Journal of
Manufacturing and Materials Processing
Article
Error Separation Method for Precision Measurement of the Run-Out of a Microdrill Bit by Using a Laser Scan Micrometer Measurement System Zengyuan Niu, Yuan-Liu Chen *
ID
, Yuki Shimizu, Hiraku Matsukuma
ID
and Wei Gao
Department of Finemechanics, Tohoku University, Sendai 980-8579, Japan;
[email protected] (Z.N.);
[email protected] (Y.S.);
[email protected] (H.M.);
[email protected] (W.G.) * Correspondence:
[email protected]; Tel.: +81-022-795-6953 Received: 27 November 2017; Accepted: 9 January 2018; Published: 12 January 2018
Abstract: This paper describes an error separation method for a precision measurement of the run-out of a microdrill bit by using a measurement system consisting of a concentricity gauge and a laser scan micrometer (LSM). The proposed error separation method can achieve a sub-micrometric measurement accuracy of the run-out of the microdrill bit without the requirement of ultra-precision rotary drive devices. In the measurement, the spindle error motion of the concentricity gauge is firstly measured by using the LSM and a small-diameter artifact, instead of the conventionally used displacement probes and large-diameter artifact, in order to determine the fine position of the concentricity gauge when the spindle error motion is at its minimum. The microdrill bit is rotated at the fine position for the measurement of the run-out, so that the influence of the spindle error motion can thus be reduced, which could not be previously realized by commercial measurement systems. Experiments were carried out to verify the feasibility of the proposed error separation method for the measurement of the run-out of the microdrill bit. The measurement results and the measurement uncertainty confirmed that the proposed method is reliable for the run-out measurement with sub-micrometric accuracy. Keywords: microdrill bit; run-out; spindle error motion; concentricity gauge; laser scan micrometer; error separation method
1. Introduction With the development of high-density printed circuit boards (PCBs) [1,2], there is an increasing demand for the microdrilling of precision holes. Compared with laser drilling [3,4] and electrochemical drilling [5,6], mechanical drilling is the most useful machining method for high aspect ratio microdrilling in practice, because it can process a variety of materials with finer quality at lower cost [7–10]. To satisfy the requirement of high aspect ratio microdrilling on the PCBs, efforts have been devoted to designing and manufacturing microdrill bits with large aspect ratios [9–14]. Due to the large aspect ratio and the low rigidity of the microdrill bit, an axial straightness error between the shank part and the body part is very likely to occur, even when manufactured by using ultra-precision grinding tools. As shown in Figure 1, when the microdrill bit is being rotated, the run-out caused by the axial straightness error is generated at the end point of the microdrill bit. The run-out of the microdrill bit would lead to an enlargement of the diameter of the drilled hole [15] and the occurrence of burrs around the hole [16], consequently reducing the hole quality in the PCBs drilling [17]. For the quality control of both PCBs drilling and microdrill bit processing, it is desired to precisely measure the degree of the run-out of the microdrill bit.
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Figure Axialstraightness straightness error bit.bit. Figure 1. 1.Axial errorofofthe themicrodrill microdrill
Previous research studies [15,16], rotated microdrill bits with ultra-precision rotary drive
Previous studies [15,16], rotated microdrill bits with ultra-precision rotary drive devices. devices. Aresearch sub-micrometric measurement accuracy of the run-out has been achieved based on the Figure 1. Axial straightness error of the microdrill bit. A sub-micrometric accuracy of the run-out been achieved based spindle. on the rotation rotation accuracymeasurement of the ultra-precision rotary drive devices,has such as the ultra-precision On the other measurement of the run-out with such sub-micrometric accuracy in spindle. machine On shops accuracy of thehand, ultra-precision rotary drive devices, as the ultra-precision theisother Previous research studies rotatedprocess microdrill bits with out ultra-precision rotary ofdrive in industries, that a[15,16], straightening can accuracy be carried for quality control the in hand,required measurement of thesorun-out with sub-micrometric in machine shops is required devices. A sub-micrometric measurement accuracy of the run-out has been achieved based on the microdrill bit. However, it is difficult to apply the ultra-precision rotary drive devices for the run-out industries, so that a straightening process can be carried out for quality control of the microdrill bit. rotation accuracy of the ultra-precision rotary drive devices, suchbecause as the ultra-precision spindle. On measurement with sub-micrometric accuracy in machine shops, the ultra-precision spindle However, it is difficult to apply the ultra-precision rotary drive devices for the run-out measurement the other hand, measurement of the run-out with sub-micrometric in machine shops is is sensitive to the large environmental disturbances of machine shops,accuracy such as vibrations. Moreover, withrequired sub-micrometric accuracy shops, because the is sensitive to the in industries, so thatinof amachine straightening canultra-precision beultra-precision carried outspindle, for spindle quality control the the sophisticated installation microdrill bitsprocess onto the in which theofaxis large environmental disturbances of machine shops, such as vibrations. Moreover, the sophisticated microdrill it is to difficult to apply the ultra-precision rotary drive devices the run-out microdrillbit. bitHowever, is required be aligned coaxially with the axis of rotation of thefor spindle, is a installation of microdrill bits onto ultra-precision spindle, in which thethe axis microdrill bitspindle is required measurement withprocedure sub-micrometric accuracy in machine shops, because ultra-precision time-consuming thatthe is not convenient for industrial measurement. to be coaxially with the axis of rotation of the spindle, is being a time-consuming procedure that is is aligned sensitive to the large environmental disturbances of machine such as in vibrations. Moreover, A laser scan micrometer (LSM) measurement system isshops, used industries for the sophisticated installation of microdrill bits onto the ultra-precision which the not the convenient for run-out industrial measurement. measuring the of microdrill bits. This process is shown in Figure 2,spindle, which isincomposed of axis the microdrill bit is required gauge. to be The aligned coaxially withmicrodrill axisused of isrotation of the spindle, is aa LSM and a concentricity shank part of the bit rotationally supported by A laser scan micrometer (LSM) measurement system isthe being in industries for the measuring pair of main rollers and the top roller of the concentricity gauge [18], which the microdrill bit can be LSM time-consuming procedure that is not convenient for industrial measurement. the run-out of microdrill bits. This process is shown in Figure 2, which is composed of the easily installed onto compared with a spindle. The motion of the body part of the microdrill bit A laser scan micrometer (LSM) measurement system is being used in industries for the and a concentricity gauge. The shank part of the microdrill bit is rotationally supported by isa pair monitoredthe byrun-out the LSMoffor the run-out measurement. The concentricity is robust enough of to be measuring process is shown Figuregauge 2, which composed of main rollers and the topmicrodrill roller ofbits. theThis concentricity gaugein[18], which the ismicrodrill bit the can be insensitive to vibrations, but the spindle error motion of the concentricity gauge is relatively large, LSM and a concentricity gauge. The shank part of the microdrill bit is rotationally supported by a easily installed onto compared with a spindle. The motion of the body part of the microdrill bit which is mainly caused by top the roller assembly errors and the roundness error of the main rollers. The pair of main rollers and the of the concentricity gauge [18], which thetwo microdrill