Sage Journals: Discover world-class research

Abstract

Bonnet polishing has been successfully used for ultra-precision machining of the large-aperture aspheric optics. To accomplish online monitoring of executive condition of the removing function and state of the polishing machine, key technological parameters and processing condition factors need to be acquired in real time and coupled back. A novel data fusion method which combines hardware synchronous signal and correcting algorithm based on the principle of linear extrapolation is proposed in allusion to data acquisition distortion caused by asynchronous sampling frequency and communication delay between different systems. The estimate values are obtained by dynamically correcting original acquired data, and the upper bound of the error is deduced with the speed and the acceleration of the signal. The simulation results showed that the data fusion method can significantly reduce the error of data acquisition. The experimental results confirmed that the data fusion method can be effectively applied to monitor the optics bonnet polishing process online.

Keywords

Bonnet polishing online monitoring data fusion

Introduction

With the wide application of large-aperture aspheric optics in many high-tech fields (e.g. aerospace, astronomy, and national defense), the requirement for ultra-precision machining and measurement of large-aperture aspheric optics has been increased.^1,2 Thus, in order to achieve the required accuracy, the manufacturing process for optics is commonly composed of two stages which are grinding and polishing. Bonnet polishing is a new polishing technology which has been increasingly applied in ultra-precision machining of large-aperture aspheric surface in recent years.³ Now, the researches on bonnet polishing are mainly concentrated in effect factors of the removing function, tool path planning, precession control, and so on.^4–7 The removing function is one of the most important factors which is calculated according to the machining results of the grinding process that is the last process before polishing. The executive condition of the removing function decides the machining results of the polishing process. And two kinds of factors have significant influence on removing function: one is key technological parameters; the other is processing condition factors. In these researches mentioned above, the values of key technological parameters such as inner air pressure of bonnet, rotation speed of the bonnet, and the concentration of polishing solution are supposed to be unchanged in the polishing process. However, it is easy to know that, as to the dynamic error of machine tool, the values of aforementioned technological parameters may fluctuate in a certain range. And it will possibly affect the polishing quality. On the other hand, it is well known that processing condition factors generated in the machining process can be used to represent the state of the machine and the process.^8,9 For the above reasons, in order to improve the polishing quality, evaluate the depletion of the equipment, and realize process control, a system for online monitoring the variation in key technological parameters and processing condition factors is necessary. The precondition and the basic demand of the monitoring system are that data acquisition distortion must not be allowed to happen. Data fusion is the main method to meet the precondition and the demand.

The online monitoring system is used to acquire both static and dynamic signals in the polishing process; therefore, errors of data acquisition would come out mainly because of two reasons: one is asynchronous sampling frequency which is mainly because of the different clock sources; the other is communication delay which is mainly because of the priorities of different systems. The data fusion method is used to solve the problems at present.¹⁰ As shown in related reports, the existing researches are mainly focused on synchronous data fusion, of which the premise is that the sampling frequencies of all sensors are the same or integral multiple.¹¹ But it cannot meet the requirements of data acquisition for monitoring bonnet polishing process online. Besides, there are also studies which pay attention to asynchronous multi-sensors data fusion. Some algorithms are proposed, such as optimal asynchronous data fusion, asynchronous data fusion based on sampling of rational number times, and data fusion based on synchronous hoisting.^12–14 However, these algorithms can hardly be applied to engineering because of the large amount of calculation.

In this study, an online monitoring system is first built to acquire and couple back key technological parameters and processing condition factors in bonnet polishing process. Then, in allusion to data acquisition distortion caused by asynchronous sampling frequency and communication delay, a novel data fusion method based on the principle of linear extrapolation is proposed, which combines hardware synchronization signal and correcting algorithm. Moreover, upper bound of the error is deduced. The correctness of the data fusion method was proved by simulations. Finally, experiments were performed to confirm the effectiveness and feasibility of the data fusion method for online monitoring of actual bonnet polishing.

