It was ZR assumedcan be extended that no to further the roughness increase in factor load-carrying ZR,VG. It was capacity assumed could that be no achieved further increasewith a further in load-carrying reduction incapacity roughness, could as be in ac Figurehieved1 [with13]. Furthera further scientific reduction investigations in roughness, ashave in Figure shown 1 that[13]. aFurther lower roughnessscientific investig can leadations to ahave further shown increase that a inlower the roughness load-carrying can leadcapacity to a further [14]. increase in the load-carrying capacity [14].

Figure 1. IncreaseIncrease of the load-carrying capacity by reducing the roughness accordingaccording toto [[13].13].

In the investigations, in which the extension of the roughness factor to Z was In the investigations, in which the extension of the roughness factor to ZR,VGR,VG was determined,determined, the the gears gears were were super super finished finished by by chemically chemically assisted assisted vibratory. vibratory. After After vibratory µ grinding, thethe investigatedinvestigated gears gears had had a a mean mean roughness roughness depth depth of approximatelyof approximately Rz =Rz 0.4 = 0.4m to Rz = 0.6 µm [13]. However, from an economic point of view this process is not favorable μm to Rz = 0.6 μm [13]. However, from an economic point of view this process is not due to long processing times and investments in new equipment. Furthermore, working favorable due to long processing times and investments in new equipment. Furthermore, with the necessary chemicals is not favorable. The increase in load-carrying capacity that working with the necessary chemicals is not favorable. The increase in load-carrying ca- is observed with chemically assisted vibratory grinding is attributed in particular to the pacity that is observed with chemically assisted vibratory grinding is attributed in partic- superfine surface qualities achieved [11]. Therefore, it can be assumed that this potential ular to the superfine surface qualities achieved [11]. Therefore, it can be assumed that this can also be achieved by grinding superfine surfaces. For this reason, the use of grinding potential can also be achieved by grinding superfine surfaces. For this reason, the use of tools with an elastic bond with a polish grinding process was investigated [10,15,16]. The grinding tools with an elastic bond with a polish grinding process was investigated processes of discontinuous profile grinding and continuous generating grinding can be [10,15,16]. The processes of discontinuous profile grinding and continuous generating used for the polish grinding of gears. For polish continuous generating gear grinding, a grinding can be used for the polish grinding of gears. For polish continuous generating two-section grinding worm is used with one section with a vitrified bond for roughing and gearfinishing, grinding, and aa secondtwo-section section grinding with an worm elastic is bond used forwith polish one section grinding with [17 ].a Anvitrified advantage bond forof the roughing two-section and finishing, grinding wormand a issecond that both section sections with canan elastic be simultaneously bond for polish dressed grinding with [17].a conventional An advantage dressing of the process two-section [17]. grinding In previous worm research is that on both polish sections gear can grinding be simulta- with neouslyan elastic dressed polyurethane with a conventional bond, grinding dressing tools with process a grain [17]. size In previous of F800 were research used. on A polish grain gear grinding with an elastic polyurethane bond, grinding tools with a grain size of F800 size of F800 corresponds to a mean grain diameter of dF800 = 6.5 ± 1 µm. With a grain size wereof F800, used. with A grain an elastic size of polyurethane F800 corresponds bond, to an a averagemean grain roughness diameter of of Rz d≈F8000.6 = 6.5µm ± could1 μm. Withbe achieved a grain insize the of polish F800, with profile an gearelastic grinding polyurethane process bond, [16]. an In aaverage polish roughness generating of gear Rz

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≈ 0.6 μm could be achieved in the polish profile gear grinding process [16]. In a polish generating gear grinding process with a grain size of F800, a mean roughness depth of Rz ≈ µ grinding≈ 0.9 μm was process achieved with [10,17]. a grain However, size of F800, the a use mean of elastic roughness bonded depth grinding of Rz tools0.9 canm have was achieveda significant [10 ,negative17]. However, effect theon usegear of geometry elastic bonded [10]. This grinding negative tools effect can havecan be a significantcaused by negative effect on gear geometry [10]. This negative effect can be caused by the elasticity of the elasticity of the polyurethane bond. the polyurethane bond. The potential of fine grinding with a vitrified grinding tool with fine grain should be The potential of fine grinding with a vitrified grinding tool with fine grain should be investigated in order to avoid the use of an additional technology of chemically assisted investigated in order to avoid the use of an additional technology of chemically assisted vibratory grinding and the use of elastic bonded grinding tools. Because of the high stiff- vibratory grinding and the use of elastic bonded grinding tools. Because of the high ness of the vitrified bond, no negative influence on the tooth flank geometry is to be ex- stiffness of the vitrified bond, no negative influence on the tooth flank geometry is to be pected. Therefore, the objective of the report was to investigate the potential of fine and expected. Therefore, the objective of the report was to investigate the potential of fine and polish grinding in order to produce super fine tooth flank surfaces, depending on the used polish grinding in order to produce super fine tooth flank surfaces, depending on the used bond. To achieve this goal, continuous generating gear grinding tests were carried out bond. To achieve this goal, continuous generating gear grinding tests were carried out with with an elastic bonded polish grinding worm as well as with a vitrified fine grinding an elastic bonded polish grinding worm as well as with a vitrified fine grinding worm. Subsequently,worm. Subsequently, the ground the ground gears were gears characterized were characterized with regard with regard to their to gear their quality gear qual- and theity and surface the roughnesssurface roughness achieved. achieved. The results The are results used in are order used to in determine order to the determine potential the of finepotential and polish of fine grinding and polish for grinding the production for the ofproduction super fine of surfaces. super fine surfaces.

2. Materials and Methods For the investigations, a proﬁleprofile andand generatinggenerating gear grindinggrinding machinemachine from KappKapp Niles GmbH of of type type KX KX 500 500 FLEX FLEX was was availa available.ble. The The grinding grinding tests tests were were performed performed on onan automotive an automotive pinion pinion shaft shaft with witha number a number of teeth of of teeth z = 26, of a z normal = 26, a module normal of module mn = 1.76 of ◦ ◦ mmm,n = a 1.76 pressure mm, a angle pressure of α anglen = 15°, of andαn =a helix 15 , and angle a helixof β = angle 33.75°. of Thisβ = 33.75gear represents. This gear a representstypical industrial a typical application industrial for application polish grinding, for polish see grinding, the left side see of the Figure left side 2. of Figure2.

Figure 2.2. Experimental setup and procedure.

