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Vibration suppression of drilling tool system during deep-hole drilling process using independence mode space control
Journal Pre-proof Vibration suppression of drilling tool system during deep-hole drilling process using independence mode space control Lingfei Kong, Shuai Cao, Jih-Hua Chin, Yue Si, Falin Miao, Yan Li PII:
S0890-6955(19)31000-4
DOI:
https://doi.org/10.1016/j.ijmachtools.2020.103525
Reference:
MTM 103525
To appear in:
International Journal of Machine Tools and Manufacture
Received Date: 4 September 2019 Revised Date:
20 January 2020
Accepted Date: 20 January 2020
Please cite this article as: L. Kong, S. Cao, J.-H. Chin, Y. Si, F. Miao, Y. Li, Vibration suppression of drilling tool system during deep-hole drilling process using independence mode space control, International Journal of Machine Tools and Manufacture (2020), doi: https://doi.org/10.1016/ j.ijmachtools.2020.103525. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2020 Published by Elsevier Ltd.
Lingfei Konga*, Shuai Caoa, Jih-Hua Chinb, Yue Sia, Falin Miaoa, Yan Lia a
School of Mechanical and Instrumental Engineering, Xi’an University of Technology, Xi’an 710048, Shaanxi, PR China b Department of Mechanical Engineering, National Chiao Tung University, Hsinchu, Taiwan, Republic of China
Vibration suppression of drilling tool system during deep-hole drilling process using independence mode space control Abstract: Deep-hole drilling technology is commonly used in the aerospace and automobile industries, for new-energy equipment manufacturing, and in the high-tech industries. While this technology produces high-quality holes, higher quality is pursued. A method to improve the processing quality is to suppress the vibration modes associated with long shafts. This problem was addressed with an aim of real-time application. In addition, a higher goal was set by way of providing a solution (in full) to the associated problem, to shed light on processes that bear similar features in manufacturing and for other industries. An operable control scheme was constructed by transforming the system dynamics to modal space for modal decoupling and truncation. The modal displacement and velocity information estimated by the modal filtering were introduced into the feedback gain matrix. All obstacles in traditional physical space were shunned. A damper/sensor position optimisation algorithm was suggested to minimise the modal spillover and acquire modal orthogonality, which led to a new method that has an edge on all preceding methods because of its stronger ability. A system capable of real-time suppression of modal vibration in a deep-hole drilling tool was built and implemented. Using hole roundness error as the criterium, it was found that further improvement of hole quality was achieved. The idea presented in this work may pave the way for elevating the quality of other manufacturing processes with similar weak stiffness features, such as those seen in long-shaft tools or thin-wall workpieces. The method may also provide a reference for other industries with relevant or comparable problems. Keywords: Deep hole drilling, Drilling tool vibration, Independence mode space, Semiactive control method to achieve the stability prediction of the drilling tool 1. Introduction [10]. However, the actual deep-hole tool system is usually a continuum consisting of auxiliary supports, oil feeders, and Deep-hole drilling technology with high precision, high specially constructed cutter heads. efficiency, and low cost is imperative in the aerospace, Given the complexity of the system, a more accurate model new-energy equipment manufacturing, and high-tech industries. to depict its dynamic characteristics is desirable. To reduce the Its quality is provided by its tool/process features. However, degrees of freedom of the tool dynamic system effectively, elevating quality by adding features of process control is being Kong et al. adopted a mode synthesis technique with a free pursued. Drilling quality control is essentially a dynamic interface, and obtained the instability mode and stability domain problem caused by unbalanced forced cutting [1], self-excited of the drilling shaft motion at a selected cutting depth and vibration [2,3], or high-pressure coolant flow performance [4,5]. cutting-speed parameter space [11]. These disturbances are caused by poor selection of cutting In 2015, Matsuzaki et al. established a tool system dynamics process parameters (such as cutting speed, feed rate, and supply model with auxiliary support, oil feeder, and tool configuration pressure) and changes in the structural parameters of the tool based on the transfer function method [3]. This was combined system (such as stiffness, damping, and placement of auxiliary with a dynamic stability criterion to study the mechanism of the supports) [6]. Accurate control of the dynamic behaviour of the rifling mark, and the tool guide pad layout was given to tool in real time and processing high-quality deep-hole parts suppress this phenomenon. In general, the method of avoiding have become critical issues in deep-hole drilling research. an unstable cutting area by adjusting cutting parameters such as To increase the cutting efficiency and processing quality, the feed rate or the cutting speed, thereby preventing external researchers have carried out considerable research on the excitation or regenerative vibration, can be attributed to the suppression of vibration in drilling tool systems. Deng and Chin passive control of the dynamic behaviour of the tool system. proposed a system equation consisting of the Euler-Bernoulli However, when a cutting system consisting of machine beam equation representing tool shaft, and an excitation force in tool-tool-workpiece changes, its stability also changes, and this the form of a Fourier series. Meanwhile, a correlation poses difficulties in practical application. expression between the roundness error of deep-hole machining In recent years, there has been a noteworthy trend to use the and the dynamic behaviour of the tool was given [7]. Mehrabadi physical characteristics of smart materials (piezoelectrics et al. constructed a dynamic model of a drilling tool system [12,13], electrorheological (ER) fluid [14], magnetorheological which also considered the influence of cutting force damping (MR) fluid [15–17] and other materials [18]) to achieve active and tool mass eccentricity, and discussed the changing or semiactive suppression of tool vibration in different characteristics and stability of the tool trajectory [2]. machining process. Fernandes et al. developed an active Roukema and Altintas first proposed a drilling dynamics vibration control system in a centreless grinding machine model with tool morphological features and nonlinear vibration containing a piezoelectric actuator [19]. In [13], piezoelectric modes. This was combined with relevant time-domain stack actuators were used to modulate the stiffness with a simulation calculations to determine the stability domain of the time-varying preload. The stiffness variation can provide an tool dynamics during drilling [8,9]. Based on this, Ahmadi and alternative technique against chatter in milling dynamics. Chen Altintas proposed a generalised dynamic stability model for the et al. increased the tool damping of the boring process using a drilling dynamics, which considers the influence of tool noncontact magnetic drive layout, which suppresses the tool torsional vibration and eddy motion on the regenerative radial and torsional vibration [18]. vibration of the tool, and used the semidiscrete time-domain However, piezoelectric materials and magnetic force are
limited by low cutting load capacity, high cost, and high energy consumption. These problems were overcome by ER fluids, which seemed to be more effective [15]. Wang and Fei designed an online adjustable control system using ER fluid materials that successfully extended the stability domain of the cutting tool using a fuzzy control strategy [14]. However, it is well understood that the lower operating temperature range and extreme nonlinearity of the ER fluid results in poor stability of the vibration suppression device [16,20]. Hence, some researchers attempted to suppress machine vibration with MR fluid because of its advantages of short response time, simple structure, and easy control. Mei et al. established a boring tool flutter suppression device based on MR fluid and its dynamic model, and explored the suppression effect of different excitation current frequencies on tool flutter [16]. Kong et al. designed a vibration suppression structure for a deep-hole drill pipe based on shear mode. It was empirically confirmed that the new deep-hole vibration damper effectively increases the structural rigidity, which improves the quality of the hole [17]. These studies provided technical support for active control of tool vibration. However, compared with the passive damping method, active damping methods did not gain popularity because they require more complex hardware and software and are more expensive. Motivated by the benefits of higher computational efficiency and lower hardware cost that an online control frame can offer, an active vibration control method derived from independent modal space is developed in this paper to avoid the defects of multiple and coupling control parameters in the classical physical space. Meanwhile, targeted suppression of the harmful vibration mode is used to achieve the ability to strike the modal accurately via modal filtering technology. In addition, this paper proposes a position optimisation algorithm that can satisfy the modal spillover minimisation and modal independence, so the above active control strategies can be implemented in actual processes with high precision but at low cost. The outline of the paper is as follows: In Section 2, an independent modal space control model is constructed for deep-hole drilling tools, and the influence of spillover effects on the modal suppression accuracy is analysed. In Section 3, low-cost target suppression of the modal is achieved by
constructing a position optimisation algorithm, which has an advantage over all previous approaches in the literature owing to its stronger ability to minimise the modal spillover. In Section 4, a finite element model of the deep-hole drilling tool is initially tuned by a modal experiment, and then the rationality of the selected position is investigated by simulation. Finally, the modal suppression effect is verified by the radial vibration information collected by the sensor. Moreover, the ability to suppress harmful modals is verified in regard to roundness errors. 2. Modeling of deep-hole drilling tool system Fig. 1 shows the structure of the deep-hole drilling system that consists of a deep-hole cutting tool, oil feeder, and MR damper [17]. The MR fluid damping configuration is geared with an adjustable annular magnetic field. It is adapted to the stiffness/damping regulation of each auxiliary support point during the deep-hole drilling process. According to the layout characteristics of the variable stiffness/damping tool system, the tool system can be discretised into a multisegment six-degree-of-freedom Euler-Bernoulli beam element. Its overall dynamic equation of motion is given by (1)
where , , and ∈ are the mass matrix, damping matrix, and stiffness matrix of the tool system in physical space, respectively; and are the damping matrix and stiffness matrix at the oil feeder, respectively, in the physical space; is the actual control force of the variable stiffness/damping damper output; is the external disturbance power which includes the tool cutting force and mass imbalance force; and respectively represent the position matrix of the external disturbance power and the actual control force; and ∈ is the physical coordinate vector, where a drilling shaft element with two nodal points is , , , , , . Note that there are a large number of coupled state variables if Eq. (1) is used directly for designing a control system, which poses a great obstacle to real-time control of the tool dynamics [21,22]. Hence, decoupling of the state variables is indispensable.
