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Condition monitoring of the feed drive system of a machine tool based on long-term operational modal analysis
International Journal of Machine Tools and Manufacture 146 (2019) 103454
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International Journal of Machine Tools and Manufacture journal homepage: www.elsevier.com/locate/ijmactool
Condition monitoring of the feed drive system of a machine tool based on long-term operational modal analysis
T
Pingjia Jiaa,b, Youmin Ronga,b, Yu Huanga,b,c,∗ a
State Key Lab of Digital Manufacturing Equipment and Technology, Huazhong University of Science and Technology, Wuhan, China School of Mechanical Science and Engineering, Huazhong University of Science and Technology, Wuhan, China c Guangdong Intelligent Robotics Institute, Dongguan, China b
ARTICLE INFO
ABSTRACT
Keywords: Condition monitoring Life cycle assessment Feed drive system Operational modal analysis Machining process
High speed and high reliability are important characteristics and are part of the inevitable development trend in many machining production lines such as those in the automotive industry and electronic manufacturing. In high-speed machining, the linear axe feed drive system is an important component that moves the cutting tool and workpiece to their desired positions for part production. Because of the long amount of time or the high power continuous machining, gradual wear of the ball screw easily occurs, which will deteriorate its performance. However, due to time-varying factors during the machining process, such as the feeding speed, cutting force and table position, condition monitoring and health assessment of the feed drive system in the long-term running status are complicated. To solve this problem, the statistical characteristics of the dynamics of the feed drive system are introduced in this paper to develop a method to long-term condition monitoring and life cycle assessment. In this method, the modal parameters are estimated from the free-vibration response excited by the inertial force of the feed drive system during its high-speed acceleration or deceleration movement. Then, the long-term statistical characteristics of the dynamics are analysed, and their effects on the machining process are further studied. The spindle current in the milling process is monitored by the current sensor and evaluated using the sparse feature vector. The results show that the variance of the modal parameter increases with the wear of the screw, which will worsen the machining process fluctuations and significantly accelerate the wear rate of the cutting tool. Therefore, the health condition of the feed drive system of the machine tool can be accurately monitored by both the statistical characteristics of modal parameters and the sparse vectors of the cutting current.
1. Introduction Manufacturing enterprises have observed high demands for the increased product quality, higher product efficiency, lower cost and global competition. In the machining field, the automated production lines effectively serve to satisfy these demands and have been widely adopted in manufacturing enterprises [1]. High speed and reliability are important characteristics and an inevitable trend for many machining production lines such as those in automotive industry and electronic manufacturing. However, the engaged automated production lines with a high operating ratio can cause various mechanical failures and reduce the product quality consistency. Generally, approximately 15%–40% of the entire production cost is consumed for the equipment maintenance, and 30% of the maintenance cost is lost for unnecessary or improper labour [2,3]. Therefore, it is essential to develop health
∗
condition monitoring and assessment technology for equipment to reduce the maintenance costs and improve product quality and efficiency. In high-speed machining, the feed drive system of the machine tool is an important component that moves the cutting tool and workpiece to desired positions for the part production. Usually, the interaction between the machining process and the dynamics of the feed drive system plays an essential role in the machining performance [4]. Due to continuous machining with high strength, the ball screw is usually in a gradual wear state or even failure, which will deteriorate its dynamic characteristics and critically affect the resulting product quality [5]. The machine tool feed drive system is a vital element that moves the cutting tool and workpiece to the desired positions. In industrial operations, 18.72% of the downtime time of the machine tool is produced by the mechanism failure of the feed drive system [2]. After a long time of running, the moving parts of the feed drive system such as the ball
Corresponding author. State Key Lab of Digital Manufacturing Equipment and Technology, Huazhong University of Science and Technology, Wuhan, China. E-mail addresses: [email protected], [email protected] (Y. Huang).
https://doi.org/10.1016/j.ijmachtools.2019.103454 Received 12 March 2019; Received in revised form 21 August 2019; Accepted 24 August 2019 Available online 28 August 2019 0890-6955/ © 2019 Elsevier Ltd. All rights reserved.
International Journal of Machine Tools and Manufacture 146 (2019) 103454
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screw and bearing will wear out, which inevitably deteriorate its dynamic characteristics [6,7]. The degradation of the dynamic characteristics could increase the tool wear and workpiece surface damage and critically affect the cutting performance and consistency of the product quality [8]. Therefore, it is important to study the dynamics of the ball-screw drive system under long-term operating conditions to improve its overall performance [9]. Li et al. proposed an output-only modal identification method to estimate the first three modal parameters of the feed drive system at different feed speeds [10,11]. The results illustrate that the estimated natural frequencies and damping ratios dramatically decrease when the feed speed increases. Feng et al. examined the relationship between the ball screw preload variation and the dynamics of the feed drive system and provided an approach to monitor the health status of the used ball screw based on the vibration signals at the ball nuts [12]. Tsai et al. conducted tests on ball screw feed drive systems with different preloads to build a performance assessment based on the ball pass frequency detection [13]. The results show that the preload loss will increase the ball pass frequency and induce its side band. This phenomenon provides promising criteria in detecting the onset of preload loss of ball screws. Vogl et al. introduced a novel inertial measurement unit (IMU)-based method for the diagnostics of machine tool linear axes [14]. Various degradation patterns were experimentally simulated, and the ability of the IMU-based method is investigated to resolve the low- and high-frequency components of error motions. However, the feed drive system dynamics is a complex problem because it is affected by many factors in the machining process. First, the feed drive system dynamics significantly and quickly changes, since it is closely related to the position of the moving worktable [1]. Second, the dynamic cutting force in the machining process will introduce considerable uncertainty into the feed drive system dynamics [15,16]. It is difficult to identify the long-term degradation of the dynamics from those variations due to these factors. Facing this challenge, a long-term experiment was performed in an actual automobile plant in this paper to study the dynamics degradation of the feed drive system and its effect on the cutting process based on the operational modal analysis and sparse feature vectors.
massive engine blocks is T22003 (diameter 99 mm, 13 teeth), produced by the GUHRING company. The speed of the feed drive system is 40–60 m/min, which is not constant during the entire milling process, whereas the spindle speed is 6000 r/min. Fig. 2b presents the finished workpiece of an engine block. The vibrations of the feed drive system are monitored by an accelerometer, and the spindle current is collected by a current sensor. The specific measurement and acquisition settings are as follows: i. A low-mass, wide-bandwidth and three-axis accelerometer is mounted at the support of the ball screw to collect the vibration signal of the feed drive system in three directions (accelerometer reference: PCB-356-A15). ii. Three current sensors are attached to the spindle power cable to collect the drive currents in three phases (current sensor reference: CSNP 661). iii. All sensors are connected to a data acquisition system (LMS SCADAS Mobile SCM05), and the sampling rate of the vibration and current are 2000 Hz and 1000 Hz, respectively. 3. Model theory 3.1. Operational modal analysis based on the free-vibration response The operational modal analysis (OMA) can estimate the modal parameters based on ambient vibration data obtained in the operation condition rather than laboratory condition [10,17]. The method requires the ambient excitation force to be approximately white noise. However, harmonic components dominate the vibration signal due to the rotational cutting forces during machining. In this case, when a natural frequency of the structure is near the excitation force of one of the harmonic components, the identification of the modal parameters (dynamics characteristics) from the operational response will be disturbed, or it cannot be estimated at all. To fix this problem, the operating modal parameters of the feed drive system are estimated from the free-vibration response excited by the worktable inertial force caused by the high-speed acceleration and deceleration. Since the inertial forces have been characterized as square-wave pulses [8], massive modal parameters can be estimated form every free-vibration response in long term running. If the machine tool is considered a viscous damping system, the general form of the equation of motion is expressed as follows:
2. Experiment As shown in Fig. 1, the free-vibration responses of the feed drive system are collected to estimate its dynamic characters such as the natural frequencies and the damping ratios. The statistics of the dynamics characteristics are used to identify the long-term dynamics degradation of the feed drive system. The cutting processes are monitored by analysing the sparse features of the spindle current. The long-term dynamics degradation of the feed drive system and its effect on cutting process are observed. The results reveal that the statistics on the dynamics characteristics can indicate the health status of the feed drive system in long-term operation. With the degradation of the feed drive system, the cutting quality fluctuations are increased, and the wear rate of the cutting tool is intensified. Experiments were performed on a real automated production line over approximately 100 days to investigate the long-term degradation of the feed drive system and its effect on the cutting process. In longterm statistics, the inertial force caused by the high-speed acceleration and deceleration and cutting force was comprehensively considered, since the entire cutting process of a workpiece is completed by a complex tool path group that consists of the multi-stage operation of the feed drive system (starting, acceleration, fast feed, milling, fast retract, deceleration, stopping, etc.), and this procedure is very complex. Acceleration and deceleration values in different cutting stages are not a constant, and their state of the feed drive system is monitored and used to extract eigenvalues. The production line, including three-axis machine tool XS 321, is shown in Fig. 2a. It is used to automatically make the upper surface of massive engine blocks. The tool used to mill
Mx¨ + Cx + Kx = f
(1)
For a free-response vibration system, the initial conditions are:
x (0) = x 0
(2)
x (0) = v0
(3)
M, C and K are the n × n mass, damping and stiffness matrices of the machine tool structure system, respectively, and n is the number of dofs for the system; x 0 and v0 are the initial displacement and velocity vectors, respectively. For the proportional viscous damping, the following relation is expressed:
C= M+ K
(4)
Constants and can be calculated based on prior knowledge from the free-vibration data [17,18]. For the normal mode analysis, the freeresponse vibration can be written as:
x = Xe i
t
(5)
Then, for the proportional viscous damping model without the prescribed force, the system equation becomes:
Mx¨ + ( M + K) x + Kx = 0 We rearrange the above equation: 2
(6)
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Fig. 1. Schematic diagram of the experimental system.