bit can be is monitored by the LSM for concentricity the run-outgauge measurement. The concentricity gauge isthe robust enough spindle error motion of the limits the measurement system to obtain required easily installed onto compared with a spindle. The motion of the body part of the microdrill bit is to be insensitive to vibrations, but the measurement. spindle errorThe motion concentricity gauge is relatively sub-micrometric measurement accuracy of the run-out. In concentricity orderof tothe achieve the required measurement monitored by the LSM for the run-out gauge is robust enough to be large, which is mainly caused by the assembly errors and the roundness error of the two main rollers. accuracy for the run-out by using the LSM measurement system, the separation of the spindle error insensitive to vibrations, but the spindle error motion of the concentricity gauge is relatively large, Thewhich spindle motion ofthe the concentricity gauge the measurement to obtain motion oferror the concentricity gauge is necessary. is mainly caused by assembly errors and thelimits roundness error of the twosystem main rollers. The the paper describes an error separation method formeasurement the precision measurement of the thethe run-out required sub-micrometric measurement accuracy the run-out. Insystem order to toobtain achieve required spindleThis error motion of the concentricity gauge limitsofthe required of a microdrill bit byfor thethe LSM measurement system. The measurement of run-out byof the measurement accuracy run-out byofusing the LSM measurement system, thethe separation sub-micrometric measurement accuracy the run-out. In order to achieveprinciple the required measurement using the LSM measurement system is presented, and the influence of the spindle error motion oferror the accuracy for the run-out by using the LSM measurement system, the separation of the spindle spindle error motion of the concentricity gauge is necessary. concentricity gauge in the measurement of the run-out is discussed. To achieve a precision motion of the concentricity gauge is necessary. This paper describes an error separation method for the precision measurement of the run-out measurement of the run-out, the method for separating thethe spindle errormeasurement motion in the of measurement This paper an error separation method precision run-out of a microdrill bitdescribes by the LSM measurement system.forThe measurement principle the of the run-out of the run-out is proposed. After a description of the measurement principle, experiments and an of a microdrill bit by the LSM measurement system. The measurement principle of the run-out by by using the LSM measurement system is presented, andand thethe influence of spindle error motion uncertainty are carried out to verify the feasibility accuracy of the the error proposed method. using the LSManalysis measurement system is presented, and the influence of the spindle motion of the of the concentricity gauge in the measurement of the run-out is discussed. To achieve a precision concentricity gauge in the measurement of the run-out is discussed. To achieve a precision measurement of the run-out, the method for separating the spindle error motion in the measurement measurement of the run-out, the method for separating the spindle error motion in the measurement of the run-out is proposed. After a description of the measurement principle, experiments and an of the run-out is proposed. After a description of the measurement principle, experiments and an uncertainty analysis are carried thefeasibility feasibilityand and the accuracy of the proposed method. uncertainty analysis are carriedout outto to verify verify the the accuracy of the proposed method.
(a)
(a) Figure 2. Cont.
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(b) Figure 2. (a) Photographs and (b) schematic of the laser scan micrometer measurement system.
Figure 2. (a) Photographs and (b) schematic of the laser scan micrometer measurement system. 2. Measurement System and Principle
2. Measurement and Principle Figure 2 System shows photographs and the schematics of the laser scan micrometer measurement
(b)the concentricity gauge and the LSM. The shank system. measurement system composed of Figure 2The shows photographs andisthe schematics of the laser scan micrometer measurement system. part of theFigure microdrill bit is gripped the two main rollers and the top roller. Two timing belts 2. (a) Photographs and (b)by schematic of the laser scan micrometer measurement system. The measurement system is composed of the concentricity gauge and the LSM. The shank part of connect the shaft of the drive handle and the shafts of the two main rollers. Through manually the microdrill bit is gripped by two main rollers and the top roller. Two timing belts connect the 2. Measurement Systemthe andthe Principle rotating the drive handle, two main rollers are simultaneously rotated by the two timing belts to shaft of the drive handle and the shafts of the two main rollers. Through manually rotating the drive drive the microdrill bit by the friction the surface of laser the shank part and the surface of the Figure 2 shows photographs andbetween the schematics of the scan micrometer measurement handle, the two main rollers are simultaneously rotated by the two timing belts to drive the microdrill main rollers. Since the diameters of the shaft of the drive handle and the shafts of the main system. The measurement system is composed of the concentricity gauge and the LSM. Therollers shank are bit by friction betweenofbit the ofbythe shank partrollers and the surface the main rollers. Since the part of the the rotations microdrill issurface gripped the two and the top of roller. Two timing belts thethe same, the drive handle and themain main rollers are synchronized. It should be noted diameters of the shaft of the drive handle and the shafts of the main rollers are the same, the connect the shaft of the drive handle and the shafts of the two main rollers. Through manually that when the diameters of the shank part of the microdrill bit and the main rollers are different,rotations one rotating the drive handle, thewould two main rollers are simultaneously by thethat two timing belts to of the drive handle and the main rollers are synchronized. It should berevolution noted the diameters revolution of the microdrill bit only correspond to a portion ofrotated one ofwhen the mail rollers. drive microdrill bit by the bit friction between surface the shank partof and surface of microdrill thepart The the LSM includes a measurement andthe arollers controller. The principle thethe measurement of the shank part of the microdrill and part the main areofdifferent, one revolution of the main rollers. Since the diameters of the shaft of the drive handle and the shafts of the main rollers are of the LSM shown in Figure 3 [19]. Aoflaser is reflected bymail a rotating polygonal mirror to scan bit would onlyiscorrespond to a portion onebeam revolution of the rollers. the same, the rotations of the drive handle and the main rollers are synchronized. It should be noted within a measurement area. The microdrill bit that has been placed into the measurement areapart The LSM includes a measurement part and a controller. The principle of the measurement that when the diameters of the shank part of the microdrill bit and the main rollers are different, one interrupts the laser beam, and cuts the measurement area into three measurement segments, which of the LSM is shown in Figure [19].only A laser beamtoisa portion reflected byrevolution a rotating polygonal mirror to revolution of the microdrill bit3would correspond of one of the mail rollers. are referred to as the top edge segment, the diameter segment, and the bottom edge segment. The top scan withinThe a measurement The microdrill that hasThe been placedofinto the measurement LSM includes aarea. measurement part and bit a controller. principle the measurement part area edge segment is the distance from the top scanning position to the upper surface of the microdrill. of the is shown Figure [19].measurement A laser beam isarea reflected a rotating polygonalsegments, mirror to scan interrupts theLSM laser beam,in and cuts3 the into by three measurement which are The diameter segment isarea. the distance between the has upper surface and surfacearea of the