Eq. (7). In an ideal state, a feedback gain matrix = can be obtained by a pole placement method or a linear quadratic regulator to construct a closed-loop control system as shown in Eq. (8), achieving the best modal suppression effect. Once an independent modal space model describing the drilling tool dynamics with modal decomposition and truncation has been developed, the feedback control frame for the vibration suppression of deep-hole drilling tools can be constructed, as shown in Fig. 2. D /$ − 2M = −2 NOPOQ M =2 L a & $ RSTUAVWXYZ BX$$YATU ` . &$ 1 . 2 $ 1 , - K < D ` &% 2 % −2OPO /% − 2 8< =2 & % K NO NO OPO % 8OQ % $ = $OQ J _ [YZWUY$ BX$$YATU \X]XZ^ BX$$YATU NOOOOOOOOOOOOOOOOOOOPOOOOOOOOOOOOOOOOOOOQ
Fig. 1. Schematic diagram of deep-hole drilling tool system.
Two topics deserve attention. First, the essence of tool vibration is a superposition of different modal features. If a vibration mode is restricted, then the damage associated with it is also restricted. Second, transforming the system from physical space to modal space for control enables decoupling of the state variables. Therefore, the dynamic equations of the system can be converted into modal coordinates. (2)
where is the n-dimensional modal space coordinate that is
completely decoupled, ! ! " , !
! , ! ! , ! , ! ,
and ! is an # # transformation matrix.
Moreover, previous studies showed that the low-frequency vibration of the tool during the drilling process has a great influence on the drilling quality [7]. To relieve the calculation of the control algorithm further, modal truncation is used to preserve the lower modes. Hence, the modal coordinates are divided into lower modes $ and higher modes % . Introducing lower-state variable &$ ' $ $ ( and higher-state variable &% ' % % ( , the system state expression is introduced in the form & / 0 &$ 2 2 +, $ - . $ 1 . 1 . $ 1 . $ 1 2% 2 % 0 /% &% & % (3) & * 3 '4$ 4% ( . $ 1 ) &% where − − $ − − % 8 1 , /% . % 1 , 2$ 7 $ 9 , /$ . $ 0 6 0 6 0 !$ 0 8% 8 $ 8 % 2% 7 9 , 2 $ 7 9 , 2 % 7 9 , 4$ , -, 0 0 0 0 !$ ! 0 4% , % - , 8 % ! % , 8% ! % , 8 $ ! $ , 0 !% and 8$ ! $ . The size of matrices $ and $ is : : , and that of % and % is # − : # − :. !$ is an ; : matrix, and !% is an ; # − : matrix (where ; is the number of sensors). Constructing a closed-loop control system, the actual vibration control force can be written as −8< (4) $ =&$ @
$ with 8< $ >8$ 8$ ? 8$ and = '=A
=$B ( . Here, “+”
denotes a pseudo-inverse matrix, and =:C
and =$B are
feedback gain matrices for the modal velocity and modal
Additionally, the lower modal coordinate &$ is estimated by D $ expressed as Eq. (5), and E is the real-time data monitored & by the sensor. ! < 0 E D$ , $ & - . 1 (5) !$ < E 0 displacement.
The ideal condition for modal filtering is that the information collected by the sensor contains only lower modes, but the higher modes are often mixed [23]. Combined with Eq. (3) and D $ can be rewritten as Eq. (5), & & D $ '/ D 2 D( . $ 1 & (6) &% D 6 and 2 D FGHI!$ < !% . where / Combined with Eq. (3), Eq. (4), and Eq. (6), the actual closed-loop control system consisting of dampers is given by
bWcV$ YZWUY$ dWTe
(
(7)
where 2$ 2M 8$ ; 2M '6 0 . & / − 2M = 0 &$ 2 , $- . $ 1 . 1 . $ 1 (8) 0 /% &% 2 % &% However, the spillover terms in Eq. (7) stand in the way of constructing a stable and capable control system. They are the D on the main diagonal, mixed spillover −2% 8< $ =2 D , and control spillover term observation spillover term −2M =2 < on the secondary diagonal which is associated with −2% 8$ = the position of the sensor or damper. To curb the spillover effects, a direct and effective method is proposed in the next section to minimise the influence of the spillover by optimising the position of the sensor and the damper. 3. Position optimisation algorithm Generally, the spillover effect of modal control includes two parts: observation spillover and control spillover [23]. The former is owing to the inability to effectively avoid higher residual modes when observing the target modal, resulting in poor accuracy of the modal estimation. The latter occurs because the vibration control force obtained by the lower-mode feedback also affects the higher residual modes, which makes the modal control independence worse. To solve these problems, a series of methods such as the effective independence method (EFI) [24,25] and modal assurance criterion (MAC) [26,27] were selected. Unfortunately, control spillover remains, although these approaches can reduce the observation spillover [23]. Additionally, other intelligence algorithms such as the genetic algorithm [23] can help us to optimise the placement of sensors and actuators for reducing the spillover effects. However, genetic algorithm cannot be easily applied to actual machining processes owing to its large computational cost and less straightforward sense in view of the physical mechanism. Therefore, this section proposes a position optimisation algorithm of the damper and sensors with consideration of high precision and low cost, and with an aim to obtain modal estimation capabilities that can minimise the spillover. The ability to minimise spillover while optimising the position is a feature silhouetted against all previous methods in the literature. 3.1 Sensor position To eliminate the observation spillover and improve the accuracy of modal estimation, it is necessary to construct an optimal objective function related to the position of the sensor.
Therefore, if the nth mode is initially considered, then the time-domain information detected by the sensor during
E f !Z f (9) where !Z is an ; # matrix, and E is an ;-dimensional vector which is a combination of lower control modes and higher residual modes. Eq. (9) can be rewritten as $ (10) E !Z '!$ !% ( 7 9 % where lower control modes are given by E $ '!$ < −!$ < !% ( 7 9 (11) % Note that in order for $ to be accurately estimated, the optimal value of the spillover term in Eq. (11) is zero. Therefore, the objective function ‖h‖ is constructed to measure the influence of the spillover term on the modal estimation, which can obtain the best solution for spillover by adjusting the position of the sensor. ‖h‖ % !YATU % (12) where !YATU '!$ < !% ( '!$ < !% ( . Next, a conversion coefficient iYATU % % is introduced that satisfies any % condition. The following inequality holds: jeXZ ∙ iYATU l ‖h‖ l iYATU ∙ jeV] (13) where jeXZ and jeV] are the minimum and maximum eigenvalues of !YATU , respectively. It can be seen from Eq. (13) that for reducing objective function ‖h‖ (namely, the spillover effect), jeV] can be reduced by adjusting the position of the sensor based on the objective function as mYATU nG#'jeV] !YATU ( (14) However, in Eq. (14), the independence of the mode and the influence of the measurement noise on the modal estimation are not considered. Therefore, an EFI is introduced to screen candidate locations for sensors [24,25]. This can further improve the accuracy of modal coordinate estimation. The sensor output containing the first nth mode and noise can be written as E !Z o p o (15) where o is stationary Gaussian white noise with zero mean and a variance of q02 . Hence, the covariance of the modal coordinate estimate error is computed using the following equation: vp vp @ t − t ( .u w qM @ u w1 r s' − v v
processing can be expressed as
Fig. 2. Schematic diagram of control algorithm.