M (¨x + x) =
(7)
K (x + x )
Thus, if the vibration responses x , x and x¨ are acquired, the matrix M 1K can be calculated by Eq. (8) and used to solve for the eigenvalues and eigenvectors. Consider the system free-response matrix as follows:
Then
M 1K =
(¨x + x)(x + x)
1
(8)
Fig. 2. Experiment system and data acquisition system: (a)machine tool; (b) engine block; (c) acceleration sensor; (d) current sensor.
3
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Fig. 3. Schematic diagram of the modal algorithm based on the free-vibration response.
X(t ) = [X ]Nk × n =
x1, k x1, k + 1
x2, k x2, k + 1
xn, k xn, k + 1
x1, k + Nk
x2, k + Nk
xn, k + Nk
x1, Nk x2, Nk xn, Nk
1
1
1
x1, Nk x2, Nk
1
1
xn, Nk
1
1
= 1
x1, k x2, k
x1, k + 1 x2, k + 1
x n, k
xn, k + 1
A=
y = Ye
¨ = [ {x¨} k {¨} X x k + 1 {x¨} k + Nk + 1]
(11)
r
r r
r = 1,2, …, n.
(18)
= R e ± iIm =
r
r
±i
r
1
2 r
(19)
Then, the natural frequency and modal damping ratio of the feed drive system can be determined: r
(12) r
(13)
= =
Re2 + Im2
(20)
Re Re2 + Im2
(21)
3.2. Sparse feature vector of the machining process
Then, the dynamic equation of the feed drive system can be rewritten as follows:
Ay + By = p
(17)
where
without loss of generality, the following equilibrium equation is introduced and combined with Eq. (1):
Mx¨ = 0
(16)
t
Yr , Yr
r
By comparing Eqs. (9)–(11), we can rewrite Eq. (9) as follows: 1
(15)
By solving the above equation, 2n pairs of complex eigenvalues and eigenvectors can be obtained:
(9)
(10)
Mx¨
x¨ , p = 0 x f
( A 1B) Y = Y
X = [ {x } k {x } k + 1 {x } k + Nk + 1]
¨ + X)(X + X) (X
M 0 , y= 0 K
Assuming that the external force vectors are zero, we substitute Eq. (16) into Eq. (14) and formulate the eigenvalue problem as:
1
where x r , k = xr (tk ) is the displacement of the rth dof at the kth sampling point as depicted in Fig. 3; k is the starting point, Nk is the number of points adopted by the modal analysis algorithm. Superscript T represents the transpose operation on the matrix. Similarly, the velocity and acceleration response matrices can be defined as follows:
M 1K =
0 M , B= M C
The sparse feature vector is extracted from the cutting current of stacked autoencoders. The autoencoder is a type of unsupervised neural network with three layers [18], and the output of the autoencoder is the reconstitution of input data with lower dimension. As depicted in Fig. 4a, the autoencoder has two basic parts: encoder network and
(14)
where
Fig. 4. Architectural graph of an auto-encoder: (a) structure of a sparse auto-encoder unit; (b) structure of a deep stack auto-encoder network. 4
International Journal of Machine Tools and Manufacture 146 (2019) 103454
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Fig. 5. Operational vibration in three directions of the feed drive system: (a) vibration signals and (b)the corresponding autopowers.
Fig. 6. Operational vibration in the x direction of the feed drive system: (a) one small portion of the vibration signal from the long-term operation; (b) free response in the vibration.
decoder network. The encoder layer transforms the input data from a high-dimensional space into sparse codes with lower dimension, and the decoder network reconstructs the sparse codes into the original input. The encoder network is defined as an encoding function denoted by f . For each measured spindle current signal ym = [y1 , y2 , y3 , , ym ] corresponding to a finished workpiece, the sparse vector of the encoder is calculated as follows:
hk = f (ym)
EAE ( ,
1 M
M
L (yi , yˆi) = i=1
1 M
M i=1
L (yi , g (f (yi)) )
(26)
where EAE ( , ) is the reconstruction error of the autoencoder, M is the number of training examples, y im is the input vector for each training example, and L (y im, yˆ im) is the corresponding loss function. In summary, the autoencoder training aims to find parameter matrices and by minimizing the reconstruction error. In Eq. (26), the commonly used forms for the encoder and decoder networks are affine mappings, which are optionally followed by a non-linearity:
(24)
where hk is the output of the encoder network, is the encoder network parameter matrices, m and k are the dimension of the input vectors and sparse vectors of the encoder network, respectively; k < m . In contrast, the decoder network is defined as a reconstruction function denoted by g . It maps hk from the low-dimensional space back into the original high-dimensional space:
yˆm = g (hk)
)=
f (y im) = sf (Wy im + b)
(27)
g (hik) = sg (W Thik + d)
(28)
where sf and sg are the encoder and decoder activation functions, respectively. Thus, the parameter matrices of the encoder and decoder are = {W, b} and = {W T, d} , where b and d are bias vectors; W and W T are the weight matrices. As shown in Fig. 4b, n autoencoders can be stacked to significantly reduce the dimensionality of the original input data and extract the relevant sparse feature vector from the spindle current.
(25)
where yˆm = [yˆ1 , yˆ2 , yˆ3 , , yˆm ] is the output vector of the decoder network, and is the decoder network parameter matrices. The parameter matrices of the encoder and decoder are simultaneously trained by reconstructing the original input as possible and attempting to incur the lowest possible reconstruction error over M training examples. The reconstruction error is defined by a loss function that measures the discrepancy between ym and yˆm : 5
International Journal of Machine Tools and Manufacture 146 (2019) 103454
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Fig. 7. Stability diagrams of the OMA algorithm based on a single free-vibration response: (a) Frequency stability diagram; (b) Damping ratio stability diagram.
Fig. 8. Time evolutions of the first three modes of the feed drive system: (a) Time evolution of the natural frequencies; (b) Time evolution of the damping ratios.