The online monitoring system

Figure 1 shows the structure of the online monitoring system which is composed of sensors, a signal acquisition and data fusion system (SADF), and a personal computer (PC). Data transmission between SADF and PC is realized by Wi-Fi because the door of the bonnet polishing machining tool must be closed in a process.

Figure 1.

Structure of the monitoring system.

SADF acquires data by two ways which are sensors and the computerized numerical control system (CNC) of bonnet polishing machining tool. The data processed by the data fusion method will then be transferred to PC and displayed on the screen.

Selection of key technological parameters and processing condition factors

The objects of the online monitoring system are key technological parameters and processing condition factors. In respect to the former, a lot of previous studies have shown that inner air pressure of bonnet, height of bonnet compression, rotation speed of bonnet, and precession angle are the key parameters which have significant effect on polishing quality.^4,5,15–17 In addition, considering the wear of the grains in polishing solution, the concentration is also regarded as a key parameter. Concerning the effects of processing condition factors, although there are rarely researches in allusion to bonnet polishing, acoustic emission, down pressure of bonnet, and vibration are supposed to be the most important factors based on the common points of the mold bonnet polishing, optics grinding, and processing technology of optics bonnet polishing.^18–22 In conclusion, the key technological parameters and processing condition factors which are selected for the online monitoring system are shown in Table 1. Values of rotation speed of bonnet, height of bonnet compression, and precession angle are obtained from CNC, and the left parameters are obtained by the measurement of sensors.

Table 1.

The selection results.

Key technological parameters	Processing condition factors
Inner air pressure of bonnet	Acoustic emission
Height of bonnet compression	Down pressure of bonnet
Concentration of polishing solution	Vibration
Rotation speed of bonnet	–
Precession angle	–

Design of SADF

As the kernel of the online monitoring system, SADF is used to acquire data from sensors and CNC. Besides, SADF is used to fuse the data and transfer the results to PC. Figure 2 illustrates the frame of SADF, which is composed of power supply module, control module, wireless communication module, multi-sensor signal acquisition module, and CNC system communication module according to the functional characteristics.

Figure 2.

Frame of SADF.

The power supply module is used to supply power to other modules. Control module is used to set up parameters of the multi-sensor signal acquisition module and the CNC system communication module, fuse the data, and control the wireless communication module to transfer the results to PC. Multi-sensor signal acquisition module is used to acquire some of the key technological parameters, that is, inner air pressure of bonnet and concentration of polishing solution, and all of the processing condition factors. The function of CNC system communication module is acquiring the left key technological parameters, that is, rotation speed of bonnet, height of bonnet compression, and precession angle, from CNC.

Data fusion method

In signal acquisition process, it can cause data distortion by two reasons as follows: (1) although the design value of the sampling frequency for each module is same, there are small differences among different modules because every module has its own clock source and (2) the priority of external communication of CNC is lower because of the closed-loop control. Thus, the communication time between the CNC system communication module and CNC may be asynchronous, that is to say, the interval of the sampling time is random.

A data fusion method which combines hardware synchronous signal and correcting algorithm based on the principle of linear extrapolation is proposed to solve the problem. This method avoids large amount of calculation caused by improving algorithm alone and complex circuit design caused by improving hardware alone.

Hardware synchronous signal

A hardware timer is added for the online monitoring system as the hardware synchronous signal. The differences between the sampling time of each test signal and the synchronous signal are then measured respectively by the timer, as shown in Figure 3. T is the sampling period of the control module. t_k is the value of the kth sampling time of the control module. Δt_k is the difference value between t_k and the sampling time of the multi-sensor signal acquisition module or the CNC system communication module which borders on and is in front of t_k.

Figure 3.

Schematic diagram for sampling time of the monitoring system.

The correcting algorithm

In this study, the correcting algorithm aims at calculating the value, which is named the estimate value, to be used for online monitoring of the process of bonnet polishing with the data acquired by SADF. For explaining the correcting algorithm clearly, make definitions as follows: y(t) is the test signal and y(t_k) is the real value of the test signal at t_k. $\bar{y} (t_{k} - Δ t_{k})$ is the acquisition value of the test signal at (t_k − Δt_k). $\hat{y} (t_{k})$ is the estimate value at t_k, which is calculated with the correcting algorithm.