The two grinding toolstools usedused werewere grindinggrinding wormsworms withwith aa numbernumber ofof startsstarts z z00 == 3 and an outer diameter of dd00 = 280 mm. In In order to ensure the same geargear conditionsconditions forfor thethe polish and the finefine grinding tests, the gears had to be pre-ground with the same grinding parameters. The The grinding grinding worms worms consisted consisted of oftwo two sections sections each each in order in order to be to able be ableto pre- to pre-grindgrind the thegears gears and and to tocarry carry out out fine fine or or po polishinglishing grinding grinding tests tests without without changing thethe clamping. The pre-grinding sectionsection ofof bothboth grindinggrinding wormsworms had had a a width width of of b bF80F80 == 110 mm and an identical specificationspecification with a corundum grain with a size of F80 in a vitrified vitrified bond. For polish grinding,grinding, aa sectionsection ofof thethe grinding grinding worm worm with with a a width width of of b F400,PUbF400,PU = 50 mm was made of corundum grains with a grain size of F400 in a polyurethane bond.bond. The grinding worm usedused forfor finefine grindinggrinding alsoalso had had a a section section with with a a width width of of b F400,VbF400,V = 50 mm, which was made size F400 corundum grains in aa vitrifiedvitrified bond.bond. Two different test series were carried out in order to investigate the potential of fine grinding to produce super fine tooth flank surfaces. The first test series had the aim to analyze the influence of the bond independent of the influence of the grain size, the

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pre-grinding process, or the process parameters with the focus on the lowest achievable roughness. In order to meet these requirements, the used tools had the same grain size of F400 and they were dressed with the same dressing parameters and the same dressing tool. For the dressing process for the analysis of bond influence, a dressing disc was used with −1 a rotational speed of nd = 5000 min and an overlap ratio of Ud = 12. The high overlap ratio was chosen in order to achieve a very low roughness during pre-grinding. The same parameters were used in order to ensure comparable conditions and be able to only detect the influence of the bond. However, it was found that the process control used was not suitable for the use of elastic grinding worms. In contrast to the analysis of bond influence, trials were also carried out in order to determine a process strategy that is suitable for both fine and polish grinding process. Within these investigations, an industrial standard −1 two-flank profile dressing tool was used with a rotational speed of nd = 5000 min . In order to ensure a good gear quality, the polish and fine grinding process parameters were individually chosen for each used bond system. Despite these differences of the two test series, the experimental procedure in terms of the pre-grinding parameters was kept constant. The pre-grinding of the gears was done by means of a standard grinding process with a cutting speed of vc = 63 m/s. For the roughing process, two roughing strokes with an axial feed of fa,Roughing = 0.33 mm and an infeed of ∆sRoughing = 37 µm were performed. The single stroke finishing process was performed with an axial feed of fa,Finishing = 0.12 mm and an infeed of ∆sFinishing = 15 µm. The ground gear geometry was corrected during pre-grinding, so that the conditions after pre-grinding were the same for both of the test series. In generating gear grinding, the grinding worm is shifted after each ground gear in order to use an unused section of the grinding worm for the next gear. Three pre-ground gears were analyzed for each test series at the beginning, in the middle, and at the end of the test series in order to determine a possible influence of the shift position and therefore an influence of the uniformity of the grinding worm during pre-grinding. Roughness measurements were carried out with a tactile roughness measuring device of the type Marsurf LD260 from the company Mahr in order to evaluate the influence of the used parameters and grinding worm specifications. The filters for the evaluation of the roughness profiles were selected according to DIN EN ISO 4288 [18]. In a range of the mean roughness depth of Rz = 0.5–10 µm, a waviness filter with a cut-off wavelength of λc = 0.8 mm has to be used according to the standard [18]. For a lower surface roughness with a mean roughness depth of Rz = 0.1–0.5 µm, the standard requires a change of the cut-off wavelength of the waviness filter to λc = 0.25 mm. A measurement with λc = 0.8 mm has first to be carried out in order to select the cut-off wavelength. If the mean roughness depth is below Rz < 0.5 µm, then the roughness must be re-evaluated with a cut-off wavelength of λc = 0.25 mm. Because the surface roughness of fine and polished surfaces was expected to be in the range Rz < 1 µm and, thus, close to the change of the cut-off wavelength, the influence of the choice of the cut-off wavelength was first evaluated. In Figure3, the mean roughness depth for one test of both a polish and fine ground surface is shown. The mean roughness depth Rz was first evaluated with a waviness filter with λc = 0.8 mm and, subsequently, with a waviness filter with λc = 0.25 mm. In the lower part of the image, a roughness profile and the corresponding Abbott curve of a polish and fine ground tooth flank are shown. J. Manuf. Mater. Process. 2021, 5, x FOR PEER REVIEW 5 of 15

urement scatter and, thus, not considered to be significant. The comparison of the roughness profiles and Abbott curve indicates that the fine ground surface has sharper roughness peaks and, thus, has a greater negative gradient in the Abbott curve in the area of a low material ratio than the Abbott curve of the polish ground surface. Because of the average value of the mean roughness depth of Rz > 0.5 μm with the default limit wavelength of the waviness filter of λc = 0.8 mm, this filter was subsequently J. Manuf. Mater. Process. 2021, 5, 4 5 of 15 used for the investigations. This ensures not only the comparability of all results within this report, but also the comparability of the results with previous research findings.

Figure 3. InfluenceInfluence of the waviness filter filter and roughness profileprofile of polish andand finefine groundground flanks.flanks.

3. AnalysisThe evaluation of Bond ofInfluence the roughness and Determination with a waviness of Process filter with Strategy a cut-off wavelength of λc = 0.25 mm results in lower mean roughness depths Rz for both of the tests in comparison to theThe evaluation results of with the apolish waviness and fine filter grinding with λc =tests 0.8 mm.are presented For the polish in the ground following. surface, The meana stronger roughness reduction depth of Rz the was mean used roughness for the eval depthuation, Rz cansince be this identified value is in often the evaluationdefined as witha target a waviness value on filtertechnical with drawingsλc = 0.25 mm.in industrial However, production. the lower In values polishing of the or polish polish ground grind- ingsurface processes, when comparedthe roughness to the peaks fine are ground flatten surfaceed and are a roughness in the range structure of the measurementwith plateaus isscatter produced. and, thus, Therefore, not considered the material to be ratio significant. Rmr(c) Thecharacterizes comparison the of surface the roughness roughness. profiles The materialand Abbott ratio curve Rmr(c) indicates corresponds that the to fine the groundpercentage surface of material has sharper in the roughness specified measuring peaks and, distancethus, has c a below greater the negative highest gradient peak of in the the roughness Abbott curve profile in the [19]. area Within of a low this material report, ratio the materialthan the Abbottratio Rmr(-0.15 curve of theμm) polish in a measuring ground surface. distance c = 0.15 μm was used in order to compareBecause the measured of the average roughness value ofprofiles. the mean The roughnesssmall peak depth distance of Rz c was > 0.5 chosenµm with due the to thedefault expected limit wavelengthflattening of of the the roughness waviness filterpeaks of inλ cthe = 0.8polish mm, grinding this filter process, was subsequently which led toused the for highest the investigations. expectable changes This ensures in the area not onlyof the the roughness comparability peaks. of In all addition results within to the evaluationthis report, of but the also roughness the comparability profile, the of thequality results of withthe gear previous geometry research was findings. analyzed in terms of the gear profile and lead. The gear quality was qualitatively evaluated by the course3. Analysis of the of profile Bond and Influence quantified and Determinationby the value of ofthe Process total profile Strategy deviation Fα. InThe the results following, of the the polish influence and fine of the grinding bond will tests be are analyzed presented with in constant the following. parameters The formean both roughness polish and depth fine Rz grinding. was used Subsequent for the evaluation,ly, the influence since this valueof different is often dressing defined tool as a technologiestarget value on for technical both polish drawings and fine in industrialgrinding will production. be evaluated. In polishing With the or polishchanged grinding dress- processes,ing tool, the the influence roughness of peaksthe cutting are flattened speed fo andr polish a roughness and fine structure grinding with will plateausbe investi- is produced.gated. Finally, Therefore, the characteristics the material of ratio the roughness Rmr(c) characterizes profiles of pre-ground, the surface roughness.polish, and Thefine groundmaterial gears ratio will Rmr(c) be compared. corresponds to the percentage of material in the specified measuring distance c below the highest peak of the roughness profile [19]. Within this report, the 3.1.material Analysis ratio of Rmr(Bond −Influence0.15 µm) in a measuring distance c = 0.15 µm was used in order to compareIn continuous the measured generating roughness gear profiles.grinding, The the smallgrinding peak worm distance is shifted c was between chosen duegrind- to ingthe expectedof gears in flattening order to of ensure the roughness that new peaksareas inof thethe polishgrinding grinding worm process,come into which contact led [8,20].to the highestThe results expectable of pre-grinding changes inat thethe areabeginning, of the roughnessmiddle, and peaks. end of In each addition test toseries the evaluation of the roughness profile, the quality of the gear geometry was analyzed in terms of the gear profile and lead. The gear quality was qualitatively evaluated by the course of the profile and quantified by the value of the total profile deviation Fα. In the following, the influence of the bond will be analyzed with constant parameters for both polish and fine grinding. Subsequently, the influence of different dressing tool technologies for both polish and fine grinding will be evaluated. With the changed dressing tool, the influence of the cutting speed for polish and fine grinding will be investigated. Finally, the characteristics of the roughness profiles of pre-ground, polish, and fine ground gears will be compared. J. Manuf. Mater. Process. 2021, 5, x FOR PEER REVIEW 6 of 15