Fig. 9. Frequency stability diagrams estimated from multiple free-vibration responses: (a) Frequency stability diagrams for the first five days; (b) Statistical characteristics of modal parameters for the first five days; (c) Frequency stability diagrams for the last five days; (d) Statistical characteristics of modal parameters for the first five days. 6
International Journal of Machine Tools and Manufacture 146 (2019) 103454
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Fig. 10. Damping ratio stability diagrams estimated from multiple free-vibration responses: (a) Damping ratio stability diagrams for the first five days; (b) Damping ratio stability diagrams for the last five days. Table 1 Statistical analysis of the modal parameters estimated from the free responses in different health statuses. Normal ball screw
Eigen frequency (Hz) Mean values Std Damping ratio (%) Mean values Std
Damaged ball screw
Mode #1
Mode #2
Mode #3
Mode #1
Mode #2
Mode #3
13.672 1.874
25.852 0.252
38.951 0.963
13.145 3.483
25.934 0.277
38.124 2.375
6.731 0.735
6.244 0.124
10.3 0.542
6.528 1.247
6.372 0.131
10.59 1.322
Fig. 11. Long-term degradation of the feed drive system during the entire life of the ball screw: (a) Long-term standard deviation of the dynamics of the feed drive system; (b) Wear characteristics of the final damaged ball screw.
4. Results and discussion
surface quality, and simultaneously accelerate the tool wear. In this section, the statistics of the dynamics of the feed drive system in the long-term operation is studied by the OMA; then, its effect on the machining process is observed and discussed.
After the long-term operation, the feed drive system inevitably wears down, which deteriorate its dynamic characteristics and vibration. The dynamics degradation affects the workpiece precision and 7
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Fig. 12. Three-phase current signals during machining process of one workpiece with 75 s related to: (a) tool #1, (b) tool #4.
Fig. 13. Process monitoring at large scale based on the similarity of the sparse feature vectors of the spindle current.
4.1. Dynamics analysis of the feed drive system based on the free-vibration response
the x direction while the green and red signals illustrate the vibrations in the y and z directions, respectively. The corresponding autopowers of the vibrations in the three different directions are shown in Fig. 5b. The amplitude and energy of the vibration in the x direction are much larger than that in the other directions. Therefore, the transient vibration curve in the x direction of the feed drive system during the machining process is analysed in Fig. 6a; then, the free-vibration response (Fig. 6b) caused by the acceleration movement is selected to validate the OMA method reliability and estimate the modal parameters of the feed drive system. The detailed dynamic characteristics of each part were not specifically elaborated, and it was almost impossible to obtain the vibration mode under the operational conditions. A free-vibration response caused by the acceleration movement in Fig. 6b was selected to validate the OMA method reliability and
The dynamics of the feed drive system is complicated in the longterm operational condition. It changes over time because it depends on the position of the moving feed drive system during machining. This type of time-varying character makes it impossible to directly identify the dynamics degradation from the estimated modal parameters. The dynamics uncertainty of the feed drive system must be considered in long-term running conditions. Generally, the dynamics uncertainty can be represented by probabilistic approaches [19–22]. Fig. 5 presents the acceleration signals and the corresponding autopowers of the feed drive system in three directions under the operational conditions. The blue signal in Fig. 5a represents the vibration in 8
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Fig. 14. Similarity index diagrams of (a) tool #1; (b) tool #2; (d) tool #3; (d) tool #4.
estimate the modal parameters of the feed drive system, whereas the free vibration is measured using an acceleration sensor, which is pasted on the surface of the support seat of the ball screw; thus, this
measurement result has no direct relationship with the natural frequency. Meanwhile, the natural frequency can be calculated by Eq. (20). Fig. 7a and b presents the stability diagrams of the OMA based on 9
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Fig. 15. Standard deviations of the similarity index calculated by the manual feature vector and sparse feature vector: (a) standard deviations based on the manual feature vectors; (b) standard deviations based on the sparse feature vectors.
the selected free-vibration response. The stability diagrams are an appropriate method for indicating the modal analysis results of the OMA algorithm. In Fig. 7a, the red curve refers to the autopower of the selected free-vibration response. The potential natural frequencies are shown on the abscissa axis, and the model orders of the algorithm are displayed on the ordinate axis. The black spot symbols in the figure suggest the relationship between the model order of the OMA and the solutions of the order. Theoretically, if a natural frequency appears at any order, there is a high probability that it is a natural frequency. There are many spot clusters in Fig. 7b, which serve as the potential modal modes estimated from the free response. The first three clusters closely match the first three peaks of the autopower, which implies that they are the real modes. Fig. 7b signifies the damping ratio stability diagram with the first three calculated damping ratios on the abscissa axis and the model orders on the ordinate axis. The clusters in both Fig. 7a and b are fairly clear, which indicates that the results of the operational modal analysis are convincing, and the method is valid.
stability diagram based on all selected free responses of the last five days of the experiment. The results in this figure illustrate the dynamics of the feed drive system under the damaged ball screw condition. Fig. 9b and d shows the statistical characteristics of the natural frequencies of the first three modes. All-natural frequencies clearly exhibit an approximately normal distribution. The natural frequency of the second mode is probably due to the mode of the machine tool frame, which is less affected by the running status of the feed drive system. The damping ratio stability diagrams estimated from the same free-vibration responses are shown in Fig. 10. Fig. 10a shows the damping ratio stability diagram in healthy condition, and Fig. 10b shows the damping ratio stability diagram in the damaged condition. The statistical characteristics of the modal parameters in different health statuses of the ball screw are presented in Table 1. The mean values of the natural frequencies and damping ratios are almost unchanged when the ball screw is damaged. Nevertheless, the standard deviations of the natural frequencies and damping ratios of mode #1 and mode #3 increase, which indicates more dynamics uncertainties of the feed drive system with a damaged ball screw. Since mode #2 results from the mode of the entire frame of the machine tool, the dynamics are less affected by the feed drive system. Hence, the standard deviations of the modal parameters are almost unchanged, and the values are much smaller than those of the other modes. In Fig. 11a, the long-term standard deviations of the dynamics uncertainties during the entire life of the ball screw are shown by the curves in four colours, which indicate the standard deviations in four different months. Fig. 11b shows the photos of the final damaged ball screw. The damaged areas of the ball screw are marked by the red dashed curves in the figures. This result shows that the wear of the ball screw increases the dynamics uncertainty and wear rate.
4.2. Time evolutions of the dynamics of the feed drive system in the longterm running status Considering the dynamics uncertainty in long-term running, it is imperative to estimate the modal parameters and their statistical characteristics through all free-vibration responses. In our modal analysis experiment, the vibration signals last for approximately 94 days, which covers the entire life of the ball screw of the feed drive system. Fig. 8 presents all estimated modal parameters of the first three modes in 94 days. The natural frequency and damping ratio of the first and third modes are increasingly dispersed from the 65th day to the 71st day. However, as shown by the green dots in Fig. 8, the natural frequency and damping ratio of the second mode are almost unchanged, and the operating modal parameters of the first and third modes vary in a wider range than those of this mode. This result suggests that the first and third modes are probably the local modes related to the feed drive system, and the second mode is related to the machine tool frame. Compared with the second mode, the first mode and third mode are more dispersed because they are more affected by the running status of the feed drive system. Fig. 9 shows the frequency stability diagrams and their statistical characteristics of the first three modes in different health statuses. In Fig. 9a, the natural frequencies of the feed drive system are estimated from all selected free responses of the first five days of the experiment. The spot symbols in this figure show that the natural frequencies of the feed drive system have significant dispersion, which is due to the timevarying worktable position and speed of the feed drive system during the machining process. In contrast, Fig. 9c presents the frequency
4.3. Effect of the feed drive system degradation on the machining process The relationship between the cutting process and the dynamics of the feed drive system is further studied in this section. Because the experiment should not disturb the routine manufacturing in the plant, the spindle current is introduced to monitor the cutting process, since it is a non-destructive measuring method. Fig. 12 shows the three-phase spindle current signals in different heath statuses of the feed drive system. Each signal corresponds to an entire machining process of one workpiece with 75 s, and different tools (1# and 4#) were selected in nearly 100-day continuous production. As shown in Fig. 12a and b, the difference between the two currents is difficult to observe due to their high data dimension. Therefore, it is crucial to select key features from the signal to construct a feature vector with low dimensionality. By applying the feature vector, the difference in spindle currents can be 10
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Fig. 16. Final worn patterns of the four cutting tools: (a) tool #1; (b) tool #2; (d) tool #3; (d) tool #4. 11
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calculated as follows and quantized:
k1, j =
m v v i = 1 1, i j, i m m 2 v v j, i i = 1 1, i i=1 2
wear situations. These results illustrate that the dynamics uncertainties caused by the deterioration of the feed system can introduce fluctuations into the cutting force in machining, which will significantly worsen the working condition of the cutting tool and accelerate its wear ratios.
