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Evaluation of removal characteristics of bonnet polishing tool using polishing forces collected online
Journal of Manufacturing Processes 47 (2019) 393–401
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Evaluation of removal characteristics of bonnet polishing tool using polishing forces collected online
T
Ri Pana, Wanying Zhaoa, Bo Zhongb,⁎, Dongju Chena, Zhenzhong Wangc, Chunqing Zhaa, Jinwei Fana a
Beijing Key Laboratory of Advanced Manufacturing Technology, Beijing University of Technology, Beijing 100124, China Research Center of Laser Fusion, China Academy of Engineering Physics, Mianyang 621900, China c Department of Mechanical and Electrical Engineering, Xiamen University, Xiamen 361005, China b
ARTICLE INFO
ABSTRACT
Keywords: Bonnet polishing Polishing force Tool removal characteristics
The polishing efficiency and accuracy for optical elements are strongly affected by the removal characteristics of the polishing tool and are commonly evaluated using a tool influencing function(TIF). During most polishing processes, the TIF is obtained through offline measurements, which are time-consuming. Consequently, the use of polishing forces collected online to evaluate TIF, including its spot shape and efficiency, was investigated as a means of reducing measurement times. Based on the elastic theory, the formation mechanism for an elliptical TIF spot during a bonnet polishing process is thought to have a long axis length that is close to a predefined value and a short axis length that is proportional to the third root of the normal force. Based on the above finding, a polishing force-based prediction model for TIF spot shape was derived and validated. The predicted results agreed well with experimental results. Afterwards, a polishing force-based, semi-quantitative prediction model for TIF efficiency was developed by combining Preston’s law and Hertz contact theory. The model was validated experimentally and successfully predicted changing trends in TIF efficiency. Based on this study, the spot shape and efficiency of the TIF can be predicted using polishing forces collected online. This approach provides a potential method that could be used in engineering applications to optimize bonnet polishing processes through a reduction in the time needed for offline measurements.
1. Introduction The tool influencing function(TIF) is an important property associated with polishing technology and represents the amount of removed material by a polishing tool in a unit of polishing time at a fixed location on a workpiece. The TIF model is usually used to calculate the dwelling time of the polishing tool on the surface of a workpiece during correction and to predict the amount of material removed from a workpiece after machining. The precision of the TIF model affects both polishing efficiency and accuracy. Thus, having an accurate TIF model is necessary for most polishing technologies [1–10]. Bonnet polishing has become more commonly used in recent years as a precise and efficient polishing technology for hard and brittle materials. Although many studies have investigated TIF modeling of a bonnet tool, the material removal mechanism during bonnet polishing process is still not fully understood. Commonly, the TIF model for a bonnet polishing tool can be obtained via a practical polishing test or
⁎
through a theoretical derivation. The TIF model achieved using the former approach is more precise but highly time-consuming, since offline measurements using an interferometer are required after the polishing test is complete. Theoretically derived TIF models for bonnet tools without offline measurement have been studied extensively. Kim et al. [1], Zhang et al. [2], Cheung et al. [3], Wang et al. [4], Zeng et al. [5], Ke et al. [6] and Feng et al. [7] analyzed bonnet polishing processes at a macroscopic level, and established theoretical TIF models in terms of Preston’s law. Different from the above studies, Cao et al. [8,9] and Shi et al. [10] selected single polishing abrasive that removed workpiece material as a target, and calculated the amount of workpiece material removed by a single abrasive based on contact mechanics, kinematic theory and wear mechanisms. Afterwards, based on the above calculation, theoretical TIF were obtained using this method by summing the removal amounts for all abrasives involving in the polishing process. For the derivation of the above theoretical TIF models, contacting
Corresponding author. E-mail address: [email protected] (B. Zhong).
https://doi.org/10.1016/j.jmapro.2019.03.029 Received 30 January 2019; Received in revised form 14 March 2019; Accepted 23 March 2019 1526-6125/ © 2019 The Society of Manufacturing Engineers. Published by Elsevier Ltd. All rights reserved.
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pressure or contacting force between the bonnet tool and workpiece computed via contact theory or simulations is crucial. However, since the removal mechanism during bonnet polishing process is still not well-understood, the theoretical contacting pressure or contacting force is different from the actual forces, which more or less limits the application scope of TIF. Based on the above analysis, both of the current approaches to obtain a TIF have disadvantages: offline measurement is time-consuming, and the contacting forces in the theoretical models are inconsistent with actual situations. The current study seeks to address the above problem by modeling the TIF using contacting forces collected online. Studies that investigated removal mechanisms and TIF modeling using collected polishing forces for other polishing technologies have been conducted [11–17]. For example, Singh et al. [11] investigated the forces acting on a material during magnetic abrasive finishing and established a correlation between surface finish and forces. Thus, the underlying mechanism for material removal is understood. Miao et al. [12] collected the contacting forces imposed on a surface during polishing processes and investigated the effects of various parameters that impact material removal for borosilicate glass. Homma et al. [13] studied the removal mechanism associated with chemical mechanical polishing using measured frictional forces and proposed an experimental TIF model. Based on the previous studies that used collected polishing forces, it is feasible to investigate the removal mechanism in bonnet polishing process and establish a TIF model for a bonnet tool via polishing forces collected online. Since it has been reported in our previous study [18] that, online collection of polishing forces during bonnet polishing processes has been achieved, this paper proposes the establishment and validation of the TIF model for a bonnet tool based on the polishing forces collected online.
Fig. 2. Typical bonnet polishing process.
consist of two parts, one for spot shape and the other for MRD of the TIF. 2.1. Prediction model for TIF spot shape based on the polishing forces collected online A typical bonnet polishing process is shown in Fig. 2. The TIF spot on the polished surface is supposed to be circular, whose radius Rc is predefined by controlling the compression of the bonnet tool. However, the actual spot shape of the TIF formed by the bonnet tool is found to be an ellipse [13] with the length of the long axis close to the defined radius Rc and a short axis length that is less than Rc. To explain these results, contact theory was studied. When hard and brittle materials such as glasses and ceramics, are polished, there are large hardness differences between the bonnet tool (made from rubber) and the workpiece. The contact type between the tool and workpiece can be regarded as an elastic ball contact with a rigid plane. Thus, as depicted in Fig. 3, in terms of elastic theory [19], when the elastic ball contacts the rigid plane under the normal force Fn, deformation occurs in the normal direction and causes the actual radius of the contacting area a to be always less than the nominal radius e. Moreover, a can be calculated by [19]
2. Modeling of TIF based on online collected polishing forces An ideal 3-dimentional TIF for a bonnet polishing tool is shown in Fig. 1. The most focused characteristics of the TIF are the maximum removal depth (MRD) shown in Fig. 1(a) and the spot shape shown in Fig. 1(b), because MRD and spot shape reflect the efficiency and regularity of the TIF, respectively. Consequently, the proposed TIF model to be established for the bonnet tool based on online collected forces
a=
3 Fn R 4 E*
1 3
Fig. 1. Typical TIF of bonnet tool. 394
(1)
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Fn R 4 E*
b= 3
1 3
(3)
Based on literature [4], E1 < < E2, consequently, the second item in the right part of the Eq. (2) can be neglected, and Eq. (2) can be expressed as 2 1
1
1 E*
(4)
E1 Combining Eq. (3) with Eq. (4), it yields
b= 3
Where Fn is the normal force, R is the radius of the elastic ball, and E* is the composite modulus, which can be calculated by
1 1 = E* E1
+
2 2
1 E2
1 2 3 1)
(5)
It should be noted that, Eq. (1) and Eq. (5) are derivated from a static contacting condition, but in dynamic polishing process, beside the variables in Eq.(5), some uncontrollable variables such as tool wear and the polishing slurry concentration also affect the length b of the contacting area, and the effect is hard to calculate. For this reason, similar to the preston coeficient k in the well-know Preston’s law, a correction factor ks which reveals the effect brought by the uncontrollable factors on the length of contacting area is introduced into Eq. (5) to yield
Fig. 3. Contact between elastic ball and rigid plane.