measurement The microdrill bit that been placed into the the lower measurement referredwithin to as athe top edge segment, the diameter segment, and the bottom edge segment. The top microdrill bit.the The bottom segment is the distance the bottom scanning position to the interrupts laser beam, edge and cuts the measurement area from into three measurement segments, which edgelower segment is thethe distance from the scanning position to edge the upper surface the microdrill. microdrill Thetop laser beams within the and top segment theofbottom edge are surface referredof to as the top edgebit. segment, the diameter segment, the bottom edgeand segment. The top The diameter segment is the distance between the upper surface and the lower surface of the microdrill segment are focused a condenser lens, then position receivedtoby photoelectric element, while the edge segment is theby distance from the top and scanning thea upper surface of the microdrill. bit. The bottom edgesegment segment is the distance from the thethe bottom scanning position thethe lower laser beam within the diameter segment isbetween blocked by microdrill bit. converting received The diameter is the distance upper surface andAfter the lower to surface of thesurface of the microdrill bit.The The laser beams thedistance topbased edge and the bottom segment signal of the bit. photoelectric element towithin time domain onthedetection, outputs of theedge top edge microdrill bottom edge segment is the fromsegment bottom scanning position to the lower by surface ofdiameter the microdrill bit. The laser beams the top segment edge segment andscanning the bottom edge segment anda the segment, as well as the within bottom edge in each cycle, are focused condenser lens, and then received by a photoelectric element, while the lasercan beam segment are focused by a condenser lens, and then received by a photoelectric element, while the be obtained by utilizing the known scan speed of the LSM. within the diameter segment is blocked by the microdrill bit. After converting the received signal of laser beam within the diameter segment is blocked by the microdrill bit. After converting the received the photoelectric element to time domain based on detection, outputs of the top edge segment and signal of the photoelectric element tounit time domain based on detection, outputs of the top edge Emission unit Reception scanning in each scanning cycle, can be obtained by the diameter segment, as well as the bottom edgeTopsegment segment and the diameter segment, as well bottom edge segmentlens in each scanning cycle, can Condenser lens as theposition Collimating Motor utilizing known speed of the scan LSM.speed of the LSM. bethe obtained by scan utilizing theEdge known detection
Reception unit Condenser lens
Photoelectric Edge element detection
Y Z
X
Micro drill Topbit scanning position
Bottom scanning
Micro position drill bit
Upper surface
Y Z
Figure
Emission unit Collimating lens Motor Polygon
Laser source
mirror
Lower surface
Photoelectricof the micro of the micro Polygon element drill bit drill bit mirror Top scanning Bottom scanning LaserBottom source scanning position position position X Top Diameter Bottom edge surface Lower surface Upper edge of the micro of the micro drill bit drill bit Time Top scanning Bottom scanning position position Diameter 3. Measurement Top principle of laserBottom scan micrometer (LSM). edge edge Time
Figure 3. Measurement principle of laser scan micrometer (LSM).
Figure 3. Measurement principle of laser scan micrometer (LSM).
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J. Manuf. Mater. Process. 2018, 2, 4 2.1. Principle Bit 2.1. Principleofofthe theRun-Out Run-OutMeasurement Measurement of of the the Microdrill Microdrill Bit
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the of of the theBit microdrillbit. bit.The Theaxis axisstraightness straightness error Figure4 4shows thedefinition definition of the theofrun-out run-out of microdrill error 2.1.Figure Principle ofshows the Run-Out Measurement the Microdrill between the body part and the shank part of the drill generates different distances from the axis of between the body part and the shank part of the drill generates different distances from the axis ofthe Figure 4 shows the definition of the run-out of the microdrill bit. The axis straightness error shank part topart twotomargins. The distance from the axis theof shank part topart each is the is rotation the shank two margins. The distance from theofaxis the shank tomargin each margin the between the body part and the shank part of the drill generates different distances from the axis of radius of each margin. When the When microdrill bit is rotated, rotation of the twoofmargins rotation radius of each margin. the microdrill bit isthe rotated, thepaths rotation paths the twoare the shank part to two margins. The distance from the axis of the shank part to each margin is the different. the run-out microdrill thus defined be the difference rotation of paths marginsThe are run-out different.ofThe of bit the ismicrodrill bit istothus defined to be of thethe difference the of rotation radius of each margin. When the microdrill bit is rotated, the rotation paths of the two paths of the two margins. therotation two margins. margins are different. The run-out of the microdrill bit is thus defined to be the difference of the rotation paths of the two margins.
Figure 4. Definition of the run-out. Figure 4. Definition of the run-out. Figure 4. Definition of the run-out.
For the measurement of the run-out, the top edge segment of the LSM, which is referred to as For measurement of the the run-out, the top θedge segment the LSM, which is referred to as TEdge (θ),the is employed to measure two margins. represents theof angular position of the microdrill For the measurement of the run-out, the top edge segment of the LSM, which is referred to as TEdge (θ), is employed to measure the two margins. θ represents the angular position of the microdrill bit along its circumference. The measurement principle is shown in Figure 5. The microdrill bit is TEdge(θ), is employed to measure the two margins. θ represents the angular position of the microdrill bitbeing alongrotated its circumference. The measurement principle is shown in Figure 5. The by the concentricity gauge, and the measurement output on Margin 1 is microdrill referred to bit as is bit along its circumference. The measurement principle is shown in Figure 5. The microdrill bit is being rotated by theTEdge concentricity gauge, and the measurement output onedge Margin 1 is referred to as TEdge(θ j), in which (θj) is the minimum measurement output of the top segment in the first being rotated by the concentricity gauge, and the measurement output on Margin 1 is referred to as half thewhich rotation of(θthe microdrill bit. j is the sampling interval in the circumference direction. TEdge (θ jof ), in TEdge ) is the minimum measurement output of the top edge segment in the first TEdge(θj), in which TEdge(θjj) is the minimum measurement output of the top edge segment in the first Hence, the measurement output on Margin 2 is referred to as T Edge (θ j + π). Based on the definition, the half of the rotation of the microdrill bit. bit. j is the interval in theincircumference direction. Hence, half of the rotation of the microdrill j is sampling the sampling interval the circumference direction. which output is the absolute value of the output difference on the two margins, can then be therun-out, measurement on Margin 2 is referred to as T (θ + π). Based on the definition, the run-out, Edge Hence, the measurement output on Margin 2 is referred to asj TEdge(θj + π). Based on the definition, the calculated as: which is the absolute value of the output difference on the two margins, can then be calculated as: run-out, which is the absolute value of the output difference on the two margins, can then be Run-out = TEdge θj - TEdge θj + π , calculated as: (1) Run − out = TEdge θ j − T Edge θ j + π , (1) Run-out = TEdge θj - TEdge θj + π , (1) Top scanning laser beam of the LSM Tedge(θj) Top scanning laser beam of the LSM Margin Tedge1(θj)
Run-out
Margin 1
Tedge(θj+π) Tedge(θj+π)
Run-out
Margin 2 Margin 2
Axis of the shank part Axis 2of the shank part Margin
Y Z Z
Y
X
Margin 2
Margin 1 Margin 1
X Figure 5. Measurement principle of the run-out.