(23)
where v1, i and vj, i are the arbitrary elements of the reference vector and the jth feature vector, respectively. In extreme cases, when the machining conditions of the two workpieces are completely different, the exponent is equal to −1; when the two workpieces have identical cutting processes, the exponent is equal to zero. Fig. 13 shows the schematic diagram of the calculation of the cutting difference over time. The first feature vector is used as a reference because it serves as the initial cutting condition with no tool wear. In a mass production line, the machining parameters of each workpiece are exactly identical. Only the tool wear condition can affect the cutting process. Thus, the difference between the feature vector at a particular moment and the reference feature vector represents the tool wear condition at that moment. For comparison, two types of features are selected from the raw current signals to construct the feature vectors. One type is a set of manually selected features, including the maximum value, root mean square (RMS), mean value and standard deviation of the current, which are stacked to form a feature vector. The other type is sparse features selected by autoencoders. There are four stacked autoencoders: the first one has 60000 input nodes and 2000 output nodes; the second one has 2000 input nodes and 400 output nodes; the last one has 400 input nodes and 100 output nodes. The last output is the sparse feature vector of the current signal. Furthermore, the entire life cycles of cutting tools #1–4 (noted in Fig. 11a) under different health states of the feed drive system are investigated. Fig. 14a–14d illustrate the difference index that is calculated by the manual feature vector and sparse feature vector during the entire life cycle of the four tools. The workpiece number, which represents the time dimension, is displayed on the abscissa axis because it is easy to record on site. Different indices of each workpiece are displayed on the ordinate axis. The red curves in the figures indicate the indices calculated from the manually selected feature vectors, and the blue curves represent the indices calculated from the sparse feature vectors. All blue curves gradually decrease, which implies the slow wear process of the cutting tools. All red curves in the figures gradually decrease except the curves of tool #4. The red curve in Fig. 14d first decreases and subsequently increases to zero, which conflicts with the phenomenon of gradual wear of the tool. Thus, the manually selected feature vectors are less reliable and consistent because they contain relatively less information than the sparse feature vectors. The standard deviations of the index of the four tools are calculated and presented in Fig. 15. Each standard deviation is calculated by 8 adjacent similarity indices, and 46 standard deviations (its one value is calculated by 10 workpieces) are acquired by sliding sampling with no overlap. Fig. 15b shows that tools #3 and #4 have larger standard deviations than tools #1 and #2. The fluctuations of the index are mainly caused by the dynamics degradation of the feed system because all control parameters of the automatic production line are stable. Tools #1 and #2 are related to the ball screw in normal conditions, and tools #3 and #4 are related to the ball screw in damaged conditions. This phenomenon can be interpreted as the fluctuation of the cutting force and spindle current are resulted from the dynamics uncertainties of the feed drive system. The curves in Fig. 15a are confusing and irregular because they are calculated from the manually selected feature vectors. Fig. 16 describes the relationship between the final worn images of the four tools. The worn areas of the cutting tool are marked by the red curves in the right figures, and the indices are presented by the blue curves in the left figures. As shown in Fig. 16a and b, the index fluctuations are relatively small, and the contours of the wear regions of the two cutting tools are smooth and almost straight. The indices in Fig. 16c and d fluctuate more significantly than 16a and 16 b, and the contours of the wear regions are irregular and distorted, which indicates worse
5. Conclusions In high-speed machining, the dynamic characteristics during longterm running deteriorate because of the mechanical wear of the ball screw in the feed drive system; thus, the dynamics of the feed drive system and its evolution were investigated. Three conclusions can be obtained as follows. (1) The statistical analysis of the dynamics is only performed based on the free-vibration signals during the entire life of the feed drive system, while modal parameters are first estimated from the freevibration responses using the OMA. (2) The standard deviations of the natural frequencies and damping ratios of mode #1 and mode #3 increase, which indicates more dynamics uncertainties of the feed drive system with a damaged ball screw. (3) The dynamics uncertainties of the feed drive system can increase the fluctuations of the cutting process, and these fluctuations will significantly worsen the working condition of the cutting tool and accelerate its wear rate. Acknowledgments The research is supported by the National Natural Science Foundation of China under Grant (51705174, 51905191), the State key laboratory smart manufacturing for special vehicles and transmission system (GZ2016KF008), Science and Technology Planning Project of Guangdong Province (2017B090913001), and DongGuan Innovative Research Team Program (201536000100031). Appendix ASupplementary data Supplementary data to this article can be found online at https:// doi.org/10.1016/j.ijmachtools.2019.103454. References [1] Y. Altintas, A. Verl, C. Brecher, et al., Machine tool feed drives, CIRP Ann. - Manuf. Technol. 60 (2) (2011) 779–796. [2] R. Teti, K. Jemielniak, G. O'Donnell, D. Dornfeld, Advanced monitoring of machining operations, CIRP Ann. - Manuf. Technol. 59 (2) (2010) 717–739. [3] K. Zhu, Y. San Wong, G.S. Hong, Wavelet analysis of sensor signals for tool condition monitoring: a review and some new results, Int. J. Mach. Tool Manuf. 49 (7) (2009) 537–553. [4] H.C. Möhring, O. Bertram, Integrated autonomous monitoring of ball screw drives, CIRP Ann. - Manuf. Technol. 61 (1) (2012) 355–358. [5] G.H. Feng, Y.L. Pan, Investigation of ball screw preload variation based on dynamic modeling of a preload adjustable feed-drive system and spectrum analysis of ballnuts sensed vibration signals, Int. J. Mach. Tool Manuf. 52 (1) (2012) 85–96. [6] C.G. Zhou, H.T. Feng, Z.T. Chen, et al., Correlation between preload and no-load drag torque of ball screws, Int. J. Mach. Tool Manuf. 102 (2016) 35–40. [7] M.C. Chang, J.L. Liou, C.C. Wei, et al., Fractal analysis for vibrational signals created in a ball-screw machine operating in short-and long-range tribological tests, J. Tribol. 135 (3) (2013) 031101. [8] K. Erkorkmaz, Y. Altintas, High speed CNC system design. Part II: modeling and identification of feed drives, Int. J. Mach. Tool Manuf. 41 (10) (2001) 1487–1509. [9] C. Brecher, M. Fey, S. Bäumler, Damping models for machine tool components of linear axes, CIRP Ann. - Manuf. Technol. 62 (1) (2013) 399–402. [10] B. Li, B. Luo, X. Mao, et al., A new approach to identifying the dynamic behavior of CNC machine tools with respect to different worktable feed speeds, Int. J. Mach. Tool Manuf. 72 (2013) 73–84. [11] B. Luo, D. Pan, H. Cai, et al., A method to predict position-dependent structural natural frequencies of machine tool, Int. J. Mach. Tool Manuf. 92 (2015) 72–84. [12] G.H. Feng, Y.L. Pan, Establishing a cost-effective sensing system and signal processing method to diagnose preload levels of ball screws, Mech. Syst. Signal Process. 28 (2012) 78–88.