were examined in order to investigate the uniformity of the grinding worm over a wide range. With this procedure, the influence of three different areas that were distributed along the width of the grinding worm on the gear was analyzed. First, the condition of J. Manuf. Mater. Process. 2021, 5, 4 6 of 15 the gears after pre-grinding was analyzed for the two grinding worms. In Figure 4, on the left-hand side of the diagrams, the results of the roughness measurements determined over the three discrete measuring points and representative profile measurements of the gears3.1. Analysis after pre-grinding of Bond Influence with the corresponding pre-grinding area of each tool used are shown.In continuous generating gear grinding, the grinding worm is shifted between grinding ofThe gears roughness in order of to the ensure pre-ground that new tooth areas flan of theks grindingfor the two worm grinding come intotools contact is compara- [8,20]. bleThe with results values of pre-grindingof the mean roughness at the beginning, depth of middle,Rz ≈ 1 μm. and For end both of of each the test grinding series tools, were itexamined is also noted in order that the to investigate right flank thehasuniformity a higher roughness of the grinding than the worm left flank. over aThe wide material range. ratioWith Rmr(-0.15 this procedure, μm) is the in influencethe range of of three Rmr(-0.15 different μm) areas = 28% that for were both distributed of the pre-grinding along the tools.width The of theprofiles grinding of the worm pre-ground on the gears gearwas do not analyzed. deviate First,between the the condition grinding of tools the gears and theafter quantified pre-grinding average was analyzedtotal profile for thedeviation two grinding Fα is approximately worms. In Figure IT =4 ,3 on for the both left-hand tools. Becauseside of thethe diagrams,grinding worms the results were of dressed the roughness in the same measurements way and profile determined as well over as lead the werethree corrected, discrete measuring these results points were and expected representative and they profile indicate measurements that the initial of thesituations gears after for polishpre-grinding and fine with grinding the corresponding were almost identical. pre-grinding area of each tool used are shown.

Gear Data Pre-Ground Feed Variation Pre-Ground Feed Variation m = 1.76 mm n 2,52.5 Left flank 60.7 z = 26 Right flank 58.9 α = 15° 2 n 56.7 β = 33.75° 1,51.5 Pre-Grinding 1 F80, vitrified 0,50.5 Depth Rz [µm] Diameter [mm] 52.8

v = 63 m/s Left Flank Profile

c Mean Roughness 0 60 µm fa = 0.12 mm Δs = 15 μm fa [mm] 0.12 0.05 0.1 fa [mm] 0.12 0.05 0.1 a [μm] 48 19 19 a [μm] 48 19 19 Polish Grinding e e F400, Polyurethane bond 100 10

vc = 30 m/s 80 8 Fine Grinding 60 6 IT5

F400, vitrified [-] IT 40 α 4 Quality vc = 30 m/s F

Material Ratio 20 2

Rmr (-0.15 µm) [%] 0 0

FigureFigure 4. 4. ResultsResults of of pre-grinding pre-grinding as as well well as as polish polish and and fine ﬁne grinding grinding with with a a feed feed variation.

AfterThe roughness pre-grinding, of the fine pre-ground grinding tooth investigations flanks for the were two carried grinding out tools with is comparablea vitrified grindingwith values worm of theand mean polish roughness grinding investigations depth of Rz ≈ with1 µm. a polyurethane For both of the bonded grinding grinding tools, worm,it is also each noted with that a grain the right size flank of F400. has aFor higher polish roughness grinding, than the thegrinding left flank. worm The specifica- material tionsratio with Rmr( a− grit0.15 sizeµm) of is F800 in the are range already of Rmr( used− 0.15as a µstandardm) = 28% [10]. for bothHowever, of the the pre-grinding grit sizes oftools. F800 The have profiles not yet of been the pre-ground tested in vitrified gears do grinding not deviate tools. between Therefore, the a grinding grit with tools the size and ofthe F400 quantified was chosen average in order total to profile analyze deviation the influence Fα is approximately of the bond system IT = 3although for both a tools. grit withBecause the size the grindingof F400 is worms relatively were large, dressed when in thecompared same way to the and standard profile as grit well size as for lead polish were corrected, these results were expected and they indicate that the initial situations for polish grinding. The cutting speed of vc = 30 m/s was kept constant during the tests. The axial and fine grinding were almost identical. feed fa was equally varied for both grinding worm specifications to fa = 0.05 mm and fa = 0.1 mm.After The pre-grinding, polish and fine fine grinding grinding were investigations carried out werein two carried strokes out with with radial a vitrified infeed grinding worm and polish grinding investigations with a polyurethane bonded grinding of ae = 19 μm each. The polish and fine grinding process were carried out with the same worm, each with a grain size of F400. For polish grinding, the grinding worm specifications grinding parameters in order to separate the influence of the bond system from other pos- with a grit size of F800 are already used as a standard [10]. However, the grit sizes of sible influences. F800 have not yet been tested in vitrified grinding tools. Therefore, a grit with the size Because of the fine dressing parameters, the roughness after pre-grinding for both of F400 was chosen in order to analyze the influence of the bond system although a grit used grinding tools with a grain size of F80 was in the range of a mean roughness depth with the size of F400 is relatively large, when compared to the standard grit size for polish of Rz = 1–1.2 μm and, thus, in the range of fine ground surfaces. These low surface rough- grinding. The cutting speed of v = 30 m/s was kept constant during the tests. The axial ness values were achieved, due toc the dressing process using a dressing disc and a high feed fa was equally varied for both grinding worm specifications to fa = 0.05 mm and fa = 0.1 mm. The polish and fine grinding were carried out in two strokes with radial infeed of ae = 19 µm each. The polish and fine grinding process were carried out with the same grinding parameters in order to separate the influence of the bond system from other possible influences. J. Manuf. Mater. Process. 2021, 5, 4 7 of 15