2 1
Fn R (1 4 E1
b = ks
3 Fn R (1 4 E1
2 1)
1 3
(6)
Strictly speaking, ks is not a constant because it changes with polishing time. However, ks is used as a constant in a certain period of polishing time for simplication. And like the calculation method of preston coefficient k [4], after a period of polishing time, a single experiment should be required to correct the ks value. Based on Eq. (6), as long as the normal force Fn can be acquired from the data collected online, the length of the short axis of the TIF can be calculated as
(2)
The parameters E1 and E2 are the elastic modulus of the bonnet tool and the workpiece, respectively. ε1 and ε2 are Poisson ratio of the bonnet tool and the workpiece, respectively. Using the above theory, the ellipse spot of the TIF formed by the compression of the bonnet tool can be explained. In Fig. 2, when the rotating bonnet tool polishes the workpiece in the long axis direction, the bonnet is supposed to be static, and the long axis length is close to the defined radius Rc. However, the short axis direction shown in Fig. 4 (left view of Fig. 2), the bonnet is cutting in and out through the whole polishing process under the action of Fn. During the cutting process elastic deformation occurs, which leads to a reduction in the length of the short axis. Since the long axis length is basically equal to Rc, the spot shape of TIF is determined by the length of the short axis. Therefore, the prediction model for TIF spot shape to be established is actually the prediction model of the length of the short axis of the TIF. In terms of Eq. (1), half of the actual length of the short axis of the TIF spot shape can be expressed as
R cs = 2 b = ks 6
Fn R (1 E1
1 2 3 1)
(7)
In addition to the previous statement that the long axis of the TIF spot is approximately equal to the defined radius, the spot shape of the TIF can be evaluated. 2.2. Predictive model for TIF efficiency based on polishing forces collected online As described in our previous study [18], the theoretical TIF for the bonnet polishing tool can be expressed using a modified Preston’s law as
RR (x , y ) = µ k P (x , y ) v (x , y ) t
(8)
where RR (i.e., TIF) is the removed workpiece material by polishing tool in certain time t. μ is the interface friction coeficient, k denotes the Preston coefficient, P and V are the pressure and relative velocity distribution on the contacting area, respectively. Based on Fig. 1, the MRD of the TIF (i.e., the maximum of RR) can be expressed as
MRD = Max(RR) = µ k Pmax vm t
(9)
Where Pmax is the maximum pressure on the polished spot, vm is the velocity corresponding to the maximum pressure. Since the TIF of bonnet tool may have different contours (Gaussian type and M type according to literatures [4,6]), it should be emphasized that only Gaussian contour TIF is considered in this section. Regarding to the Gaussian TIF, the maximum RR and the maximum pressure Pmax is supposed to be located at a point near the centre of the TIF (where the position parameters in Eq.(8) x = 0 and y = 0). However, the
Fig. 4. The deformation during bonnet polishing process.
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maximum velocity on the spot is usually locating at the edge of the TIF, that is why only the maximum pressure is involved in Eq.9. Based on Fig. 2 and literature [18], there is (10)
µ = Ft Fn vm =
interferometer (model SSI, made by QED). After that, the TIFs were extracted from the measurement data. Thus, in order to obtain the TIF, the workpiece needs to be disassembled from the worktable after polishing and moved to the interferometer. (2) The polishing forces are collected online by a 3-components dynamometer (model 9257B, made by Kistler) during polishing process and are transmitted real time to the computer [20].
((R
y cos n 2 /60) 2 + (x cos n 2 /60)2
h) sin n 2 /60
(11) Where Ft is the frictional force, Fn is the normal force, ρ is the incline angle of tool spin, n is the tool rotational speed, R is bonnet radius and h is the compression of the bonnet. As stated before, vm is the velocity corresponding to the maximum pressure, therefore, both x and y in Eq. (11) are equal to 0, which yields:
vm = (R
It is obvious that the offline measurement of the TIF is time consuming in comparison to the online collection of polishing forces. Consequently, if the polishing forces collected online can be used to evaluate the offline measured TIF, the bonnet polishing process could be optimized by reducing the processing time. All of the TIFs and the corresponding force data to be analyzed in the following section were obtained using the above approach. The data consists of three groups of experiments that used different bonnet tools and were conducted at different times [18,21]. The key parameters applied for the three groups of experiments are listed in Tables 1–3. In addition, the workpiece were BK7 glasses, the employed polishing tool is an improved semirigid bonnet tool [22], of which the radius was R = 80 mm. The elastic modulus and the Poisson ratio of the bonnet tool were E1≈1.5Mpa and ε1≈0.47 [4], respectively. Note that, the elastic modulus of rubber material is used here to approximate the elastic modulus of the bonnet tool, because small compression of bonnet tool is adopted in the polishing process, the contacting type between bonnet tool and workpiece is elastic contact, which is approximate to the rubber properties. The experimental results are revealed and discussed in the following section.
