A Novel artifact for evaluating accuracies of gear profile and pitch measurements of gear measuring instruments

Transcription

1 A Novel artfact for evaluatng accuraces of gear profle and ptch measurements of gear measurng nstruments Sonko Osawa, Osamu Sato, Yohan Kondo, Toshyuk Takatsuj (NMIJ/AIST) Masaharu Komor (Kyoto Unversty)

2 Contents Background DBA used for evaluaton of GMIs on the gear profle measurement capablty Two types of MBAs for evaluaton of GMIs on the gear ptch measurement capablty Characterstcs Calbraton method Evaluaton of gear measurng nstruments usng calbrated MBA Summares

3 Background Requrements: reducton of nose and vbraton Test for the gear profle, lead, ptch, etc. Gear measurng nstrument (GMI) The nose and vbraton form the gears are caused by the form devaton n mcro meter level of gears. Therefore, the requrement of the gear form devaton s sub mcrometer level. Capabltes of GMIs are mostly evaluated by measurng a calbrated gear artfact Dffcult to manufacture wth hgh accuracy We propose new concept artfacts used smple geometres

4 Gear artfacts Introducton Proposed artfacts NMIJ: U 95 Profle:.6 µm Smple geometres U 95 Profle:.3 µm Profle artfact Ball Cylnder Plane Helx artfact Ptch artfact Profle (DBA) Ptch (MBA) Helx (WA) Dffcult to manufacture the artfact wth hgh accuracy Easy to manufacture the artfact wth hgh accuracy The Am of New artfacts s to calbrate the gear measurng nstrument at shop floor wth a mnmum uncertanty.

5 Advantages of usng smple geometres Form devaton s smaller than that of gear Smooth surface (small roughness) Easy to manufacture wth good qualty Form and dameter are calbrated wth small uncertantes Easy to assemble dfferent sze artfact Inexpensve

6 Introducton Contents DBA used for evaluaton of GMIs on the gear profle measurement capablty Two types of MBAs for evaluaton of GMIs on the gear ptch measurement capablty Characterstcs Calbraton method Evaluaton of gear measurng nstruments usng calbrated MBA Summares

7 Double Ball Artfact (DBA) Use for evaluatng GMI s capablty of a profle measurement Reference axs s used as a center axs of gear Form checkng ball s used as a tooth form Cross-secton of the DBA Form checkng ball Centerng ball Datum plane Started from fy Sprng Reference axs Prototype of DBA

8 Prncple of profle evaluaton stylus X Involute curve M M Involute curve Base crcle r b M Y Involute curve: can be expressed mathematcally. O DBA measurement However, manufacturng deal nvolute s dffcult. Involute and arc (a part of crcle) are smlar. The dfference can be expressed mathematcally. Therefore, arc can be used nstead of nvolute.

9 Tooth form devaton [µm] Calculated value - measurement [µm] Example of evaluaton result Roll angle [deg] Dfference between two curves after fttng (rght scale) Calculated curve (left scale) Measured curve (left scale) Detals: ISO/TR 164-5

10 Introducton Contents DBA used for evaluaton of GMIs on the gear profle measurement capablty Two types of MBAs for evaluaton of GMIs on the gear ptch measurement capablty Characterstcs Calbraton method Evaluaton of gear measurng nstruments usng calbrated MBA Summares

11 Ptch artfact usng balls Expand the DBA method to ptch evaluaton

12 How to assume as a gear The centerng ball s used to set the reference axs assumed as the center axs of a gear The reference axs s perpendcular to the datum plane and passes through the center of the centerng ball The ptch balls are used nstead of gear teeth Ptch ball Measurement plane Centerng ball Datum plane Sprng Reference axs