Figure5.5.Measurement Measurement principle Figure principleof ofthe therun-out. run-out.
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J. Manuf. Mater. Process. 2018, 2, spindle 4 5 of 12 On the other hand, the error motion of the concentricity gauge changes the height position (Y-direction) of the microdrill bit. This process is shown in Figure 6, in which the spindle error motion On the other hand, the spindle error motion of the concentricity gauge changes the height is t referred to as eSpindle_1,2 . Then, the run-out influenced by eSpindle_1,2 can be written as: position (Y-direction) of the microdrill bit. This process is shown in Figure 6, in which the spindle . Then,the run-out influenced can be written as: error motion is t referred to as eSpindle_1,2 by eSpindle_1,2 Run − out = TEdge θ j − TEdge θ j + π + eSpindle_1,2 , (2) Run-out = TEdge θj − TEdge θj + π + (2) _ , , It can be seen from Equation (2) that the value of eSpindle_1,2 directly determines the measurement It can be seen from Equation (2) that the value of eSpindle_1,2 directly determines the measurement accuracy of of thethe run-out. accuracy,the thespindle spindleerror errormotion motion accuracy run-out.For Forachieving achievingsatisfied satisfied measurement measurement accuracy, ofof thethe concentricity gauge must be separated. As expressed above—that one revolution of the microdrill concentricity gauge must be separated. As expressed above—that one revolution of the microdrill bit bit corresponds to to a portion gauge—themicrodrill microdrillbitbitcan can corresponds a portionofofone onerevolution revolutionof ofthe the concentricity concentricity gauge—the bebe measured accurately gauge, where wherethe thespindle spindleerror errormotion motion measured accuratelyatata afine fineposition positionofofthe theconcentricity concentricity gauge, reaches thethe minimum. An An accurate measurement of the errorerror motion of the gauge reaches minimum. accurate measurement of spindle the spindle motion ofconcentricity the concentricity of the measurement system is a pre-condition in order to locate the fine position. gauge of the measurement system is a pre-condition in order to locate the fine position.
Top scanning laser beam of the LSM Tedge(θj)
Tedge(θj+π) - eSpinde_1,2
Margin 1
Run-out Margin 2
Y Z
Spindle error motion eSpinde_1,2 Margin 2 X
Margin 1
eSpinde_1,2
Ideal position eSpinde_1,2
Figure 6. Influence of the spindle error motion on the run-out measurement. Figure 6. Influence of the spindle error motion on the run-out measurement.
2.2. Spindle Error Motion Measurement Using the Laser Scan Micrometer 2.2. Spindle Error Motion Measurement Using the Laser Scan Micrometer The reversal technique has been proposed for the measurement of the slide error motions and The reversal has been proposed for the the spindle slide error motions the spindle errortechnique motions of machine tools [20–24]. Themeasurement measurement of of the error motion and is theusually spindleperformed error motions machine tools [20–24]. Theameasurement the spindle error with of two displacement probes and measurement of artifact, in which themotion two is usually performed with displacement and sides a measurement artifact, which thethe two displacement probes aretwo arranged at twoprobes opposing of the artifact. Toinovercome displacement probes are arranged at two opposing sides of the artifact. To overcome the measurement measurement error caused by the misalignment error of the two displacement probes, a large-diameter error caused by the misalignment erroremployed of the twoindisplacement probes, a large-diameter measurement measurement artifact is frequently practice for the measurement of the spindle error artifact is frequently in practice for the measurement of thebespindle error However, motion. However, employed the large-diameter measurement artifact cannot used for the motion. measurement of spindle error motion of the concentricity gauge, due tofor itsthe limited gripping capacity. In ordererror to thethe large-diameter measurement artifact cannot be used measurement of the spindle an achieve accurate measurement the spindle error motionInof the to concentricity motion of the concentricity gauge, dueresult to its of limited gripping capacity. order an achieve gauge, accurate instead of using probes, top edge segment the bottom edge measurement resulttwo of additional the spindledisplacement error motion of thethe concentricity gauge,and instead of using two segment of the LSM are employed to detect the two opposing sides of a measurement artifact with a additional displacement probes, the top edge segment and the bottom edge segment of the LSM small diameter for measurement of the spindle error motion. Since the linearity of the LSM over the are employed to detect the two opposing sides of a measurement artifact with a small diameter for whole measurement rangeerror has been wellSince calibrated, the misalignment thewhole top edge segment measurement of the spindle motion. the linearity of the LSMerror overofthe measurement andhas thebeen bottom edge segmentthe is only on the level of 10 nm.top Therefore, the misalignment-induced range well calibrated, misalignment error of the edge segment and the bottom edge measurement error of the spindle error motion is negligible, even when employing the segment is only on the level of 10 nm. Therefore, the misalignment-induced measurement error of the small-diameter measurement artifact. spindle error motion is negligible, even when employing the small-diameter measurement artifact. A schematic of the spindle error motion measurement of the concentricity gauge by using the A schematic of the spindle error motion measurement of the concentricity gauge by using the LSM is shown in Figure 7. The spindle error motion is referred to as eSpindle(θM). θM represents the LSM is shown in Figure 7. The spindle error motion is referred to as eSpindle (θ M ). θ M represents the angular position of the main rollers along its circumference, which is provided by the attached scale angular position of the main rollers along its circumference, which is provided by the attached scale on the drive handle. A pin gauge with a small diameter is used as the measurement artifact. It is on rotationally the drive handle. A pin gauge with a small diameter is used asand the the measurement artifact. It is supported by the concentricity gauge. The upper surface lower surface of the pin rotationally supported by the concentricity gauge. The upper surface and the lower surface of the gauge are simultaneously measured by the top edge segment and the bottom edge segment of the pinLSM, gauge simultaneously by the the bottom top edge segment and bottomasedge in are which the top edge measured segment and edge segment arethe denoted TEdge segment and BEdge,of respectively. The spindle error motion of the concentricity gauge is measured before and after a