The correcting algorithm for y(t) is described using equation (1)

\hat{y} (t_{k}) = \bar{y} (t_{k} - Δ t_{k}) + \hat{v} (t_{k} - Δ t_{k}) Δ t_{k}

(1)

where $\hat{v} (t_{k} - Δ t_{k})$ is the estimate value of the average speed which presents the trend of the variation of the signal in Δt_k and is calculated based on the principle of linear extrapolation using equation (2)

\hat{v} (t_{k} - Δ t_{k}) = \frac{\bar{y} (t_{k} - Δ t_{k}) - \bar{y} (t_{k - 1 - m} - Δ t_{k - 1 - m})}{(t_{k} - Δ t_{k}) - (t_{k - 1 - m} - Δ t_{k - 1 - m})}

(2)

where m is the integer part of Δt_k/T and is calculated using equation (3)

m = ⌊ \frac{Δ t_{k}}{T} ⌋

(3)

Analysis of the error caused by the correcting algorithm

The following equations can be got according to the relationship between the sampling frequency of the test signal and the synchronous signal

| v | < a_{1} | \overset{\cdot}{v} | < a_{2}

(4)

Δ t_{k} \leq T_{M}

(5)

T_{m} \leq t_{k} - t_{k - 1 - m} - (Δ t_{k} - Δ t_{k - 1 - m}) \leq T_{M}

(6)

where v is the variation speed of the test signal, $\overset{\cdot}{v}$ is the acceleration, a₁ is the maximum value of v, a₂ is the maximum value of $\overset{\cdot}{v}$ , T_M is the maximum value of the sampling period, and T_m is the minimum value of the sampling period.

y(t) can be calculated using equation (7)

y (t_{k}) = y (t_{k} - Δ t_{k}) + \int_{t_{k} - Δ t_{k}}^{t_{k}} v (τ) d τ

(7)

So the error caused by the correcting algorithm is obtained by equation (8)

\tilde{y} (t_{k}) = \hat{y} (t_{k}) - y (t_{k})

(8)

where $\tilde{y} (t_{k})$ is used to present the error. Equation (9) is got according to equations (1), (7), and (8)

\begin{array}{l} | \tilde{y} (t_{k}) | \leq | y (t_{k} - Δ t_{k}) - \bar{y} (t_{k} - Δ t_{k}) | \\ + | \int_{t_{k} - Δ t_{k}}^{t_{k}} v (τ) d τ - \hat{v} (t_{k} - Δ t_{k}) Δ t_{k} | \end{array}

(9)

The error caused by measurement uncertainty is presented by δ₀. Thus, equation (10) can be got according to equations (4)–(9)

| \tilde{y} (t_{k}) | \leq δ_{0} + 2 a_{2} T_{M}^{2} + 2 δ_{0} \frac{T_{M}}{T_{m}}

(10)

The upper bound of the error is given by equation (10). And there are specific physical significances as follows: (1) the first item of the expression is δ₀ caused by measurement uncertainty which includes many factors, such as the measured error of sensors and the instability of the wireless transmission network, and it should be reduced as little as possible, but it cannot be avoided completely; (2) the second item presents the relationship between the error and the variation trend of the signal, and it will be zero in condition of the static or uniform variation signal; and (3) the minimal error can be got in condition of equal interval sampling.

Simulation of the data fusion method

The simulation of the data fusion method was performed using MATLAB in allusion to the two cases which caused data distortion, and the configuration of the computer during the simulation in MATLAB environment was 64 bits. The clock frequency was set as 1 kHz.

The condition of differences existing in different clocks

In simulation process, T was set as 1 ms and was considered to be invariant. There were small differences between T and the sampling period of the other modules which was presented by T₁. In this study, two cases had been considered: one was that T₁ equal to 1.001 ms, and the other was that T₁ equal to 0.999 ms. δ₀ was set as 0.001, and the test signal was set as sinusoidal signal with the frequency of 50 Hz, that is to say, y(t) = sin(100πt). Figure 4 shows the variation curve of the differences between T and T₁ for the two cases. Figures 5 and 6 show the error caused by the data which had been fused by the method and the error caused by the data which had not been fused for two cases of T₁, respectively.