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P. Jia, et al. [13] P.C. Tsai, C.C. Cheng, Y.C. Hwang, Ball screw preload loss detection using ball pass frequency, Mech. Syst. Signal Process. 48 (1) (2014) 77–91. [14] G.W. Vogl, M.A. Donmez, A. Archenti, Diagnostics for geometric performance of machine tool linear axes, CIRP Ann. - Manuf. Technol. 65 (1) (2016) 377–380. [15] Y. Altintas, P. Kersting, D. Biermann, et al., Virtual process systems for part machining operations, CIRP Ann. - Manuf. Technol. 63 (2) (2014) 585–605. [16] E. Diez, E. Leal-Muñoz, H. Perez, et al., Dynamic analysis of a piezoelectric system to compensate for workpiece deformations in flexible milling, Mech. Syst. Signal Process. 91 (2017) 278–294. [17] F. Magalhães, Á. Cunha, E. Caetano, et al., Damping estimation using free decays and ambient vibration tests, Mech. Syst. Signal Process. 24 (5) (2010) 1274–1290. [18] B.T. Wang, D.K. Cheng, Modal analysis by free vibration response only for discrete
and continuous systems, J. Sound Vib. 330 (16) (2011) 3913–3929. [19] G.E. Hinton, R.R. Salakhutdinov, Reducing the dimensionality of data with neural networks, Science 313 (5786) (2006) 504–507. [20] F. Jia, Y. Lei, J. Lin, et al., Deep neural networks: a promising tool for fault characteristic mining and intelligent diagnosis of rotating machinery with massive data, Mech. Syst. Signal Process. 72 (2016) 303–315. [21] M. Dohler, X.B. Lam, L. Mevel, Uncertainty quantification for modal parameters from stochastic subspace identification on multi-setup measurements, Mech. Syst. Signal Process. 36 (2) (2013) 562–581. [22] C. Soize, Stochastic modeling of uncertainties in computational structural dynamics-recent theoretical advances, J. Sound Vib. 332 (10) (2013) 2379–2395.
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International Journal of Machine Tools and Manufacture journal homepage: www.elsevier.com/locate/ijmactool
Condition monitoring of the feed drive system of a machine tool based on long-term operational modal analysis
T
Pingjia Jiaa,b, Youmin Ronga,b, Yu Huanga,b,c,∗ a
State Key Lab of Digital Manufacturing Equipment and Technology, Huazhong University of Science and Technology, Wuhan, China School of Mechanical Science and Engineering, Huazhong University of Science and Technology, Wuhan, China c Guangdong Intelligent Robotics Institute, Dongguan, China b
ARTICLE INFO
ABSTRACT
Keywords: Condition monitoring Life cycle assessment Feed drive system Operational modal analysis Machining process
High speed and high reliability are important characteristics and are part of the inevitable development trend in many machining production lines such as those in the automotive industry and electronic manufacturing. In high-speed machining, the linear axe feed drive system is an important component that moves the cutting tool and workpiece to their desired positions for part production. Because of the long amount of time or the high power continuous machining, gradual wear of the ball screw easily occurs, which will deteriorate its performance. However, due to time-varying factors during the machining process, such as the feeding speed, cutting force and table position, condition monitoring and health assessment of the feed drive system in the long-term running status are complicated. To solve this problem, the statistical characteristics of the dynamics of the feed drive system are introduced in this paper to develop a method to long-term condition monitoring and life cycle assessment. In this method, the modal parameters are estimated from the free-vibration response excited by the inertial force of the feed drive system during its high-speed acceleration or deceleration movement. Then, the long-term statistical characteristics of the dynamics are analysed, and their effects on the machining process are further studied. The spindle current in the milling process is monitored by the current sensor and evaluated using the sparse feature vector. The results show that the variance of the modal parameter increases with the wear of the screw, which will worsen the machining process fluctuations and significantly accelerate the wear rate of the cutting tool. Therefore, the health condition of the feed drive system of the machine tool can be accurately monitored by both the statistical characteristics of modal parameters and the sparse vectors of the cutting current.
1. Introduction Manufacturing enterprises have observed high demands for the increased product quality, higher product efficiency, lower cost and global competition. In the machining field, the automated production lines effectively serve to satisfy these demands and have been widely adopted in manufacturing enterprises [1]. High speed and reliability are important characteristics and an inevitable trend for many machining production lines such as those in automotive industry and electronic manufacturing. However, the engaged automated production lines with a high operating ratio can cause various mechanical failures and reduce the product quality consistency. Generally, approximately 15%–40% of the entire production cost is consumed for the equipment maintenance, and 30% of the maintenance cost is lost for unnecessary or improper labour [2,3]. Therefore, it is essential to develop health
∗
condition monitoring and assessment technology for equipment to reduce the maintenance costs and improve product quality and efficiency. In high-speed machining, the feed drive system of the machine tool is an important component that moves the cutting tool and workpiece to desired positions for the part production. Usually, the interaction between the machining process and the dynamics of the feed drive system plays an essential role in the machining performance [4]. Due to continuous machining with high strength, the ball screw is usually in a gradual wear state or even failure, which will deteriorate its dynamic characteristics and critically affect the resulting product quality [5]. The machine tool feed drive system is a vital element that moves the cutting tool and workpiece to the desired positions. In industrial operations, 18.72% of the downtime time of the machine tool is produced by the mechanism failure of the feed drive system [2]. After a long time of running, the moving parts of the feed drive system such as the ball
Corresponding author. State Key Lab of Digital Manufacturing Equipment and Technology, Huazhong University of Science and Technology, Wuhan, China. E-mail addresses: [email protected], [email protected] (Y. Huang).
https://doi.org/10.1016/j.ijmachtools.2019.103454 Received 12 March 2019; Received in revised form 21 August 2019; Accepted 24 August 2019 Available online 28 August 2019 0890-6955/ © 2019 Elsevier Ltd. All rights reserved.
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screw and bearing will wear out, which inevitably deteriorate its dynamic characteristics [6,7]. The degradation of the dynamic characteristics could increase the tool wear and workpiece surface damage and critically affect the cutting performance and consistency of the product quality [8]. Therefore, it is important to study the dynamics of the ball-screw drive system under long-term operating conditions to improve its overall performance [9]. Li et al. proposed an output-only modal identification method to estimate the first three modal parameters of the feed drive system at different feed speeds [10,11]. The results illustrate that the estimated natural frequencies and damping ratios dramatically decrease when the feed speed increases. Feng et al. examined the relationship between the ball screw preload variation and the dynamics of the feed drive system and provided an approach to monitor the health status of the used ball screw based on the vibration signals at the ball nuts [12]. Tsai et al. conducted tests on ball screw feed drive systems with different preloads to build a performance assessment based on the ball pass frequency detection [13]. The results show that the preload loss will increase the ball pass frequency and induce its side band. This phenomenon provides promising criteria in detecting the onset of preload loss of ball screws. Vogl et al. introduced a novel inertial measurement unit (IMU)-based method for the diagnostics of machine tool linear axes [14]. Various degradation patterns were experimentally simulated, and the ability of the IMU-based method is investigated to resolve the low- and high-frequency components of error motions. However, the feed drive system dynamics is a complex problem because it is affected by many factors in the machining process. First, the feed drive system dynamics significantly and quickly changes, since it is closely related to the position of the moving worktable [1]. Second, the dynamic cutting force in the machining process will introduce considerable uncertainty into the feed drive system dynamics [15,16]. It is difficult to identify the long-term degradation of the dynamics from those variations due to these factors. Facing this challenge, a long-term experiment was performed in an actual automobile plant in this paper to study the dynamics degradation of the feed drive system and its effect on the cutting process based on the operational modal analysis and sparse feature vectors.