@
7 z !Z !Z 9
xy @
{
(16)
t is the unbiased estimator of . To accurately Here, estimate the modal, the determinant or trace of the Fisher matrix { must be maximised. If the column in the !Z formed by the initial sensor position is linearly independent, then the matrix !Z !Z is a positive definite symmetric matrix. Then, the corresponding position optimisation matrix is given by (17) | !Z !Z !Z @ !Z
According to Eq. (18), the position of the sensor corresponding to the smallest value on the diagonal of the matrix | is removed, thereby reducing the candidate position of the sensor. By combining the two optimisation methods, the state estimation ability of the target modal can be effectively improved. However, to improve the feasibility of the position optimisation algorithm further, it is also essential to perform an orthogonality test on the mode matrix composed of the selected sensor positions. The orthogonality test generally uses the MAC to establish the relevant objective function meV [26,27], where the value of the MAC is inversely related to the orthogonality of the mode. Additionally, the optimal solution of the two sensor positions satisfies the duality condition. $ meV nG#}∑$@ (18) V ∑SV< !V , !S Combining Eq. (14), Eq. (17), and Eq. (18), it is possible to construct a sensor position optimisation algorithm (as shown in Fig. 3), which guarantees the ability of the state estimation, modal independence, and minimisation of observation spillover during modal filtering. 3.2 Damper position
The following optimisation algorithm constructs the position optimisation of the damping, which reduces the control spillover of higher residual modes and achieves high-precision, low-cost modal control requirements. If the number of dampers is assumed to be :V , then the force is divided into an l-dimensional lower modal control force $ and an (n l)-dimensional higher residual modal control force % . The specific expression is given by
$ 8$
The control spillover
% 8% term % can be expressed % 8% 8< $ $
(19) (20) as
(21) As discussed in the observation spillover, the objective function that minimises the control spillover is also given by ‖h‖ > $ ? 8YATU $ (22)
< with 8YATU 8% 8< $ 8% 8$ . The corresponding objective
function boundary is as follows: jeXZ ∙ YATU l ‖h‖ l YATU ∙ jeV]
where YATU >$ ? $ , and jeXZ and jeV] are the minimum and maximum eigenvalues of 8YATU , respectively. Note that the value of jeV] is proportional to the control spillover, for which the objective function mYATU of the corresponding damper position optimisation is mYATU nG#'jeV] 8YATU ( (24) As discussed in the sensor position optimisation algorithm, an EFI is also used to initially optimise the position of the damper to ensure the controllability of the lower modes. Then, the objective function in Eq. (24) is used to minimise the control spillover of higher residual modes, thereby precisely controlling the lower modes. Based on the above optimisation procedures, an effective guarantee for the closed-loop control system design of the tool independent mode is provided, and the spillover effect is reduced when the model truncation is introduced simultaneously. This stronger spillover reducing ability is an innovative contribution on the methodology level. Therefore, a modal vibration suppression system with lower computing demand and hardware cost can be realised in the actual machining process. Any process that bears similarity to this, regardless of its carrier, can use the method to optimise the positions of supports or fixing equipment and actuators on the basis of the vibration mode features whether using passive or active control.
(23)
A schematic frame of the independent mode space control concept is shown in Fig. 2. Here, the green domain consisting of the current output (with the reference values according to the MR model [28] and its exact formulation listed in Appendix A) comprises the feedforward control for the MR damping force. The blue domain consisting of a weighted linear combination of the target modal velocity and displacement in Eq. (4), optimal position of the sensor from Section 3.1, and optimal position of the damper from Section 3.2 comprise the modal filtering feedback control strategy described in Section 3. Then, combining theoretical calculations and experimental results, the feasibility and effectiveness of the vibration suppression method for drilling tools proposed in this paper are verified. 4.1 Modified model To suppress tool vibration from the modal space, it is necessary to know the parameters and boundary conditions of the tool dynamic model. LMS Test. Lab’s modal test system (SCM02) was used to identify the self-made deep-hole machining machine as shown in Fig. 4, where the excitation force generated by the hammer stroke is taken as input, and the vibration information is obtained by the two prefixed acceleration sensors (PCB333B30). The corresponding results are listed in Tables 1 and 2. Table 3 presents an experimental and theoretical comparison of the natural frequency of the deep-hole tool system, in which the error is less than 5%, the maximum error is 3.43%, and the minimum error is only 0.02%. In addition, Fig. 5 shows the dynamic frequency response curves of the experiment and theoretical calculation for sensors #1 and #2, where the curves have a good fit. It can be concluded that the dynamic model of the deep-hole machining system has sufficient accuracy to predict the dynamic characteristics of the system.
Fig. 4. Parameter identification experiment. Table 1 Drill shaft parameters. Elastic modulus (Pa)
Area moment of inertia (m4)
Sectional area (m2)
Density (kg/m3)
Length (m)
Mass (kg)
1.35 × 1011
2.6 × 10-9
1.1 × 10-4
7860
1.45
1.3
Table 2 Identification results of tool system boundary conditions.
Fig. 3. Sensor location optimisation algorithm.
4. Experimental results
Position
Tool chuck
Oil feeder
Stiffness
1 × 109 N/m
1 × 106 N/m
Damping
0
4 × 103 N·S/m
Table 3 Comparison of natural frequencies between experiment and modified model. Modal
Experimental results (Hz)
Modified model results (Hz)
Error (%)
1
199.84
199.80
0.02
4
878.90
874.48
0.50
2
272.78
281.00
3.01
5
1146.44
1176.80
2.65
3
677.46
654.22
3.43
The initially considered modal is # = 5, and the two modes (: = 2) are selected as closed-loop control targets. In view of low cost, two sensors (; = 2) are selected for state observation, and one damper (:V = 1) is used as the vibration suppression device. Combining the algorithm proposed in Section 3 to optimise the position, the objective function meV was initially set as meV l 0.1 related to the MAC. Note that the position close to the cutter head or the oil feeder is not suitable for placing the sensor and the damper during the actual drilling process. Thus, the actual observation or vibration suppression 4.2 Optimal position discussion
position can also be suboptimal. Fig. 6 shows the location optimisation process and results for the sensor and damper, where the symmetry of optimisation solutions is also clearly demonstrated. As the meshing becomes finer, the results of location optimisation will also be more reasonable. To demonstrate the plausibility of the sensor location further, Fig. 7 shows the resulting meV calculated at the relevant sensor location. It can be seen that the information measured at the preferred location of the sensor satisfies the orthogonality of the modes.
Fig. 5. Comparison of frequency responses between experiment and modified model: (a) sensor #1, (b) sensor #2.
Fig. 6. Schematic diagram of optimal positions: (a) optimal positions of sensors, (b) optimal position of damper.
Fig. 7. Corresponding optimal results of sensor positions: (a) 3D display, (b) 2D display.
Fig. 8. Simulation verification of modal estimation: (a) diagram of modal shapes, (b) frequency responses after modal separation.
A meaningful way to judge the rationality of the position is to observe the mode shape. As shown in Fig. 8(a), the optimal position of the sensor is far from the mode node and is distributed on both sides of the damper, so that lower control modal information can be collected to avoid mutual interference. Meanwhile, the damper is close to the peak of the two mode shapes, which is beneficial to the effective control of multiple lower modes using only one damper. Fig. 8(b) shows the simulation results obtained by modal filtering based on the selected optimal position. It can be seen that the modes are entirely separated and the information of higher modes is minimal, which significantly improves the observation spillover in the modal coordinate estimation. 4.3 Modal control experiment In the following, a more detailed description of the experimental test rig is provided to verify the effectiveness of the modal space suppression algorithm outlined in Fig. 9. A dSPACE MicroLabBox control system platform is used as real-time hardware to record the measurement signals and to accommodate the observer and controller implementation. Moreover, the tool vibration signal obtained by the eddy current
sensor (with a response frequency of 5 KHz) is brought into the modal filter by analog-to-digital (A/D) conversion, and the sampling frequency is 8 KHz. Then, the independent mode control algorithm is used to obtain the control analogue quantity , which is output to the power amplifier by digital-to-analog (D/A) conversion. The power amplifier applies the corresponding excitation current to the MR damper to achieve precise suppression of harmful vibration modes. The tool vibration signal was obtained under the conditions of a feed rate of 0.04 mm/r, tool speed of 800 r/min, and cutting depth of 60 mm. Figs. 10 and 11 show the modal control (control of first mode, and simultaneous control of the first and second modes) and the vibration comparison under uncontrolled conditions. It can be seen that the response peak of the tool mainly exists in the vicinity of a cutting frequency of 26.7 Hz (tool cutting edge is 2), first natural frequency of 210.2 Hz, second natural frequency of 344.0 Hz, and third natural frequency of 639.2 Hz. To reduce the cost of suppression, the control system uses only two sensors and one damper. In Fig. 10(b), the peak value at the first modal frequency is significantly reduced, and the residual higher modes are less
affected, which indicates that the control system has a pinpoint effect on the target mode. At the same time, the peak reductions at the first-mode and second-mode frequencies in Fig. 11(b) also exceed 2/3 and 1/3, respectively. The ability for targeted suppression of harmful vibration modes during drilling by the control algorithm is very encouraging, and the sensor/damper position optimisation algorithms also meet the requirements of modal spillover minimisation. Furthermore, although the different modal numbers are suppressed by the independent
modal control algorithm, the amplitude at the cutting frequency becomes smaller. The main reason for affecting the amplitude of the cutting frequency is that the damper is similar to auxiliary support with a variable damping force when the modal is controlled. If only the first mode is controlled, then the amplitude at the cutting frequency is attenuated by 81%, while the amplitude attenuation is 85% when suppressing both the first and second modes.