Figure 4.

The variation curve of the differences between T and T₁.

Figure 5.

The error curve of the case that T₁ equal to 1.001 ms.

Figure 6.

The error curve of the case that T₁ equal to 0.999 ms.

Losing data or data coverage was brought out because of the differences, though the differences were small. The mutation of the time differences appeared every 1000 periods, and the maximum error of the output of the online monitoring system appeared too. It can be concluded that the error was significantly reduced after fused by the data fusion method.

The condition of random interval of the measured time

For the simulation of this case, the interval of the measured time was set from 0.8 to 1.2 ms, of which the variation was random. The test signal was set as sinusoidal signal with the frequency of 10 Hz, that is to say, y(t) = sin(20πt). The differences between T and the period of the measured time were random because of the random interval, as shown in Figure 7. Figure 8 shows the error caused by the data which had been fused by the method and the error caused by the data which had not been fused, respectively. It can be concluded that the error was significantly reduced after fused by the data fusion method.

Figure 7.

The variation curve of the differences between T and the period of the measured time.

Figure 8.

The error curve caused by the random interval.

Experiments

Experiments were performed to verify whether the data fusion method can be used for online monitoring of actual optics bonnet polishing. SADF was developed, of which the control module adopted MicroZed development board whose main control chip was field-programmable gate array (FPGA) made by AVNET company and the other modules were self developed. Wireless transmitting equipment adopted router of which the model was WS326 made by Huawei company. In order to be used easily, all the boards mentioned above, transformer, fan, and power supply interface were assembled in a 25 cm × 21 cm × 12 cm box. Netting twine was through the back of the box and connected with the router. Figure 9 shows the physical map of SADF. Experiments were performed on 2MK460 bonnet polishing machine tool, as shown in Figure 10.

Figure 9.

Physical map of SADF.

Figure 10.

2MK460 bonnet polishing machine tool.

The scheme of the experiments was designed as follows: optics were polished in six groups of different technological parameters as shown in Table 2. In polishing process, the key technological parameters and processing condition factors were acquired in real time. The reference parameters of sensors and the parameters set for the experiments are shown in Table 3. Using the data acquired above, the key characteristic parameters, that is, the maximum removing depth and the size, of the removing function were predicted based on the online monitoring algorithm. This algorithm was built based on high-order polynomial fitting method, of which the input vectors were key technological parameters and processing condition factors, and the output vectors were the key characteristic parameters of the removing function. It is applied to monitor and couple back the executive condition of the removing function in a bonnet polishing process in real time.²³ The results obtained by comparing the predicted values with the measured values were used to evaluate the effectiveness and feasibility of the data fusion method for online monitoring of bonnet polishing. Figure 11 shows the installation methods for all sensors used in the experiments and the panorama.

Table 2.

Technological parameters.

Serial number of experiment	Technological parameters
Serial number of experiment	Precession angle (°)	Height of bonnet compression (mm)	Rotation speed of bonnet (r/min)	Inner air pressure of bonnet (MPa)	Concentration of polishing solution (%)
1	15	0.6	1000	0.20	2.0
2	15	0.8	2000	0.25	2.0
3	20	0.6	2000	0.15	2.0
4	20	0.8	500	0.20	2.0
5	25	0.6	500	0.25	2.0
6	25	0.8	1000	0.15	2.0

Table 3.

Parameters of sensors.

Kinds of parameters	Types of sensors
Kinds of parameters	Acoustic emission	Down pressure of bonnet	Vibration
Manufacturer	Beijing Shenghua	KISTLER	PCB
Model	SAEU2S	9255C	356A16
Frequency response range	156–625 (kHz)	0–200 (kHz)	0.3 Hz–6 kHz
Sensitivity	4.88 mV	−3.7 pC/N	100 mV/g
Measuring range	−10 to +10 (V)	−10 to +40 (kN)	−50 to +50 (g)
Sampling frequency for the experiments (Hz)	1.56 × 10⁵	5 × 10³	1.5 × 10³
Quantity for the experiments	2	1	2

Figure 11.