(12)
h) sin n 2 /60
Additionally, according to Section 2.1, the contacting type between the bonnet tool and the workpiece can be regarded as hertz elastic contact. Consequently, Pmax in Eq. (9) can be expressed in terms of the hertz elastic contact theory [19] as
Pmax =
6 Fn (E *)2 3 R2
1 3
=
6 Fn (E1 E2 )2 2 3 R2 (E (1 1 1 ) + E2 (1
1 3 2 2 2 ))
(13)
Combining Eqs. (10)–(13) with Eq. (9) yields
MRD =
Ft k Fn
6Fn (E1 E2 ) 2 2 3R2 (E (1 1 1 ) + E2 (1
1 3 2 2 2 ))
2 n (R
h) t sin 60 (14)
Since h < < R, Eq. (14) can be simplified as
MRD =
Ft k Fn
6Fn (E1 )2 2 2 3R2 (1 1)
1 3
2 nRt sin 60
4. Results and discussion
(15)
4.1. Validation of the prediction capabilities of the model for TIF spot shape
In the above equation, since the values of all variables except Ft, Fn and n are presetted, Eq. (15) can be represented using the product of two parts, i.e., as shown in Eq. (16)
MRD =
Ft n 2 (Fn ) 3
k
6(E1 ) 2R 2 2 (1 1)
1 3
t sin 30
Experimental results including the collected polishing force and measured TIF spots shape are shown in Table 4. Note that, each measured data of 5th and 6th row in Table 4 was obtained from the average of 3 polishing spots. It is interesting that for all the experimental groups, the measured length of the long axis (LLA) of the TIF spot shown in the 5th row of Table 4, are close to the predefined spot radius in the 4th row. The maximum derivation is only (15.50-15)/ 15 = 3.33％. The results are consistent with the aforementioned derivation which suggests that the LLA is close to the predefined radius in Section 2.1. On the other hand, the length of short axis (LsA) of the TIF spots predicted by the proposed model based on the polishing force collected online are shown in the 7th row of Table 4 and then compared with the measured LsA in the 6th row of Table 4. Since the predicted model Eq. (7) for LsA of TIF is derived from the elastic theory, which suggests that LsA is proportional to the third root of the normal force as shown in Eq. (1), thus, before the proposed model is verified, relation between LsA and the third root of the normal force was investigated firstly. Fig. 6 illustrates the nomalized data of the 9 measured LsAs from the 6th row of Table 4 and the nomolized data of the third root of the 9 normal forces collected online during the experiment from the 3rd row of Table 4. According to Fig. 6, although the two curves do not fit very well, the changing trend of the LsAs and the third root of the normal force is totally the same. Thus, if the measurement errors of the LsAs and forces in the experiment is taken into consideration, it is reasonable to conclude that LsA is proportional to the third root of the normal force. According to Eq. (7), except for the third root of the normal force, ks is the other factor affects the LsA. As stated previously, the 3 experimental groups in Table 4 were conducted at different times with different bonnet tools. Thus, according to the defination of ks in Eq. (7), for each experimental group, ks should be corrected before it is used for the
(16)
Based on the equations presented above, as long as the normal force Fn and the tangential force Ft in the first part are collected online, the MRD can be calculated because other variables in the equation are known, therefore the efficiency of the polishing tool can be evaluated. Note that similar to the correction factor ks in Eq. (6), k in the Eq. (16) also varies with the polishing time. Consequently, for every polishing process, a single experiment should be conducted before polishing to determine the standard value for k. Based on the above derivation, the forces-based TIF model, consisting of two parts (Eqs. (7) and (16)) was established. To validate the above model, polishing experiments were conducted and the results were discussed in the following section. 3. Experimental details To validate the derived TIF models based on polishing forces collected online, practical TIF of bonnet tool and polishing forces were collected experimentally as shown in Fig. 5 [13]. A spherical coronal bonnet filled with gas was used as polishing tool, the workpiece was fixed on the worktable and polished using the rotating bonnet tool. The polishing forces acting on the workpiece were the normal force Fn, the frictional forces Ftx and Fty. As shown in Fig. 5, the collection principles for the TIF of bonnet tool and the polishing forces have the following differences: (1) The workpiece was polished and then measured by the sub-aperture 396
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Fig. 5. Collection principle of TIF and polishing forces. Table 1 Key parameters associated with the 1st group [21]. Pad condition
Rotational speed (rpm)
Predefined spot size (mm)
Inner pressure (MPa)
Precession angle ρ(°)
Polishing time(s)
New pad New pad after 1st conditioning New pad after 2nd conditioning
1000
20
0.15
23
4
Table 2 Key parameters associated with the 2nd group. Pad condition
Rotational speed (rpm)
Predefined spot size (mm)
Inner pressure (MPa)
Precession Angle ρ (°)
Polishing time (s)
Worn pad Worn pad after 1st conditioning Worn pad after 2nd conditioning
1000
20
0.15
23
4
group, the predicted LsAs are: 18.20ks, 19.06ks and 19.32ks, respectively. (2) Use the second test as the standard for the 1st experimental group to calculate ks, i.e., set the predicted LsA obtained from Eq. (7) of the second test equal to the measured LsA, then it yields:
Table 3 Key parameters associated with the 3rd group [18]. Pad condition
Rotational Speed (rpm)
Predefined spot size (mm)
Inner pressure (MPa)
Precession angle ρ(°)
Polishing time (s)
New pad after conditioning
250 500 750 1000 1500 2000 250 500 750 1000 1500 2000
15
0.15
23
4
19.06ks = 16.07 (the measured LsA of the 2nd test) The substitution yields ks = 0.84
20
(3) Substitute the above ks value into the other two tests of the 1st experimental group such that the predicted LsAs of the other two tests can be obtained. The predicted LsAs obtained using the proposed model and the measured LsAs from the 1st experimental group are shown in Fig. 7(a), Fig. 7(b) illustrates the error bar of the measured LsAs of the 3 tests in 1st experimental group.
prediction of the LsA of TIF because ks varies with polishing time and other conditions. Using the 1st experimental group of Table 4 as an example, the prediction of the LsA based on Eq. (7) include the correction of ks is shown as following:
For the other two experimental groups shown in Table 4, the pad conditions are different as indicated in the 2nd row of Table 4. The above steps should be repeated to correct the corresponding ks and used to predict the LsAs. The predicted LsAs for the other two experimental groups and the measured LsAs are shown in Fig. 8 and Fig. 9. Some measured data obtained from polishing spots are shown in Fig. 10. The results shown in Figs. 7–9 suggest that for all of the experimental groups, the predicted LsAs obtained using the proposed model
(1) Substitute the Fn collected online and shown in the 3rd row of Table 4 and the other variables mentioned in the experimental details into Eq. (7). For the three tests in the 1st experimental 397
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Table 4 Experimental determination of the TIF spot shape. Experimental group
Pad condition
Collected normal force(N)
Predefined spot radius(mm)
Measured LLA(mm)
Measured LsA(mm)
Predicted LsA(mm)
1st
New
20.00
2nd
Worn pad
3rd
New after conditioning
96.59 110.89 115.69 62.42 110.69 117.34 47.96 120.08 207.76
19.53 19.67 20.00 20.13 19.80 20.30 15.50 20.03 24.53
15.33 16.07 16.33 14.47 17.27 18.17 12.50 16.57 20.27
15.35 16.07 16.30 14.27 17.27 17.61 12.50 16.97 20.38
15.00 20.00 25.00
Fig. 6. Relation between LsA and the third root of the normal force.
Fig. 8. Result of 2nd experimental group in Table 4.
to explain the formation of the TIF spot shape for the bonnet tool, and the LsA of the TIF spot is proportional to the third root of the normal force. Moreover, the proposed model for the LsA associated with the TIF is correct and effective for various TIF shapes (shown in Fig. 9, both Mshape and Gaussian shape). However, there is a disadvantage of the proposed model that a single experiment should be carried out to correct for the value of ks before every series of polishing processes. 4.2. Validation of the model for predicting TIF efficiency
Fig. 7. Result of 1st experimental group in Table 4.
To validate the predicted model for TIF efficiency using polishing forces collected online, results from the 12 tests in the 3rd experimental group in Table 3 were used, which are shown in Table 5 [18]. Similar to the calculation of the predicted LsA in Section 3.1, calculation of predicted MRD included the following steps:
agrees well with the measured LsAs. Specifically, the maximum differences for the 3 experimental groups are (16.33−16.30)/ 16.33 = 0.18%, (18.17−17.61)/18.17 = 3.08% and (16.97−16.57) /16.57 = 2.41%. Thus, the predictive capabilities of the model are demonstrated. Based on the analysis of the above results, elastic theory can be used
(1) Substitute Ft and Fn collected online and shown in Table 5 and the other variables described in the experimental details into Eq. (16). For each test in Table 5, the predicted MRD obtained with the proposed model is as a function of variable k. (2) Take the first test as the standard, i.e., set the predicted MRD obtained from the first test using Eq. (16) equal to the measured MRD, then kcan be determined. 398
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Fig. 9. Result of 3rd experimental group in Table 4.
