"Machining with geometrically undefined Cutting Edges Surface and"
Chair of Manufacturing Technology Machining with geometrically undefined Cutting Edges – Surface and Cylindrical Grinding Manufacturing Technology I Exercise 9 Laboratory for Machine Tools and Production Engineering Chair of Manufacturing Technology Prof. Dr.-Ing. Dr.-Ing. E.h. F. Klocke Machining with geometrically undefined Cutting Edges Table of Contents Table of Contents ......................................................................................................2 Symbols, Units, Terms ..............................................................................................3 1 Process options ..................................................................................................4 2 Surface circumferential plunge grinding a rectangular groove ......................7 3 Surface circumferential plunge grinding a V-shaped groove .........................8 4 External cylindrical circumferential crosswise grinding ...............................10 5 External cylindrical circumferential traverse grinding ..................................11 Manufacturing Techgnology I – Exercise 9 2 Machining with geometrically undefined Cutting Edges Symbols, Units, Terms Index a axial Axialrichtung c cutting Schnitt d dressing Abrichten f feed Vorschub V’w n normal Normalenrichtung r radial Radialrichtung R roller Rotierendes Abrichtwerkzeug s grinding wheel Schleifscheibe t tangential Tangentialrichtung w workpiece Werkstück Symbols b mm width Breite d mm diameter Durchmesser f mm feed Vorschub F N force Kraft l mm length Länge n min-1 no. of revolutions Drehzahl Q mm³/s material removal rate Zeitspanungsvolumen t s time Zeit U overlap ratio Überdeckungsgrad v m/s, velocity Geschwindigkeit mm/min V mm³ material removal Zerspanungsvolumen q speed ratio Geschwindigkeitsquotient F’ ·mm-1 specific value (per mm Bezogene Größe (pro mm V’ grinding wheel width) Schleifscheibenbreite) Q’ Further: ae µm depth of cut Zustellung, Schnitttiefe ap µm width of cut Eingriffsbreite ∆rs µm radial wear Radialverschleiß Manufacturing Techgnology I – Exercise 9 3 Machining with geometrically undefined Cutting Edges 1 Process options cylindrical external surface rotary internal between centers centerless bs circum- ap ferential vs vw crosswise vr grinding vfr bs circum- ap ferential vs vw traverse vr grinding vfa face crosswise grinding face traverse grinding Vw Material removal rate Q w = (1) tc Qw V' Specific material removal rate Q' w = = w (2) b seff tc If ap = bseff, then: Qw = ae· ap ·vw (3) Q’w = ae · vw (4) Manufacturing Techgnology I – Exercise 9 4 Machining with geometrically undefined Cutting Edges cylindrical external internal surface z = dw0 - dwend z = dwmax - dwmin between centers centerless Qw = vw•ap•ae Qw = vw•ap•ae Qw = vw•ap•ae Qw = vw•ap•ae = π•dw•vfr •ap = ½ π•dw•vfr•bs = π•dw •vfr•ap circum- ferential Q‘w = ae • vw Q‘w= ae • vw Q‘w = ae • vw Q‘w = ae • vw crosswise = π•dw•vfr = ½ π•dw•vfr = π•dw•vfr grinding vfr = ae•nw vfr = 2ae•nw vfr = ae•nw ap = bs= bs eff ap = bs= bs eff ap = bs= bs eff ap = bs= bs eff no slippage: vw = vr Qw = π•dw•vfa•ae Qw = π•dw•vfa•ae Qw = π•dw•vfa•ae Qw= vw•ap•ae = vfa = ap•nw vfa = ap•nw vfa = ap•nw ap = bs eff ap =bs eff ap = bs eff cylindrical no slippage : cylindrical grinding wheel: vw = vr • cosαr grinding wheel : ap= bs eff vfa = vr • sinαr Q‘w = z/2 • vw Q‘w = z/2 • vw bs bs ae ae z/2 z/2 circum- af af ferential traverse conical grinding conical grinding conical grinding grinding wheel: wheel : wheel : Q‘w = ap •tanα •vw Q‘w = ½ a p •tanα •vw Q‘w = ap •tanα •vw bs bs bs bss bsa bss bsa bss bsa ap ap ap z/2 z/2 z α α α 2ae ae ae a e z/2 2a e z a e z/2 tan α = = tan α = = tan α = = ap b ss ap b ss ap b ss In peripheral plunge grinding the depth of cut ae is not the same as the total depth of cut like in traverse or surface grinding. It has to be calculated for each workpiece revolution (formula (5)). Between centres v fr = a e ⋅ n w (5) Manufacturing Techgnology I – Exercise 9 5 Machining with geometrically undefined Cutting Edges Centerless grinding like grinding between centers nr nr control wheel control wheel nw nw grinding wheel grinding wheel ns ns vfr vfr 2ae workpiece grinding wheel grinding wheel in-feed in-feed control work wheel ae rest blade v fr = 2 ⋅ a e ⋅ n w v fr = a e ⋅ n w Fig. 1 Centerless plunge cut grinding In centerless crosswise grinding (plunge grinding) the workpiece will act like in grind- ing between centres, if it lies on shoulders which are not ground (Fig. 1 right). If it lies on its circumference, the feed rate vfr will directly operate on the diameter, not on the radius (with fixed regulating or grinding wheel) (Fig. 1 left). Then formula (6) is essential. Centerless v fr = 2 ⋅ ae ⋅ nw (6) The cut of depth ae differs from the radial total allowance z in the cylindrical cross- wise grinding processes! The speed ratio q is defined as quotient of grinding