Because of the fine dressing parameters, the roughness after pre-grinding for both used grinding tools with a grain size of F80 was in the range of a mean roughness depth of Rz = 1–1.2 µm and, thus, in the range of fine ground surfaces. These low surface roughness values were achieved, due to the dressing process using a dressing disc and a high overlap ratio of Ud = 12. However, this dressing process took a long time. In addition, the fine structure of the grinding worm can reduce the cutting performance of the tool. They both negatively affect the productivity. By comparing the polish and fine ground with the pre-ground gears, it can be seen that the mean roughness depth of Rz = 1–1.2 µm after pre-grinding was reduced to a mean roughness depth of Rz = 0.6–0.8 µm. An influence of the feed rate used fa = 0.05 mm and fa = 0.1 mm is not recognizable. Furthermore, the results of the mean roughness depth do not directly indicate the bond system used. By analyzing the material ratio Rmr(−0.15 µm), no increase in the material ratio Rmr(−0.15 µm) can be determined for the polish ground gears as compared to the pre-ground gears. In contrast, an increase in the material ratio of the fine ground gears from Rmr(−0.15 µm) = 28% after pre-grinding to Rmr(−0.15 µm) = 40–50% can be detected, whereby the fine grinding process with an axial feed of fa = 0.05 mm led to a higher material ratio. The comparison highlights the advantage of a vitrified worm with a grain size of F400 for increasing the material ratio and, thus, the contact ratio of the tooth flank with the used set of parameters. The difference in roughness between the left and right flank after pre-grinding can result from the kinematics during generating gear grinding, since the contact conditions between the worm thread of the leading and trailing flank are different. The dressing process can be used as a further explanation for the slightly higher roughness of the right flank. During the dressing of −1 the grinding worm, the dressing tool rotates at a constant speed of nd = 5000 min and a constant rotational direction. Consequently, the dressing process alternates between counter-rotating and synchronized dressing. This can lead to different topographies of the left and right flanks. In addition, the left and right grinding worm flanks are dressed with different radii of the dressing tool, which can also lead to this slight difference in roughness. Furthermore, the elasticity of the polish grinding worm can lead to geometric deviations during dressing, which was also shown for elastic diamond grinding tools [21]. Based on the evaluations of the mean roughness depth Rz that are presented in Figure4, only a slight correlation can be found between the polish respective fine grinding parameters and mean roughness depth. However, the correlation is in the range of the scatter of the roughness values and, therefore, not clearly detectable. In the polish grinding of surfaces, the peaks of the roughness profile are typically removed and, thus, the surface is smoothened. The resulting surfaces are characterized by a high material radio Rmr(c) at small distances c [10]. This tendency cannot be observed for the examined polish ground gears. The reason for this might be the relatively large grain size of F400 for polish grinding. With those grains, some roughness peaks might be removed, but relatively large grains can cause new, deep grinding scratches, which results in new roughness peaks. Because of the elasticity of the bond, the polish grinding worm can cause a wavy roughness, which can result in a low material ratio. In further investigations, therefore, a finer grain size of F800 will be used to test whether the expected effect occurs or the polish grinding parameters have to be changed to machine only the roughness peaks and avoid too much material removal. The profiles and the profile qualities Fα are compared on the right side of Figure4 in order to visualize the gear quality achieved by polish and fine grinding. In case of the fine ground gears, for both axial feeds fa = 0.05 mm and fa = 0.1 mm, no change in the profile can be determined visually, but the measured quality Fα becomes slightly better when compared to the pre-ground gears. The profile of the polish ground gear deviates significantly from the pre-ground and fine ground profile. This can also be seen in the decreasing profile quality Fα up to an IT value of IT = 8. The significant loss of gear quality when compared to pre-grinding can be caused by a different contact pressure between grinding worm and tooth flank over the tooth height. Furthermore, the grinding J. Manuf. Mater. Process. 2021, 5, 4 8 of 15

worm can expand due to the centrifugal force that is caused by the rotational speed of −1 n0 = 2100 min to reach the cutting speed vc = 30 m/s. The grinding worm expands until it is restricted from expanding by the teeth with which the worm is in contact. This effect has already been observed by WAGNER for profile gear grinding [10]. According to WAGNER, the systematic deviations of the flank profile can be compensated by means of time and material consuming corrections. The increase in the material ratio after fine grinding can be attributed to the significantly finer grain size when compared to pre-grinding. By using a comparable vitrified bond, after fine grinding a surface that is similar to the pre-ground surface is produced. Because of the finer grain size in a rigid vitrified bond, the resulting surface structure is also finer, which can be measured with the help of the material ratio. The slightly positive influence on the gear quality allows for the conclusion that the grinding worm is not, or is only slightly, elastically deformed in contact with the gear and thus the set nominal geometry of the gear is achieved. In polish grinding, the significant negative influence on gear quality is caused by the selected disadvantageous parameters for the elastic polyurethane bond. The parameters used were the equal for both polish and fine grinding worm to expose the influence of the bond. However, in the tests to determine a process strategy that is suitable for each of the grinding worm specifications, process parameters were chosen to avoid a negative influence on the profile. Furthermore, the used dressing tool led to very high and unacceptable dressing times; therefore, the use of an industrial standard dressing tool will be investigated in the following.

3.2. Determination of Process Strategy Further tests had to be carried out in order to determine a suitable process strategy for both polish and fine grinding process. The process strategy had to be adjusted particularly for the polish grinding process due to the negative influence of the elastic bonded polish grinding worm. In the first tests, a dressing disc was used. This led to high dressing process times. In industrial applications, two-flank profile dressing tools are commonly used in order to minimize the dressing process times. Furthermore, the pre-ground roughness was significantly lower than that commonly achieved in industrial grinding. In order to determine the dressing tool influence, the same gear geometry was ground with the same grinding worms and with the same grinding parameters as in the first tests.

3.2.1. Dressing Tool Technology Influence on the Pre-Ground Roughness In the following, the influence of different dressing tool technologies is analyzed by means of the achieved roughness after pre-grinding, as well as the pre-ground profile and lead. The roughness after pre-grinding with a grain size of F80 is evaluated by means of the mean roughness depth Rz and the arithmetic mean roughness Ra, left side of Figure5 . After pre-grinding with the conventional grinding worm with a grain size of F80 dressed with a dressing disc, the roughness is approximately Rz = 1 µm, respectively, Ra = 0.13 µm. By using an industry standard two-flank profile dressing tool with industry standard dressing parameters, the roughness is approximately Rz = 1.9 µm, respectively, Ra = 0.29 µm. On the right side of Figure5, the profile and lead of the left and right flanks of two pre-ground gears are shown. The profile and lead correspond to the specifications of the technical drawing. The visible lead angle deviation is part of a modification of the gear used and, therefore, is not an error. J. Manuf. Mater. Process. 2021, 5, x FOR PEER REVIEW 9 of 15

J. Manuf. Mater. Process. 2021, 5, 4 9 of 15 profile dressing tool to achieve a low roughness might not yet be fully exploited with the industrial standard dressing parameters.

Gear Data Pre-Ground Roughness Pre-Ground Profile and Lead mn = 1.76 mm 3 60.7 z= 26 58.9 α = 15° n 2 56.7 β = 33.75° Pre-Grinding 1 Profile F80, vitrified Depth Rz [µm] Diameter [mm] Diameter Mean Roughness 52.8 vc = 63 m/s 0 60 µm fa = 0.12 mm Dress. Tool Disc Profile Δs = 15 μm Fine Grinding Tool Polish Grinding Tool Ud [-] 12 - -1 Left Right Left Right Polish Grinding qd [min ] 36 18 60 µm F400, Polyurethane bond 0.40,4 left flank 33 right flank 0.30,3 Fine Grinding 0.20,2

Lead 17.5 F400, vitrified Ra [mm] 0.10,1 left flank Roughness Face Width [mm] Face right flank Arithmetic Mean 0 2

Figure 5.5. Results of pre-grinding withwith differentdifferent dressingdressing tooltool technologies.technologies.

