Estimation Algorithm of Minimum Dwell Time in Precision Cylindrical ...

INTERNATIONAL JOURNAL OF PRECISION ENGINEERING AND MANUFACTURING Vol. 15, No. 4, pp. 601-607

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DOI: 10.1007/s12541-014-0377-y

Estimation Algorithm of Minimum Dwell Time in Precision Cylindrical Plunge Grinding Using Acoustic Emission Signal Chen Jiang1,#, Qi Song1, Debao Guo1, and Haolin Li1 1 College of Mechanical Engineering, University of Shanghai for Science and Technology, Shanghai, China, 200093 # Corresponding Author / E-mail: [email protected], TEL: +86-21-5527-0938, FAX: +86-21-5527-0938 KEYWORDS: Acoustic emissions, Cylindrical-plunge grinding, Dwell time, Grinding quality

This work presents an investigation of the minimum dwell time during the precision cylindrical-plunge grinding process. According to the model of acoustic emissions proposed in earlier work, two estimation algorithms of the dwell time, focused on the size error and the surface roundness of the machined workpiece, are deduced from the models of the material removal and the surface roundness, respectively. Based on the proposed estimation algorithms, an on-line estimation method of the minimum dwell time is developed using the measurement and analysis of the acoustic emission signal. A series of experiments of grinding C45 steel are conducted to confirm the validity of the proposed estimation algorithms and determine the model coefficient. The ability of the estimation algorithms to predict the minimum dwell time is deemed necessary for optimal control of the grinding process. In addition, the proposed model provides a new approach to estimate the machined qualities of a workpiece such as the surface roughness and size error using the dwell time of the grinding process. Manuscript received: September 16, 2013 / Revised: January 25, 2014 / Accepted: January 29, 2014

1. Introduction The grinding process has been used for the final finishing of part products due to its ability to satisfy strict requirements for machining qualities. Of the several common types of grinding, cylindrical-plunge grinding has been widely used to machine the precision axis parts in today’s industry. Since precision cylindrical-plunge grinding is commonly used as a final finishing operation, its performance is bound to have the most significant effect on the overall yield and productivity of the whole production line. As an important grinding variable, the dwell time is related with the machining qualities and efficiency. Previous experiments found that the proper dwell time should be about three to five times the time constant of the grinding system. In the present study, specific mathematical relations between dwell time and the machining qualities, including size error and surface roundness, are discussed. Following earlier work on modeling the root mean square (RMS) of acoustic emissions (AEs),1 a new method of estimating the minimum dwell time of the cylindrical-plunge grinding process using AE signals is presented to improve the efficiency of cylindrical-plunge grinding and ensure good grinding qualities in the process control of

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grinding. The monitoring and control of the grinding process requires robust estimation and prediction of important process variables such as workpiece qualities and wheel conditions. Many attempts have been made to describe more effectively and adequately models for monitoring and controlling the grinding process.2-4 Lee et al. proposed a controloriented model for the cylindrical grinding process to estimate workpiece qualities such as the surface roughness and actual part size with the measurement of grinding power.5 Morgan et al. proposed a fully integrated intelligent grinding system for adaptive controlled cycle optimization, thermal damage avoidance, dressing interval optimization and data retention. Grinding performance was monitored and assessed in real time.6 Kwak et al. used the parameters of the AE signals as the inputs of a neural network in developing a diagnostic technique for chatter vibration and burning phenomena in the grinding process and evaluated the performance of the diagnostic technique.7 They then developed the response surface models to predict the grinding power and the surface roughness in the external cylindrical grinding of the hardened SCM440 steel and also to help the selection of grinding conditions.8 Sutowski et al. presented a possible diagnostic method to

