A high precision collaborative vision measurement of gear chamfering profile

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1 Internatonal Conference on Advances n Mechancal Engneerng and Industral Informatcs (AMEII 05) A hgh precson collaboratve vson measurement of gear chamferng profle Conglng Zhou, a, Zengpu Xu, b, Chunmng Ca, c, Yongqang Wang, d College of Mechancal Engneerng, Tanjn Unversty of Scence and Technology, Tanjn, 300, Chna a zhouclng@tust.edu.cn, b xuzp@tust.edu.cn, c c08300@6.com, d wangyq@tust.edu.cn Keywords: collaboratve vson, precson measurement, gear chamferng Abstract. In order to acheve hgher measurement precson of the surface profle on chamferng gears n auto gearbox, ths paper proposed a collaboratve vsual surface profle measurement system, researched mage processng and measurement path plannng algorthm n the system. The measurng process ncludes: collectng gear mage usng the area array mage sensor, processng mage edge, fttng gear center by utlzng edge ponts of the gear mage, postonng local area through combnng calbraton algorthm. Then, plannng measurement path accordng requrements, drvng XY platform to carry hgh-precson pont vsual laser dsplacement sensors achevng local area of gear chamferng along the measurement path. Fnally, processng the data obtaned by laser dsplacement sensors and outputtng measurement report. Experments show that measurement accuracy of the system can attan μm when measurng the heght (Z drecton) of gear chamferng profle and 5μm when measurng the length(x drecton) and wdth (Y drecton) of gear chamferng profle. By combnng ther respectve advantages of the two sensors, the collaboratve vson measurement method whch uses area array mage sensor to acheve hgh-speed postonng and laser sensor can be used to mprove the measurement precson for measurement of gear chamferng profle. Introducton In machne vson technology, measurement usng only one sngle mage sensor cannot meet the hgh accuracy, speed, and many other requrements n precson manufacturng. Therefore, t s very mportant to study a collaboraton precson measurement method combned wth two or even mult-level vsual sensors on ther dfferent merts. In a two-step collaboraton measurement system, vsual sensors are used to complete the wde range of rough measurement or measurng locaton on the frst stage, and the local small-scale precson measurement on the second stage. The vsual sensors on the second stage may be the vsual sensor of dfferent resoluton or hgh-precson laser dsplacement sensor. Due to the pxel sze of the current D CCD s usually larger than.5μm.5μm, and t s not enough to meet the measurement accuracy requrement. In ths paper, a two-stage collaboraton measurement system s desgned to measure the gear chamferng profle. On the frst stage of the measurement, combned wth the calbraton algorthm, work pece locatng s completed usng a D mage sensor. On the second stage, the hgh accuracy of measurement s completed usng a pont vsual laser dsplacement sensor carred by the D hgh precson electrc platform on the planned path. Measurement prncple and coordnate relatonshp Measurement prncple. In ths paper, the measurement system s used for measurement on the gear chamferng profle, and the precson s requred to μm n the heght value. Based on the calbraton method, mage processng and locaton of measurng part are fnshed n the frst stage through collectng the gear mage by a D camera. Then the gear chamferng contour measurement s completed by a laser dsplacement sensor wth repeat measurement accuracy of 0.μm on the second 05. The authors - Publshed by Atlants Press 689

2 stage. The desgned measurement system s shown as Fg., whch ncludes D camera, computer, XY platforms, laser dsplacement sensor, marble base, lght source, and prnter. Frstly, collect mage of the gear through the CCD sensor, after the calbraton and the gear mages processng, computer wll send planned path orders to the move the XY platform, then the XY platform wll carry the laser dsplacement sensor to measure the contour of the gear chamferng profle. Fnally, the measurement result wll be saved n the computer and can be prnted out. Fg. Measurement system. XY platform,. laser dsplacement senor, 3. D camera, 4. marble base, 5. Gear, 6. lght source, 7. Computer, 8. Prnter. Coordnate systems. Durng the measurement, the movng path of the XY platforms s desgned after the calbraton between the mage and the world coordnaton, so t s needed to get the relatonshp between the dfferent coordnate systems n the measurement system, whch ncludes the world coordnate system (Xw, Yw, Zw), the XY platform coordnate system (X, Y, Z), the mage sensor coordnate system (X, Y, Z) and the mage pont coordnate system (U,V), as shown n Fg.. Fg. The four coordnates n the system In ths measurement system, the world coordnate system (Xw, Yw, Zw) s set to concde wth the XY platform coordnate system (X, Y, Z). Z drecton n the mage sensor coordnate system (X, Y, Z) s set as the optcal axs of the camera, the other two drectons are set parallel wth the U drecton and V drecton n the mage pont coordnate system (U, V), respectvely. The coordnaton n the mage pont coordnate system (U, V) shows the pont poston n the mage. Put the gear to be measured on the XY platform, and calbrate the relatonshp between the XY platform coordnate system (X, Y, Z) and the mage pont coordnate system (U, V). Calbraton method. After collectng the gear mage on the XY platform, the gear poston n the world coordnate system can be presented on the mage coordnate system. Calbraton means to get the relatonshp between the two coordnate systems. The relatonshp between the coordnate (x, y) on the object plane n the world coordnate system and the coordnate (u, v) on the mage plane n the mage coordnate can be shown as Eq. [] : 690