Fig. 9. Schematic diagram of tool vibration real-time control system.
Fig. 10. Comparison of vibration signals between uncontrolled mode and controlled 1st mode: (a) comparison of vibration signals, (b) comparison of frequency responses.
Fig. 11. Comparison of vibration signals between uncontrolled mode and controlled 1st + 2nd modes: (a) comparison of vibration signals, (b) comparison of frequency responses.
4.4 Roundness error The purpose of vibration suppression is to improve the quality of the hole, which is directly related to the vibration mode of the tool. ZEISS CONTURA G2 instruments were used for measuring the profile of the hole, and the roundness error was computed based on [29]. Table 4 and Fig. 12 show the roundness errors of a hole with a target diameter of 17.75 mm obtained by suppressing different target modes. It can be seen that the roundness error of the hole was improved. In addition, the suppression of different modes leads to a significant difference in the improvement of the roundness error, which is mainly owing to the superposition of various mode functions in the vibration process affecting the roundness of the hole. The roundness error of the hole under uncontrolled conditions is concentrated from 18.3 to 23.3 µm, while the roundness error of the hole is concentrated from 12.1 to 17.5 µm when the first mode is controlled. It can be seen from Fig. 13 that the quality of the hole increased by at least 1/4. In addition, when two modes were controlled, the roundness error of the hole was suppressed in the range of 7.5–13.1 µm, which significantly improved the hole quality. The experimental results also confirm that the independent control modal algorithm can achieve target suppression of vibration modes and bring about significant improvement to the roundness error of the deep hole. 4.5 Process fidelity It should be pointed out that the experimental rig setup in this study is an exact reproduction of the Boring and Trepanning
Association (BTA) drilling process. On a deep-drilling machine tool, the machine structures do not exhibit noticeable influences on the process because the process is sealed by a chuck on one side and by the workpiece on the other side. At the bottom is a machine bed which is usually assumed to have no dynamic behaviour. In extreme cases, i.e. in high-speed drilling, the chuck may be affected by centrifugal forces and become slightly loose, and the drill head may experience slightly different hydrodynamic lubrication. However, neither effect changes the boundary conditions of the drilling tool significantly, and the working range in this study is not in the high-speed domain. The only limitation is the shorter drilling depth owing to the existence of the sensor, but the results obtained from the created experimental rig are still fundamental and contribute to advancing the knowledge of deep-hole drilling. Table 4 Comparison of roundness errors at different depths. Drilling depth (mm)
Roundness error ∆ (µm) With control Without control (control mode)
10
18.3
20
19.5
30
18.5
40
21.2
Error reduction (%)
12.1 (1st)
33.9
7.5 (1st + 2nd)
59.0
13.2 (1st)
32.3
7.9 (1st + 2nd)
59.5
13.1 (1st)
29.2
8.5 (1st + 2nd)
54.1
15.4 (1st)
27.4
11.2 (1st + 2nd)
47.2
50
23.3
17.5 (1st)
24.9
13.1 (1st + 2nd)
43.8
Fig. 12. Comparison of roundness errors.
Fig. 13. Percentage of roundness error reductions.
5. Future applications The solutions shown in this work can be used in applications in other processes or even fields with relevant features. The damper in this work is still an alien entity attached to the target. Making the damper part of the target structure would revolutionise its application. That is, a “structurisation” of the MR-fluid damper or a morphing of the target structure to embed the on-call damper can assist in some fields that still rely on alien tuned mass-damper inerters for vibration suppression. The online, on-call, quick-response, and low-cost advantages can then be harvested. However, this will not occur in a plug-and-play method. Significant research and time are needed, and limitations do exist. 6. Conclusions
roundness errors proved the value of the idea, damping mechanism, and proposed algorithms. The physical phenomenon of suppressing even the lowest two Eigen vibration modes can essentially elevate the already high manufacturing quality in the sense of “roundness”. This was definitely proven by this work. The concept and methodology proposed can be applied directly to BTA deep-hole drilling requirements with a rotating or stationary tool. For gun drilling, some adaptations are needed which require further research. The general significance of this work is on two levels: process and methodology. On the process level, the real-time precision suppression of undesirable modal vibration in a process as confronted in deep-hole drilling was shown in full. Any process that bears relevant features, i.e. cantilevered or weakly and/or peripherally supported beams, plates, shells, blades, etc., can derive ideas from this work. Possible applications include manufacturing and other industries such as crane, bridge (especially suspension bridges), aerial refuelling hoses/pipes (probe & drogue or flying boom), rotor blades of wind power generators, electricity post/transmission towers, and even kilns and chimneys. Process-specific dampers and a mechanism for attaching and actuating them to the identified nodes are needed. The solutions can follow a similar line of thought as that shown in this work. On the methodology level, this paper combined the minimum spillover objective function Jover based on the vibration principle with EFI and MAC to create a new methodology that achieves what all previous literature attempted, but with stronger ability in reducing the spillover effect. In addition, the proposed sensor (damper) position optimisation algorithm makes it possible to suppress multiple-order modes with fewer sensors and a damper. This greatly reduces the cost of technical implementation, which is of interest to various industries. References [1] X. Q. Zhang, G. L. Tnay, K. Liu, A. S. Kumar, Effect of apex offset inconsistency on hole straightness deviation in deep hole gun drilling of Inconel 718, Int. J. Mach. Tool Manuf. 125 (2018) 123-132. [2] I. M. Mehrabadi, M. Nouri, R. Madoliat, Investigating chatter vibration in deep drilling, including process damping and the gyroscopic effect, Int. J. Mach. Tool Manuf. 49 (2009) 939-946. [3] K. Matsuzaki, T. Ryu, A. Sueoka, K. Tsukamoto, Theoretical and experimental study on rifling mark generating phenomena in BTA deep
Deep-hole drilling is a manufacturing process that produces high-quality holes. To upgrade its processing quality, the basic physics of the process should be addressed. This paper presents an investigation into the idea of suppressing the vibration modes of a long-tool shaft, and proposes a damping mechanism capable of target-suppressing the first and second vibration modes with pinpoint precision and in real-time. To derive an operable control law, modal decoupling and truncation were performed on a model of tool system dynamics, which overcame the obstacles in the classical physical space. A damper/sensor position optimisation algorithm was also suggested to minimise the modal spillover and acquire modal orthogonality. Experiments were conducted. A check of the hole
hole drilling process (generating mechanism and countermeasure), Int. J. Mach. Tool Manuf. 88 (2015) 194-205. [4] G. L. Tnay, S. Wan, K. S. Woon, S. H. Yeo, The effects of dub-off angle on chip evacuation in single-lip deep hole gun drilling, Int. J. Mach. Tools Manuf. 108 (2016) 66-73. [5] K. S. Woon, G. L. Tnay, M. Rahman, S. Wan, S. H. Yeo, A computational fluid dynamics (CFD) model for effective coolant application in deep hole gun drilling, Int. J. Mach. Tools Manuf. 113 (2017) 10-18. [6] H. Zhang, X. Q. Shen, A. Bo, Y. M. Li, H. F. Zhan, Y. T. Gu, A multiscale evaluation of the surface integrity in boring trepanning association deep hole drilling, Int. J. Mach. Tools Manuf. 123 (2017) 48-56. [7] C. S. Deng, J. H. Chin, Roundness errors in BTA drilling and a model of
waviness and lobing caused by resonant forced vibrations of its long drill shaft, J. Manuf. Sci. Eng., Trans. ASME 126 (2004) 524-534. [8] J. C. Roukema, Y. Altintas, Generalized modeling of drilling vibrations. Part I: time domain model of drilling kinematics, dynamics and hole formation, Int. J. Mach. Tool Manuf. 47 (2007) 1455-1473. [9] J. C. Roukema, Y. Altintas, Generalized modeling of drilling vibrations. Part II: chatter stability in frequency domain, Int. J. Mach. Tool. Manuf. 47 (2007) 1474-1485.