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be applied in the grinding process using the AE signal and image analysis. The experimental results showed the proposed method enables the detection of signs of wear on the grinding wheel active surface components, during the machining process, as well as allowing for the assessment of their influence on grinding power and workpiece surface roughness parameters.9 Subrahmanya et al. proposed a systematic approach, which allows the development and deployment of processmonitoring systems via automated sensor and feature selection combined with parameter-free model training, both of which are especially crucial for implementation in industry. Different sensors are used to measure acoustic emission, spindle power, and workpiece vibration signals, which are used to monitor three of the most common faults in grindingworkpiece burn, chatter, and wheel wear.10 AE measurement has been the most popular approach used to monitor grinding processes for the last two decades and has proven advantages such as low cost, easy installation and low latency, with no reduction in machine tool stiffness.11 Much progress has been made in understanding the relationship between the features of AE signals and the physics of the grinding process through the pioneering work of many researchers. However, most of the methods require the calibration of the AE signal or must self-learn the samples before monitoring and cannot be adapted to real-time monitoring with changing parameters. Using the mathematical model of AE proposed in earlier study,1 the presented study analyzes the process of the dwell period during precision cylindrical-plunge grinding to propose an estimation algorithm of the minimum dwell time using an AE measurement made during the grinding process. The proposed estimation algorithm provides a new approach to realize the on-line optimal control of cylindrical-plunge grinding according to machining requirements including those of the size error and surface roundness. Compared with the force, power and displacement sensors, the AE sensor has some advantages such as low cost and easy installation, with no reduction in machine tool stiffness. It is very suitable for industrial application of process control and can be deployed as an alternative to force, power or displacement monitoring during the cylindrical-plunge grinding. In this work, using the model of the AE RMS signal, an online calculation of the time constant of the dwell period is first presented and two estimation algorithms of dwell time of the precision cylindrical-plunge grinding are deduced from the relationship between the dwell time and the grinding qualities, namely the size error and surface roundness. An on-line estimation method of the minimum dwell time is then developed using the AE RMS signal, and the prediction of the minimum dwell time is obtained from the experimental data. Finally, the results of experiment and simulation are compared.

2. Estimation of the Dwell Time A model of the AE RMS signal is introduced briefly following earlier work.1 Using the introduced model of the AE RMS signal, a quick on-line method of calculating the time constant during the dwell period is established. The relationship between the curve of the AE RMS signal and the dwell time is then deduced from the models of the material removal and the traditional surface roundness. According to this relationship, the estimation algorithms of the minimum dwell time, satisfying the requirements of the grinding qualities, are discussed using

the calculated time constant.

2.1 Model of AE signals In earlier work,1 a mathematical model of the AE signal during a grinding cycle was proposed for the monitoring of material removal in precision cylindrical-plunge grinding. In the proposed model, the curves of AE RMS signals in both the infeed period and dwell period can be obtained: kae kc u· –t/τ –t/τ - (1 – e ) = Ks ( 1 – e ) , (0 < t < t1) VAE = ------------ωw t – t1

(1)

t – t1

– ---------kae kc u· –--------τ τ -e = Ks e VAE = ------------, (t > t1) ωw

(2)

where VAE is the averaged AE RMS, ωw is the workpiece rotational speed, kc is the grinding force coefficient, kae is the proportionality coefficient of the averaged AE RMS and normal force, u· is the command feed velocity and t1 is the infeed time in the grinding cycle. The AE coefficient Ks in Eqs. (1) and (2) is expressed as: kae kc u· Ks = ------------ωw

(3)

The time constant τ is a measure of the relationship between the stiffness and the grinding force coefficient and can be expressed as:12 kc τ = ---------ke n w

(4)

where nw is the rotational speed of the workpiece and kc is the grinding force coefficient.

2.2 Calculation of the time constant during the dwell period According to the model of the AE RMS signal, the time constant τ during the dwell period can be calculated in one grinding process. The time constant τ is generally on the order of a second in precision cylindrical-plunge grinding. In the infeed period, the AE coefficient Ks can be easily obtained using Eq. (1) by looking at the steady-state AE RMS. kae kc u· - ≡ Ks (t >> τ) VAE = V′ AE ≈ ------------ωw

(5)

where V′ AE is the averaged AE RMS of the steady state. Once Ks is known, the AE RMS signal during the dwell period is obtained as t – t1

t – t1

t – t1

– ---------– ---------kae kc u· –--------τ τ τ VAE = -------------e = Kse = V′AE e (t > t1) ωw

(6)

According to the transformation of Eq. (6), the calculation of τ is t – t1 τ = – -------------------VAE ( t ) ln --------------V′AE

(7)

Therefore, using Eq. (7), the time constant τ can be obtained by the real-time measurement of the AE signal.

2.3 Estimation algorithms of the minimum dwell time At the beginning of the dwell period of the grinding process, the

INTERNATIONAL JOURNAL OF PRECISION ENGINEERING AND MANUFACTURING Vol. 15, No. 4

command feed rate of the computer numerically controlled (CNC) system is zero. However, owing to the elastic deformation of the contact area between the wheel and workpiece, the removal of workpiece material continues. With the removal of workpiece material, the elastic deformation decreases and the grinding depth gradually decreases to zero. To ensure machining efficiency, the dwell period may finish as the elastic deformation is eliminated. Therefore, two specific estimation algorithms of the minimal dwell times are developed to obtain satisfactory grinding qualities, namely the size error and surface roundness, and efficiency in this section.

