Machining with geometrically undefined Cutting Edges Surface and by sanmelody

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									                    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

								
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