(3) Substitute the above value of k into the predicted MRD for the other tests obtained in step (1) so that the predicted MRD of the other tests are obtained. The comparing result of the predicted MRD values for the other tests can be calculated. The predicted MRD values obtained using the proposed model and the measured MRD values are shown in Table 6 and Fig. 11. As shown in Fig. 11, both the predicted and measured MRDs follow similar trends as the rotational speed of the bonnet tool increases. Specifically, for both the figures in Fig. 11, when n < = 1000 rpm, the predicted MRDs agree well with the measured MRDs. The maximum deviation is only ˜0.05λ. However, when n > 1000 rpm, the deviations between the predicted and measured MRD values are much larger. Thus, the range in which the proposed force-based TIF efficiency model (i.e., Eq. (16)) is valid can be determined by the explanation as follows: See Table 5, for the first four tests of both experimental series (n < = 1000 rpm), the rotational speed of the tool increases greatly, the normal force Fn changes slightly, while the frictional force Ft decreases significantly. Thus, by using the Eq. (16), the effects of increasing of n on the MRD would be partially counteracted by the decreases in Ft. Therefore, the increasing rate of the predicted MRD with Eq. (16) should not be as high as n. The results that the predicted MRD values are very close to the measured MRD values shown in the both figures of Fig. 11 validate the effectiveness of the proposed model. However, in the final two tests for both experimental series (n > 1000 rpm), the rotational speed of the tool increases at a higher rate, the normal force Fn still changes slightly, but the frictional force decreases at a lower rate than before; thus, by using Eq. (16), only a small part of the effect due to the increase of n on the MRD is counteracted by the decrease of Ft. Therefore, the predicted MRD should increase at a larger rate than the previous four tests as shown in Fig. 11. The large variations between the predicted and measured MRD after n > 1000 rpm may be attribute to the following reason [18]: along with the increase in the tool rotational speed, liquid film may form in the interface between bonnet tool and workpiece, thus the interfacial
Fig. 10. Measured LsAs for the TIFs.
friction coeficient decreases because the friction type at the interface between the bonnet tool and workpiece may converse from solid friction to mix friction. Moreover, this phenomenon is not linear to the increase in the tool rotational speed. However, the above in not included in the proposed efficiency prediction model, which affects the prediction accuracy. Based on the above analysis, the proposed model for determination 399
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Table 5 Experimental results of the 12 tests shown in Table 3 [18]. Experimental serie
Test number
Predefined spot size (mm)
Tool rotational speed n (rpm)
Online collected normal force(N)
Online collected frictional force (N)
Measured MRD (λ)
1
1 2 3 4 5 6 7 8 9 10 11 12
15
250 500 750 1000 1500 2000 250 500 750 1000 1500 2000
43.66 47.96 47.14 49.57 50.43 49.43 116.42 120.08 118.75 123.39 123.58 120.83
28.58 21.60 17.92 15.69 14.47 11.92 73.71 55.23 45.34 38.76 36.53 33.94
0.535 0.82 0.989 1.041 1.227 1.405 0.646 1.023 1.286 1.391 1.642 1.861
2
20
Table 6 Comparison of the predicted and measured MRD values. Test number
Tool rotational speed n (rpm)
Measured MRD (λ)
Predicted MRD with force-based model (λ)
Derivation (λ)
1 2 3 4 5 6 7 8 9 10 11 12
250 500 750 1000 1500 2000 250 500 750 1000 1500 2000
0.535 0.82 0.989 1.041 1.227 1.405 0.646 1.023 1.286 1.391 1.642 1.861
0.5346 0.759 0.9554 1.079 1.475 1.642 0.717 1.053 1.306 1.451 2.049 2.577
0.0004 0.061 0.034 −0.038 −0.25 −0.24 −0.07 −0.03 −0.02 −0.06 −0.407 −0.696
of MRD values can be used when tool rotational speed n < = 1000 rpm. If n > 1000 rpm, the predictive model based on the polishing forces should only be used as a semi-quantitative model that evaluates variation trends in TIF efficiency. On the basis of the results described in above sections, the polishing forces collected online can be used to predict TIF spot shape and efficiency under certain conditions. The above finding provides a potential way to optimize bonnet polishing processes by reducing the time for offline measurements in engineering applications. 5. Conclusions To optimize the bonnet polishing process through reductions in processing time, predictive models for TIF spot shape and efficiency based on polishing forces collected online were investigated, and the following conclusions were obtained: (1) The formation mechanism for the elliptical TIF spot for the bonnet tool was investigated, and it was found that the length of the long axis of the TIF for the bonnet tool is equal to the predefined value and the length of the short axis of TIF is proportion to the third root of the normal force. Based on the above findings, a polishing forcebased prediction model for the TIF spot shape is presented and validated. The results reveal that the maximum deviation between the predicted and measured lengths is only 3.08％, which validated the model. Consequently, the spot shape of the TIF can be predicted using the normal force value collected online, instead of offline measurements. (2) Using a combination of Hertz elastic theory and an improved version of Preston’s law, a semi-qualitative predictive model for TIF efficiency based on polishing forces was derived and validated. Result from the model suggest that the changing trend for MRD
Fig. 11. Comparison of the predicted and measured MRD values.
values predicted by the proposed force-based model agree well with the measured MRD values, even when the values for the predicted MRD are close to the measure MRD if the tool rotational speed n≤1000 rpm.Consequently, the effectiveness of the proposed model for evaluating changing trends in TIF efficiency is verified. Through this study, it was found that prediction of a TIF spot shape and efficiency can be achieved based on polishing forces collected online. Consequently, it is feasible that the tool removal characteristics, which are often obtained using offline measurements, can be replaced by predictive models based on polishing forces collected online, without the processes of mounting-dismounting of the workpiece, 400
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workpiece measurement, or changing of tool settings. The above findings provide a practical approach to reducing the processing time associated with bonnet polishing processes.
[9] [10]
Acknowledgements
[11]
We appreciate the invaluable expert comments and advices on the manuscript from all anonymous reviewers. This work was financially supported by the the National Natural Science Foundation of China [grant number: 51705011], the Science Challenge Project [grant number: JCKY2016212A506-0502], the National Science and Technology Major Project of China [grant number: 2016ZX04003001] and the Science and Technology Projects of Shenzhen [grant number: JCYJ 20180306172924636].