massive engine blocks is T22003 (diameter 99 mm, 13 teeth), produced by the GUHRING company. The speed of the feed drive system is 40–60 m/min, which is not constant during the entire milling process, whereas the spindle speed is 6000 r/min. Fig. 2b presents the finished workpiece of an engine block. The vibrations of the feed drive system are monitored by an accelerometer, and the spindle current is collected by a current sensor. The specific measurement and acquisition settings are as follows: i. A low-mass, wide-bandwidth and three-axis accelerometer is mounted at the support of the ball screw to collect the vibration signal of the feed drive system in three directions (accelerometer reference: PCB-356-A15). ii. Three current sensors are attached to the spindle power cable to collect the drive currents in three phases (current sensor reference: CSNP 661). iii. All sensors are connected to a data acquisition system (LMS SCADAS Mobile SCM05), and the sampling rate of the vibration and current are 2000 Hz and 1000 Hz, respectively. 3. Model theory 3.1. Operational modal analysis based on the free-vibration response The operational modal analysis (OMA) can estimate the modal parameters based on ambient vibration data obtained in the operation condition rather than laboratory condition [10,17]. The method requires the ambient excitation force to be approximately white noise. However, harmonic components dominate the vibration signal due to the rotational cutting forces during machining. In this case, when a natural frequency of the structure is near the excitation force of one of the harmonic components, the identification of the modal parameters (dynamics characteristics) from the operational response will be disturbed, or it cannot be estimated at all. To fix this problem, the operating modal parameters of the feed drive system are estimated from the free-vibration response excited by the worktable inertial force caused by the high-speed acceleration and deceleration. Since the inertial forces have been characterized as square-wave pulses [8], massive modal parameters can be estimated form every free-vibration response in long term running. If the machine tool is considered a viscous damping system, the general form of the equation of motion is expressed as follows:
2. Experiment As shown in Fig. 1, the free-vibration responses of the feed drive system are collected to estimate its dynamic characters such as the natural frequencies and the damping ratios. The statistics of the dynamics characteristics are used to identify the long-term dynamics degradation of the feed drive system. The cutting processes are monitored by analysing the sparse features of the spindle current. The long-term dynamics degradation of the feed drive system and its effect on cutting process are observed. The results reveal that the statistics on the dynamics characteristics can indicate the health status of the feed drive system in long-term operation. With the degradation of the feed drive system, the cutting quality fluctuations are increased, and the wear rate of the cutting tool is intensified. Experiments were performed on a real automated production line over approximately 100 days to investigate the long-term degradation of the feed drive system and its effect on the cutting process. In longterm statistics, the inertial force caused by the high-speed acceleration and deceleration and cutting force was comprehensively considered, since the entire cutting process of a workpiece is completed by a complex tool path group that consists of the multi-stage operation of the feed drive system (starting, acceleration, fast feed, milling, fast retract, deceleration, stopping, etc.), and this procedure is very complex. Acceleration and deceleration values in different cutting stages are not a constant, and their state of the feed drive system is monitored and used to extract eigenvalues. The production line, including three-axis machine tool XS 321, is shown in Fig. 2a. It is used to automatically make the upper surface of massive engine blocks. The tool used to mill
Mx¨ + Cx + Kx = f
(1)
For a free-response vibration system, the initial conditions are:
x (0) = x 0
(2)
x (0) = v0
(3)
M, C and K are the n × n mass, damping and stiffness matrices of the machine tool structure system, respectively, and n is the number of dofs for the system; x 0 and v0 are the initial displacement and velocity vectors, respectively. For the proportional viscous damping, the following relation is expressed:
C= M+ K
(4)
Constants and can be calculated based on prior knowledge from the free-vibration data [17,18]. For the normal mode analysis, the freeresponse vibration can be written as:
x = Xe i
t
(5)
Then, for the proportional viscous damping model without the prescribed force, the system equation becomes:
Mx¨ + ( M + K) x + Kx = 0 We rearrange the above equation: 2
(6)
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Fig. 1. Schematic diagram of the experimental system.
M (¨x + x) =
(7)
K (x + x )
Thus, if the vibration responses x , x and x¨ are acquired, the matrix M 1K can be calculated by Eq. (8) and used to solve for the eigenvalues and eigenvectors. Consider the system free-response matrix as follows:
Then
M 1K =
(¨x + x)(x + x)
1
(8)
Fig. 2. Experiment system and data acquisition system: (a)machine tool; (b) engine block; (c) acceleration sensor; (d) current sensor.
3
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Fig. 3. Schematic diagram of the modal algorithm based on the free-vibration response.
X(t ) = [X ]Nk × n =
x1, k x1, k + 1
x2, k x2, k + 1
xn, k xn, k + 1
x1, k + Nk
x2, k + Nk
xn, k + Nk
x1, Nk x2, Nk xn, Nk
1
1
1
x1, Nk x2, Nk
1
1
xn, Nk
1
1
= 1
x1, k x2, k
x1, k + 1 x2, k + 1
x n, k
xn, k + 1
A=
y = Ye
¨ = [ {x¨} k {¨} X x k + 1 {x¨} k + Nk + 1]
(11)
r
r r
r = 1,2, …, n.
(18)
= R e ± iIm =
r
r
±i
r
1
2 r
(19)
Then, the natural frequency and modal damping ratio of the feed drive system can be determined: r
(12) r
(13)
= =
Re2 + Im2
(20)
Re Re2 + Im2
(21)
3.2. Sparse feature vector of the machining process
Then, the dynamic equation of the feed drive system can be rewritten as follows:
Ay + By = p
(17)
where
without loss of generality, the following equilibrium equation is introduced and combined with Eq. (1):
Mx¨ = 0
(16)
t
Yr , Yr
r
By comparing Eqs. (9)–(11), we can rewrite Eq. (9) as follows: 1
(15)
By solving the above equation, 2n pairs of complex eigenvalues and eigenvectors can be obtained:
(9)
(10)
Mx¨
x¨ , p = 0 x f
( A 1B) Y = Y
X = [ {x } k {x } k + 1 {x } k + Nk + 1]
¨ + X)(X + X) (X
M 0 , y= 0 K
Assuming that the external force vectors are zero, we substitute Eq. (16) into Eq. (14) and formulate the eigenvalue problem as:
1
where x r , k = xr (tk ) is the displacement of the rth dof at the kth sampling point as depicted in Fig. 3; k is the starting point, Nk is the number of points adopted by the modal analysis algorithm. Superscript T represents the transpose operation on the matrix. Similarly, the velocity and acceleration response matrices can be defined as follows:
M 1K =
0 M , B= M C
The sparse feature vector is extracted from the cutting current of stacked autoencoders. The autoencoder is a type of unsupervised neural network with three layers [18], and the output of the autoencoder is the reconstitution of input data with lower dimension. As depicted in Fig. 4a, the autoencoder has two basic parts: encoder network and
(14)
where
Fig. 4. Architectural graph of an auto-encoder: (a) structure of a sparse auto-encoder unit; (b) structure of a deep stack auto-encoder network. 4
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Fig. 5. Operational vibration in three directions of the feed drive system: (a) vibration signals and (b)the corresponding autopowers.
Fig. 6. Operational vibration in the x direction of the feed drive system: (a) one small portion of the vibration signal from the long-term operation; (b) free response in the vibration.
decoder network. The encoder layer transforms the input data from a high-dimensional space into sparse codes with lower dimension, and the decoder network reconstructs the sparse codes into the original input. The encoder network is defined as an encoding function denoted by f . For each measured spindle current signal ym = [y1 , y2 , y3 , , ym ] corresponding to a finished workpiece, the sparse vector of the encoder is calculated as follows:
hk = f (ym)
EAE ( ,
1 M
M
L (yi , yˆi) = i=1
1 M
M i=1
L (yi , g (f (yi)) )
(26)
where EAE ( , ) is the reconstruction error of the autoencoder, M is the number of training examples, y im is the input vector for each training example, and L (y im, yˆ im) is the corresponding loss function. In summary, the autoencoder training aims to find parameter matrices and by minimizing the reconstruction error. In Eq. (26), the commonly used forms for the encoder and decoder networks are affine mappings, which are optionally followed by a non-linearity:
(24)
where hk is the output of the encoder network, is the encoder network parameter matrices, m and k are the dimension of the input vectors and sparse vectors of the encoder network, respectively; k < m . In contrast, the decoder network is defined as a reconstruction function denoted by g . It maps hk from the low-dimensional space back into the original high-dimensional space:
yˆm = g (hk)
)=
f (y im) = sf (Wy im + b)
(27)
g (hik) = sg (W Thik + d)
(28)
where sf and sg are the encoder and decoder activation functions, respectively. Thus, the parameter matrices of the encoder and decoder are = {W, b} and = {W T, d} , where b and d are bias vectors; W and W T are the weight matrices. As shown in Fig. 4b, n autoencoders can be stacked to significantly reduce the dimensionality of the original input data and extract the relevant sparse feature vector from the spindle current.
(25)
where yˆm = [yˆ1 , yˆ2 , yˆ3 , , yˆm ] is the output vector of the decoder network, and is the decoder network parameter matrices. The parameter matrices of the encoder and decoder are simultaneously trained by reconstructing the original input as possible and attempting to incur the lowest possible reconstruction error over M training examples. The reconstruction error is defined by a loss function that measures the discrepancy between ym and yˆm : 5
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Fig. 7. Stability diagrams of the OMA algorithm based on a single free-vibration response: (a) Frequency stability diagram; (b) Damping ratio stability diagram.
