EFFECTS OF STYLUS POSITION SHIFTING TO ECCENTRICITY AND ROUNDNESS VALUE IN GLASS HEMISPHERE
MEASUREMENTS
PENGARUH PERGESERAN POSISI STILUS TERHADAP EKSENTRISITAS DAN NILAI KEBUNDARAN PADA PENGUKURAN GELAS SETENGAH BOLA
Nadya Larasati Kartika, Ardi Rahman, Asep Ridwan Nugraha Research Center for Metrology, Indonesian Institute of Science (LIPI) Complex of Puspiptek Building 420, Serpong, Tangerang Selatan 15314 [email protected]
ABSTRACT
In this research, the testing of the effect of stylus position shifting to eccentricity on hemisphere roundness measurement was done in Research Center for Metrology LIPI (RCM-LIPI). The effect would give the acceptable eccentricity value for center adjustment of hemisphere. Least Square Circle (LSC) data fitting and Gaussian filtering were used in data processing. The result showed that the roundness values were constant until 3.3 µm shifting value with 3.23 µm in eccentricity. However, it started to increase significantly when the eccentricity value reached above that, so it gave an uncertainty contribution to the hemisphere measurement.
Keywords: roundness metrology, stylus position shifting, eccentricity, glass hemisphere, LSC, Gaussian filtering
ABSTRAK
Pada penelitian ini, pengujian efek dari variasi pergeseran posisi stilus terhadap eksentrisitas dalam pengukuran kebundaran hemisfer dilakukan di Pusat Penelitian Metrologi LIPI (RCM-LIPI). Pengaruh tersebut akan menghasilkan besaran nilai eksentrisitas yang diterima dalam pengaturan posisi hemisfer terhadap stilus. Filter Gaussian dan fitting Least Square Circle (LSC) digunakan dalam proses pengolahan data. Hasil menunjukkan bahwa nilai kebundaran masih stabil sampai posisi 3,3 µm dengan nilai eksentrisitas 3,23 µm. Namun, nilai kebundaran mulai mengalami kenaikan secara signifikan ketika nilai yang dihasilkan melebihi angka tersebut yang berakibat pada besarnya unsur ketidakpastian dalam pengukuran hemisfer.
Kata kunci: metrologi kebundaran, pergeseran posisi stilus, eksentrisitas, hemisfer, LSC, Gaussian filter
A. INTRODUCTION
As National Metrology Institute (NMI) in Indonesia, Research Center for Metrology (RCM)-LIPI has some important roles in maintaining and disseminating the national standard for unit measurement. One of these national standard for measurement units is roundness.
Roundness measurement has important roles in industries and becomes one of several elements on quality control for mechanic production process. When a roundness value has a big deviation from required specification, it will give negative impacts for the products like noises, unproper rotation, and alignment error on shaft (Juhanko, 2011).
Roundness measurement is carried out by rotating instruments (Thalmann & Spiller, 2005). Roundness does not describe radial
displacement of a shape from some notional centre point, merely it describes all over the shape (Reeve, 1979). Roundness is measured using rotational techniques by measuring radial deviation from a rotating datum axis.
Every rotating object is always related to a parameter, that indicates the distance between the object and the axis datum, called as eccentricity. In mathematics, an object can be classified as perfectly round if it has zero in eccentricity.
Several studies about roundness and eccentricity have been conducted in recent times.
Sieniło and Żebrowska-Łucyk (2014) have studied a proper method for errors compensation in roundness measurement, such as the effect of the center position and cylindricity. On their experiments, they used cylinder artifacts and was measured using roundness measurement
instrument, but the effect of eccentricity on the roundness value was not clearly seen yet because the eccentricity and cylindricity errors were still merged. Zakharov and Brzhozovskii (2006) studied about the effect of centering accuracy on the error for measurement using roundness gauge as a workpiece. They used harmonic analysis in compensating a given error.
Eccentricity is related to centering position of hemisphere to the spindle rotation center.
Ideally, the profile of measurement will have a circle form. Due to the eccentricity, however, measurement profile will not show as a circle form. It will give some distortion at several points of radius. Furthermore, eccentricity effect in roundness measurement is quite difficult to avoid.
Several publications has stated that centering position of setting glass hemisphere standard on roundness machine should be smaller than 1 µm (Neugebauer, 2000; Reeve, 1979;
Sieniło & Żebrowska-Łucyk, 2014; Thalmann, 2006). So far, there are no technical reasons which supported that statement. Even though, the initial centering position of workpiece is necessary as one of several parameters to avoid eccentricity.
Stylus position plays an important role on measurement techniques, especially when the object has multi-structure or a combination between round object and another object. This paper explained the effect of stylus position shifting to the eccentricity and the roundness value based on computational algorithm application. The stylus shifting positions to the eccentricity values were investigated, thus the maximum value for initial setting measurement could be predicted. The result can be applied for high precision roundness measurement practitioners especially on glass hemisphere.