wheel speed and workpiece speed (formula (7)). It is an important parameter of the chip formation. When the speed vectors point to the same direction in the machining area, the grinding process is called down-grinding and the speed ratio q is positive. In up-grinding the speed vectors are directed contrary and q is negative. vs q=± (7) vw Manufacturing Techgnology I – Exercise 9 6 Machining with geometrically undefined Cutting Edges 2 Surface circumferential plunge grinding a rectangular groove Up to now the groove shown in Fig. 2 has been produced in a pendulum grinding process with a specific material removal rate of Q’w = 10 mm³/mms. Now the intention is to switch to a creep feed grinding operation, in which the entire volume of material is machined in one stroke. If Q’w remains constant, which work- piece speed vw is taken? 10 Fig. 2 Workpiece with groove Explain, why the pendulum grinding process takes more time in total than the creep feed grinding process with the same material removal Vw. Manufacturing Techgnology I – Exercise 9 7 Machining with geometrically undefined Cutting Edges 3 Surface circumferential plunge grinding a V-shaped groove A V-shaped groove with a width b and height h is to be produced (Fig. 3). The groove was pre-milled from a solid rectangular material to an allowance of 180 µm (orthogonal to the surface to be produced in each case). In a second step, the part is to be finished in a surface profile grinding operation in one machining stroke. The dimensional fault of the ground profile in y-direction allowed is ∆y = 50 µm. Y Grinding wheel Z b l = 1500 mm α h 180 µm Workpiece: cross view Workpiece: length view Fig. 3 Machining a pre-machined groove (drawing not scaled!) Information provided: Workpiece material: 100Cr6 Length of workpiece: lw = 1500 mm Allowance: A = 0.18 mm Workpiece feed speed: vw = 3000 mm/min Helix angle of the groove: α = 53° Max. dimensional fault in y-direction: ∆y = 50 µm Cutting speed: vc = 45 m/s Grinding wheel diameter: ds = 400 mm Manufacturing Techgnology I – Exercise 9 8 Machining with geometrically undefined Cutting Edges Is it possible to meet the requirements specified in terms of dimensional accuracy in the profile grinding process described? (Use Fig. 4 for your solution). 100 ∆ rs Q'w = 20 mm³/mms radial grinding wheel wear µm Q'w = 15 mm³/mms 60 Q'w = 12 mm³/mms Q'w = 8,5 mm³/mms 40 300 450 mm³/mm 750 Spec. material removal V'w Fig. 4 Dependence of radial grinding wheel wear on specific material removal V’w and on specific material removal rate Q‘w Manufacturing Techgnology I – Exercise 9 9 Machining with geometrically undefined Cutting Edges Which options do you have to reduce the grinding wheel wear? 4 External cylindrical circumferential crosswise grinding You have to set-up an external cylindrical plunge grinding process between centers for a hydraulic piston. Because you have to react very quickly, no procedures which need time-consuming set-up or preliminary tests are possible. You have to achieve the demanded workpiece quality and grinding time by a clever variation of machine parameters. Fig. 5 Hydraulic piston Boundary conditions and requirements: Workpiece diameter before grinding dw0 = 50.3 mm Process control One cycle Demanded roughness Rz ≤ 1.3 µm Demanded grinding time ts ≤ 12 s Determine a suitable cutting speed vc and specific material removal rate Q’w with the following chart (Fig. 6). Calculate the grinding time ts! Manufacturing Techgnology I – Exercise 9 10 Machining with geometrically undefined Cutting Edges Specific material removal rate Q’w [mm³/mms] Cutting speed vc [m/s] 1 1.5 2 30 Rz ≤ 1.2 µm Rz ≤ 1.8 µm Rz ≤ 2.1µm 45 Rz ≤ 0.9 µm Rz ≤ 1.7 µm Rz ≤ 1.9 µm 70 Rz ≤ 0.6 µm Rz ≤ 0.9 µm Rz ≤ 1.2 µm Fig. 6 Known process settings 5 External cylindrical circumferential traverse grinding The external cylindrical traverse grinding technique is used to machine a bearing sur- face of a spindle rotor. A conical grinding wheel is used (Fig. 7), which conducts the roughing operation and the sparking out in one travel. Whilst the majority of the ma- terial removal occurs in the conical grinding zone bSS, the cylindrical part of the grind- ing wheel bSA is used for sparking out. Workpiece material: 16MnCr5, 53 HRC Mean workpiece diameter: dw = 80 mm Rotational speed of workpiece: nw = 27 min-1 Cutting speed: vc = 105 m/s Width of the spark-out zone: bSA = 4 mm Feed: fa = 1 mm Profile angle: α = 10° Manufacturing Techgnology I – Exercise 9 11 Machining with geometrically undefined Cutting Edges bS bSS bSA vfa ae α ap ap nw Q'W I II III Fig. 7 Engagement conditions in an traverse grinding operation by use of a conically dressed grinding wheel The conical roughing zone results in a characteristic curve of the specific material removal rate Q’w along the width of the wheel. Sketch the qualitative progression of Q’w in areas I to III in Fig. 7 and calculate the value of Q’w for area II. Manufacturing Techgnology I – Exercise 9 12