2.3.1 Estimation algorithm of the dwell time based on the size error (EADSE) With the elastic deformation decreasing, the size error of the workpiece decreases during the dwell period. The size of the workpiece is strongly related with the material removal theoretically. Using the relationship between the AE signal and the material removal, the size of the workpiece can be estimated using the real-time AE signal. Therefore, a method of calculating the size error of the workpiece using the AE measurement is developed to estimate the minimum dwell time. In the dwell period of the precision cylindrical-plunge grinding, the change in the workpiece size during the dwell period is:1 ⎛ r ( t) = u· ⎜ t1 – τe ⎝

t – t1 – ----------⎞ τ

⎟ ⎠

(8)

Suppose that the targeted change in the workpiece size and the required size accuracy are rd and ∆r, respectively. In the dwell period, the final change in the workpiece size rt should satisfy rt ≤ rd – ∆r

(9)

2.3.2 Estimation algorithm of the dwell time based on the surface roundness (EADSR) As an important variable of the grinding quality, the surface roundness must be considered in estimating the minimum dwell time of precision cylindrical-plunge grinding. The surface roundness Ra, which is arithmetic mean deviation of contour of grinding workpiece, can be expressed as:13 0.8

+ R∞

L = ade

(12)

The instantaneous depth of the cut a is related to the actual feed velocity r· and angular workpiece velocity ωw according to: r· a = ------ωw

(13)

Eqs. (12) and (13) are substituted into Eq. (11) to obtain an equation relating the surface roundness of the workpiece to the actual feed velocity r· , the rate of the workpiece vw and the rate of the wheel vs: 0.5 0.8

s ⎛ ⎛ d----v r·⎞ ⎞ R0 ⎞ ⎜ ⎝ 2 w ⎠ ⎟ ⎛ - -----------------------⎟ Ra = -------⎝ 0.5⎠ ⎜⎜ vs ⎟ m ⎝ ⎠

+ R∞

(14)

In the dwell period, the actual feed velocity r· can be obtained using Eq. (8): r· = u· e

t – t1 – ---------τ

(15)

Before the surface roundness of the workpiece reaches a steady state (R∞), the change in the surface roundness of the workpiece during the dwell period ∆Ra can be expressed by substituting Eq. (15) into Eq. (14): t–t

0.5 0.8

1 – ----------⎞ ⎞ ⎛ ⎛ ds ⎜ ⎜ ----vw u· e τ ⎟ ⎟ R0 ⎞ ⎜ ⎝ 2 ⎠ ⎟ - ------------------------------------⎟ ∆Ra = ⎛ -------⎝ 0.5⎠ ⎜⎜ v ⎟ s m ⎜ ⎟ ⎝ ⎠

(10)

Therefore, once the time constant of the dwell period is calculated and the required size accuracy is known, using Eq. (10), the required theoretical minimum dwell time tDmin can be obtained by the real-time measurement of the AE signal.

R0 ⎞ ⎛ vw L ⎞ - -----------Ra = ⎛ -------⎝ 0.5⎠ ⎜⎝ 0.5⎟⎠ vs de m

of the cut is a. L can be geometrically expressed as:

(16)

At the beginning of the dwell time, the change in the surface roundness of the workpiece ∆Ra reaches a maximum value and may be obtained from Eq. (16):

Combining Eqs. (8) and (9), the minimal dwell time tDmin is: rt – ∆r⎞ ⎞ 1 tDmin ≤ t1 – τ ln ⎛ --- ⎛ t1 – ------------⎝τ ⎝ u· ⎠ ⎠

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(11)

where R0 and m are constants, R is the minimum surface roundness deviation of the workpiece after a sufficient dwell time during the grinding process, vw is the speed of the workpiece, vs is the speed of the wheel, de is the equivalent diameter of the wheel, and L is the arc length of the contact of the wheel and workpiece when the instantaneous depth

0.5 0.8

s ⎛ ⎛ d----v u· ⎞ ⎞ R0 ⎞ ⎜ ⎝ 2 w ⎠ ⎟ ⎛ - ------------------------⎟ ∆Ra-max = -------⎝ 0.5⎠ ⎜⎜ vs ⎟ m ⎝ ⎠

(t = t1)

(17)