Installation methods of all sensors and experimental panorama.

The maximum removing depth and the size of the removing function were predicted with the online monitoring algorithm and were then compared with the measured values. The compared results are shown in Figure 12, of which (a) represents the maximum removing depth and (b) represents the size.

Figure 12.

The compared results between the predicted and the measured values: (a) the predicted and the measured values of the maximum removing deep and (b) the predicted and the measured values of the size.

As can be observed from Figure 12, for the maximum removing depth, the maximum and minimum error of the predicted values were 0.1578 and −0.1496 µm respectively, and the average value of the absolute difference between the predicted values and the measured values was 0.0741 µm which was just 4.72% of the average value of the measured values; for the size, the maximum and minimum error of the predicted values were 0.8539 and −0.6102 µm, respectively, and the average value of the absolute difference between the predicted values and the measured values was 0.4727 µm which was just 2.70% of the average value of the measured values. The trend of the variation in the predicted values had high correlation with that of the measured values for both the maximum removing depth and the size. The above comparisons confirmed that the data fusion method can be effectively applied to online monitoring of optics bonnet polishing.

Discussion

The correcting algorithm of the data fusion method proposed in the study was simple; in other words, it was not the best choice from accuracy and intelligence opinion. However, the top-priority selection criteria of correcting algorithms in this study were real-time and engineering application. In these respects, this correcting algorithm was a good choice because it had small amount of calculation and could be easily realized for engineering. It needs much more work to develop a correcting algorithm which considers all the criteria besides these mentioned above.

On the other hand, reducing the measurement uncertainty was also important, although the error caused by measurement uncertainty could not be avoided completely. Several methods were adopted to improve the possibilities to reduce the measurement uncertainty in the study as follows: (1) good performance sensors had be chosen because sensors were the data sources and had significant influence on the accuracy, (2) the wireless transmission network used for the online monitoring system was established separately because the special network had better instability than that of the public network, and (3) many different kinds of rigorous tests in allusion to the software used for the online monitoring system had been performed, for example, known data were transmitted and stored by the software; after that, the results obtained by comparing the received data with the known data were used to evaluate the software. Besides these methods, there must be more and better methods that can reduce the measurement uncertainty, and they need more researches in the future work.

Conclusion

The online monitoring system was built to realize acquiring and coupling back key technological parameters and processing condition factors in real time according to the characteristics of the optics bonnet polishing process. A summary of the findings are given below:

A novel data fusion method which combined hardware synchronous signal and correcting algorithm based on the principle of linear extrapolation was proposed in allusion to data acquisition distortion. The simulation results showed that the error was significantly reduced by the method which had the small amount of calculation and was easily used for engineering.

The experiments for online monitoring of actual optics bonnet polishing were performed. The data were fused by the data fusion method. The fused results were used to predict the maximum removing depth and the size of the removing function with the online monitoring algorithm, and the average errors of the predicted values were just 4.72% and 2.70% of the measured values, respectively. This confirmed that the data fusion method can be effectively applied to online monitoring of optics bonnet polishing.

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported by the China Postdoctoral Science Foundation (No. 2016M591285 and 2015M570920) and Laboratory of precision manufacturing technology, CAEP (No. ZZ14006).

References

Gao

Huang

Zhang

An improved discrete system model for form error control in surface grinding. J Mater Process Tech 2010; 210: 1794–1804.

Harvey

. Next generation optics manufacturing technologies. In: Proceedings of the SPIE 4231 on advanced optical manufacturing and testing technology, Chengdu, China, 1 November 2000, pp.8–15. Bellingham, WA: SPIE.

Walker

Brooks

King

et al . The “Precessions” tooling for polishing and figuring flat, spherical and aspheric surfaces. Opt Express 2003; 8(11): 958–964.

Wei

Hongyu

Hai

Research on digital simulation and experiment of removal function of bonnet tool polishing. J Mech Eng 2009; 45(2): 308–312.