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[1] Kim DW, Kim SW. Static tool influence function for fabrication simulation ofhexagonal mirror segments for extremely large telescopes. Opt Express 2005;13:910–7. [2] Zhang W, Li HY, Jin H. Research on digital simulation and experiment of removal function of bonnet tool polishing. Chin J Mech Eng-Cn 2009;45:308–12. [3] Cheung CF, Kong LB, Ho LT, To S. Modelling and simulation of structure surface generation using computer controlled ultra-precision polishing. Precis Eng 2011;35:574–90. [4] Wang CJ, Wang ZZ, Yang X, Sun Z, Peng Y, Guo Y, et al. Modeling of the static tool influence function of bonnet polishing based on FEA. Int J Adv Manuf Technol 2014;74:341–9. [5] Zeng S, Blunt L. Experimental investigation and analytical modelling of the effects of process parameters on material removal rate for bonnet polishing of cobalt chrome alloy. Precis Eng 2014;38:348–55. [6] Ke XL, Wang CJ, Guo YB, Xu Q. Modeling of tool influence function for high-efficiency polishing. Int J Adv Manuf Technol 2016;84:2479–89. [7] Feng Y, Wu H, Cheng H. Tool removal function modeling and processing parameters optimization for bonnet polishing. Int J Optomechatroni 2016;10:141–53. [8] Cao ZC, Cheung CF. Multi-scale modeling and simulation of material removal
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characteristics in computer-controlled bonnet polishing. Int J Mech Sci 2016;106:147–56. Cao ZC, Cheung CF, Xing Z. A theoretical and experimental investigation of material removal characteristics and surface generation in bonnet polishing. Wear 2016;360361:137–46. Shi CC, Peng YF, Hou L, Wang ZZ. Micro-analysis model for material removal mechanisms of bonnet polishing. Appl Opt 2018;57:2861–72. Singh DK, Jain VK, Raghuram V. Experimental investigations into forces acting during a magnetic abrasive finishing process. J. Int J Adv Manuf Technol 2006;30:652–62. Miao C, Lambropoulos JC, Jacobs SC. Process parameter effects on material removal in magnetorheological finishing of borosilicate glass. Appl Opt 2010;49:1951–63. Homma Y, Fukushima K, Kondo S, Sakuma N. Effects of mechanical parameters on CMP characteristics analyzed by two-dimensional frictional-force measurement. J Electrochem Soc 2003;150:245–6. Mizugaki Y, Sakamoto M, Kamijo K. Development of metal-mold polishing robot system with contact pressure control using CAD/CAM data. CIRP Ann Manuf Technol 1990;39:523–6. Guo J, Suzuki H, Morita SY, Yamagata Y, Higuchi T. A real-time polishing force control system for ultraprecision finishing of micro-optics. Precis Eng 2013;37:787–92. Guo J, Tan ZEE, Au KH, Liu K. Experimental investigation into the effect of abrasive and force conditions in magnetic field-assisted finishing. Int J Adv Manuf Technol 2016;90:1–8. Guo J, Jong HJH, Kang RK, Guo DM. New vibration-assisted magnetic abrasive polishing (VAMAP) method for microstructured surface finishing. Opt Express 2018;26:11608–19. Pan R, Zhong B, Chen DJ, Wang ZZ, Fan JW, Zhang CY, et al. Modification of tool influence function of bonnet polishing based on interfacial friction coefficient. Int J Mach Tool Manuf 2018;124:43–52. Wen SZ, Huang P. Principle of Tribology. Fourth Edition 2012. Pan R, Zhong B, Wang ZZ, Ji ST, Chen DJ, Fan JW. Influencing mechanism of the key parameters during bonnet polishing process. Int J Adv Manuf Technol 2018;94:643–53. Zhong B, Huang HZ, Chen XH, Wang J, Pan R, Wen ZJ. Impact of pad conditioning on the bonnet polishing process. Int J Adv Manuf Technol 2018;98:539–49. Wang CJ, Wang ZZ, Wang QJ, Ke XL, Zhong B, Guo YB, et al. Improved semirigid bonnet tool for high-efficiency polishing on large aspheric optics. Int J Adv Manuf Technol 2017;88:1607–17.
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Evaluation of removal characteristics of bonnet polishing tool using polishing forces collected online
T
Ri Pana, Wanying Zhaoa, Bo Zhongb,⁎, Dongju Chena, Zhenzhong Wangc, Chunqing Zhaa, Jinwei Fana a
Beijing Key Laboratory of Advanced Manufacturing Technology, Beijing University of Technology, Beijing 100124, China Research Center of Laser Fusion, China Academy of Engineering Physics, Mianyang 621900, China c Department of Mechanical and Electrical Engineering, Xiamen University, Xiamen 361005, China b
ARTICLE INFO
ABSTRACT
Keywords: Bonnet polishing Polishing force Tool removal characteristics
The polishing efficiency and accuracy for optical elements are strongly affected by the removal characteristics of the polishing tool and are commonly evaluated using a tool influencing function(TIF). During most polishing processes, the TIF is obtained through offline measurements, which are time-consuming. Consequently, the use of polishing forces collected online to evaluate TIF, including its spot shape and efficiency, was investigated as a means of reducing measurement times. Based on the elastic theory, the formation mechanism for an elliptical TIF spot during a bonnet polishing process is thought to have a long axis length that is close to a predefined value and a short axis length that is proportional to the third root of the normal force. Based on the above finding, a polishing force-based prediction model for TIF spot shape was derived and validated. The predicted results agreed well with experimental results. Afterwards, a polishing force-based, semi-quantitative prediction model for TIF efficiency was developed by combining Preston’s law and Hertz contact theory. The model was validated experimentally and successfully predicted changing trends in TIF efficiency. Based on this study, the spot shape and efficiency of the TIF can be predicted using polishing forces collected online. This approach provides a potential method that could be used in engineering applications to optimize bonnet polishing processes through a reduction in the time needed for offline measurements.
1. Introduction The tool influencing function(TIF) is an important property associated with polishing technology and represents the amount of removed material by a polishing tool in a unit of polishing time at a fixed location on a workpiece. The TIF model is usually used to calculate the dwelling time of the polishing tool on the surface of a workpiece during correction and to predict the amount of material removed from a workpiece after machining. The precision of the TIF model affects both polishing efficiency and accuracy. Thus, having an accurate TIF model is necessary for most polishing technologies [1–10]. Bonnet polishing has become more commonly used in recent years as a precise and efficient polishing technology for hard and brittle materials. Although many studies have investigated TIF modeling of a bonnet tool, the material removal mechanism during bonnet polishing process is still not fully understood. Commonly, the TIF model for a bonnet polishing tool can be obtained via a practical polishing test or
⁎
through a theoretical derivation. The TIF model achieved using the former approach is more precise but highly time-consuming, since offline measurements using an interferometer are required after the polishing test is complete. Theoretically derived TIF models for bonnet tools without offline measurement have been studied extensively. Kim et al. [1], Zhang et al. [2], Cheung et al. [3], Wang et al. [4], Zeng et al. [5], Ke et al. [6] and Feng et al. [7] analyzed bonnet polishing processes at a macroscopic level, and established theoretical TIF models in terms of Preston’s law. Different from the above studies, Cao et al. [8,9] and Shi et al. [10] selected single polishing abrasive that removed workpiece material as a target, and calculated the amount of workpiece material removed by a single abrasive based on contact mechanics, kinematic theory and wear mechanisms. Afterwards, based on the above calculation, theoretical TIF were obtained using this method by summing the removal amounts for all abrasives involving in the polishing process. For the derivation of the above theoretical TIF models, contacting
Corresponding author. E-mail address: [email protected] (B. Zhong).
https://doi.org/10.1016/j.jmapro.2019.03.029 Received 30 January 2019; Received in revised form 14 March 2019; Accepted 23 March 2019 1526-6125/ © 2019 The Society of Manufacturing Engineers. Published by Elsevier Ltd. All rights reserved.
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pressure or contacting force between the bonnet tool and workpiece computed via contact theory or simulations is crucial. However, since the removal mechanism during bonnet polishing process is still not well-understood, the theoretical contacting pressure or contacting force is different from the actual forces, which more or less limits the application scope of TIF. Based on the above analysis, both of the current approaches to obtain a TIF have disadvantages: offline measurement is time-consuming, and the contacting forces in the theoretical models are inconsistent with actual situations. The current study seeks to address the above problem by modeling the TIF using contacting forces collected online. Studies that investigated removal mechanisms and TIF modeling using collected polishing forces for other polishing technologies have been conducted [11–17]. For example, Singh et al. [11] investigated the forces acting on a material during magnetic abrasive finishing and established a correlation between surface finish and forces. Thus, the underlying mechanism for material removal is understood. Miao et al. [12] collected the contacting forces imposed on a surface during polishing processes and investigated the effects of various parameters that impact material removal for borosilicate glass. Homma et al. [13] studied the removal mechanism associated with chemical mechanical polishing using measured frictional forces and proposed an experimental TIF model. Based on the previous studies that used collected polishing forces, it is feasible to investigate the removal mechanism in bonnet polishing process and establish a TIF model for a bonnet tool via polishing forces collected online. Since it has been reported in our previous study [18] that, online collection of polishing forces during bonnet polishing processes has been achieved, this paper proposes the establishment and validation of the TIF model for a bonnet tool based on the polishing forces collected online.