Fig. 8. Time evolutions of the first three modes of the feed drive system: (a) Time evolution of the natural frequencies; (b) Time evolution of the damping ratios.
Fig. 9. Frequency stability diagrams estimated from multiple free-vibration responses: (a) Frequency stability diagrams for the first five days; (b) Statistical characteristics of modal parameters for the first five days; (c) Frequency stability diagrams for the last five days; (d) Statistical characteristics of modal parameters for the first five days. 6
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Fig. 10. Damping ratio stability diagrams estimated from multiple free-vibration responses: (a) Damping ratio stability diagrams for the first five days; (b) Damping ratio stability diagrams for the last five days. Table 1 Statistical analysis of the modal parameters estimated from the free responses in different health statuses. Normal ball screw
Eigen frequency (Hz) Mean values Std Damping ratio (%) Mean values Std
Damaged ball screw
Mode #1
Mode #2
Mode #3
Mode #1
Mode #2
Mode #3
13.672 1.874
25.852 0.252
38.951 0.963
13.145 3.483
25.934 0.277
38.124 2.375
6.731 0.735
6.244 0.124
10.3 0.542
6.528 1.247
6.372 0.131
10.59 1.322
Fig. 11. Long-term degradation of the feed drive system during the entire life of the ball screw: (a) Long-term standard deviation of the dynamics of the feed drive system; (b) Wear characteristics of the final damaged ball screw.
4. Results and discussion
surface quality, and simultaneously accelerate the tool wear. In this section, the statistics of the dynamics of the feed drive system in the long-term operation is studied by the OMA; then, its effect on the machining process is observed and discussed.
After the long-term operation, the feed drive system inevitably wears down, which deteriorate its dynamic characteristics and vibration. The dynamics degradation affects the workpiece precision and 7
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Fig. 12. Three-phase current signals during machining process of one workpiece with 75 s related to: (a) tool #1, (b) tool #4.
Fig. 13. Process monitoring at large scale based on the similarity of the sparse feature vectors of the spindle current.
4.1. Dynamics analysis of the feed drive system based on the free-vibration response
the x direction while the green and red signals illustrate the vibrations in the y and z directions, respectively. The corresponding autopowers of the vibrations in the three different directions are shown in Fig. 5b. The amplitude and energy of the vibration in the x direction are much larger than that in the other directions. Therefore, the transient vibration curve in the x direction of the feed drive system during the machining process is analysed in Fig. 6a; then, the free-vibration response (Fig. 6b) caused by the acceleration movement is selected to validate the OMA method reliability and estimate the modal parameters of the feed drive system. The detailed dynamic characteristics of each part were not specifically elaborated, and it was almost impossible to obtain the vibration mode under the operational conditions. A free-vibration response caused by the acceleration movement in Fig. 6b was selected to validate the OMA method reliability and
The dynamics of the feed drive system is complicated in the longterm operational condition. It changes over time because it depends on the position of the moving feed drive system during machining. This type of time-varying character makes it impossible to directly identify the dynamics degradation from the estimated modal parameters. The dynamics uncertainty of the feed drive system must be considered in long-term running conditions. Generally, the dynamics uncertainty can be represented by probabilistic approaches [19–22]. Fig. 5 presents the acceleration signals and the corresponding autopowers of the feed drive system in three directions under the operational conditions. The blue signal in Fig. 5a represents the vibration in 8
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Fig. 14. Similarity index diagrams of (a) tool #1; (b) tool #2; (d) tool #3; (d) tool #4.
estimate the modal parameters of the feed drive system, whereas the free vibration is measured using an acceleration sensor, which is pasted on the surface of the support seat of the ball screw; thus, this
measurement result has no direct relationship with the natural frequency. Meanwhile, the natural frequency can be calculated by Eq. (20). Fig. 7a and b presents the stability diagrams of the OMA based on 9
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Fig. 15. Standard deviations of the similarity index calculated by the manual feature vector and sparse feature vector: (a) standard deviations based on the manual feature vectors; (b) standard deviations based on the sparse feature vectors.
the selected free-vibration response. The stability diagrams are an appropriate method for indicating the modal analysis results of the OMA algorithm. In Fig. 7a, the red curve refers to the autopower of the selected free-vibration response. The potential natural frequencies are shown on the abscissa axis, and the model orders of the algorithm are displayed on the ordinate axis. The black spot symbols in the figure suggest the relationship between the model order of the OMA and the solutions of the order. Theoretically, if a natural frequency appears at any order, there is a high probability that it is a natural frequency. There are many spot clusters in Fig. 7b, which serve as the potential modal modes estimated from the free response. The first three clusters closely match the first three peaks of the autopower, which implies that they are the real modes. Fig. 7b signifies the damping ratio stability diagram with the first three calculated damping ratios on the abscissa axis and the model orders on the ordinate axis. The clusters in both Fig. 7a and b are fairly clear, which indicates that the results of the operational modal analysis are convincing, and the method is valid.
stability diagram based on all selected free responses of the last five days of the experiment. The results in this figure illustrate the dynamics of the feed drive system under the damaged ball screw condition. Fig. 9b and d shows the statistical characteristics of the natural frequencies of the first three modes. All-natural frequencies clearly exhibit an approximately normal distribution. The natural frequency of the second mode is probably due to the mode of the machine tool frame, which is less affected by the running status of the feed drive system. The damping ratio stability diagrams estimated from the same free-vibration responses are shown in Fig. 10. Fig. 10a shows the damping ratio stability diagram in healthy condition, and Fig. 10b shows the damping ratio stability diagram in the damaged condition. The statistical characteristics of the modal parameters in different health statuses of the ball screw are presented in Table 1. The mean values of the natural frequencies and damping ratios are almost unchanged when the ball screw is damaged. Nevertheless, the standard deviations of the natural frequencies and damping ratios of mode #1 and mode #3 increase, which indicates more dynamics uncertainties of the feed drive system with a damaged ball screw. Since mode #2 results from the mode of the entire frame of the machine tool, the dynamics are less affected by the feed drive system. Hence, the standard deviations of the modal parameters are almost unchanged, and the values are much smaller than those of the other modes. In Fig. 11a, the long-term standard deviations of the dynamics uncertainties during the entire life of the ball screw are shown by the curves in four colours, which indicate the standard deviations in four different months. Fig. 11b shows the photos of the final damaged ball screw. The damaged areas of the ball screw are marked by the red dashed curves in the figures. This result shows that the wear of the ball screw increases the dynamics uncertainty and wear rate.
4.2. Time evolutions of the dynamics of the feed drive system in the longterm running status Considering the dynamics uncertainty in long-term running, it is imperative to estimate the modal parameters and their statistical characteristics through all free-vibration responses. In our modal analysis experiment, the vibration signals last for approximately 94 days, which covers the entire life of the ball screw of the feed drive system. Fig. 8 presents all estimated modal parameters of the first three modes in 94 days. The natural frequency and damping ratio of the first and third modes are increasingly dispersed from the 65th day to the 71st day. However, as shown by the green dots in Fig. 8, the natural frequency and damping ratio of the second mode are almost unchanged, and the operating modal parameters of the first and third modes vary in a wider range than those of this mode. This result suggests that the first and third modes are probably the local modes related to the feed drive system, and the second mode is related to the machine tool frame. Compared with the second mode, the first mode and third mode are more dispersed because they are more affected by the running status of the feed drive system. Fig. 9 shows the frequency stability diagrams and their statistical characteristics of the first three modes in different health statuses. In Fig. 9a, the natural frequencies of the feed drive system are estimated from all selected free responses of the first five days of the experiment. The spot symbols in this figure show that the natural frequencies of the feed drive system have significant dispersion, which is due to the timevarying worktable position and speed of the feed drive system during the machining process. In contrast, Fig. 9c presents the frequency
4.3. Effect of the feed drive system degradation on the machining process The relationship between the cutting process and the dynamics of the feed drive system is further studied in this section. Because the experiment should not disturb the routine manufacturing in the plant, the spindle current is introduced to monitor the cutting process, since it is a non-destructive measuring method. Fig. 12 shows the three-phase spindle current signals in different heath statuses of the feed drive system. Each signal corresponds to an entire machining process of one workpiece with 75 s, and different tools (1# and 4#) were selected in nearly 100-day continuous production. As shown in Fig. 12a and b, the difference between the two currents is difficult to observe due to their high data dimension. Therefore, it is crucial to select key features from the signal to construct a feature vector with low dimensionality. By applying the feature vector, the difference in spindle currents can be 10
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Fig. 16. Final worn patterns of the four cutting tools: (a) tool #1; (b) tool #2; (d) tool #3; (d) tool #4. 11
International Journal of Machine Tools and Manufacture 146 (2019) 103454
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calculated as follows and quantized:
k1, j =
m v v i = 1 1, i j, i m m 2 v v j, i i = 1 1, i i=1 2
wear situations. These results illustrate that the dynamics uncertainties caused by the deterioration of the feed system can introduce fluctuations into the cutting force in machining, which will significantly worsen the working condition of the cutting tool and accelerate its wear ratios.