In the grinding process, supposing that the grinding conditions except for the commanded feed rate, including the rate of the workpiece vw, the rate of the wheel vs and the equivalent diameter of the wheel de, are invariant, the proportionality coefficient of the real-time change in the surface roundness and the maximum change in the surface roundness can be expressed as: t – t1 ⎛ – ---------- ⎞ ⎜ u· 1 e τ ⎟ ∆R1a - ------------KR = ------------------- = ⎜ ---⎟ ∆R2a-max ⎜ u· 2 –t-----------1 – t 1⎟ ⎝ e τ ⎠

0.4

t – t1 0.4

⎛ u· 1 –--------τ ⎞ = ⎜ ---e ⎟ ⎝ u· 2 ⎠

(18)

Assuming that the maximum proportional coefficient is KRmax, the minimum dwell time tDmin can be obtained from Eq. (18): tDmin = t1 – 2.5τ ln KRmax – τ ln u· 2 + τ ln u· 1

(19)

The maximum proportional coefficient KRmax may be determined

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Table 1 Machining conditions Machining conditions Wheel width (mm) Wheel radius (mm) Wheel speed (m/s) Feed rate (mm/min) Workpiece speed (m/s) Workpece diameter (mm)

Value of Parameters 60 245 35 0.3 0.3123 59

Fig. 1 Grinding experimental setup

from experiment. Once the time constant of the dwell time τ is calculated from AE measurement, the minimum dwell time can be predicted using Eq. (19). Therefore, the dwell time of the grinding process can be estimated from the real-time AE RMS signal.

3. Experimental Setup

Fig. 2 Calculation of the time constant τ of the dwell period

A series of experiments was performed using a CNC cylindrical grinding machine to verify that the estimation algorithms of the minimum dwell time allow precise and repeatable control of the dwell time using the AE signal measurements. Fig. 1 shows a STUDER KC33 multi-purpose CNC cylindrical grinding machine, a Al2O3 wheel (53A80L15V) and a C45 steel with diameter of 59 mm selected as the workpiece material. The change in the workpiece diameter was monitored with an inductance micrometer. The micrometer was located to minimize sensitivity to the effects of workpiece movement resulting from the grinding force. As shown in Fig. 1, an AE sensor was installed on the footstock of the grinding apparatus to monitor the grinding process. The AE RMS signal and the data of part size were filtered and digitized using a data acquisition card. The surface roundness of the workpiece was inspected by a Mitutoyo SJ-201P surface-roundness tester.

dwell period was first calculated in real-time in the experimental work to estimate the dwell time of the grinding cycle. The machining conditions are given in Table 1. Using Eq. (5), the coefficient Ks was directly obtained from the record of the AE RMS signal V′AE observed during the steady state of the infeed period. To reduce the effect of noise, only AE RMS data within a selected portion of the decay were used during the dwell period. Meanwhile, Ks was substituted into Eq. (7), and the time constant τ was calculated using the least mean squares of AE RMS data in real time. Fig. 4 shows that the calculation result for the time constant is 2.99 s during the dwell period. The AE RMS curve was obtained using Eq. (2) with the calculated time constant. As shown in Fig. 2, the prediction of the AE curve was similar to the measured AE RMS signal.

4. Experimental Results and Discussion The experimental work is divided into three parts according to the proposed estimation algorithms of the minimum dwell times. First, an experiment was performed to verify the calculation method of the time constant during the dwell period. Second, several grinding experiments, focused on the relationship between the dwell time and the workpiece size, were performed to verify the EADSE. Finally, several grinding experiments, focused on the relationship between the dwell time and the surface roundness of the workpiece, were performed to verify the EADSR.

4.1 Calculation of the time constant As a key variable in the proposed models, the time constant τ of the

4.2 Estimation of dwell time The dwell time affects the machining precision and the surface quality of the workpiece. For specific limits, the longer the dwell time is, the better the machining accuracy and the surface roundness are. However, to ensure machining efficiency, the dwell time should be shortened. Therefore, using the proposed estimation algorithms, proper dwell times affecting the machining accuracy and surface roundness were investigated in a series of experiments. 4.2.1 Estimation of dwell time using the EADSE Three grinding experiments, with a feed rate of 0.3 mm/min, were preformed to verify the EADSE. In each whole grinding cycle, the infeed period lasted 14 s and the dwell period lasted 22 s. The measurement of the workpiece size, which is the mean value for three experimental results, and the predicted workpiece size are shown in Fig. 3. According to the requirement of machining accuracy (1 µm), the theoretical