[27] S. K. Au, F. L. Zhang, On assessing the posterior mode shape uncertainty in ambient modal identification, Probab. Eng. Mech. 26 (2011) 427-434. [28] S. J. Dyke, Jr. B. F. Spencer, M. K. Sain, J. D. Carlson, Modelling and control of magnetorheological dampers for seismic response reduction, Smart Mater. Struct. 5 (1996) 565-575. [29] M. S. Shunmugam, Criteria for computer-aided form evaluation, J. Ind., Trans. ASME 113 (1991) 233-238.
[10] K. Ahmadi, Y. Altintas, Stability of lateral, torsional and axial vibrations in drilling, Int. J. Mach. Tool. Manuf. 68 (2013) 63-74. [11] L. F. Kong, Y. Li, Z. Y. Zhao, Numerical investigating nonlinear dynamic responses to rotating deep-hole drilling shaft with multi-span intermediate supports, Int. J. Non-Linear Mech. 55 (2013) 170-179. [12] A. Matsubara, M. Maeda, I. Yamaji, Vibration suppression of boring bar by piezoelectric actuators and LR circuit, CIRP Ann. Manuf. Technol. 63 (2014) 373-376. [13] C. X. Wang, X. W. Zhang, Y. L. Liu, H. R. Cao, X. F. Chen, Stiffness variation method for milling chatter suppression via piezoelectric stack actuators, Int. J. Mach. Tool. Manuf. 124 (2018) 53-66. [14] M. Wang, R. Fei, On-line chatter detection and control in boring based on an electrorheological fluid, Mechatronics 11 (2001) 779-792. [15] D. S. Pour, S. Behbahani, Semi-active fuzzy control of machine tool chatter vibration using smart MR dampers, Int. J. Adv. Manuf. Technol. 83 (2016) 421-428. [16] D. Q. Mei, T. R. Kong, A. J. Shih, Z. C. Chen, Magnetorheological fluid-controlled boring bar for chatter suppression, J. Mater. Process. Technol. 209 (2009) 1861-1870. [17] L. F. Kong, J. H. Chin, Y. Li, Y. J. Lu, P. Y. Li, Targeted suppression of
Appendix A The Bouc-Wen model is extremely versatile and can exhibit a wide variety of hysteretic behaviour [28]. An applied force based on a shear model is given by M (A.1) where M and are the damping coefficient and hysteresis coefficient, respectively. The evolutionary variable z is governed by −| |||Z@ − ||Z (A.2)
By adjusting the parameters of the model (, and , one can control the shape of the hysteresis loops for the yielding element. To account for the dependence of the force on the electrical current q, M , and can be suggested as Eq. (A.3): MV MS q M V S q
(A.3)
where MV , MS , V , and V are constant values, and the resulting parameters as listed in Table 5 are obtained from identification experiments.
vibration in deep hole drilling using magneto-rheological fluid damper, J. Mater. Process. Technol. 214 (2014) 2617-2626. [18] F. Chen, X. D. Lu, Y. Altintas, A novel magnetic actuator design for active damping of machining tools, Int. J. Mach. Tool Manuf. 85 (2014) 58-69. [19] M.H. Fernandes, I. Garitaonandia, J. Albizuri, J. M. Hernández, D. Barrenetxea, Simulation of an active vibration control system in a centerless grinding machine using a reduced updated FE model, Int. J. Mach. Tool Manuf. 49 (2009) 239-245. [20] G. Park, M. T. Bement, D. A. Hartman, R. E. Smith, C. R. Farrar, The use of active materials for machining processes: a review, Int. J. Mach. Tool Manuf. 47 (2007) 2189-2206. [21] S. Cinquemani, F. Resta, A mechanical approach to the design of independent modal space control for vibration suppression, J. Vibr. Acoust., Trans. ASME 135 (2013) 051002. [22] F. Resta, F. Ripamonti, G. Cazzulani, M. Ferrari, Independent modal control for nonlinear flexible structures: an experimental test rig, J. Sound Vib. 329 (2010) 961-972. [23] S. Cinquemani, D. Ferrari, I. Bayati, Reduction of spillover effects on independent modal space control through optimal placement of sensors and actuators, Smart Mater. Struct. 24 (2015) 085006. [24] T. Hanis, M. Hromcik, Optimal sensors placement and spillover suppression, Mech. Syst. Signal Process. 28 (2012) 367-378. [25] M. Meo, G. Zumpano, On the optimal sensor placement techniques for a bridge structure, Eng. Struct. 27 (2005) 1488-1497. [26] M. Brehm, V. Zabel, C. Bucher, An automatic mode pairing strategy using an enhanced modal assurance criterion based on modal strain energies, J. Sound Vib. 329 (2010), 5375-5392.
Table 5 Identification results of Bouc-Wen model parameters. Parameters
Values
Parameters
Values
MV
168 (N·s-1/m)
220 (m-2)
MS V S
2820 (N·s-1/I·m) 0.16 (N/m) 3.9 (N/I·m)
#
225 (m-2) 37255 2
Acknowledgements: This work was supported by National Natural Science Foundation of China (Grant No. 51475367 and 51905421), Natural Science Foundation of Shaanxi province (Grant No. 2018JM5113) and Natural Science Foundation of Department of Education of Shaanxi Province of China (Grant No. 17JS093).
Highlights Real-time targeted suppression of drilling tool vibration modes is presented for improving the hole processing quality. An operable damper/sensor position optimization strategy was constructed to minimize the modal spillover. The presented idea may pave the way for elevating the quality of other manufacturing processes with similar weak stiffness features, such as long shaft tools or thin-wall workpieces.
In this paper, the contribution is on two levels, namely process and methodology. On the process level the real time, precision suppression of undesirable modal vibration in a process like that of deep hole drilling is shown in full. Any process that bears relevant features, i.e. cantilevered or weakly and/or peripherally supported beams, plates, shells, blades, etc., can derive ideas from this work. On the methodology level, this paper combines the minimum spillover objective function based on vibration principle with the effective independence method (EFI) and modal assurance criterion (MAC) to create a new methodology which achieves all those literatures are trying to do but with tougher ability in reducing the spillover effect. Besides, the proposed sensor (damper) position optimization algorithm makes it possible to suppress the multiple order modes with fewer sensors and a damper thus greatly reduce the cost of technical implementation which is definitely of interest to the industry.
We declare that we do not have any commercial or associative interest that represents a conflict of interest in connection with the work submitted
S0890-6955(19)31000-4
DOI:
https://doi.org/10.1016/j.ijmachtools.2020.103525
Reference:
MTM 103525
To appear in:
International Journal of Machine Tools and Manufacture
Received Date: 4 September 2019 Revised Date:
20 January 2020
Accepted Date: 20 January 2020
Please cite this article as: L. Kong, S. Cao, J.-H. Chin, Y. Si, F. Miao, Y. Li, Vibration suppression of drilling tool system during deep-hole drilling process using independence mode space control, International Journal of Machine Tools and Manufacture (2020), doi: https://doi.org/10.1016/ j.ijmachtools.2020.103525. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2020 Published by Elsevier Ltd.