(23)
where v1, i and vj, i are the arbitrary elements of the reference vector and the jth feature vector, respectively. In extreme cases, when the machining conditions of the two workpieces are completely different, the exponent is equal to −1; when the two workpieces have identical cutting processes, the exponent is equal to zero. Fig. 13 shows the schematic diagram of the calculation of the cutting difference over time. The first feature vector is used as a reference because it serves as the initial cutting condition with no tool wear. In a mass production line, the machining parameters of each workpiece are exactly identical. Only the tool wear condition can affect the cutting process. Thus, the difference between the feature vector at a particular moment and the reference feature vector represents the tool wear condition at that moment. For comparison, two types of features are selected from the raw current signals to construct the feature vectors. One type is a set of manually selected features, including the maximum value, root mean square (RMS), mean value and standard deviation of the current, which are stacked to form a feature vector. The other type is sparse features selected by autoencoders. There are four stacked autoencoders: the first one has 60000 input nodes and 2000 output nodes; the second one has 2000 input nodes and 400 output nodes; the last one has 400 input nodes and 100 output nodes. The last output is the sparse feature vector of the current signal. Furthermore, the entire life cycles of cutting tools #1–4 (noted in Fig. 11a) under different health states of the feed drive system are investigated. Fig. 14a–14d illustrate the difference index that is calculated by the manual feature vector and sparse feature vector during the entire life cycle of the four tools. The workpiece number, which represents the time dimension, is displayed on the abscissa axis because it is easy to record on site. Different indices of each workpiece are displayed on the ordinate axis. The red curves in the figures indicate the indices calculated from the manually selected feature vectors, and the blue curves represent the indices calculated from the sparse feature vectors. All blue curves gradually decrease, which implies the slow wear process of the cutting tools. All red curves in the figures gradually decrease except the curves of tool #4. The red curve in Fig. 14d first decreases and subsequently increases to zero, which conflicts with the phenomenon of gradual wear of the tool. Thus, the manually selected feature vectors are less reliable and consistent because they contain relatively less information than the sparse feature vectors. The standard deviations of the index of the four tools are calculated and presented in Fig. 15. Each standard deviation is calculated by 8 adjacent similarity indices, and 46 standard deviations (its one value is calculated by 10 workpieces) are acquired by sliding sampling with no overlap. Fig. 15b shows that tools #3 and #4 have larger standard deviations than tools #1 and #2. The fluctuations of the index are mainly caused by the dynamics degradation of the feed system because all control parameters of the automatic production line are stable. Tools #1 and #2 are related to the ball screw in normal conditions, and tools #3 and #4 are related to the ball screw in damaged conditions. This phenomenon can be interpreted as the fluctuation of the cutting force and spindle current are resulted from the dynamics uncertainties of the feed drive system. The curves in Fig. 15a are confusing and irregular because they are calculated from the manually selected feature vectors. Fig. 16 describes the relationship between the final worn images of the four tools. The worn areas of the cutting tool are marked by the red curves in the right figures, and the indices are presented by the blue curves in the left figures. As shown in Fig. 16a and b, the index fluctuations are relatively small, and the contours of the wear regions of the two cutting tools are smooth and almost straight. The indices in Fig. 16c and d fluctuate more significantly than 16a and 16 b, and the contours of the wear regions are irregular and distorted, which indicates worse
5. Conclusions In high-speed machining, the dynamic characteristics during longterm running deteriorate because of the mechanical wear of the ball screw in the feed drive system; thus, the dynamics of the feed drive system and its evolution were investigated. Three conclusions can be obtained as follows. (1) The statistical analysis of the dynamics is only performed based on the free-vibration signals during the entire life of the feed drive system, while modal parameters are first estimated from the freevibration responses using the OMA. (2) The standard deviations of the natural frequencies and damping ratios of mode #1 and mode #3 increase, which indicates more dynamics uncertainties of the feed drive system with a damaged ball screw. (3) The dynamics uncertainties of the feed drive system can increase the fluctuations of the cutting process, and these fluctuations will significantly worsen the working condition of the cutting tool and accelerate its wear rate. Acknowledgments The research is supported by the National Natural Science Foundation of China under Grant (51705174, 51905191), the State key laboratory smart manufacturing for special vehicles and transmission system (GZ2016KF008), Science and Technology Planning Project of Guangdong Province (2017B090913001), and DongGuan Innovative Research Team Program (201536000100031). Appendix ASupplementary data Supplementary data to this article can be found online at https:// doi.org/10.1016/j.ijmachtools.2019.103454. References [1] Y. Altintas, A. Verl, C. Brecher, et al., Machine tool feed drives, CIRP Ann. - Manuf. Technol. 60 (2) (2011) 779–796. [2] R. Teti, K. Jemielniak, G. O'Donnell, D. Dornfeld, Advanced monitoring of machining operations, CIRP Ann. - Manuf. Technol. 59 (2) (2010) 717–739. [3] K. Zhu, Y. San Wong, G.S. Hong, Wavelet analysis of sensor signals for tool condition monitoring: a review and some new results, Int. J. Mach. Tool Manuf. 49 (7) (2009) 537–553. [4] H.C. Möhring, O. Bertram, Integrated autonomous monitoring of ball screw drives, CIRP Ann. - Manuf. Technol. 61 (1) (2012) 355–358. [5] G.H. Feng, Y.L. Pan, Investigation of ball screw preload variation based on dynamic modeling of a preload adjustable feed-drive system and spectrum analysis of ballnuts sensed vibration signals, Int. J. Mach. Tool Manuf. 52 (1) (2012) 85–96. [6] C.G. Zhou, H.T. Feng, Z.T. Chen, et al., Correlation between preload and no-load drag torque of ball screws, Int. J. Mach. Tool Manuf. 102 (2016) 35–40. [7] M.C. Chang, J.L. Liou, C.C. Wei, et al., Fractal analysis for vibrational signals created in a ball-screw machine operating in short-and long-range tribological tests, J. Tribol. 135 (3) (2013) 031101. [8] K. Erkorkmaz, Y. Altintas, High speed CNC system design. Part II: modeling and identification of feed drives, Int. J. Mach. Tool Manuf. 41 (10) (2001) 1487–1509. [9] C. Brecher, M. Fey, S. Bäumler, Damping models for machine tool components of linear axes, CIRP Ann. - Manuf. Technol. 62 (1) (2013) 399–402. [10] B. Li, B. Luo, X. Mao, et al., A new approach to identifying the dynamic behavior of CNC machine tools with respect to different worktable feed speeds, Int. J. Mach. Tool Manuf. 72 (2013) 73–84. [11] B. Luo, D. Pan, H. Cai, et al., A method to predict position-dependent structural natural frequencies of machine tool, Int. J. Mach. Tool Manuf. 92 (2015) 72–84. [12] G.H. Feng, Y.L. Pan, Establishing a cost-effective sensing system and signal processing method to diagnose preload levels of ball screws, Mech. Syst. Signal Process. 28 (2012) 78–88.
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