3 m m m wx 3 u wy m m m v = 3 w m m m () Where w s a relaton factor,and m33=. Then: x = mu + mv + m3 xm3u xm3v y = mu + mv + m3 ym3u ym3v () So, f the 8 relaton factors n Eq., m to m 3, are known, the real coordnaton of any pont on the object plane can be receved basng on Eq. from the coordnate on the mage plane. And the 8 relaton factors can be calbrated by the coordnates of the corner ponts of the grds on the calbraton board. Collaboratve measurement of gear chamferng profle Frst measurement step - center locaton. Measurement object. The measurement object s the gear chamferng profle as shown n Fg.3. The lnes n the (a) are the connecton lnes between the crcle center and the addendum crcle arc mdpont of each toot, and the 3 polylnes n (b) are the measurement planes, whch are perpendcular to the lnes n the left sde. (a) (b) Fg.3 Real Object and partal enlarged detal fgure of chamferng gear Center locaton method. Snce LED backlght resource s nvolved n the measurement system, edge of a clear grayscale mage can be receved from the mage collecton. After the mage processng, the coordnates of boundary ponts can be extracted by the software. Fttng the root crcle basng on the ponts extracted by least-squares fttng algorthm, the center pont coordnate of the root crcle can be receved. Denote all the ponts extracted from the gear mage as Set D, the dstance from any pont n set D, D (u, v ), to the crcle center pont s marked as R, and the crcle area wth rad R s s. The crcle area of the ft crcle wth rad R s s, and the ft crcle center coordnate s (x 0, y 0 ). Then the error between the crcle areas s expressed as Eq. 3: ε = s s = πr πr = π[( u x ) + ( v y ) R ] 0 0 (3) And the squared error can be shown as Eq. 4: 69

4 n 0 0 = π = F( x, y, R) [( u x ) ( v y ) R ] (4) Make F (x0, y0, R) to be the mnmum, the value of x 0 y 0 and R can be taken through Eq. 5: F F F = = = 0 x y R 0 0 (5) Whch can also be shown as Eq. 6: F n = π ( 4)[( ) ( ) u x0 + v y0 R ]( u x0) = 0 x0 = F n ( 4)[( ) ( ) = π u x0 + v y0 R ]( v y0) = 0 y0 = F n π ( 4)[( u x ) ( ) = 0 + v y0 R ] R= 0 R = (6) Solvng Eq. 6, then the exact crcle center coordnate O (Ou, Ov) of gear can be receved by Eq.7. hq tc x0 = ( pq c ) tp hc y0 = ( pq c ) (7) where: p = n u ( u ) q = n v ( v ) h= n u + n uv ( u + v ) u 3 t= n v + n uv ( u + v) v 3 c= n uv ( u) v Gear chamferng profle measurement. Man parameter to measure. The man parameter of gear chamferng profle to be measured ncludes: the angle between the two chamferng surface M, the dstance from the chamferng surface to the specfed plane N, as shown n Fg.4. Measurement requrement. The measurng planes on the tooth of the gear chamferng profle s shown as Fg. 5, and the data, 43.7, 45. and 46.5 means the dstance from the measurng plane to the crcle center, and t wll be dfferent to gears of dfferent sze. Assumng the crcle center s marked as O, the addendum crcle arc mdpont of a tooth s marked as P, and the measurng planes must be perpendcular to lne OP. Measurement path plannng. The prncple of measurement path plannng s shown n Fg.6. Lne AB s the measurement path for the laser dsplacement sensor, whch s requred to be perpendcular to OP, P s the ntersecton of OP and AB, and the dstance L from AB to O s a known value. Because the coordnate of pont O n the mage plane can be acheved by equ.7, lne OP can be decded by determnng the coordnate of pont P (P u, P v ) n the mage plane. Lne CD s the chord to the arc of the addendum crcle, P s the mdpont of CD. 69