3.2.2.To Influence conclude, of the the Used results Dressing of pre-grinding Tool Technology can be for summarized, Polish and Fine where Grinding the selected dressingAfter tools determining had neither the a influence positive norof the a negative dressing influence tool on the on thepre-grinding workpiece roughness, geometry. However,the two-flank the dressing used dressing tool is parameters subsequently and used. use ofThe a two-flankfurther investigations profile dressing will follow tool led a tomore a roughness industrial that process was strategy. approximately In the twiceprevious as high investigations, as when using the gear a dressing profile discwas withneg- anative overlap influenced. ratio of In U and = industrial 12. Nevertheless, application, the timethis negative that is required influence for is a singlenot acceptable. dressing processTherefore, with it will the dressingbe ensured disc that was the approximately profile of the gear td,disc is =not 120 negatively min, whereas influenced the dressing during process with the two-flank profile dressing tool took only approximately t = 5 min. polish or fine grinding. In addition, in industrial grinding processes, higherd,profile cutting speeds The use of a dressing disc is preferred, but not recommended from an economic point of are used in order increase the productivity. Therefore, the influence of cutting speed has view, in order to achieve a very low roughness. However, the full potential of the two-flank to be vc = 63 m/s in order to correspond more to an industrial process strategy. profile dressing tool to achieve a low roughness might not yet be fully exploited with the In the previous tests, the profile was negatively affected. This could be explained by industrial standard dressing parameters. the elasticity and the resulting expansion of the grinding worm. For this reason, the first 3.2.2.step of Influence the polish of grinding the Used tests Dressing is to verify Tool Technology the initial machine for Polish infeed and Fineposition Grinding ae,Initial-Contact, where the grinding worm and gear have the first contact. In order to find the initial con- After determining the influence of the dressing tool on the pre-grinding roughness, tact, first, all of the gear was pre-ground. The second step was to paint the gear in order the two-flank dressing tool is subsequently used. The further investigations will follow to make the contact between the grinding worm and the gear visible. Afterwards, the first a more industrial process strategy. In the previous investigations, the gear profile was set infeed of the grinding worm was e.g., ae = −80 μm. At this distance, no material was negative influenced. In an industrial application, this negative influence is not acceptable. Therefore,removed. Further, it will be the ensured infeed that was the set profileto a lower of the infeed. gear isWhen not negativelythe grinding influenced worm removed during polishsome of or the fine paint, grinding. the infeed In addition, of the in initial industrial contact grinding was found, processes, e.g., higherae,Initial-Contact cutting = − speeds60 μm. areStarting used from in order this increase initial contact, the productivity. the machine Therefore, infeed theis successively influence of cuttingincreased. speed The has gear to quality is systematically checked. Thus, in polish grinding, the infeed Δae is relative to the be vc = 63 m/s in order to correspond more to an industrial process strategy. initialIn contact, the previous as in Equation tests, the (1). profile was negatively affected. This could be explained by

the elasticity and the resulting expansionΔae = ae,Polish of the − a grindinge,Initial-Contact worm. For this reason, the first(1) step of the polish grinding tests is to verify the initial machine infeed position ae,Initial-Contact, whereBecause the grinding the vitrified worm andfine geargrinding have theworm first is contact. assumed In to order be stiff, to find the the initial initial contact contact, of first,the fine all grinding of the gear worm was and pre-ground. gear is at Theae,Initial-Contact second = step 0 μm. was Therefore, to paint thein fine gear grinding, in order the to makeinfeed the ae is contact equal to between the relative the grinding infeed Δ wormae. and the gear visible. Afterwards, the first set infeedAfter ofthe the gears grinding were pre-ground, worm was e.g., the ainitiale = − 80contactµm. Atwas this determined. distance, noFrom material this initial was removed.contact, the Further, infeed thewas infeed successively was set increased. to a lower Figure infeed. 6 When shows the the grinding measurement worm results removed of somepolish of ground the paint, gears the with infeed a ofrelative the initial infeed contact of Δa wase = found,20 μm e.g.,and aΔe,Initial-Contactae = 40 μm. =A− relative60 µm. Startinginfeed of from Δae = this 20 μ initialm led contact,to a slight the decrease machine of infeedthe roughness, is successively but the increased. material ratio The is gear not qualityaffected. is With systematically an increasing checked. relative Thus, infeed in polish to of grinding, Δae = 40 the μm, infeed the roughness∆ae is relative decreases to the initialmore, contact,and the material as in Equation ratio increases (1). slightly. Because of the limitation of the test that the profile should not be influenced negatively, the profile, as well as the profile quality, are ∆ae = ae,Polish − ae,Initial-Contact (1)

J. Manuf. Mater. Process. 2021, 5, 4 10 of 15

Because the vitrified fine grinding worm is assumed to be stiff, the initial contact of the fine grinding worm and gear is at ae,Initial-Contact = 0 µm. Therefore, in fine grinding, the infeed ae is equal to the relative infeed ∆ae. After the gears were pre-ground, the initial contact was determined. From this initial contact, the infeed was successively increased. Figure6 shows the measurement results of polish ground gears with a relative infeed of ∆ae = 20 µm and ∆ae = 40 µm. A relative µ J. Manuf. Mater. Process. 2021, 5, x FORinfeed PEER REVIEW of ∆ae = 20 m led to a slight decrease of the roughness, but the material10 ratio of 15 is not affected. With an increasing relative infeed to of ∆ae = 40 µm, the roughness decreases more, and the material ratio increases slightly. Because of the limitation of the test that the profile should not be influenced negatively, the profile, as well as the profile quality, not affected by a relative infeed of Δae = 20 μm or by a relative infeed of Δae = 40 μm. In are not affected by a relative infeed of ∆ae = 20 µm or by a relative infeed of ∆ae = 40 µm. e conclusion,In conclusion, a higher a higher relative relative infeed infeed Δa ∆ canae can lead lead to a to lower a lower surface surface roughness roughness and and an in- an creasingincreasing material material ratio. ratio. However, However, the the high high re requirementsquirements on on the the gear gear geometry geometry set set a limit toto the the increase increase of the relative infeed Δ∆ae..

Gear Data Pre-Ground Variation Δae Pre-Ground Variation Δae m = 1.76 mm n 2,52.5 Left flank 60.7 z = 26 Right flank 58.9 α = 15° 2 n 56.7 β = 33.75° 1,51.5 Pre-Grinding 1 F80, vitrified 0,50.5 Depth Rz [µm] Diameter [mm] 52.8

v = 63 m/s Left Flank Profile

c Mean Roughness 0 60 µm fa = 0.12 mm Δs = 15 μm fa [mm] 0.12 0.1 0.1 fa [mm] 0.12 0.1 0.1 Polish Grinding Δae [μm] 48 20 40 Δae [μm] 48 20 40 F400, Polyurethane bond 100 10

vc = 30 m/s 80 8 f = 0.1 mm a 60 6 IT5 IT [-] IT

40 α 4 Quality F

Material Ratio Material 20 2 Rmr (-0.15 µm) [%] 0 0

Figure 6. TheThe results results of polish ground gears with different relative infeed.