B. THEORY
Based on International Standard, there are several methods to determine the roundness value from a polar graph measurement result (ISO 4291, 1985; ISO 6318, 1985). They are
Reference Circle (MZC), Minimum Reference Circumscribed Circle (MCC), and Maximum Inscribed Circle (MIC) (Juhanko, 2011; Reeve, 1979). Some journals stated that LSC method gives more accurate roundness value than the other methods (Piengbangyang, Somthong, Buajarern, & Tonmueanwai, 2009; Reeve, 1979; Yalovoy, Zakharov, & Kochetkov, 2015;
Zakharov & Brzhozovskii, 2006).
A polar graph in a rectangular coordinate system is shown in Figure 1. O is the centre of rotation of the spindle during measurement; yi is the distance between O to P on the curve at the rectangular position of each θi; point (a,b) is the centre of LSC curve fitting; R is the radius of LSC curve fitting, E is the distance between center of workpiece and center point of curve fitting, and ∆ is the difference between LSC curve fitting and workpiece trace.
LSC curve fitting was applied by minimizing the difference between measured roundness data and predicted roundness data.
cos sin
i i i
y R a= + θ +b θ (1)
( )
21
, , min N ( i i)
i
LSC R a b d y
=
= −
∑
(2)( ) ( )
21
, , min N ( i cos i sin i)
i
LSC R a b d R a θ b θ
=
= − + +
∑
(
) ( )
21
, , min N ( i cos i sin i)
i
LSC R a b d R a θ b θ
=
= − + +
∑
(3)Source: Reeve (1979)
where di is the measured roundness value, yi
is the predicted roundness value, θi is the step angle in measurement, R is the radius from LSC curve fitting, a and b are the central point (a, b) of reference circle which is determined through LSC fitting curve. Spragg approach (Spragg, 1967) was used to calculate R, a and b parameters due to its simplicity.
(4) Eccentricity value was obtained from the distance between measured central point and LSC central point (a, b), according to equation below,
2 2
E = a +b (5)
where E is eccentricity, a and b are x-axis and y-axis correction respectively.
C. METHODOLOGY
Roundness measurement was carried out in RCM-LIPI with ambient (20.0 ± 0.5)oC temperature and humidity (55.0 ± 10)%. The measurement was done using a glass hemisphere standard (Figure 2 (a)) with 50 mm diameter as a workpiece from Taylor Hobson type 112/436, serial number 170 D that was placed on a rotating table. A probe with spherical tip 0.79
mm in diameter from tungsten carbide materials was used with effective arm length 63.5 mm measured from its pivot point. The spindle was rotated at speed of 6 rpm around the workpiece area. Talyround 3 from Taylor Hobson as shown in Figure 2 (b) was employed as a standard roundness machine, which was calibrated using magnification standard (flick) and traceable to SI through TUBITEK UME, Turkey.
Position of measuring point on hemisphere was located at 3 mm height from the bottom of a hemisphere with the angle between the hemisphere and the stylus was around 20o as shown in Figure 2 (b). The red point on hemisphere was located at 270 degree on the rotary table roundness machine.
The influence of the eccentricity on the value of roundness was carried out in several steps by involving eccentricity variations. Eccentricity value was varied by changing the spindle position to the x axis. Deviation positions of spindle were set within range 0–6.5 µm and with 0.1 µm increments. Scheme of roundness measurement is simply summarized in Figure 3.
(a) (b)
Figure 2. Roundness Artefact, (a) The Top View of Glass Hemisphere and (b) The Roundness
Measurement Set Up for Glass Hemisphere Figure 3. Scheme of Roundness Measurement
D. RESULT AND DISCUSSION
Roundness measurement will provide the deviation value or out-of-roundness from the real hemisphere radius based on the reference as a raw data. The output of roundness measurement consisted of a set of n numbers which represented the radial deviations of the workpiece at each point. Roundness profiles were transferred to the polar graph according to Spragg equation (Spragg, 1967).
Measurements were conducted using sixty- six stylus positions from 0–6.5 µm with 0.1 µm increment of the workpiece and contained two thousands data points from 0–360o around the hemisphere.
The raw data showed that the data was needed to be centered by LSC. This step was necessary because the data contained roughness and other harmonic components such as mechanic chatter, electric noises, mechanical gear movement, spindle error, and eccentricity.
Other components besides the roundness deviation value are needed to be filtered after LSC methods was applied.