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the180-degree LSM, in which the top edge segment and as the bottom edge are denoted as TEdge of and reversal operation of in 8.8.Before 180-degree reversal operation ofthe thepin pingauge, gauge, asshown shown inFigure Figuresegment Beforethe thereversal reversaloperation operation of BEdge , respectively. The spindle error motion of the concentricity gauge is measured before and after the the pin pin gauge, gauge, the the pin pin gauge gauge isis driven driven by by the the two two main main rollers, rollers, and and the the outputs outputs of of the the top top edge edge a 180-degree operation of the pinsegment gauge, Bas shown inrespectively Figure 8. Before the reversal operation segment the edge are expressed as: segmentTreversal TEdge_Before Edge_Beforeand and thebottom bottom edge segment BEdge_Before Edge_Before are respectively expressed as: of the pin gauge, the pin gauge is driven by the two main rollers, and the outputs of the top edge TTEdge_Before θθ ==eeForm θθ ++eeSpindle θθ , , (3) (3) segment TEdge_Before and the bottomEdge_Before edge segmentForm BEdge_BeforeSpindle are respectively expressed as: + −− eeSpindle (4) (4) Edge_Before Edge_Before θθ ==eeForm Form θθ + Spindle θθ , , (3) TEdge_Before (θ M ) = eForm θ p + eSpindle (θ M ), where whereeeForm Form(θ (θpp))isisthe theform formerror errorof ofthe thepin pingauge, gauge,including includingan anout-of-roundness out-of-roundnesserror errorcomponent componentand and position of aa straightness θp represents the angular straightness error error component. component. angular of the the pin pin gauge gauge along along its its(4) BEdge_Beforeθ(pθ Mrepresents θp + π − eposition ) = eFormthe Spindle ( θ M ), circumference. circumference.After Afterthe thepin pingauge gaugeisisrotated rotatedby by180 180degrees degreeswith withrespect respectto tothe theangular angularposition positionof of where eForm (θ p ) rollers, is the form error of the pin gauge, including anand out-of-roundness error component the main the measurement isisconducted again, the outputs of thetwo two main rollers, thesame same measurement conducted again, and themeasurement measurement outputs ofthe the two edge are and a straightness error component. two edgesegments segments areexpressed expressedas: as: θ p represents the angular position of the pin gauge along its circumference. After the pin gauge is rotated by 180 θdegrees with respect to the angular position of the TTEdge_After + ++eeSpindle (5) (5) Edge_After θθ ==eeForm Form θpp+ Spindle θθdd , , two main rollers, the same measurement is conducted again, and the measurement outputs of the two − eeSpindle (6) (6) Edge_After θθ ==eeForm Form θθpp − Spindle θθdd , , edge segments are expressed as: BBEdge_After Based Basedon onthe theoutputs outputsof ofthe thetwo twosegment segmentof ofthe theLSM LSMbefore beforeand andafter afterthe thereversal reversaloperation operationof of θ p +the π + eSpindleof(θedForm (5) TEdge_After (θevaluated ), (θpp))as: M ) = eForm then without the Spindle(θ (θMM))can can thenbe beevaluated without theinfluence influence of eForm(θ as: thepin pingauge, gauge,eeSpindle 11 θθ (θ− ,, eeSpindle BEdge_After = eForm θθθ p +− eEdge_After (7) = 4 TTEdge_Before −)BBEdge_Before +TTEdge_After −BBEdge_Before (7) (6) M d ), − Spindle ( θθθ Spindle θθ = Edge_Before Edge_Before Edge_Before θθ 4
Figure the measurement of gauge. Figure 7.Schematic Schematic ofthe themeasurement measurementof ofthe thespindle spindleerror errormotion motion of concentricity gauge. Figure 7.7.Schematic ofof the spindle error motionof ofconcentricity concentricity gauge.
Figure 8.8.8.Measurement of the spindle errormotion. motion. Figure Measurement principle Figure Measurementprinciple principleof ofthe thespindle spindleerror error motion.
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Based on the outputs of the two segment of the LSM before and after the reversal operation of the pin gauge, eSpindle (θ M ) can then be evaluated without the influence of eForm (θ p ) as: i 1h TEdge_Before (θ M ) − BEdge_Before (θ M ) + TEdge_After (θ M ) − BEdge_Before (θ M ) , (7) 4 2, 4 J. Manuf. Mater. Process. 2018, 7 of 12 eSpindle (θ M ) =
3. 3. Experiments Experiments Measurement thethe spindle error motion of theofconcentricity gauge and the and run-out Measurement experiments experimentsofof spindle error motion the concentricity gauge the of the microdrill bit were carried out based on the measurement setup in Figure 2. The concentricity run-out of the microdrill bit were carried out based on the measurement setup in Figure 2. The gauge (Manufacturer: Universal Punch Corp., Santa CA,Santa USA,Ana, Model: had JSLP-10C) two main concentricity gauge (Manufacturer: Universal PunchAna, Corp., CA,JSLP-10C) USA, Model: rollers and a top roller. diameters of diameters the main rollers wererollers 22 mm, and22that ofand the that top of roller had two main rollers andThe a top roller. The of the main were mm, the was 6.3 mm. A LSM (Manufacturer: Mitutoyo Corp., Kwasaki, Japan, Model: LSM-902/6900) had top roller was 6.3 mm. A LSM (Manufacturer: Mitutoyo Corp., Kwasaki, Japan, Model: LSMa902/6900) scanninghad range of 32 mm, a resolution 0.00001–0.01 mm (selectable), a linearity of ±0.03 µm a scanning range of 32 mm, of a resolution of 0.00001–0.01 mm (selectable), a linearity of (narrow scanning range), and a measurement speed of 800 cycles/second. The LSM had two average ±0.03 μm (narrow scanning range), and a measurement speed of 800 cycles/second. The LSM had two methods, which were the arithmetical average and the moving average, with an average average methods, which were the arithmetical average and the movingrespectively, average, respectively, with range of 1–2048 points, which can be selectable in the instrument. The outputs of the LSM were an average range of 1–2048 points, which can be selectable in the instrument. The outputs of the LSM recorded by a 64-bit PC through a RS-232 interface. Figure 9 shows a pina gauge andand a microdrill bit, were recorded by a 64-bit PC through a RS-232 interface. Figure 9 shows pin gauge a microdrill in which the pin gauge was employed as the measurement artifact for the measurement of the spindle bit, in which the pin gauge was employed as the measurement artifact for the measurement of the error motion the concentricity gauge, and the microdrill bit is the measurement target for the run-out spindle errorofmotion of the concentricity gauge, and the microdrill bit is the measurement target for measurement. The pin gauge had a diameter of 3 mm and a length of 50 mm. The diameter and the the run-out measurement. The pin gauge had a diameter of 3 mm and a length of 50 mm. The length of the part of bitofwere 3 mm and bit 26 mm, those themm, body part of the diameter andshank the length ofthe themicrodrill shank part the microdrill wereand 3 mm andof26 and those of microdrill bit were 0.75 mm and 24 mm, respectively. the body part of the microdrill bit were 0.75 mm and 24 mm, respectively.