Lingfei Konga*, Shuai Caoa, Jih-Hua Chinb, Yue Sia, Falin Miaoa, Yan Lia a
School of Mechanical and Instrumental Engineering, Xi’an University of Technology, Xi’an 710048, Shaanxi, PR China b Department of Mechanical Engineering, National Chiao Tung University, Hsinchu, Taiwan, Republic of China
Vibration suppression of drilling tool system during deep-hole drilling process using independence mode space control Abstract: Deep-hole drilling technology is commonly used in the aerospace and automobile industries, for new-energy equipment manufacturing, and in the high-tech industries. While this technology produces high-quality holes, higher quality is pursued. A method to improve the processing quality is to suppress the vibration modes associated with long shafts. This problem was addressed with an aim of real-time application. In addition, a higher goal was set by way of providing a solution (in full) to the associated problem, to shed light on processes that bear similar features in manufacturing and for other industries. An operable control scheme was constructed by transforming the system dynamics to modal space for modal decoupling and truncation. The modal displacement and velocity information estimated by the modal filtering were introduced into the feedback gain matrix. All obstacles in traditional physical space were shunned. A damper/sensor position optimisation algorithm was suggested to minimise the modal spillover and acquire modal orthogonality, which led to a new method that has an edge on all preceding methods because of its stronger ability. A system capable of real-time suppression of modal vibration in a deep-hole drilling tool was built and implemented. Using hole roundness error as the criterium, it was found that further improvement of hole quality was achieved. The idea presented in this work may pave the way for elevating the quality of other manufacturing processes with similar weak stiffness features, such as those seen in long-shaft tools or thin-wall workpieces. The method may also provide a reference for other industries with relevant or comparable problems. Keywords: Deep hole drilling, Drilling tool vibration, Independence mode space, Semiactive control method to achieve the stability prediction of the drilling tool 1. Introduction [10]. However, the actual deep-hole tool system is usually a continuum consisting of auxiliary supports, oil feeders, and Deep-hole drilling technology with high precision, high specially constructed cutter heads. efficiency, and low cost is imperative in the aerospace, Given the complexity of the system, a more accurate model new-energy equipment manufacturing, and high-tech industries. to depict its dynamic characteristics is desirable. To reduce the Its quality is provided by its tool/process features. However, degrees of freedom of the tool dynamic system effectively, elevating quality by adding features of process control is being Kong et al. adopted a mode synthesis technique with a free pursued. Drilling quality control is essentially a dynamic interface, and obtained the instability mode and stability domain problem caused by unbalanced forced cutting [1], self-excited of the drilling shaft motion at a selected cutting depth and vibration [2,3], or high-pressure coolant flow performance [4,5]. cutting-speed parameter space [11]. These disturbances are caused by poor selection of cutting In 2015, Matsuzaki et al. established a tool system dynamics process parameters (such as cutting speed, feed rate, and supply model with auxiliary support, oil feeder, and tool configuration pressure) and changes in the structural parameters of the tool based on the transfer function method [3]. This was combined system (such as stiffness, damping, and placement of auxiliary with a dynamic stability criterion to study the mechanism of the supports) [6]. Accurate control of the dynamic behaviour of the rifling mark, and the tool guide pad layout was given to tool in real time and processing high-quality deep-hole parts suppress this phenomenon. In general, the method of avoiding have become critical issues in deep-hole drilling research. an unstable cutting area by adjusting cutting parameters such as To increase the cutting efficiency and processing quality, the feed rate or the cutting speed, thereby preventing external researchers have carried out considerable research on the excitation or regenerative vibration, can be attributed to the suppression of vibration in drilling tool systems. Deng and Chin passive control of the dynamic behaviour of the tool system. proposed a system equation consisting of the Euler-Bernoulli However, when a cutting system consisting of machine beam equation representing tool shaft, and an excitation force in tool-tool-workpiece changes, its stability also changes, and this the form of a Fourier series. Meanwhile, a correlation poses difficulties in practical application. expression between the roundness error of deep-hole machining In recent years, there has been a noteworthy trend to use the and the dynamic behaviour of the tool was given [7]. Mehrabadi physical characteristics of smart materials (piezoelectrics et al. constructed a dynamic model of a drilling tool system [12,13], electrorheological (ER) fluid [14], magnetorheological which also considered the influence of cutting force damping (MR) fluid [15–17] and other materials [18]) to achieve active and tool mass eccentricity, and discussed the changing or semiactive suppression of tool vibration in different characteristics and stability of the tool trajectory [2]. machining process. Fernandes et al. developed an active Roukema and Altintas first proposed a drilling dynamics vibration control system in a centreless grinding machine model with tool morphological features and nonlinear vibration containing a piezoelectric actuator [19]. In [13], piezoelectric modes. This was combined with relevant time-domain stack actuators were used to modulate the stiffness with a simulation calculations to determine the stability domain of the time-varying preload. The stiffness variation can provide an tool dynamics during drilling [8,9]. Based on this, Ahmadi and alternative technique against chatter in milling dynamics. Chen Altintas proposed a generalised dynamic stability model for the et al. increased the tool damping of the boring process using a drilling dynamics, which considers the influence of tool noncontact magnetic drive layout, which suppresses the tool torsional vibration and eddy motion on the regenerative radial and torsional vibration [18]. vibration of the tool, and used the semidiscrete time-domain However, piezoelectric materials and magnetic force are
limited by low cutting load capacity, high cost, and high energy consumption. These problems were overcome by ER fluids, which seemed to be more effective [15]. Wang and Fei designed an online adjustable control system using ER fluid materials that successfully extended the stability domain of the cutting tool using a fuzzy control strategy [14]. However, it is well understood that the lower operating temperature range and extreme nonlinearity of the ER fluid results in poor stability of the vibration suppression device [16,20]. Hence, some researchers attempted to suppress machine vibration with MR fluid because of its advantages of short response time, simple structure, and easy control. Mei et al. established a boring tool flutter suppression device based on MR fluid and its dynamic model, and explored the suppression effect of different excitation current frequencies on tool flutter [16]. Kong et al. designed a vibration suppression structure for a deep-hole drill pipe based on shear mode. It was empirically confirmed that the new deep-hole vibration damper effectively increases the structural rigidity, which improves the quality of the hole [17]. These studies provided technical support for active control of tool vibration. However, compared with the passive damping method, active damping methods did not gain popularity because they require more complex hardware and software and are more expensive. Motivated by the benefits of higher computational efficiency and lower hardware cost that an online control frame can offer, an active vibration control method derived from independent modal space is developed in this paper to avoid the defects of multiple and coupling control parameters in the classical physical space. Meanwhile, targeted suppression of the harmful vibration mode is used to achieve the ability to strike the modal accurately via modal filtering technology. In addition, this paper proposes a position optimisation algorithm that can satisfy the modal spillover minimisation and modal independence, so the above active control strategies can be implemented in actual processes with high precision but at low cost. The outline of the paper is as follows: In Section 2, an independent modal space control model is constructed for deep-hole drilling tools, and the influence of spillover effects on the modal suppression accuracy is analysed. In Section 3, low-cost target suppression of the modal is achieved by
constructing a position optimisation algorithm, which has an advantage over all previous approaches in the literature owing to its stronger ability to minimise the modal spillover. In Section 4, a finite element model of the deep-hole drilling tool is initially tuned by a modal experiment, and then the rationality of the selected position is investigated by simulation. Finally, the modal suppression effect is verified by the radial vibration information collected by the sensor. Moreover, the ability to suppress harmful modals is verified in regard to roundness errors. 2. Modeling of deep-hole drilling tool system Fig. 1 shows the structure of the deep-hole drilling system that consists of a deep-hole cutting tool, oil feeder, and MR damper [17]. The MR fluid damping configuration is geared with an adjustable annular magnetic field. It is adapted to the stiffness/damping regulation of each auxiliary support point during the deep-hole drilling process. According to the layout characteristics of the variable stiffness/damping tool system, the tool system can be discretised into a multisegment six-degree-of-freedom Euler-Bernoulli beam element. Its overall dynamic equation of motion is given by (1)
where , , and ∈ are the mass matrix, damping matrix, and stiffness matrix of the tool system in physical space, respectively; and are the damping matrix and stiffness matrix at the oil feeder, respectively, in the physical space; is the actual control force of the variable stiffness/damping damper output; is the external disturbance power which includes the tool cutting force and mass imbalance force; and respectively represent the position matrix of the external disturbance power and the actual control force; and ∈ is the physical coordinate vector, where a drilling shaft element with two nodal points is , , , , , . Note that there are a large number of coupled state variables if Eq. (1) is used directly for designing a control system, which poses a great obstacle to real-time control of the tool dynamics [21,22]. Hence, decoupling of the state variables is indispensable.
Eq. (7). In an ideal state, a feedback gain matrix = can be obtained by a pole placement method or a linear quadratic regulator to construct a closed-loop control system as shown in Eq. (8), achieving the best modal suppression effect. Once an independent modal space model describing the drilling tool dynamics with modal decomposition and truncation has been developed, the feedback control frame for the vibration suppression of deep-hole drilling tools can be constructed, as shown in Fig. 2. D /$ − 2M = −2 NOPOQ M =2 L a & $ RSTUAVWXYZ BX$$YATU ` . &$ 1 . 2 $ 1 , - K < D ` &% 2 % −2OPO /% − 2 8< =2 & % K NO NO OPO % 8OQ % $ = $OQ J _ [YZWUY$ BX$$YATU \X]XZ^ BX$$YATU NOOOOOOOOOOOOOOOOOOOPOOOOOOOOOOOOOOOOOOOQ
Fig. 1. Schematic diagram of deep-hole drilling tool system.
Two topics deserve attention. First, the essence of tool vibration is a superposition of different modal features. If a vibration mode is restricted, then the damage associated with it is also restricted. Second, transforming the system from physical space to modal space for control enables decoupling of the state variables. Therefore, the dynamic equations of the system can be converted into modal coordinates. (2)
where is the n-dimensional modal space coordinate that is
completely decoupled, ! ! " , !
! , ! ! , ! , ! ,
and ! is an # # transformation matrix.