INTERNATIONAL JOURNAL OF PRECISION ENGINEERING AND MANUFACTURING Vol. 15, No. 4

Fig. 3 Change in workpiece size during the dwell period

Fig. 4 Predicted results of TDmin for different size error

prediction of the minimum dwell time TDmin is obtained as 8.1 s using Eq. (10) and the calculated time constant (2.99 s). The workpiece size measured by the inductance micrometer shows that the machining accuracy is satisfactory when the dwell time is 10.7 s. The experiments indicate that the difference between the measured minimum dwell time and the predicted result is 2.60 s which is less than one time constant. Furthermore, some experiments were preformed to investigate the predicted accuracy of the workpiece size at different requirement of size error. As shown in Fig. 4, the measured minimum dwell times, which are obtained by the mean value of five experiments, are decreased, as the required size error varies from 0.1 to 2 µm. In this range of the required size error, the change of the predicted minimum dwell time is similar to that of the measured minimum dwell time and the difference of them only varies from 1.9 to 2.72 s. The experimental results also indicate that the spread of the mean values of measured minimum dwell time is decreased while the required size error varies from 0.1 to 2 µm. Several other experiments were preformed to verify the validity of the EADSE at different feed rates. The two additional feed rates were 0.6 and 1.2 mm/min. When the infeed period enters a steady state, the minimum dwell times, which ensure that the size error of the workpiece is below 1 µm, are measured on-line by the inductance micrometer. The measured workpiece size is the mean value in three experiments at each feed rate. Fig. 5 shows the measurement results for the minimum dwell

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Fig. 5 Results of the EADSE for different feed rates

Fig. 6 Measured surface roundness for different dwell times at a feed rate 0.3 mm/min

time. The calculated time constants and TDmin predicted using Eq. (10) are also shown in the figure. It is seen that the calculated minimum time constants vary slightly, by less than 0.02 s, for different feed rates. The predicted results of minimum dwell times TDmin are similar to the measurements, and the minimum dwell times predicted by the EADSE increase with an increasing feed rate. The maximum difference between the predicted results and measurements is 2.19 s at a feed rate of 0.3 mm/min, and the minimum difference is 0.52 s at a feed rate of 1.2 mm/ min. It is seen that the prediction accuracy increases with an increasing feed rate.

4.2.2 Estimation of dwell time using the EADSR Several experiments were preformed to verify the validity of the EADSR. First, three grinding experiments, with a feed rate of 0.3 mm/ min, were conducted to obtain the minimum dwell time when the surface roundness of the workpiece is steady. Fig. 6 shows the change trend of the mean value of surface roundness in the grinding experiments while the dwell time is changed from 0 to 22 s. The surface roundness is steady at around 0.32 µm after the dwell time reaches 11 s. This means that the minimum dwell time TDmin obtained by the mean value of the surface roundness in experiments is 11 s and the minimum surface roundness deviation R is 0.32 µm at a feed rate 0.3 mm/min. Substituting the calculated time constant τ (2.99 s) and the measured

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Table 2 Results of the experiments and predictions Grinding conditions Infeed time (s) Measured minimum dwell time (s) Measured minimum surface roundness deviation R Calculated KRmax KRmax used in EADSR Predicted minimum dwell time (s) Predicted error of EADSR (s)

Feed rate 0.3 Feed rate 0.6 Feed rate 1.2 (mm/min) (mm/min) (mm/min) 0~22 0~20 0~20 11

12

12

0.32

0.32

0.31

0.22 /

/ 0.22

/ 0.22

/

13.1

15.1

/

1.1

3.1 Fig. 8 Measured roundness error RONt for different dwell times at feed rate 0.3 mm/min

Fig. 7 Measured surface roundness for different dwell times

minimum dwell time TDmin (11 s) into Eq. (19), KRmax can be calculated as 0.22. Using the calculated KRmax, the minimum dwell times for different feed rates may be estimated from Eq. (19). The predicted minimum dwell times TDmin at the feed rates of 0.6 and 1.2 mm/min, obtained by the EADSR, are given in Table 2. Grinding experiments with feed rates 0.6 and 1.2 mm/min were conducted to verify the minimum dwell time predicted by the EADSR. To obtain the surface roundness at different dwell times and analyze the impact of the dwell time on the surface roundness, the wheel is stopped feeding and returned for different dwell times from 0 to 20 s during the dwell period of the grinding process. The surface roundness of the workpiece at each dwell time is measured by the surface roundness instrument. The experiment results, which are the mean value of the surface roundness in three experiments for both feed rates, are shown in Fig. 7. It is seen that the surface roundness for both feed rates decreases with increasing dwell time and enters a steady state after approximately 12 s. The minimum surface roundness deviation R can be obtained after a sufficient dwell period, and the measurements of R are given in Table 2. This indicates that the predicted minimum dwell times are close to the experimental results under the presented grinding conditions and the prediction error of the EADSR increases with the increasing feed rate. The above experimental results of the minimum dwell times are similar to the simulation results obtained with the EADSE and EADSR. According to the EADSE, to satisfy the requirement that the size error of the workpiece be within 1 µm, the minimum dwell time should last