Hongyu

Guoyu

Walker

et al . Modeling and measurement of polishing tool influence functions for edge control. J Eur Opt Soc 2011; 6: 1–6.

Yindong

Research on robot-assisted gasbag polishing motion control and trajectory planning for mould. Master Thesis, Zhejiang University of Technology, Hangzhou, China, 2009.

Zhenzhong

Chunjin

et al . Control techniques of bonnet polishing for free-form optical lenses with precession. J Mech Eng 2012; 48(4): 92–99.

Liang

Hecker

Landers

RG.

Machining process monitoring and control: the-state-of-the-art. J Manuf Sci Eng 2004; 126(5): 297–310.

Stephenson

Sun

Zervos

A study on ELID ultra precision grinding of optical glass with acoustic emission. Int J Mach Tool Manu 2006; 46: 1053–1063.

10.

Rhee

Lee

Kim

Clock synchronization in wireless sensor networks: an overview. Sensors 2009; 9: 56–85.

11.

Shalom

Kirbrarajam

Estimation with application to tracking and navigation. New York: John Wiley & Sons, 2001.

12.

Ai-Bing

Cheng-Lin

Bin

Optimal state fusion estimate based on asynchronous multi-sensor sampled measurements. Acta Electron Sinica 2010; 38(7): 1483–1488.

13.

Quan-Bo

Guo-An

Tian-Hao

et al . The research on asynchronous data fusion algorithm based on sampling of rational number times. Acta Electron Sinica 2006; 34(3): 221–223.

14.

Besada Portas

Lopez Orozco

Besada

et al . Multisensor fusion for linear control systems with asynchronous, out-of-sequence and erroneous data. Automatica 2011; 47(7): 1399–1408.

15.

Zhenzhong

Chunjin

et al . Optimization of key technological parameters in bonnet polishing using FEA. J Chin Soc Mech Eng 2012; 33(5): 373–382.

16.

Zhenzhong

Tao

et al . A novel method for aspheric polishing based on abrasive trajectories analysis on contact region. Proceedings IMechE, Part B: J Engineering Manufacture 2015; 229(2): 275–285.

17.

Walker

Beaucamp

ATH

Doubrovski

et al . Recent advances in the control of form and texture on free-form surfaces. In: Proceedings of the SPIE 5965, optical fabrication, testing, and metrology II, Jena, 12 September 2005, pp.59650S-1–59650S-7. Bellingham, WA: SPIE.

18.

Oliveira

JFG

Franca

Wang

JP.

Experimental analysis of wheel/workpiece dynamic interactions in grinding. CIRP Ann-Manuf Techn 2008; 57(1): 329–332.

19.

Lezanski

An intelligent system for grinding wheel condition monitoring. J Mater Process Tech 2004; 109: 258–263.

20.

Kwak

M-K.

Detection of dressing time using the grinding force signal based on the discrete wavelet decomposition. Int J Adv Manuf Tech 2004; 23: 87–92.

21.

Wegener

Hoffmeister

H-W

Karpuschewski

et al . Conditioning and monitoring of grinding wheels. CIRP Ann-Manuf Techn 2011; 60: 757–777.

22.

Zhang

Sun

et al . On-line monitoring of precision optics grinding using acoustic emission based on support vector machine. Int J Adv Manuf Tech 2015; 80(5): 761–774.

23.

Dongxu

Research on online monitoring of grinding and polishing process and measuring technology for large aspheric optical components. Xiamen, China: Xiamen University, 2015.

Research on data fusion technology of the online monitoring system for optics bonnet polishing

Abstract

Keywords

Introduction

The online monitoring system

Selection of key technological parameters and processing condition factors

Design of SADF

Data fusion method

Hardware synchronous signal

The correcting algorithm

Analysis of the error caused by the correcting algorithm

Simulation of the data fusion method

The condition of differences existing in different clocks

The condition of random interval of the measured time

Experiments

Discussion

Conclusion

Footnotes

Declaration of conflicting interests

Funding

References