Moreover, previous studies showed that the low-frequency vibration of the tool during the drilling process has a great influence on the drilling quality [7]. To relieve the calculation of the control algorithm further, modal truncation is used to preserve the lower modes. Hence, the modal coordinates are divided into lower modes $ and higher modes % . Introducing lower-state variable &$ ' $ $ ( and higher-state variable &% ' % % ( , the system state expression is introduced in the form & / 0 &$ 2 2 +, $ - . $ 1 . 1 . $ 1 . $ 1 2% 2 % 0 /% &% & % (3) & * 3 '4$ 4% ( . $ 1 ) &% where − − $ − − % 8 1 , /% . % 1 , 2$ 7 $ 9 , /$ . $ 0 6 0 6 0 !$ 0 8% 8 $ 8 % 2% 7 9 , 2 $ 7 9 , 2 % 7 9 , 4$ , -, 0 0 0 0 !$ ! 0 4% , % - , 8 % ! % , 8% ! % , 8 $ ! $ , 0 !% and 8$ ! $ . The size of matrices $ and $ is : : , and that of % and % is # − : # − :. !$ is an ; : matrix, and !% is an ; # − : matrix (where ; is the number of sensors). Constructing a closed-loop control system, the actual vibration control force can be written as −8< (4) $ =&$ @
$ with 8< $ >8$ 8$ ? 8$ and = '=A
=$B ( . Here, “+”
denotes a pseudo-inverse matrix, and =:C
and =$B are
feedback gain matrices for the modal velocity and modal
Additionally, the lower modal coordinate &$ is estimated by D $ expressed as Eq. (5), and E is the real-time data monitored & by the sensor. ! < 0 E D$ , $ & - . 1 (5) !$ < E 0 displacement.
The ideal condition for modal filtering is that the information collected by the sensor contains only lower modes, but the higher modes are often mixed [23]. Combined with Eq. (3) and D $ can be rewritten as Eq. (5), & & D $ '/ D 2 D( . $ 1 & (6) &% D 6 and 2 D FGHI!$ < !% . where / Combined with Eq. (3), Eq. (4), and Eq. (6), the actual closed-loop control system consisting of dampers is given by
bWcV$ YZWUY$ dWTe
(
(7)
where 2$ 2M 8$ ; 2M '6 0 . & / − 2M = 0 &$ 2 , $- . $ 1 . 1 . $ 1 (8) 0 /% &% 2 % &% However, the spillover terms in Eq. (7) stand in the way of constructing a stable and capable control system. They are the D on the main diagonal, mixed spillover −2% 8< $ =2 D , and control spillover term observation spillover term −2M =2 < on the secondary diagonal which is associated with −2% 8$ = the position of the sensor or damper. To curb the spillover effects, a direct and effective method is proposed in the next section to minimise the influence of the spillover by optimising the position of the sensor and the damper. 3. Position optimisation algorithm Generally, the spillover effect of modal control includes two parts: observation spillover and control spillover [23]. The former is owing to the inability to effectively avoid higher residual modes when observing the target modal, resulting in poor accuracy of the modal estimation. The latter occurs because the vibration control force obtained by the lower-mode feedback also affects the higher residual modes, which makes the modal control independence worse. To solve these problems, a series of methods such as the effective independence method (EFI) [24,25] and modal assurance criterion (MAC) [26,27] were selected. Unfortunately, control spillover remains, although these approaches can reduce the observation spillover [23]. Additionally, other intelligence algorithms such as the genetic algorithm [23] can help us to optimise the placement of sensors and actuators for reducing the spillover effects. However, genetic algorithm cannot be easily applied to actual machining processes owing to its large computational cost and less straightforward sense in view of the physical mechanism. Therefore, this section proposes a position optimisation algorithm of the damper and sensors with consideration of high precision and low cost, and with an aim to obtain modal estimation capabilities that can minimise the spillover. The ability to minimise spillover while optimising the position is a feature silhouetted against all previous methods in the literature. 3.1 Sensor position To eliminate the observation spillover and improve the accuracy of modal estimation, it is necessary to construct an optimal objective function related to the position of the sensor.
Therefore, if the nth mode is initially considered, then the time-domain information detected by the sensor during
E f !Z f (9) where !Z is an ; # matrix, and E is an ;-dimensional vector which is a combination of lower control modes and higher residual modes. Eq. (9) can be rewritten as $ (10) E !Z '!$ !% ( 7 9 % where lower control modes are given by E $ '!$ < −!$ < !% ( 7 9 (11) % Note that in order for $ to be accurately estimated, the optimal value of the spillover term in Eq. (11) is zero. Therefore, the objective function ‖h‖ is constructed to measure the influence of the spillover term on the modal estimation, which can obtain the best solution for spillover by adjusting the position of the sensor. ‖h‖ % !YATU % (12) where !YATU '!$ < !% ( '!$ < !% ( . Next, a conversion coefficient iYATU % % is introduced that satisfies any % condition. The following inequality holds: jeXZ ∙ iYATU l ‖h‖ l iYATU ∙ jeV] (13) where jeXZ and jeV] are the minimum and maximum eigenvalues of !YATU , respectively. It can be seen from Eq. (13) that for reducing objective function ‖h‖ (namely, the spillover effect), jeV] can be reduced by adjusting the position of the sensor based on the objective function as mYATU nG#'jeV] !YATU ( (14) However, in Eq. (14), the independence of the mode and the influence of the measurement noise on the modal estimation are not considered. Therefore, an EFI is introduced to screen candidate locations for sensors [24,25]. This can further improve the accuracy of modal coordinate estimation. The sensor output containing the first nth mode and noise can be written as E !Z o p o (15) where o is stationary Gaussian white noise with zero mean and a variance of q02 . Hence, the covariance of the modal coordinate estimate error is computed using the following equation: vp vp @ t − t ( .u w qM @ u w1 r s' − v v
processing can be expressed as
Fig. 2. Schematic diagram of control algorithm.
@
7 z !Z !Z 9
xy @
{
(16)
t is the unbiased estimator of . To accurately Here, estimate the modal, the determinant or trace of the Fisher matrix { must be maximised. If the column in the !Z formed by the initial sensor position is linearly independent, then the matrix !Z !Z is a positive definite symmetric matrix. Then, the corresponding position optimisation matrix is given by (17) | !Z !Z !Z @ !Z
According to Eq. (18), the position of the sensor corresponding to the smallest value on the diagonal of the matrix | is removed, thereby reducing the candidate position of the sensor. By combining the two optimisation methods, the state estimation ability of the target modal can be effectively improved. However, to improve the feasibility of the position optimisation algorithm further, it is also essential to perform an orthogonality test on the mode matrix composed of the selected sensor positions. The orthogonality test generally uses the MAC to establish the relevant objective function meV [26,27], where the value of the MAC is inversely related to the orthogonality of the mode. Additionally, the optimal solution of the two sensor positions satisfies the duality condition. $ meV nG#}∑$@ (18) V ∑SV< !V , !S Combining Eq. (14), Eq. (17), and Eq. (18), it is possible to construct a sensor position optimisation algorithm (as shown in Fig. 3), which guarantees the ability of the state estimation, modal independence, and minimisation of observation spillover during modal filtering. 3.2 Damper position
The following optimisation algorithm constructs the position optimisation of the damping, which reduces the control spillover of higher residual modes and achieves high-precision, low-cost modal control requirements. If the number of dampers is assumed to be :V , then the force is divided into an l-dimensional lower modal control force $ and an (n l)-dimensional higher residual modal control force % . The specific expression is given by
$ 8$
The control spillover
% 8% term % can be expressed % 8% 8< $ $
(19) (20) as
(21) As discussed in the observation spillover, the objective function that minimises the control spillover is also given by ‖h‖ > $ ? 8YATU $ (22)
< with 8YATU 8% 8< $ 8% 8$ . The corresponding objective
function boundary is as follows: jeXZ ∙ YATU l ‖h‖ l YATU ∙ jeV]
where YATU >$ ? $ , and jeXZ and jeV] are the minimum and maximum eigenvalues of 8YATU , respectively. Note that the value of jeV] is proportional to the control spillover, for which the objective function mYATU of the corresponding damper position optimisation is mYATU nG#'jeV] 8YATU ( (24) As discussed in the sensor position optimisation algorithm, an EFI is also used to initially optimise the position of the damper to ensure the controllability of the lower modes. Then, the objective function in Eq. (24) is used to minimise the control spillover of higher residual modes, thereby precisely controlling the lower modes. Based on the above optimisation procedures, an effective guarantee for the closed-loop control system design of the tool independent mode is provided, and the spillover effect is reduced when the model truncation is introduced simultaneously. This stronger spillover reducing ability is an innovative contribution on the methodology level. Therefore, a modal vibration suppression system with lower computing demand and hardware cost can be realised in the actual machining process. Any process that bears similarity to this, regardless of its carrier, can use the method to optimise the positions of supports or fixing equipment and actuators on the basis of the vibration mode features whether using passive or active control.