(a)
(b)
Figure 9. 9. Photographs of (a) (a) the the pin pin gauge gauge and and (b) (b) the the microdrill microdrill bit. bit. Figure Photographs of
Top edge segment
Temperature
Bottom edge segment Measurement time 10 min./div.
Temperature change 0.1 deg./div.
Outputs of the laser scan micrometer 2μm/div.
The stabilities of the LSM measurement system were firstly investigated. The temperature during The stabilities of the LSM measurement system were firstly investigated. The temperature during the measurement was measured as well by using a thermal sensor with a resolution of 0.001 ◦°C. In the the measurement was measured as well by using a thermal sensor with a resolution of 0.001 C. In the measurement of the stabilities, the LSM was set by using the moving average method, with averaging measurement of the stabilities, the LSM was set by using the moving average method, with averaging points of 512 to reduce the noise level. The measurement interval and the measurement resolution of points of 512 to reduce the noise level. The measurement interval and the measurement resolution of the LSM were 0.64 s and 0.01 μm, respectively. The measurement of the stabilities lasted for one hour, the LSM were 0.64 s and 0.01 µm, respectively. The measurement of the stabilities lasted for one hour, while all of the parts of the LSM measurement system were kept stationary. The measurement result is while all of the parts of the LSM measurement system were kept stationary. The measurement result is shown in Figure 10. The peak-to-valley (PV) stabilities of the top edge segment and the bottom edge shown in Figure 10. The peak-to-valley (PV) stabilities of the top edge segment and the bottom edge segment were evaluated as 0.57 μm and 0.65 μm, respectively, while the temperature drift during the segment were evaluated as 0.57 µm and 0.65 µm, respectively, while the temperature drift during the measurement was characterized as 0.269 °C (PV). The stabilities of the measurement system were measurement was characterized as 0.269 ◦ C (PV). The stabilities of the measurement system were influenced by the mechanical stability between the concentricity gauge and the LSM, the drift of the influenced by the mechanical stability between the concentricity gauge and the LSM, the drift of the scanning beam of the LSM, the temperature drift during the measurement procedure, etc. scanning beam of the LSM, the temperature drift during the measurement procedure, etc.
Temperature change 0.1 deg./div.
Outputs of the laser scan micrometer 2μm/div.
the LSM were 0.64 s and 0.01 μm, respectively. The measurement of the stabilities lasted for one hour, while all of the parts of the LSM measurement system were kept stationary. The measurement result is shown in Figure 10. The peak-to-valley (PV) stabilities of the top edge segment and the bottom edge segment were evaluated as 0.57 μm and 0.65 μm, respectively, while the temperature drift during the measurement was characterized as 0.269 °C (PV). The stabilities of the measurement system were J. Manuf. Mater. Process. 2, 4 influenced by the2018, mechanical stability between the concentricity gauge and the LSM, the drift of the8 of 12 scanning beam of the LSM, the temperature drift during the measurement procedure, etc.
Top edge segment
Temperature
Bottom edge segment Measurement time 10 min./div.
Figure 10.10. Stability micrometermeasurement measurement system. Figure Stabilityofofthe thelaser laser scan scan micrometer system. J. Manuf. Mater. Process. 2018, 2, 4
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18.650 18.650 18.645 18.645
No.2 No.2
No.3 No.3
10.655 10.655 10.650 10.650 10.645 10.645
18.640 18.640
10.640 10.640
18.635 18.635
10.635 10.635
18.630 18.630
10.630 10.630
18.625 18.625
10.625 10.625
BEdge_Before
BEdge_Before 10.620 18.620 18.620 Angular position of main roller 90 deg./div. 10.620
Output of of Top edge segment (mm) Output Top edge segment (mm)
No.1 No.1 TEdge_Before TEdge_Before
18.655 18.655 18.650 18.650 18.645 18.645
No.1 No.1
No.2 No.2
No.3 No.3
TEdge_After TEdge_After
10.655 10.655 10.650 10.650 10.645 10.645
18.640 18.640
10.640 10.640
18.635 18.635
10.635 10.635
18.30 18.30
10.630 10.630
18.625 18.625
BEdge_After
10.625 10.625
BEdge_After 10.620 18.620 18.620 Angular position of main roller 90 deg./div. 10.620
Output of of Bottom edge segment (mm) Output Bottom edge segment (mm)
18.655 18.655
Output of of Bottom edge segment (mm) Output Bottom edge segment (mm)
Output of of Top edge segment (mm) Output Top edge segment (mm)
3.1. Experimental Result of the Spindle Error Motion Measurement eSpindle (θM ) of the concentricity gauge evaluated based on the proposed measurement method, 3.1. Experimental Result of the Spindle Errorwas Motion Measurement e Spindle (θ M ) of the concentricity gauge was evaluated based on the proposed measurement method, as showneSpindle in Figure 8. concentricity The concentricity gauge was driven manually, and measurement the angular position (θM) of the gauge was evaluated based on the proposed method, was as shown in Figure 8. The concentricity gauge was driven manually, and the angular position was provided by the attached to the drive handle. Thedriven measurement sampling eSpindle (θ M ) was as shown in scale Figure 8. The concentricity gauge was manually, and the interval angular of position was provided by the scale attached to the drive handle. The measurement sampling interval of e Spindle(θM) ◦ 5.625provided . The measurement of e (θ ) was repeated by three revolutions, and the measurement outputs M drive handle. The measurement sampling interval of eSpindle(θM) by the scale attached Spindleto the was 5.625°. The measurement of eSpindle(θM) was repeated by three revolutions, and the measurement of TEdge BEdge before and afterofthe reversal operation in Figure 11. on Equation (7), wasand 5.625°. The measurement eSpindle (θM) was repeatedare by shown three revolutions, andBased the measurement outputs of TEdge and BEdge before and after the reversal operation are shown in Figure 11. Based on outputs of TEdge and Bof Edge before and aftercalculated, the reversal operation are in shown Figure 11. BasedPV onvalue the measurement results eSpindle (θM ) were and are shown Figurein12. The average Equation (7), the measurement results of eSpindle(θM) were calculated, and are shown in Figure 12. The Equation (7), the measurement results of e Spindle (θ M ) were calculated, and are shown in Figure 12. The of eSpindle (θMPV ) ofvalue the repeated measurement result was 7.10 µm, and the measurement repeatability was average of eSpindle(θM) of the repeated measurement result was 7.10 μm, and the measurement PV value of eSpindle (θM) of themainly repeated measurement result was 7.10 μm,ofand measurement 2.54 average µm. The repeatability error caused by the rotation accuracy thethe concentricity gauge, repeatability was 2.54 μm. Thewas repeatability error was mainly caused by the rotation accuracy of the repeatability was 2.54 μm. The repeatability error was mainly caused by the rotation accuracy of the sinceconcentricity the concentricity gauge was driven manually. Also, the non-repeatable rotation errors of the gauge, since the concentricity gauge was driven manually. Also, the non-repeatable two concentricity gauge, since the concentricity gauge was driven manually. Also, the non-repeatable mainrotation rollers errors were also a factor thatrollers induced the repeatability of the two main were also a factor thaterror. induced the repeatability error. rotation errors of the two main rollers were also a factor that induced the repeatability error.