BesidesBesides the constantconstant pre-grindingpre-grinding process process parameters, parameters, the the process process parameters, parameters, respec- re- spectively,tively, the processthe process strategy, strategy, was was only only adjusted adjusted for thefor polishthe polish grinding grinding process. process. Therefore, There- fore,the relative the relative infeed infeed was was set toset∆ toa eΔ=ae 40= 40µm μm for for polish polish grinding. grinding. TheThe finefine grinding pro- pro- cesscess was was kept kept constant constant compared compared to to the first first test with the dressing disc with an infeed of Δ∆aaee == 19 19 μµm.m. The The axial axial feed feed and and the cutting speed for both polish and fine fine grinding was setset to f a == 0.1 0.1 mm, mm, respectively, respectively, vc = 30 30 m/s. m/s. In In Figure Figure 7,7, the the results results of pre-ground, polish,polish, andand fine fine ground gears are shown. The The grinding worms were dressed with a two-flanktwo-flank dressingdressing tool with standard industrial dressingdressing parameters.parameters. After After pre-grinding with a graingrain size of F80, F80, the the mean mean roughness roughness depth is approximately Rz = 1.9 μµm and the material material ratioratio is approximately Rmr(Rmr(-0.15−0.15 μµm)m) = = 20%. 20%. The The profile profile is is within within the the tolerance and the worst measured profileprofile qualitiesqualities areare FFαα,left,left IT = 2 andand FFαα,right,right ITIT = = 4. 4. The The achieved mean roughnessroughness depth depth with with the polish grinding process is approximately Rz = 1.3 µμm. While usingusing fine fine grinding, a mean roughness depth of Rz = 1.1 μµm can be achieved. The material ratioratio Rmr(-0.15 Rmr(−0.15 μµm)m) is is only only slightly slightly increased increased by by the the use use of of polish polish or or fine fine grinding grinding process process asas compared compared to to the the pre-ground pre-ground gears. gears. The The profile profile and and profile profile quality quality are not are affected not affected neg- ativelynegatively by fine by fineor by or polishing by polishing grinding. grinding. Theref Therefore,ore, the profiles the profiles are almost are almost identical identical to the pre-groundto the pre-ground variant variant and quality and qualityFα changes Fα changes to IT = 3 to for IT both = 3for the both polish the and polish fineand ground fine gears.ground gears. Because of the two-flank profile dressing tool, the roughness of the pre-ground gears is quite high when compared to the tests with a dressing disc. With the subsequent fine grinding process, the roughness in terms of the mean roughness depth and the material ratio is only slightly reduced. Because the same dressing parameters are used for the vitrified pre-grinding and the vitrified fine grinding section, not only is the pre-grinding area dressed rougher, but also the fine grinding area. This leads to a higher roughness after pre-grinding and after fine grinding. For the grinding worm with the elastic bonded polish grinding section, the same dressing parameters were used and, thus, the roughness was reduced to approximately the same mean roughness depth with the polish grinding process as with the fine grinding process. Because the profile has not been affected negatively, the selected procedure for polish grinding can be considered to be suitable. The cutting should be increased to an industrial standard cutting speed of vc = 63 m/s, because, in the first tests, and in the tests with the changed dressing tool, a cutting speed

J. Manuf. Mater. Process. 2021, 5, x FOR PEER REVIEW 11 of 15

of vc = 30 m/s was used. Following, the influence of the cutting speed for fine and polish grinding has to be analyzed with respect to the gained knowledge. Therefore, gears fine J. Manuf. Mater. Process. 2021, 5, 4 11 of 15 and polish ground with these two cutting speeds are investigated by means of the roughness and achieved profile quality.

Gear Data Pre-Ground Worm Variation Pre-Ground Worm Variation m = 1.76 mm n 2,52.5 Left flank 60.7 z = 26 Right flank 58.9 α = 15° 2 n 56.7 β = 33.75° 1,51.5 Pre-Grinding 1 F80, vitrified 0,50.5 Depth Rz [µm] Diameter [mm] 52.8

v = 63 m/s Left Flank Profile

c Mean Roughness 0 60 µm fa = 0.12 mm Δs = 15 μm fa [mm] 0.12 0.1 0.1 fa [mm] 0.12 0.1 0.1 Polish Grinding Δae [μm] 48 40 19 Δae [μm] 48 40 19 F400, Polyurethane bond 100 10

vc = 30 m/s 80 8 Fine Grinding 60 6 IT5

F400, vitrified [-] IT 40 α 4 Quality vc = 30 m/s F

Material Ratio 20 2

Rmr (-0.15 µm) [%] 0 0

Figure 7. ResultsResults of polish and fine fine grinding wi withth a two-flank two-flank profileprofile dressing tool.

3.2.3.Because Cutting ofSpeed the two-flank Influence profile dressing tool, the roughness of the pre-ground gears is quiteIn the high first when test compared series with to the the dressing tests with disc, a dressing the cutting disc. speed With thefor subsequentpolish and finefine grinding process, the roughness in terms of the mean roughness depth and the material grinding was set to vc = 30 m/s. In the tests with the industrial standard dressing tool, this cuttingratio is speed only slightly was kept reduced. constant. Because In industrial the same grinding dressing processes, parameters higher are cutting used forspeeds the arevitrified necessary pre-grinding in order andto increase the vitrified the producti fine grindingvity. Therefore, section, not the only cutting is the speed pre-grinding has to be area dressed rougher, but also the fine grinding area. This leads to a higher roughness after increased to an industrial standard of vc = 63 m/s, and the dressing tool was changed to anpre-grinding industrial andstandard after finetwo-flank grinding. profile For dressing the grinding tool. worm For this with reason, the elastic the influence bonded polishof the differentgrinding cutting section, speeds the same used dressing for polish parameters and fine weregrinding used on and, the thus,roughness, the roughness and the pro- was reduced to approximately the same mean roughness depth with the polish grinding process file quality has to be investigated. Therefore, gears are polished and fine ground with as with the fine grinding process. Because the profile has not been affected negatively, the grinding worms dressed with the used industrial standard dressing process. Because of selected procedure for polish grinding can be considered to be suitable. the different used cutting speeds and, therefore, the different rotational speeds, the defor- The cutting should be increased to an industrial standard cutting speed of v = 63 m/s, mation of the elastic polyurethane bonded grinding worm is also expected to bec different. because, in the first tests, and in the tests with the changed dressing tool, a cutting speed For this reason, the first step for the polish grinding process is to determine the infeed of of v = 30 m/s was used. Following, the influence of the cutting speed for fine and polish initialc contact between grinding worm and gear, according to Equation (1). Subsequently, grinding has to be analyzed with respect to the gained knowledge. Therefore, gears fine and the relative infeed is set to Δae = 40 μm while using the polish grinding worm for both polish ground with these two cutting speeds are investigated by means of the roughness cutting speeds. The relative infeed of the vitrified fine grinding worm equals the infeed, and achieved profile quality. and it is set to Δae = 19 μm for both cutting speeds. The results of the cutting speed varia- tion3.2.3. are Cutting compared Speed in InfluenceFigure 8 for both polish and fine grinding. In the first test series with the dressing disc, the cutting speed for polish and fine grinding was set to vc = 30 m/s. In the tests with the industrial standard dressing tool, this cutting speed was kept constant. In industrial grinding processes, higher cutting speeds are necessary in order to increase the productivity. Therefore, the cutting speed has to be increased to an industrial standard of vc = 63 m/s, and the dressing tool was changed to an industrial standard two-flank profile dressing tool. For this reason, the influence of the different cutting speeds used for polish and fine grinding on the roughness, and the profile quality has to be investigated. Therefore, gears are polished and fine ground with grinding worms dressed with the used industrial standard dressing process. Because of the different used cutting speeds and, therefore, the different rotational speeds, the deformation of the elastic polyurethane bonded grinding worm is also expected to be different. For this reason, the first step for the polish grinding process is to determine the infeed of initial contact between grinding worm and gear, according to Equation (1). Subsequently, the relative infeed is set to ∆ae = 40 µm while using the polish grinding worm for both cutting speeds. The relative infeed of the vitrified fine grinding worm equals the infeed, and it is

set to ∆ae = 19 µm for both cutting speeds. The results of the cutting speed variation are compared in Figure8 for both polish and ﬁne grinding. J. Manuf. Mater. Process. 2021, 5, 4x FOR PEER REVIEW 1212 of of 15