Fig. 2. Typical bonnet polishing process.
consist of two parts, one for spot shape and the other for MRD of the TIF. 2.1. Prediction model for TIF spot shape based on the polishing forces collected online A typical bonnet polishing process is shown in Fig. 2. The TIF spot on the polished surface is supposed to be circular, whose radius Rc is predefined by controlling the compression of the bonnet tool. However, the actual spot shape of the TIF formed by the bonnet tool is found to be an ellipse [13] with the length of the long axis close to the defined radius Rc and a short axis length that is less than Rc. To explain these results, contact theory was studied. When hard and brittle materials such as glasses and ceramics, are polished, there are large hardness differences between the bonnet tool (made from rubber) and the workpiece. The contact type between the tool and workpiece can be regarded as an elastic ball contact with a rigid plane. Thus, as depicted in Fig. 3, in terms of elastic theory [19], when the elastic ball contacts the rigid plane under the normal force Fn, deformation occurs in the normal direction and causes the actual radius of the contacting area a to be always less than the nominal radius e. Moreover, a can be calculated by [19]
2. Modeling of TIF based on online collected polishing forces An ideal 3-dimentional TIF for a bonnet polishing tool is shown in Fig. 1. The most focused characteristics of the TIF are the maximum removal depth (MRD) shown in Fig. 1(a) and the spot shape shown in Fig. 1(b), because MRD and spot shape reflect the efficiency and regularity of the TIF, respectively. Consequently, the proposed TIF model to be established for the bonnet tool based on online collected forces
a=
3 Fn R 4 E*
1 3
Fig. 1. Typical TIF of bonnet tool. 394
(1)
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Fn R 4 E*
b= 3
1 3
(3)
Based on literature [4], E1 < < E2, consequently, the second item in the right part of the Eq. (2) can be neglected, and Eq. (2) can be expressed as 2 1
1
1 E*
(4)
E1 Combining Eq. (3) with Eq. (4), it yields
b= 3
Where Fn is the normal force, R is the radius of the elastic ball, and E* is the composite modulus, which can be calculated by
1 1 = E* E1
+
2 2
1 E2
1 2 3 1)
(5)
It should be noted that, Eq. (1) and Eq. (5) are derivated from a static contacting condition, but in dynamic polishing process, beside the variables in Eq.(5), some uncontrollable variables such as tool wear and the polishing slurry concentration also affect the length b of the contacting area, and the effect is hard to calculate. For this reason, similar to the preston coeficient k in the well-know Preston’s law, a correction factor ks which reveals the effect brought by the uncontrollable factors on the length of contacting area is introduced into Eq. (5) to yield
Fig. 3. Contact between elastic ball and rigid plane.
2 1
Fn R (1 4 E1
b = ks
3 Fn R (1 4 E1
2 1)
1 3
(6)
Strictly speaking, ks is not a constant because it changes with polishing time. However, ks is used as a constant in a certain period of polishing time for simplication. And like the calculation method of preston coefficient k [4], after a period of polishing time, a single experiment should be required to correct the ks value. Based on Eq. (6), as long as the normal force Fn can be acquired from the data collected online, the length of the short axis of the TIF can be calculated as
(2)
The parameters E1 and E2 are the elastic modulus of the bonnet tool and the workpiece, respectively. ε1 and ε2 are Poisson ratio of the bonnet tool and the workpiece, respectively. Using the above theory, the ellipse spot of the TIF formed by the compression of the bonnet tool can be explained. In Fig. 2, when the rotating bonnet tool polishes the workpiece in the long axis direction, the bonnet is supposed to be static, and the long axis length is close to the defined radius Rc. However, the short axis direction shown in Fig. 4 (left view of Fig. 2), the bonnet is cutting in and out through the whole polishing process under the action of Fn. During the cutting process elastic deformation occurs, which leads to a reduction in the length of the short axis. Since the long axis length is basically equal to Rc, the spot shape of TIF is determined by the length of the short axis. Therefore, the prediction model for TIF spot shape to be established is actually the prediction model of the length of the short axis of the TIF. In terms of Eq. (1), half of the actual length of the short axis of the TIF spot shape can be expressed as
R cs = 2 b = ks 6
Fn R (1 E1
1 2 3 1)
(7)
In addition to the previous statement that the long axis of the TIF spot is approximately equal to the defined radius, the spot shape of the TIF can be evaluated. 2.2. Predictive model for TIF efficiency based on polishing forces collected online As described in our previous study [18], the theoretical TIF for the bonnet polishing tool can be expressed using a modified Preston’s law as
RR (x , y ) = µ k P (x , y ) v (x , y ) t
(8)
where RR (i.e., TIF) is the removed workpiece material by polishing tool in certain time t. μ is the interface friction coeficient, k denotes the Preston coefficient, P and V are the pressure and relative velocity distribution on the contacting area, respectively. Based on Fig. 1, the MRD of the TIF (i.e., the maximum of RR) can be expressed as
MRD = Max(RR) = µ k Pmax vm t
(9)
Where Pmax is the maximum pressure on the polished spot, vm is the velocity corresponding to the maximum pressure. Since the TIF of bonnet tool may have different contours (Gaussian type and M type according to literatures [4,6]), it should be emphasized that only Gaussian contour TIF is considered in this section. Regarding to the Gaussian TIF, the maximum RR and the maximum pressure Pmax is supposed to be located at a point near the centre of the TIF (where the position parameters in Eq.(8) x = 0 and y = 0). However, the
Fig. 4. The deformation during bonnet polishing process.
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maximum velocity on the spot is usually locating at the edge of the TIF, that is why only the maximum pressure is involved in Eq.9. Based on Fig. 2 and literature [18], there is (10)
µ = Ft Fn vm =
interferometer (model SSI, made by QED). After that, the TIFs were extracted from the measurement data. Thus, in order to obtain the TIF, the workpiece needs to be disassembled from the worktable after polishing and moved to the interferometer. (2) The polishing forces are collected online by a 3-components dynamometer (model 9257B, made by Kistler) during polishing process and are transmitted real time to the computer [20].
((R
y cos n 2 /60) 2 + (x cos n 2 /60)2
h) sin n 2 /60
(11) Where Ft is the frictional force, Fn is the normal force, ρ is the incline angle of tool spin, n is the tool rotational speed, R is bonnet radius and h is the compression of the bonnet. As stated before, vm is the velocity corresponding to the maximum pressure, therefore, both x and y in Eq. (11) are equal to 0, which yields:
vm = (R
It is obvious that the offline measurement of the TIF is time consuming in comparison to the online collection of polishing forces. Consequently, if the polishing forces collected online can be used to evaluate the offline measured TIF, the bonnet polishing process could be optimized by reducing the processing time. All of the TIFs and the corresponding force data to be analyzed in the following section were obtained using the above approach. The data consists of three groups of experiments that used different bonnet tools and were conducted at different times [18,21]. The key parameters applied for the three groups of experiments are listed in Tables 1–3. In addition, the workpiece were BK7 glasses, the employed polishing tool is an improved semirigid bonnet tool [22], of which the radius was R = 80 mm. The elastic modulus and the Poisson ratio of the bonnet tool were E1≈1.5Mpa and ε1≈0.47 [4], respectively. Note that, the elastic modulus of rubber material is used here to approximate the elastic modulus of the bonnet tool, because small compression of bonnet tool is adopted in the polishing process, the contacting type between bonnet tool and workpiece is elastic contact, which is approximate to the rubber properties. The experimental results are revealed and discussed in the following section.