13 Ptch artfacts (Mult Ball Artfacts) Combnaton type Separaton type (low cost) Separaton type (envronment robust)

14 Combnaton type Glass plate Ptch ball Cylnder: reference axs Advantages: Smple prncple Easy to assemble Many combnatons are avalable Calbraton s not necessary deally Combnaton type MBA Spheres are fxed by magnetc force. It s mpossble to assemble a MBA wth perfect ptch angle. Makng a gap dsadvantage: Combnatons not apply for steel stylus

15 Repeatablty of cumlatve ptch devaton[m] Repeatablty of sngle ptch devaton[m] Stabltes of combnaton type MBA Reproducblty of 5 tmes assembles Number Repeatablty of sngle ptch devaton Number Repeatablty of cumulatve ptch devaton

16 Centerng ball Ptch ball Curvc couplng Low cost type Ptch ball Datum plane Separaton type Datum plane Centerng ball Envronment robust type Ptch angles are defned by a curvc couplng. Advantages: Inexpensve Easy to manufacture Calbraton s not necessary (ptch angles are defned by those of a curvc couplng) Dsadvantages: Stablty? (Balls are fxed by glue) Base plane s made of a zero expanson ceramcs (NEXCERA). Advantage: Envronment robust Dsadvantage: Calbraton s necessary Expensve

17 Introducton Contents DBA used for evaluaton of GMIs on the gear profle measurement capablty Three types of MBAs for evaluaton of GMIs on the gear ptch measurement capablty Characterstcs Calbraton method Evaluaton of gear measurng nstruments usng calbrated MBA Summares

18 Ptch angle calbraton MBA Probng system of CMM MBA Probng system of GMI Index table Calbraton by a CMM Calbraton by a GMI

19 Multple-orentaton technque Ths method elmnate the systematc errors of an nstrument Geometrcal error, probng error, etc f j = Frst orentaton j m j 1 ( j 1,,, m) Second orentaton where j: orentaton number m:total number of orentatons

20 Dfference [mm] [µm] Dfference [mm] [µm] Ptch calbraton results (usng a CMM and two GMIs) GMI-I NMIJ GMI-II NMIJ Uncertanty of NMIJ 1,,8,6,4,, -, -,4 -,6 -,8-1, Sngle ptch devaton for rght flank Tooth number 1,6 1,,8,4, -,4 -,8-1, -1,6 Cumulatve ptch devaton for rght flank Tooth number Sngle ptch devaton result Cumulatve ptch devaton result

21 Introducton Contents DBA used for evaluaton of GMIs on the gear profle measurement capablty Three types of MBAs for evaluaton of GMIs on the gear ptch measurement capablty Characterstcs Calbraton method Evaluaton of gear measurng nstruments usng calbrated MBA Summares

22 Measurement setup Gear measurng nstrument:mgl-6a Manufactured by Osaka Semtsu Kka

23 Reproducblty [m] Reproducblty [m] Repeatablty [m] Repeatablty [m] Repeatablty and reproducblty of GMI Ptch number Repeatablty of sngle ptch devaton Ptch number Repeatablty of cumulatve ptch devaton Ptch number Reproducblty of sngle ptch devaton Ptch number Reproducblty of cumulatve ptch devaton

24 Cumulatve ptch devaton [m] OSK - NMIJ [m] Sngle ptch devaton [m] OSK - NMIJ [m] Evaluaton result 6 4 OSK-NMIJ NMIJ OSK Ptch number 6 4 OSK-NMIJ - -. NMIJ OSK Ptch number.6.4. Measurement uncertanty U 95 k uw ur u p us u w : standard uncertanty of calbraton value u r : standard uncertanty of repeatablty u p : standard uncertanty of reproducblty u s : standard uncertanty of systematc error k: coverage factor set to k = Left flank U 95 (f p ) U 95 (F p ) Rght flank Left flank Rght flank.4 m.5 m.46 m.49 m

25 Summares We proposed new artfacts for evaluaton of GMI s measurement capabltes. MBAs are avalable for the gear profle and ptch evaluatons. We proposed the multple-orentaton technque for calbratng the angular ptch devaton of the MBA. We evaluated the ptch measurng accuracy of the gear measurng nstrument usng the calbrated MBA. MBA s effectve for calbratng the gear measurng nstrument at shop floor wth a mnmum uncertanty.