for about 3τ. The prediction changes with the targeted size error of the workpiece, theoretically. The experimental results show the predicted minimum dwell time is less 2.60 s than the actual measured minimum dwell time. A possible explanation for the difference is the absence of thermal deformation in the prediction model for estimating minimum dwell time. The thermal deformation affects the cutting depth of the wheel, and the higher cutting depth of the wheel affects the change in workpiece size. According to the EADSR, to obtain the minimum surface roundness deviation during the dwell period, the minimum dwell time should last for no less than 3.7τ. The predicted minimum dwell time theoretically increases with the increasing feed rate, but the experiment results show the feed rate has no obvious effect on the minimum dwell time under the presented grinding conditions. The roundness error related to the dwell time was also investigated by nine experiments which were divided into three groups averagely. The wheel was dressed before the first experiment of each group. The roundness errors were measured by a roundness measuring instrument (Talyrond 565 by Taylor Hobson Inc.) after each grinding experiment at feed rate 0.3 mm/min. The measured results of roundness errors of each group, which are the mean value for three experimental results, for different dwell time are shown in Fig. 8. The trends of the roundness errors of the experiments seem to decrease with the increasing dwell time. However, the convergence of roundness error is not as obvious as that of the surface roundness in Fig. 7. A possible explanation for the phenomenon is the absence of transformation of the cross section of the workpiece in the prediction model for estimating dwell time. It will be focused in the next work of this research.

5. Conclusions This study presented the on-line calculation of the time constant of the dwell period and deduced the estimation algorithms of dwell time in cylindrical-plunge grinding from the relationships between the dwell time and grinding qualities, namely the size error and surface roundness. An on-line method of estimating the minimum dwell time was developed using the AE RMS signal. The results of experiment and simulation were compared. The following conclusions can be drawn.

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1. The time constants for different feed rates, calculated from the AE RMS signals, vary only slightly by less than 0.02 s. This indicates that the feed rate has little effect on the time constants of the grinding system. Using the on-line AE measurement, the estimation algorithms of minimum dwell time, the EADSE and EADSR, were developed. Experiments indicate that both the EADSE and EADSR can be used in estimating the dwell time in precision cylindrical-plunge grinding with excellent sensitivity. 2. To satisfy the requirement of the size error of the workpiece being within 1 µm, the minimum dwell time, predicted by the EADSE, should last for 3τ at least. The predicted minimum dwell time increases with the increasing feed rate, which is in agreement with experimental results. However, the predicted minimum dwell times are always slightly shorter than the actual measured results. 3. To obtain steady surface roundness, the minimum dwell time, predicted by the EADSR, should be last for 3.7τ at least. The experimental results show the minimum dwell time should be no less than 4τ to obtain the steady minimum surface roundness deviation under the presented grinding conditions. The predicted minimum dwell time theoretically increases with the increasing feed rate, but there was no obvious increase in the experiments. This discrepancy should be the focus of future research. 4. Because the time constant is related to the grinding system, both estimation algorithms of minimum dwell times, the EADSE and EADSR, are suited to cylindrical-plunge grinding with different machine tools, workpiece materials and grinding wheels. Compared with traditional control motheds, the predictions of the EADSE and EADSR are determined by the requirement of the machining accuracy and the surface quality. This allows repeatable prediction of the proper dwell time for both workpiece quality and machining efficiency by characterizing the grinding system with a few simple measurements and then monitoring the AE signals. The dwell time satisfying constraints for industrial application can be selected easily using the proposed estimation algorithms. It is also possible to estimate the size error and surface roundness of a workpiece using the dwell time and the EADSE and EADSR.

ACKNOWLEDGEMENT The authors gratefully acknowledge the Research Fund for the Doctoral Program of Ministry of Education of China (20133120120005), the Shanghai Municipal Natural Science Foundation (13ZR1428000) and the Innovation Program of Shanghai Municipal Education Commission (No. 13YZ068) by which the paper was supported.

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