(12)
h) sin n 2 /60
Additionally, according to Section 2.1, the contacting type between the bonnet tool and the workpiece can be regarded as hertz elastic contact. Consequently, Pmax in Eq. (9) can be expressed in terms of the hertz elastic contact theory [19] as
Pmax =
6 Fn (E *)2 3 R2
1 3
=
6 Fn (E1 E2 )2 2 3 R2 (E (1 1 1 ) + E2 (1
1 3 2 2 2 ))
(13)
Combining Eqs. (10)–(13) with Eq. (9) yields
MRD =
Ft k Fn
6Fn (E1 E2 ) 2 2 3R2 (E (1 1 1 ) + E2 (1
1 3 2 2 2 ))
2 n (R
h) t sin 60 (14)
Since h < < R, Eq. (14) can be simplified as
MRD =
Ft k Fn
6Fn (E1 )2 2 2 3R2 (1 1)
1 3
2 nRt sin 60
4. Results and discussion
(15)
4.1. Validation of the prediction capabilities of the model for TIF spot shape
In the above equation, since the values of all variables except Ft, Fn and n are presetted, Eq. (15) can be represented using the product of two parts, i.e., as shown in Eq. (16)
MRD =
Ft n 2 (Fn ) 3
k
6(E1 ) 2R 2 2 (1 1)
1 3
t sin 30
Experimental results including the collected polishing force and measured TIF spots shape are shown in Table 4. Note that, each measured data of 5th and 6th row in Table 4 was obtained from the average of 3 polishing spots. It is interesting that for all the experimental groups, the measured length of the long axis (LLA) of the TIF spot shown in the 5th row of Table 4, are close to the predefined spot radius in the 4th row. The maximum derivation is only (15.50-15)/ 15 = 3.33％. The results are consistent with the aforementioned derivation which suggests that the LLA is close to the predefined radius in Section 2.1. On the other hand, the length of short axis (LsA) of the TIF spots predicted by the proposed model based on the polishing force collected online are shown in the 7th row of Table 4 and then compared with the measured LsA in the 6th row of Table 4. Since the predicted model Eq. (7) for LsA of TIF is derived from the elastic theory, which suggests that LsA is proportional to the third root of the normal force as shown in Eq. (1), thus, before the proposed model is verified, relation between LsA and the third root of the normal force was investigated firstly. Fig. 6 illustrates the nomalized data of the 9 measured LsAs from the 6th row of Table 4 and the nomolized data of the third root of the 9 normal forces collected online during the experiment from the 3rd row of Table 4. According to Fig. 6, although the two curves do not fit very well, the changing trend of the LsAs and the third root of the normal force is totally the same. Thus, if the measurement errors of the LsAs and forces in the experiment is taken into consideration, it is reasonable to conclude that LsA is proportional to the third root of the normal force. According to Eq. (7), except for the third root of the normal force, ks is the other factor affects the LsA. As stated previously, the 3 experimental groups in Table 4 were conducted at different times with different bonnet tools. Thus, according to the defination of ks in Eq. (7), for each experimental group, ks should be corrected before it is used for the
(16)
Based on the equations presented above, as long as the normal force Fn and the tangential force Ft in the first part are collected online, the MRD can be calculated because other variables in the equation are known, therefore the efficiency of the polishing tool can be evaluated. Note that similar to the correction factor ks in Eq. (6), k in the Eq. (16) also varies with the polishing time. Consequently, for every polishing process, a single experiment should be conducted before polishing to determine the standard value for k. Based on the above derivation, the forces-based TIF model, consisting of two parts (Eqs. (7) and (16)) was established. To validate the above model, polishing experiments were conducted and the results were discussed in the following section. 3. Experimental details To validate the derived TIF models based on polishing forces collected online, practical TIF of bonnet tool and polishing forces were collected experimentally as shown in Fig. 5 [13]. A spherical coronal bonnet filled with gas was used as polishing tool, the workpiece was fixed on the worktable and polished using the rotating bonnet tool. The polishing forces acting on the workpiece were the normal force Fn, the frictional forces Ftx and Fty. As shown in Fig. 5, the collection principles for the TIF of bonnet tool and the polishing forces have the following differences: (1) The workpiece was polished and then measured by the sub-aperture 396
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Fig. 5. Collection principle of TIF and polishing forces. Table 1 Key parameters associated with the 1st group [21]. Pad condition
Rotational speed (rpm)
Predefined spot size (mm)
Inner pressure (MPa)
Precession angle ρ(°)
Polishing time(s)
New pad New pad after 1st conditioning New pad after 2nd conditioning
1000
20
0.15
23
4
Table 2 Key parameters associated with the 2nd group. Pad condition
Rotational speed (rpm)
Predefined spot size (mm)
Inner pressure (MPa)
Precession Angle ρ (°)
Polishing time (s)
Worn pad Worn pad after 1st conditioning Worn pad after 2nd conditioning
1000
20
0.15
23
4
group, the predicted LsAs are: 18.20ks, 19.06ks and 19.32ks, respectively. (2) Use the second test as the standard for the 1st experimental group to calculate ks, i.e., set the predicted LsA obtained from Eq. (7) of the second test equal to the measured LsA, then it yields:
Table 3 Key parameters associated with the 3rd group [18]. Pad condition
Rotational Speed (rpm)
Predefined spot size (mm)
Inner pressure (MPa)
Precession angle ρ(°)
Polishing time (s)
New pad after conditioning
250 500 750 1000 1500 2000 250 500 750 1000 1500 2000
15
0.15
23
4
19.06ks = 16.07 (the measured LsA of the 2nd test) The substitution yields ks = 0.84
20
(3) Substitute the above ks value into the other two tests of the 1st experimental group such that the predicted LsAs of the other two tests can be obtained. The predicted LsAs obtained using the proposed model and the measured LsAs from the 1st experimental group are shown in Fig. 7(a), Fig. 7(b) illustrates the error bar of the measured LsAs of the 3 tests in 1st experimental group.
prediction of the LsA of TIF because ks varies with polishing time and other conditions. Using the 1st experimental group of Table 4 as an example, the prediction of the LsA based on Eq. (7) include the correction of ks is shown as following:
For the other two experimental groups shown in Table 4, the pad conditions are different as indicated in the 2nd row of Table 4. The above steps should be repeated to correct the corresponding ks and used to predict the LsAs. The predicted LsAs for the other two experimental groups and the measured LsAs are shown in Fig. 8 and Fig. 9. Some measured data obtained from polishing spots are shown in Fig. 10. The results shown in Figs. 7–9 suggest that for all of the experimental groups, the predicted LsAs obtained using the proposed model
(1) Substitute the Fn collected online and shown in the 3rd row of Table 4 and the other variables mentioned in the experimental details into Eq. (7). For the three tests in the 1st experimental 397
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Table 4 Experimental determination of the TIF spot shape. Experimental group
Pad condition
Collected normal force(N)
Predefined spot radius(mm)
Measured LLA(mm)
Measured LsA(mm)
Predicted LsA(mm)
1st
New
20.00
2nd
Worn pad
3rd
New after conditioning
96.59 110.89 115.69 62.42 110.69 117.34 47.96 120.08 207.76
19.53 19.67 20.00 20.13 19.80 20.30 15.50 20.03 24.53
15.33 16.07 16.33 14.47 17.27 18.17 12.50 16.57 20.27
15.35 16.07 16.30 14.27 17.27 17.61 12.50 16.97 20.38
15.00 20.00 25.00
Fig. 6. Relation between LsA and the third root of the normal force.
Fig. 8. Result of 2nd experimental group in Table 4.
to explain the formation of the TIF spot shape for the bonnet tool, and the LsA of the TIF spot is proportional to the third root of the normal force. Moreover, the proposed model for the LsA associated with the TIF is correct and effective for various TIF shapes (shown in Fig. 9, both Mshape and Gaussian shape). However, there is a disadvantage of the proposed model that a single experiment should be carried out to correct for the value of ks before every series of polishing processes. 4.2. Validation of the model for predicting TIF efficiency
Fig. 7. Result of 1st experimental group in Table 4.