26 Thank you for your attenton!!

27 Angular ptch devaton If the ptch balls are arranged at equal ntervals, we defne the nomnal angular poston as the center of the th ptch ball by q n 1 1,, n, where : ptch ball number n the clockwse drecton n: the total number of ptch balls Centerng ball Y O Reference crcle r X T(q ) We defne the angular ptch devaton by P q Tq q where T(q ): the true angular poston n the actual MBA W Center of th ptch ball -1th ptch ball

28 Calbraton parameter The sngle ptch devaton for a vrtual gear s calculated by f f pl pr r r P P q Pq Ω Ω q Pq Ω Ω Centerng ball Y Reference crcle where r: reference crcle radus W : angle between the measurement pont and the center of the th ptch ball Ω cos 1 r C r C r c where r c : radus of th ptch ball C : ball center dstance between the centerng ball and the th ptch ball W Center of th ptch ball r O T(q ) -1th ptch ball X

29 M(q, f j ) and (q ) [arcsec] Nomnal angular poston q [deg] Law of the Fourer seres Measurement value Measurement value M q, j P q E q j Erand Mean value 1 m m q M q, 1 m P m j1 q Eq m q E q When m-number of curve wth a phase shft of /m at a tme are averaged, the averaged curve shows the sum of an ntegral multple of mth-order Fourer components of the orgnal curve. P j1 E(q ): Systematc error E rand : Non systematc error j j E rand

30 Average [arcsec] Ampltude [arcsec] Angular ptch devaton [arcsec] Ampltude [arcsec] Example of law of Fourer seres Orgnal curve Shfted curve -1 Phase shft of Nomnal angular poston q [deg] Fourer component Nomnal angular poston q [deg] Average Mean curve Fourer component

31 r b How to set vrtual gear dmenson rc sn cos cos C rc cos Reference crcle Lne of acton Base crcle Y A P I r b r O c r c Ptch ball α C X O B

32 Measurement value M 1 q, j P q E q j Erand Mean value m P q E q j Erand m j 1 P P(q ): Angular ptch devaton E(q ): Systematc error E rand : Non systematc error m q E q Measurement value Expected value s zero By law of Fourer seres M(q, f j ) and (q ) [arcsec] the sum of an ntegral multple of mth-order Fourer components of the systematc error Nomnal angular poston q [deg]

33 M M To obtan the systematc error: 1st step Measurement value q, j P q E q j Erand Phase shft of j at each orentaton Shfted value q j, j Pq j Eq Erand M(q, f j ) [arcsec] M(q - f j, f j ) [arcsec] Nomnal angular poston q [deg] Nomnal angular poston q [deg]

34 Mean value [arcsec] M To obtan the systematc error: nd step q j, j Pq j Eq Erand 1 m m j1 P ( m) P Shfted value Average Mean value of shfted curves q Eq q Eq j E rand P (16) (q ) s never analyzed n accordance wth the samplng theory M(q - f j, f j ) [arcsec] Nomnal angular poston q [deg] Nomnal angular poston q [deg]

35 Shfted value [arcsec] Mean value [arcsec] To obtan the systematc error: 3rd step The phase of the systematc error n the measurement value s dfferent at each orentaton Systematc error E q Nomnal angular poston q [deg] E q Phase shft of j at each orentaton j Nomnal angular poston q [deg]

36 Dsperson [arcsec] M 1 m q, Eq P m j1 P q Average for all orentatons Calbraton Value j q Erand P q E rand j Measurement uncertanty Calbraton value M(q, f j ) - E(q +f j ) [arcsec] Nomnal angular poston q [deg] s =.4 arcsec Nomnal angular poston q [deg]

37 Calbraton for length CMM wth an nterferometer U 34 6 L (k=) [µm] 37