5 Fg.4 Measurement Parameters n secton Fg.5 fgure of Sngle-tooth measurement locaton Fg.6 Prncple fgure of system of mage When the system starts to measure the gear chamferng profle, clck the mouth at a pont near the gear tooth of gear on the gear mage, the poston of the pont wll be saved by the program. Supposng the pont s marked as Q, ts coordnaton s (Qu, Qv) n the mage coordnate system (U, V). Scan a small area near the pont to fnd all of the edge pont of the gear tooth, whch ncludes all of the ponts on the addendum arc CPD, mark the frst pont on arc CPD as pont C and the last pont as D, extract the coordnaton of pont C and D, get the mdpont poston of lne CD, and mark t as P (Pu, Pv). Because pont P, P, and O are on the same lne, and the equaton of the lne can be solved out by the three ponts. Converse the coordnate of pont O and P n the mage coordnate system to the XOY plan n the XY platform coordnate system and marked as (Ox, Oy) and (Px, Py). The slop of lne OP s k, and the length of OP s L,the coordnate of P(Px, Py) on XOY plan can be solved by Eq. 8: ( ( )) ( ( )) Px = Ox L cos arctan k P y = Oy L sn arctan k (8) Snce lne AB s perpendcular to lne OP, and the length of AB s set as L, so the coordnate of pont A (Ax, Ay) s shown as Eq. 9: L Ax = P cos k L Ay = P sn k k = k ( π arctan ( )) x ( π arctan ( )) y (9) Coordnate of pont B (Bx, By) can be solved by the same method. Second measurement step-precson measurement by laser dsplacement sensor. The second measurement step depends on the laser dsplacement sensor to complete the precson measurement, and the measurement data are the heght nformaton n Z drecton, cooperated wth the movement of XY platform nformaton, the 3D dmenson measurement of the gear chamferng profle can be completed. System movement. The movement s realzed by the XY platform along the planned path. Commands controllng the movement of the XY platform are sent from the computer to the stepper 693

6 motors, and then the stepper motors drve the precson ball screw to complete the platform moton, whch can control the movement precson to μm. And the laser dsplacement sensor can be moved to the specfed poston on the XY plan by the platform under the dfferent commands from the computer. Measurng method. To fnsh the measurement, the laser dsplacement sensor can be moved along the planned path n the XY platform coordnate system, after the coordnaton of pont A and B s solved by Eq. 9. Gear chamferng profle measurement. The measurement result from the laser dsplacement sensor s the heght value of the ponts on gear chamferng profle n Z drecton, and the X and Y coordnaton can be acheved from the XY platform movements. So the 3D coordnate of ponts on the gear chamferng profle can be acheved by composng the above nformaton from the laser dsplacement sensor and the XY platform movements. Set the Y coordnate as 0, then the gear chamferng profle can be drawn on one plan as shown n Fg.7. And Fg.8 shows the gear chamferng measurement results wth dfferent Y values n the 3D space. Fg.7 Drawng result of gear profle Fg.8 Surface profle of gear tooth Conclusons Ths paper desgned a hgh precson collaboratve measurement system for gear chamferng profle basng on the advantages of two dfferent vson sensors. The system can meet the requrements of the hgh speed, precson and non-connect measurement. And ths system s used to measure the gear chamferng profle, and the measurement precson s not lower than μm. Moreover, ths system needs no mechancal fxture, whch makes a easy usng and low cost measurement system. Acknowledgements Ths work was fnancally supported by the Tanjn Scence and Technology Supportng Program (No.3ZCZDGX0400) and Tanjn Unversty of Scence and Technology Foundaton (0309). References [] XU Z P, YU D M. Journal of Tanjn nsttute of lght ndustry, S (993), p4. (n Chnese) [] LI Z Q, DONG X L, LI Q L, GUO C L. Coastal enterprse and scence & technology, 00(5). (n Chnese) [3] XU Z P, ZH SH. AMR, 0, p [4] ZH X H. Tanjn: Tanjn Unversty of Scence & Technology, 00. (n Chnese). [5] ZH SH. Tanjn: Tanjn Unversty of Scence & Technology, 0. (n Chnese). 694