Angular position of main roller 90 deg./div.
Angular position of main roller 90 deg./div.
(a) (a)
(b) (b)
Figure 11. Measurement outputs (a) before and (b) after reversing the pin gauge.
4.016 4.016 4.012 4.012
No.1 No.1
No.2 No.2
Result of three-time measurement Result of three-time measurement
4.000 4.000
Fine position Fine position
Average Average
4.022 4.022
4.014 4.014 4.010 4.010 4.006 4.006
3.996 3.996 3.992 3.992
4.026 4.026
4.018 4.018
4.008 4.008 4.004 4.004
No.3 No.3
4.002
Angular position of main roller 90 deg./div. 4.002 Angular position of main roller 90 deg./div.
(a) (a)
Average of of spindle error motion (mm) Average spindle error motion (mm)
Measurement result of of spindle Measurement result spindle error motion (mm) error motion (mm)
Figure 11.11. Measurement beforeand and(b) (b)after after reversing gauge. Figure Measurementoutputs outputs (a) before reversing thethe pinpin gauge.
(b) (b)
Figure 12. (a) Measurement result of the spindle error motion and (b) the fine position for the run-out Figure 12. (a) Measurement result of the spindle error motion and (b) the fine position for the run-out
Figure 12. (a) Measurement result of the spindle error motion and (b) the fine position for the measurement measurement run-out measurement. It can be seen from the measurement result that a fine position, which is located from the angular It can be seen from the measurement result that a fine position, which is located from the angular range of approximate 70° to 110°, had the minimum eSpindle(θM), which was 1.86 μm (PV). The fine range of approximate 70° to 110°, had the minimum eSpindle(θM), which was 1.86 μm (PV). The fine position corresponds to a 0.111 revolution of the concentricity gauge. Since the diameter of the shank position corresponds to a 0.111 revolution of the concentricity gauge. Since the diameter of the shank part of the microdrill bit and the diameter of the main rollers are 3 mm and 22 mm, one revolution of part of the microdrill bit and the diameter of the main rollers are 3 mm and 22 mm, one revolution of the microdrill bit corresponded to 0.136 revolution of the concentricity gauge. The range of the fine the microdrill bit corresponded to 0.136 revolution of the concentricity gauge. The range of the fine position of the concentricity gauge satisfied the required range for the measurement of the run-out
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It can be seen from the measurement result that a fine position, which is located from the angular range of approximate 70◦ to 110◦ , had the minimum eSpindle (θ M ), which was 1.86 µm (PV). The fine position corresponds to a 0.111 revolution of the concentricity gauge. Since the diameter of the shank part of the microdrill bit and the diameter of the main rollers are 3 mm and 22 mm, one revolution of the microdrill bit corresponded to 0.136 revolution of the concentricity gauge. The range of the fine position of the concentricity gauge satisfied the required range for the measurement of the run-out of the microdrill bit. 3.2. Experimental Result of the Run-Out Measurement
Run-out measured at fine position (μm)
Outputs on the two margins (mm)
In order to separate eSpindle (θ M ) out of the concentricity gauge to meet the required measurement accuracy, theProcess. microdrill J. Manuf. Mater. 2018, 2,bit 4 was measured at the identified fine position of the concentricity gauge. 9 of 12 The microdrill bit was gripped at the beginning of the fine position of the concentricity, as shown Figure 12b,12b, andand rotated oneone revolution to measure the two by the of theof LSM. in Figure rotated revolution to measure the margins two margins bytop thesegment top segment the Then, the microdrill bit was rotated backback to the beginning of of the LSM. Then, the microdrill bit was rotated to the beginning thefine fineposition positionfor for the the second measurement. repeated 1010 times, and thethe measurement outputs on the measurement. This Thisset setofofmeasurements measurementswas was repeated times, and measurement outputs on two margins are shown in Figure 13a.13a. The The measurement repeatability on Margin 1 and1 Margin 2 was2 the two margins are shown in Figure measurement repeatability on Margin and Margin 0.51 μm By utilizing Equation (1) and(1) the measurement outputsoutputs in Figure was 0.51and µm 0.96 and μm, 0.96respectively. µm, respectively. By utilizing Equation and the measurement in 13a, the13a, average of theofmeasured run-out of the microdrill bitbit was 13.57 Figure the average the measured run-out of the microdrill was 13.57μm, µm,with withaameasurement measurement repeatability of 1.16 μm, µm, as shown in Figure 13b. The standard deviation of the measurement results was 0.40 μm. The repeatability error was mainly caused by the uneven rotational speed and the drift µm. of the scanning beam of the LSM during the measurement.
19.034 19.030
Output on Margin 1
19.026 19.022
Output on Margin 2
19.018 19.014
16 15 14 13
1.16 μm
12 11 10
Measurement time of micro drill bit 1 meas./div.
Measurement time of micro drill bit 1 Meas./div.
(a)
(b)
Figure 13. (a) (a)Measurement Measurementoutputs outputs margins andthe (b)measurement the measurement result of the Figure 13. onon thethe twotwo margins and (b) result of the run-out run-out at the fine position of the concentricity gauge. at the fine position of the concentricity gauge.