To validate the predicted model for TIF efficiency using polishing forces collected online, results from the 12 tests in the 3rd experimental group in Table 3 were used, which are shown in Table 5 [18]. Similar to the calculation of the predicted LsA in Section 3.1, calculation of predicted MRD included the following steps:
agrees well with the measured LsAs. Specifically, the maximum differences for the 3 experimental groups are (16.33−16.30)/ 16.33 = 0.18%, (18.17−17.61)/18.17 = 3.08% and (16.97−16.57) /16.57 = 2.41%. Thus, the predictive capabilities of the model are demonstrated. Based on the analysis of the above results, elastic theory can be used
(1) Substitute Ft and Fn collected online and shown in Table 5 and the other variables described in the experimental details into Eq. (16). For each test in Table 5, the predicted MRD obtained with the proposed model is as a function of variable k. (2) Take the first test as the standard, i.e., set the predicted MRD obtained from the first test using Eq. (16) equal to the measured MRD, then kcan be determined. 398
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Fig. 9. Result of 3rd experimental group in Table 4.
(3) Substitute the above value of k into the predicted MRD for the other tests obtained in step (1) so that the predicted MRD of the other tests are obtained. The comparing result of the predicted MRD values for the other tests can be calculated. The predicted MRD values obtained using the proposed model and the measured MRD values are shown in Table 6 and Fig. 11. As shown in Fig. 11, both the predicted and measured MRDs follow similar trends as the rotational speed of the bonnet tool increases. Specifically, for both the figures in Fig. 11, when n < = 1000 rpm, the predicted MRDs agree well with the measured MRDs. The maximum deviation is only ˜0.05λ. However, when n > 1000 rpm, the deviations between the predicted and measured MRD values are much larger. Thus, the range in which the proposed force-based TIF efficiency model (i.e., Eq. (16)) is valid can be determined by the explanation as follows: See Table 5, for the first four tests of both experimental series (n < = 1000 rpm), the rotational speed of the tool increases greatly, the normal force Fn changes slightly, while the frictional force Ft decreases significantly. Thus, by using the Eq. (16), the effects of increasing of n on the MRD would be partially counteracted by the decreases in Ft. Therefore, the increasing rate of the predicted MRD with Eq. (16) should not be as high as n. The results that the predicted MRD values are very close to the measured MRD values shown in the both figures of Fig. 11 validate the effectiveness of the proposed model. However, in the final two tests for both experimental series (n > 1000 rpm), the rotational speed of the tool increases at a higher rate, the normal force Fn still changes slightly, but the frictional force decreases at a lower rate than before; thus, by using Eq. (16), only a small part of the effect due to the increase of n on the MRD is counteracted by the decrease of Ft. Therefore, the predicted MRD should increase at a larger rate than the previous four tests as shown in Fig. 11. The large variations between the predicted and measured MRD after n > 1000 rpm may be attribute to the following reason [18]: along with the increase in the tool rotational speed, liquid film may form in the interface between bonnet tool and workpiece, thus the interfacial
Fig. 10. Measured LsAs for the TIFs.
friction coeficient decreases because the friction type at the interface between the bonnet tool and workpiece may converse from solid friction to mix friction. Moreover, this phenomenon is not linear to the increase in the tool rotational speed. However, the above in not included in the proposed efficiency prediction model, which affects the prediction accuracy. Based on the above analysis, the proposed model for determination 399
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Table 5 Experimental results of the 12 tests shown in Table 3 [18]. Experimental serie
Test number
Predefined spot size (mm)
Tool rotational speed n (rpm)
Online collected normal force(N)
Online collected frictional force (N)
Measured MRD (λ)
1
1 2 3 4 5 6 7 8 9 10 11 12
15
250 500 750 1000 1500 2000 250 500 750 1000 1500 2000
43.66 47.96 47.14 49.57 50.43 49.43 116.42 120.08 118.75 123.39 123.58 120.83
28.58 21.60 17.92 15.69 14.47 11.92 73.71 55.23 45.34 38.76 36.53 33.94
0.535 0.82 0.989 1.041 1.227 1.405 0.646 1.023 1.286 1.391 1.642 1.861
2
20
Table 6 Comparison of the predicted and measured MRD values. Test number
Tool rotational speed n (rpm)
Measured MRD (λ)
Predicted MRD with force-based model (λ)
Derivation (λ)
1 2 3 4 5 6 7 8 9 10 11 12
250 500 750 1000 1500 2000 250 500 750 1000 1500 2000
0.535 0.82 0.989 1.041 1.227 1.405 0.646 1.023 1.286 1.391 1.642 1.861
0.5346 0.759 0.9554 1.079 1.475 1.642 0.717 1.053 1.306 1.451 2.049 2.577
0.0004 0.061 0.034 −0.038 −0.25 −0.24 −0.07 −0.03 −0.02 −0.06 −0.407 −0.696
of MRD values can be used when tool rotational speed n < = 1000 rpm. If n > 1000 rpm, the predictive model based on the polishing forces should only be used as a semi-quantitative model that evaluates variation trends in TIF efficiency. On the basis of the results described in above sections, the polishing forces collected online can be used to predict TIF spot shape and efficiency under certain conditions. The above finding provides a potential way to optimize bonnet polishing processes by reducing the time for offline measurements in engineering applications. 5. Conclusions To optimize the bonnet polishing process through reductions in processing time, predictive models for TIF spot shape and efficiency based on polishing forces collected online were investigated, and the following conclusions were obtained: (1) The formation mechanism for the elliptical TIF spot for the bonnet tool was investigated, and it was found that the length of the long axis of the TIF for the bonnet tool is equal to the predefined value and the length of the short axis of TIF is proportion to the third root of the normal force. Based on the above findings, a polishing forcebased prediction model for the TIF spot shape is presented and validated. The results reveal that the maximum deviation between the predicted and measured lengths is only 3.08％, which validated the model. Consequently, the spot shape of the TIF can be predicted using the normal force value collected online, instead of offline measurements. (2) Using a combination of Hertz elastic theory and an improved version of Preston’s law, a semi-qualitative predictive model for TIF efficiency based on polishing forces was derived and validated. Result from the model suggest that the changing trend for MRD
Fig. 11. Comparison of the predicted and measured MRD values.
values predicted by the proposed force-based model agree well with the measured MRD values, even when the values for the predicted MRD are close to the measure MRD if the tool rotational speed n≤1000 rpm.Consequently, the effectiveness of the proposed model for evaluating changing trends in TIF efficiency is verified. Through this study, it was found that prediction of a TIF spot shape and efficiency can be achieved based on polishing forces collected online. Consequently, it is feasible that the tool removal characteristics, which are often obtained using offline measurements, can be replaced by predictive models based on polishing forces collected online, without the processes of mounting-dismounting of the workpiece, 400
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R. Pan, et al.
workpiece measurement, or changing of tool settings. The above findings provide a practical approach to reducing the processing time associated with bonnet polishing processes.
[9] [10]
Acknowledgements
[11]
We appreciate the invaluable expert comments and advices on the manuscript from all anonymous reviewers. This work was financially supported by the the National Natural Science Foundation of China [grant number: 51705011], the Science Challenge Project [grant number: JCKY2016212A506-0502], the National Science and Technology Major Project of China [grant number: 2016ZX04003001] and the Science and Technology Projects of Shenzhen [grant number: JCYJ 20180306172924636].
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