Gear Data Pre-Ground Variation vc Pre-Ground Variation vc m = 1.76 mm n 2,52.5 Left flank 60.7 z = 26 Right flank 58.9 α = 15° 2 n 56.7 β = 33.75° 1,51.5 Pre-Grinding 1 F80, vitrified 0,50.5 Depth RzDepth [µm] Diameter [mm] Diameter 52.8

v = 63 m/s Left Profile Flank

c Roughness Mean 0 60 µm fa = 0.12 mm Δs = 15 μm vc [m/s]6330 63 vc [m/s] 63 30 63 Polish Grinding F400, Polyurethane bond 100 10

Δae = 40 μm 80 8 f = 0.1 mm a 60 6 IT5

Fine Grinding [-] IT 40 α 4 Quality F400, vitrified F

Material Ratio Material 20 2 Δae = 19 μm

f = 0.1 mm Rmr (-0.15 µm) [%] a 0 0

Figure 8. Results of polish and fine ﬁne grinding with varied cutting speeds.

With a a cutting cutting speed speed of ofvc v= c30= m/s, 30 m/s,the mean the meanroughness roughness depth is depth reduced is reduced to Rz = 1.4 to μRzm =by 1.4 polishµm by grinding polish and grinding to Rz and= 1.1 to μm Rz by = fine 1.1 µgrinding.m by fine While grinding. using a While cutting using speed a ofcutting vc = 63 speed m/s for of vthec = polish 63 m/s and for fine the grinding, polish and a mean fine grinding, roughness a mean depth roughness of Rz = 1.1 depth μm can of beRz achieved, = 1.1 µm canbut bethe achieved, roughness but of the left roughness fine ground of left flank fine is ground Rz = 1.5 flank μm. isBy Rz analyzing = 1.5 µm. the By materialanalyzing ratio the Rmr(-0.15 material ratioμm), Rmr(with −a 0.15cuttingµm), speed with of a v cuttingc = 30 m/s, speed only of a vveryc = 30slight m/s, increase only a invery the slight material increase ratio in can the be material detected ratio when can co bempared detected to when the pre-ground compared togear the for pre-ground both the polishgear for and both fine the ground polish gears. and fine The ground use of gears.a cutting The speed use of of a cuttingvc = 63 speedm/s only of vresultsc = 63 m/sin a slightonlyresults increase in of a slightthe material increase ratio of theof the material fine ground ratio ofgear. the In fine cont groundrast, after gear. polish In contrast, grinding,after the polish material grinding, ratio theof Rmr(-0.15 material ratioμm) of= 40% Rmr(-0.15 is nearlyµm) twice = 40% as high is nearly as the twice material as high ratio as ofthe the material pre-ground ratio ofgear. the pre-groundThis can be gear.explained This candue be to explainedthe use of duean elastic to the usebond of for an polish elastic grinding.bond for polishEvery grinding.single grain Every is elastic single bonded. grain is Therefore, elastic bonded. the grains Therefore, can be the forced grains into can the be bondforced during into the the bond engagement during the and, engagement thus, the ac and,tive thus,grain the protrusion active grain can protrusionbe different can from be thedifferent vitrified from fine the grinding vitrified worm. fine grinding Another worm. explanation Another can explanation be that the can grain be that engagement the grain pathengagement with the path elastic with bond the elasticcan be bonddifferent can befrom different the vitrified from the grinding vitrified worm grinding due wormto the elasticity.due to the These elasticity. two Theseeffects two can effects also occur can also duri occurng the during dressing the dressingprocess, which process, can which have can an effecthave anon effectthe topography on the topography of the polish of the grinding polish grinding worm and, worm consequently, and, consequently, an effect an on effect the roughnesson the roughness of the polish of the polishground ground gear. The gear. profile The profile is neither is neither negatively negatively influenced influenced by any by ofany the of used the usedset of set parameters of parameters nor by nor the by grin theding grinding worms worms used. used.The quantified The quantified profile profile qual- quality becomes a little better by using a cutting speed of v = 30 m/s with both the polish ity becomes a little better by using a cutting speed of vc = 30c m/s with both the polish and fineand grinding. fine grinding. For both For bothprocesses, processes, polish polish and fine and grinding, fine grinding, the profile the profile quality quality is not isposi- not positively or negatively affected by using a cutting speed of vc = 63 m/s. tively or negatively affected by using a cutting speed of vc = 63 m/s. Because the the aim aim for for the the test test with with the the two-flank two-flank profile profile dressing dressing tool tool was was to to not not nega- nega- tively influence the gear quality, the results of the course of the profile and profile quality tively influence the gear quality, the results of the course of the profile and profile quality were to be expected. The influence of the polish and fine grinding on the roughness is were to be expected. The influence of the polish and fine grinding on the roughness is comparable to the first tests with the dressing disc. In both of the test series, the roughness comparable to the first tests with the dressing disc. In both of the test series, the roughness could be reduced to nearly half of the roughness of the corresponding pre-ground gears. could be reduced to nearly half of the roughness of the corresponding pre-ground gears. The only remarkable result is that the material ratio Rmr(−0.15 µm) was significantly The only remarkable result is that the material ratio Rmr(-0.15 μm) was significantly in- increased by polish grinding with a cutting speed of vc = 63 m/s. This can be explained creased by polish grinding with a cutting speed of vc = 63 m/s. This can be explained with with the use of an elastic bonded polish grinding tool. It was already shown that, with the use of an elastic bonded polish grinding tool. It was already shown that, with elastic elastic bonded polish grinding tools, only roughness peaks are machined [10]. Because of bonded polish grinding tools, only roughness peaks are machined [10]. Because of this, this, the peaks of the ground surface are flattened and, therefore, the material ratio in a the peaks of the ground surface are flattened and, therefore, the material ratio in a peak peak distance of c = 0.15 µm increases. distance of c = 0.15 μm increases. The results of the second test series to determine the process strategy are comparable toThe previous results investigations.of the second test In series a previous to determine investigation, the process a mean strategy roughness are comparable depth of toRz previous≤ 1.2 µm investigations.was achieved. In The a previous running investigation, tests of these gearsa mean have roughness shown adepth higher of wearRz ≤ 1.2resistance μm was and, achieved. therefore, The a higherrunning number tests of of thes loade cyclesgears thathave can shown be sustained a higher [17 wear]. resistance and, therefore, a higher number of load cycles that can be sustained [17].