4. Uncertainty of the Run-Out Measurement 4. Uncertainty of the Run-Out Measurement To confirm the reliability of the proposed methods for measurement of the run-out of the To confirm the reliability of the proposed methods for measurement of the run-out of the microdrill microdrill bit, an uncertainty evaluation of the measurement of the run-out was carried out based on bit, an uncertainty evaluation of the measurement of the run-out was carried out based on Guide to Guide to Expression of Uncertainty in Measurement (GUM) [25]. Figure 14 shows a schematic of the Expression of Uncertainty in Measurement (GUM) [25]. Figure 14 shows a schematic of the uncertainty uncertainty sources. The measurement uncertainty on each margin was composed of the sources. The measurement uncertainty on each margin was composed of the measurement resolution measurement resolution of the LSM, the linearity of the LSM, the thermal drift, and the mechanical of the LSM, the linearity of the LSM, the thermal drift, and the mechanical vibration during the vibration during the measurement. The combined measurement uncertainty of each margin, which measurement. The combined measurement uncertainty of each margin, which is referred to as uMargin , is referred to as uMargin, can be evaluated based on the following equation: can be evaluated based on the following equation: = 2 u2Resolution + u2Linearity + u2 2 + u2Vibration , uMarginq uMargin = uResolution + u2Linearity +Thermal uThermal + u2Vibration ,
(8) (8)
According to Equation (2), the measurement uncertainty of the run-out was composed of the uMargin of the two margins and the uncertainty uSpindle of the spindle error motion of the concentricity gauge, as well as the uncertainty uReading of the measurement repeatability of the run-out, in which uSpindle is the spindle error motion at the fine position of the concentricity gauge. The combined measurement uncertainty of the run-out, which is referred to as uRun-out, can be expressed as: u
= 2u2Margin +
+ u2
,
(9)
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According to Equation (2), the measurement uncertainty of the run-out was composed of the uMargin of the two margins and the uncertainty uSpindle of the spindle error motion of the concentricity gauge, as well as the uncertainty uReading of the measurement repeatability of the run-out, in which uSpindle is the spindle error motion at the fine position of the concentricity gauge. The combined measurement uncertainty of the run-out, which is referred to as uRun-out , can be expressed as: uRun−out =
q
2u2Margin + u2Spindle + u2Reading ,
(9)
Table 1 shows the uncertainty budget for the measurement of the run-out. uMargin was evaluated to be 0.34 µm. The combined uncertainty of uRun-out based on Equation (9) was evaluated to be 0.61 µm. The expanded uncertainty with a coverage factor of k = 2 for the measurements of the run-out was evaluated to be 1.22 µm, in which the evaluated uncertainty had a level of confidence of approximately 95%. The measurement results and the measurement uncertainty confirmed that the proposed error J. Manuf. Mater. Process. 2018, 2, 4 10 of 12 separation method is reliable for the measurement of the run-out with sub-micrometric accuracy.
Figure 14. Schematic of the uncertainty sources of the run-out measurement. Figure 14. Schematic of the uncertainty sources of the run-out measurement. Table 1. Uncertainty budget of the run-out measurement. Table 1. Uncertainty budget of the run-out measurement.
Uncertainty Source Uncertainty Source Resolution
LSM
LSM
Resolution Linearity Linearity
Thermal drift
Thermal drift vibration Mechanical Mechanical vibration Combined uncertainty uMargin Combined uncertainty uMargin Spindle error motion Spindle error motion Reading repeatability Reading repeatability Combined uncertainty uRun-out uRun-out Combined uncertainty
Type Standard Uncertainty (μm) Standard B Type 2.89 × 10−4 Uncertainty (µm) B B 0.02 2.89 × 10−4 0.02 B B 0.16 0.16 A B 0.04 A 0.04 0.17 0.17 B B 0.54 0.54 A A 0.13 0.13 0.61 0.61
Compared with the used ultra-precision rotary drive devices, the Compared theprevious previousresearch researchstudies studiesthat that used ultra-precision rotary drive devices, proposed error separation method can also achieve sub-micrometric accuracy for the measurement the proposed error separation method can also achieve sub-micrometric accuracy for the measurement of the the run-out run-outof ofmicrodrill microdrillbit, bit,even eventhough thoughthe thespindle spindle error motion concentricity gauge of error motion of of thethe concentricity gauge waswas as as large as 7.10 Although the realized accuracy hassufficient been sufficient for industrial application, large as 7.10 µm. μm. Although the realized accuracy has been for industrial application, from the from the uncertainty budget, it can seen that the spindle motion of the fine position of the uncertainty budget, it can be seen thatbethe spindle error motionerror of the fine position of the concentricity concentricity gauge was still thecontributing major sourcetocontributing to theuncertainty. measurement For gauge was still the major source the measurement Foruncertainty. improving the improving theaccuracy measurement to the nanometric order, it necessary to further separate the measurement to theaccuracy nanometric order, it is necessary toisfurther separate the spindle error spindle error asof the next step of the research. motion, whichmotion, remainswhich as theremains next step the research. 5. Conclusions An error separation method has been proposed for a precision measurement of the run-out of a microdrill bit by using a measurement system consisting of a concentricity gauge and a laser scan micrometer (LSM). In order to achieve a precision measurement of the run-out, rotating the microdrill
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5. Conclusions An error separation method has been proposed for a precision measurement of the run-out of a microdrill bit by using a measurement system consisting of a concentricity gauge and a laser scan micrometer (LSM). In order to achieve a precision measurement of the run-out, rotating the microdrill bit at the fine position of the concentricity gauge with the minimum spindle error motion for the measurement of the run-out was proposed for separating the influence of the spindle error motion. Taking into consideration the limited gripping capacity of the concentricity gauge, the LSM and a small-diameter artifact—instead of the conventionally used displacement probes and large-diameter artifact—were employed to measure the spindle error motion of the concentricity gauge for determining the fine position. Then, the measurement of the run-out was conducted at the determined fine position to achieve high measurement accuracy, which previously cannot be realized by the commercial concentricity gauge combined LSM measurement system. The measurement result showed that the average of the measured run-out was 13.57 µm. The measurement uncertainty of the run-out by using the measurement system and the proposed error separation method was estimated to be 0.61 µm. It has been confirmed that the proposed error separation method is reliable for a run-out measurement with sub-micrometric measurement accuracy. As the first step of the research, this paper has focused on achieving the precision measurement of the run-out. It should be noted that the measurement position along the axial direction of the microdrill bit hasn’t been accurately determined in this research. Instead, an additional positioning stage is necessary to determine the axial measurement position on the microdrill bit, which will be carried out as next step of this research. Author Contributions: Z.N. conducted experiments and paper writing. Y.-L.C., Y.S., H.M. and W.G. designed the study, supervised the work and modified the manuscript. Conflicts of Interest: The authors declare no conflict of interest.
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