1. LSC Curve Fitting
LSC method was applied to the raw data. The effect of stylus shifting to the roundness polar graph using LSC fitting at 0 µm shifting position and at 6.5 µm the extreme position is shown in Figure 4 (a) and Figure 4 (b) respectively. LSC fitting result on 0 µm shifting position showed nearly perfect fitted in the center of the raw fluctuation data, while some part of the data on
6.5 µm were fluctuated above LSC fit at 60–90o and 240–270o. This result explained that there was a slight shape evolution from the perfect circle to eliptical form due to stylus shifting position.
Smaller noise intensity was appeared on 6.5 µm position due to the force between the stylus and the surface of hemisphere on 6.5 µm position which was bigger than on 0 µm position. This can be explained that the vibration between stylus and hemisphere was attenuated.
The number of spindle revolution on the surface of hemisphere can also be contributed by minimizing the roughness.
After the value of a and b were obtained from LSC, both parameters were used to centering the raw data. The a value was varied from -6.31 µm to 0.03 µm, while b value was varied from -287.30 µm to 144.53 µm.
2. Gaussian Filtering
Data filtering was done after the raw data were already located on the center using LSC.
LSC fitting was applied to homogenize the data trends in order to avoid any additional harmonic components from shifting the center of measurement which belongs to hemisphere as shown in Figure 5. If the center shifting position was bigger, the intensity of additional harmonic would be bigger and could corrupt the real information. Roughness data were needed to be removed from measurement result (Juhanko, 2011). Roughness and undesirable elements were removed using Gaussian filter at spacial
Figure 5. Data Before and After LSC Fitting for 0.02 µm Eccentricity
domain to reduce high frequency component on measurement data result.
Gaussian UPR-50 was used for each two thousand-data point as a filter to remove the roughness data. The Fourier spectra before and after filtering for 0 µm stylus position shifting is shown in Figure 6. The Fourier spectra is shown in undulation per revolutions (UPR) unit. The -3 dB cut off began at 145.15 upr and fully filtered data above 249.24 upr.
The radius profile differences between before and after filtering for 0 µm stylus position shifting is shown in Figure 7. After filtering, the data became smooth and consisted of roundness value only. Radial deviation mainly appeared at 60–90o and 240–270o from the contribution of the stylus shift positions. It was also assumed that the dust particles or residues from cleaning process had given an influence to the deviation on hemisphere measurement.
However, Neugebauer (2000) showed that the dust particle was negligible because the effect was much smaller than other contributions such as vibration, mechanical gear movement, thermal drift, and error from the spindle itself.
3. Eccentricity Effect on Out-of-Roundness The relationship between stylus position shifting to eccentricity is shown in Figure 8. Initial setting stylus position was -0.30 µm from hemisphere. Generally, the relationship tends to be linear.
When stylus position reached -0.20 µm, the eccentricity value close was to zero and at ±1 µm, the eccentricity value was 1.21 µm. These result showed that technically this condition is an ideal condition for initial setting of hemisphere measurement.
Figure 9 shows a graph of the eccentricity effect to the out-of-roundness value. However, artifacts and range value measurement were used is different, this result is in a good agreement with Sieniło & Żebrowska-Łucyk (2014). As can be seen in Figure 9 during the motion of stylus shifting position from 0.03 µm until 1.21 µm in eccentricity, the out-of-roundness value relative was in the range 0.02 µm to 0.03 µm.
Above 1.21 µm of stylus position shifting, the out-of-roundness value was still in the range of 0.02−0.03 µm until eccentricity reached 3.23 µm.
The roundness deviation was starting to increase over 3.23 µm eccentricity. This phenomena showed the acceptance eccentricity value when initial position setting was greater than ±1 µm because the roundness deviation value was relatively stable within range 0.02 µm to 0.03 µm.
Finally, the acceptance eccentricity value for initial centering position setting of hemisphere is 3.23 µm with stylus position at 3.3 µm. It should be noted that this result only applies for artifacts that have high precision such as hemisphere.
Since the result shows greater than ±1 µm, the eccentricity effect can negligible in hemisphere measurement because a promising method for roundness measurement has been provided namely multistep method. Multistep method is used to minimizing undesirable elements using error separation methods (Neugebauer, 2000; Piengbangyang et al., 2009; Chetwynd
& Siddal, 1976).
Figure 6. The Fourier Spectra Before and After Filtering for 0 µm Stylus Position Shifting
E. CONCLUSION
The effect of stylus position shifting to eccentricity was examined. The result shows that initial centering position could be greater than ±1 µm. This result can be applied to high precision artifacts such as glass hemisphere.
This technique is expected to be applied for roundness measurement practitioners in other NMIs, especially in high precision roundness measurement.
ACKNOWLEDGEMENT
The authors would like to thank head and staffs of Length Laboratory in RCM-LIPI for providing all measurement equipments. The authors also would like to thank Dr. Sensus
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