J. Manuf. Mater. Process. 2021, 5, x FOR PEER REVIEW 13 of 15

4. Discussion and Conclusions The first test series was carried out in order to analyze the bond influence. The process parameters were kept constant to determine the influence of the used bond system independent from the process parameters or the grain size. As a result of this test series, the roughness could be reduced with both the polish and the fine grinding process. How- ever, the use of the elastic bonded grinding worm for polish grinding led to a significant

J. Manuf. Mater. Process. 2021, 5, 4 negative influence of the profile. During the second test series, it was mandatory that13 ofthe 15 gear profile should not be negatively influenced. Therefore, the procedure was changed. Because of the elasticity of the polish grinding worm, the worm can expand and, thus, can lead to too high material removal during polish grinding. Therefore, as a first step, the initial4. Discussion contact between and Conclusions the polish grinding worm and gear was determined. Subsequently, a relativeThe firstinfeed test of series Δae was= 40 carriedμm was out used in order for polish to analyze grinding. the bond With influence. this procedure, The process the profileparameters was not were negatively kept constant influenced. to determine the influence of the used bond system inde- pendentIn addition from the to process the results parameters shown, or the the roughness grain size. profilesAs a result of the of polish this test and series, the fine the groundroughness surfaces could shall be reduced be visually with examined. both the polish Figure and 9 shows the fine the grinding visual comparison process. However, of the roughnessthe use of the profiles elastic afte bondedr pre-, grinding polish, and worm fine for grinding. polish grinding The difference led to a between significant the negative rough- nessinfluence profiles of the is profile.shown by During the profile the second height tests series,along itthe was evaluation mandatory length, that the which gear nearly profile matchesshould not the be whole negatively gear profile influenced. length. Therefore, Furthermore, the procedure the Abbott was curve changed. is shown, Because corre- of spondingthe elasticity to each of the roughness polish grinding profile. worm, the worm can expand and, thus, can lead to too highThe material roughness removal profile during of the polish pre-ground grinding. su Therefore,rface has clearly as a first visible step, theroughness initial contact peaks andbetween valleys. the On polish the contrary, grinding the worm profile and height gear was of the determined. polish ground Subsequently, variant only a relative shows barelyinfeed visible of ∆ae =valleys 40 µm and was almost used for no polishclear ro grinding.ughness Withpeaks. this The procedure, roughness the profile profile of wasthe finenot negativelyground variant influenced. is similar in height to the height of the polish ground variant. How- ever, Inthe addition roughness to profile the results of the shown, fine ground the roughness variant shows profiles many of thesmall polish roughness and the peaks fine andground valleys. surfaces The Abbott shall be curve visually sums examined. up the percen Figuretage9 shows of material the visual in a certain comparison height ofof thethe profile. roughness Because profiles of this, after the pre-, Abbott polish, curves and of fine the grinding. roughness The profiles difference have a between high gradi- the entroughness at the beginning profiles isand shown end. In by the the middle profile sect heightsion of alongthe curve, the evaluationthe gradient length, is lower. which The lowestnearly gradient matches is the detectable whole gear for profilethe polish length. ground Furthermore, surface. the Abbott curve is shown, corresponding to each roughness profile.

FigureFigure 9. 9. RoughnessRoughness profiles proﬁles of pre-, poli polish,sh, and fine ﬁne ground gears.

ByThe comparing roughness the profile roughness of the pre-groundprofiles and surface the Abbott has clearlycurves visibleof the different roughness ground peaks and valleys. On the contrary, the profile height of the polish ground variant only shows surfaces, it becomes clear that the polish ground surface is the smoothest achieved surface. barely visible valleys and almost no clear roughness peaks. The roughness profile of the However, the structure after polish grinding does not yet fully have the expected plateau- fine ground variant is similar in height to the height of the polish ground variant. However, like shape. Therefore, further investigations will be made in order to determine whether the roughness profile of the fine ground variant shows many small roughness peaks and this can be achieved with a grinding tool with a grain size of F800. valleys. The Abbott curve sums up the percentage of material in a certain height of the profile. Because of this, the Abbott curves of the roughness profiles have a high gradient at the beginning and end. In the middle section of the curve, the gradient is lower. The lowest gradient is detectable for the polish ground surface. By comparing the roughness profiles and the Abbott curves of the different ground surfaces, it becomes clear that the polish ground surface is the smoothest achieved surface. However, the structure after polish grinding does not yet fully have the expected plateau- like shape. Therefore, further investigations will be made in order to determine whether this can be achieved with a grinding tool with a grain size of F800. The presented results give a further understanding of the processes of fine and polish grinding of gears. Both of the processes are designed to reduce the roughness of gear flanks J. Manuf. Mater. Process. 2021, 5, 4 14 of 15

in order to improve the load-carrying capacity. From the knowledge gained by using an automotive pinion shaft and a process commonly used in the automotive production for the investigations, the automotive branch can especially benefit from the investigation presented. However, other branches where fine or polish ground gears are needed can benefit from these investigations. Furthermore, the results can be transferred to other grinding processes as surface of cutting tool grinding processes.

5. Summary and Outlook Because of the constantly increasing performance requirements of gears, hard fine machining of gears is necessary in many cases to correct the deviations from the gear hobbing process and heat treatment. One of the established processes for hard fine machining is continuous generating gear grinding. The reduction of the tooth flank roughness by means of grinding increases the load-carrying capacity of the tooth flank. The often required roughness of Rz < 1 µm can, in many cases, not be achieved with conventional vitrified corundum grinding tools. Therefore, gears are increasingly super finished after hard finishing. Chemically supported vibratory grinding and polish grinding with elastic bonded tools are used for super finishing. However, in order to avoid the use of a further process, such as vibratory grinding or polishing with elastic bonded tools, the objective of this report was to analyze the potential of fine grinding with vitrified grinding tools as compared to polish grinding with elastic bonds. Grinding tests were carried out on identically pre-ground gears in order to determine the potential of fine grinding compared to polish grinding. The same grain size of F400 was used for both polish and fine grinding to minimize the influence of the grain size used. Furthermore, two test series were carried out. One test series with the same grinding parameters for both grinding tools and a dressing disc for a fine dressing process. With the polish and fine grinding process, the tooth flank roughness could be reduced to nearly the same values. A dependence of the tooth flank condition on the selected grinding parameters could not be determined. The material ratio could be increased in all of the test points during fine grinding at the examined distances when compared to pre-grinding. An increase of the material ratio could not be achieved with polish grinding. However, it could be determined that the profile geometry after polish grinding significantly deviates from the preset values if no significant corrections are applied. In contrast, a slight improvement in the achieved gear quality could be determined for fine ground gears. The second test series was carried out with an industrial standard dressing tool and the restriction that the gear profile should not be negatively influenced. Because of the restrictions, one result of this test series was that the gear geometry was not negatively influenced. In contrast, the roughness after pre-grinding was significantly higher when compared to the first test series, due to the used two-flank profile dressing tool and industrial standard dressing parameters. An increase of the cutting speed to an industrial standard cutting speed led to a significant increase of the material ratio of the polish ground gear. In future, the investigations should be continued in order to determine the influence of the grain size in both fine and polish grinding. Grit sizes of F800 have already been used in earlier investigations on polish grinding. Therefore, the presented investigations should also be carried out with a finer grain size in order to achieve a further increase in the surface quality. In addition, the potential of the dressing process with a two-flank profile dressing tool to achieve a lower roughness by means of the dressing parameters should be investigated.

Author Contributions: Funding acquisition, T.B., J.B., M.S.; Investigation, M.S.; Project administra- tion, J.B.; Writing—original draft, M.S.; Writing—review & editing, J.B., M.S. All authors have read and agreed to the published version of the manuscript. Funding: This research was ﬁnancially supported by the WZL Gear Research Circle. J. Manuf. Mater. Process. 2021, 5, 4 15 of 15

Data Availability Statement: The data presented in this study are available on request from the corresponding author. The data are not publicly available due to confidential information of an industry collaborator. Conflicts of Interest: The authors declare no conflict of interest.

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