(23)
A schematic frame of the independent mode space control concept is shown in Fig. 2. Here, the green domain consisting of the current output (with the reference values according to the MR model [28] and its exact formulation listed in Appendix A) comprises the feedforward control for the MR damping force. The blue domain consisting of a weighted linear combination of the target modal velocity and displacement in Eq. (4), optimal position of the sensor from Section 3.1, and optimal position of the damper from Section 3.2 comprise the modal filtering feedback control strategy described in Section 3. Then, combining theoretical calculations and experimental results, the feasibility and effectiveness of the vibration suppression method for drilling tools proposed in this paper are verified. 4.1 Modified model To suppress tool vibration from the modal space, it is necessary to know the parameters and boundary conditions of the tool dynamic model. LMS Test. Lab’s modal test system (SCM02) was used to identify the self-made deep-hole machining machine as shown in Fig. 4, where the excitation force generated by the hammer stroke is taken as input, and the vibration information is obtained by the two prefixed acceleration sensors (PCB333B30). The corresponding results are listed in Tables 1 and 2. Table 3 presents an experimental and theoretical comparison of the natural frequency of the deep-hole tool system, in which the error is less than 5%, the maximum error is 3.43%, and the minimum error is only 0.02%. In addition, Fig. 5 shows the dynamic frequency response curves of the experiment and theoretical calculation for sensors #1 and #2, where the curves have a good fit. It can be concluded that the dynamic model of the deep-hole machining system has sufficient accuracy to predict the dynamic characteristics of the system.
Fig. 4. Parameter identification experiment. Table 1 Drill shaft parameters. Elastic modulus (Pa)
Area moment of inertia (m4)
Sectional area (m2)
Density (kg/m3)
Length (m)
Mass (kg)
1.35 × 1011
2.6 × 10-9
1.1 × 10-4
7860
1.45
1.3
Table 2 Identification results of tool system boundary conditions.
Fig. 3. Sensor location optimisation algorithm.
4. Experimental results
Position
Tool chuck
Oil feeder
Stiffness
1 × 109 N/m
1 × 106 N/m
Damping
0
4 × 103 N·S/m
Table 3 Comparison of natural frequencies between experiment and modified model. Modal
Experimental results (Hz)
Modified model results (Hz)
Error (%)
1
199.84
199.80
0.02
4
878.90
874.48
0.50
2
272.78
281.00
3.01
5
1146.44
1176.80
2.65
3
677.46
654.22
3.43
The initially considered modal is # = 5, and the two modes (: = 2) are selected as closed-loop control targets. In view of low cost, two sensors (; = 2) are selected for state observation, and one damper (:V = 1) is used as the vibration suppression device. Combining the algorithm proposed in Section 3 to optimise the position, the objective function meV was initially set as meV l 0.1 related to the MAC. Note that the position close to the cutter head or the oil feeder is not suitable for placing the sensor and the damper during the actual drilling process. Thus, the actual observation or vibration suppression 4.2 Optimal position discussion
position can also be suboptimal. Fig. 6 shows the location optimisation process and results for the sensor and damper, where the symmetry of optimisation solutions is also clearly demonstrated. As the meshing becomes finer, the results of location optimisation will also be more reasonable. To demonstrate the plausibility of the sensor location further, Fig. 7 shows the resulting meV calculated at the relevant sensor location. It can be seen that the information measured at the preferred location of the sensor satisfies the orthogonality of the modes.
Fig. 5. Comparison of frequency responses between experiment and modified model: (a) sensor #1, (b) sensor #2.
Fig. 6. Schematic diagram of optimal positions: (a) optimal positions of sensors, (b) optimal position of damper.
Fig. 7. Corresponding optimal results of sensor positions: (a) 3D display, (b) 2D display.
Fig. 8. Simulation verification of modal estimation: (a) diagram of modal shapes, (b) frequency responses after modal separation.
A meaningful way to judge the rationality of the position is to observe the mode shape. As shown in Fig. 8(a), the optimal position of the sensor is far from the mode node and is distributed on both sides of the damper, so that lower control modal information can be collected to avoid mutual interference. Meanwhile, the damper is close to the peak of the two mode shapes, which is beneficial to the effective control of multiple lower modes using only one damper. Fig. 8(b) shows the simulation results obtained by modal filtering based on the selected optimal position. It can be seen that the modes are entirely separated and the information of higher modes is minimal, which significantly improves the observation spillover in the modal coordinate estimation. 4.3 Modal control experiment In the following, a more detailed description of the experimental test rig is provided to verify the effectiveness of the modal space suppression algorithm outlined in Fig. 9. A dSPACE MicroLabBox control system platform is used as real-time hardware to record the measurement signals and to accommodate the observer and controller implementation. Moreover, the tool vibration signal obtained by the eddy current
sensor (with a response frequency of 5 KHz) is brought into the modal filter by analog-to-digital (A/D) conversion, and the sampling frequency is 8 KHz. Then, the independent mode control algorithm is used to obtain the control analogue quantity , which is output to the power amplifier by digital-to-analog (D/A) conversion. The power amplifier applies the corresponding excitation current to the MR damper to achieve precise suppression of harmful vibration modes. The tool vibration signal was obtained under the conditions of a feed rate of 0.04 mm/r, tool speed of 800 r/min, and cutting depth of 60 mm. Figs. 10 and 11 show the modal control (control of first mode, and simultaneous control of the first and second modes) and the vibration comparison under uncontrolled conditions. It can be seen that the response peak of the tool mainly exists in the vicinity of a cutting frequency of 26.7 Hz (tool cutting edge is 2), first natural frequency of 210.2 Hz, second natural frequency of 344.0 Hz, and third natural frequency of 639.2 Hz. To reduce the cost of suppression, the control system uses only two sensors and one damper. In Fig. 10(b), the peak value at the first modal frequency is significantly reduced, and the residual higher modes are less
affected, which indicates that the control system has a pinpoint effect on the target mode. At the same time, the peak reductions at the first-mode and second-mode frequencies in Fig. 11(b) also exceed 2/3 and 1/3, respectively. The ability for targeted suppression of harmful vibration modes during drilling by the control algorithm is very encouraging, and the sensor/damper position optimisation algorithms also meet the requirements of modal spillover minimisation. Furthermore, although the different modal numbers are suppressed by the independent
modal control algorithm, the amplitude at the cutting frequency becomes smaller. The main reason for affecting the amplitude of the cutting frequency is that the damper is similar to auxiliary support with a variable damping force when the modal is controlled. If only the first mode is controlled, then the amplitude at the cutting frequency is attenuated by 81%, while the amplitude attenuation is 85% when suppressing both the first and second modes.
Fig. 9. Schematic diagram of tool vibration real-time control system.
Fig. 10. Comparison of vibration signals between uncontrolled mode and controlled 1st mode: (a) comparison of vibration signals, (b) comparison of frequency responses.
Fig. 11. Comparison of vibration signals between uncontrolled mode and controlled 1st + 2nd modes: (a) comparison of vibration signals, (b) comparison of frequency responses.
4.4 Roundness error The purpose of vibration suppression is to improve the quality of the hole, which is directly related to the vibration mode of the tool. ZEISS CONTURA G2 instruments were used for measuring the profile of the hole, and the roundness error was computed based on [29]. Table 4 and Fig. 12 show the roundness errors of a hole with a target diameter of 17.75 mm obtained by suppressing different target modes. It can be seen that the roundness error of the hole was improved. In addition, the suppression of different modes leads to a significant difference in the improvement of the roundness error, which is mainly owing to the superposition of various mode functions in the vibration process affecting the roundness of the hole. The roundness error of the hole under uncontrolled conditions is concentrated from 18.3 to 23.3 µm, while the roundness error of the hole is concentrated from 12.1 to 17.5 µm when the first mode is controlled. It can be seen from Fig. 13 that the quality of the hole increased by at least 1/4. In addition, when two modes were controlled, the roundness error of the hole was suppressed in the range of 7.5–13.1 µm, which significantly improved the hole quality. The experimental results also confirm that the independent control modal algorithm can achieve target suppression of vibration modes and bring about significant improvement to the roundness error of the deep hole. 4.5 Process fidelity It should be pointed out that the experimental rig setup in this study is an exact reproduction of the Boring and Trepanning
Association (BTA) drilling process. On a deep-drilling machine tool, the machine structures do not exhibit noticeable influences on the process because the process is sealed by a chuck on one side and by the workpiece on the other side. At the bottom is a machine bed which is usually assumed to have no dynamic behaviour. In extreme cases, i.e. in high-speed drilling, the chuck may be affected by centrifugal forces and become slightly loose, and the drill head may experience slightly different hydrodynamic lubrication. However, neither effect changes the boundary conditions of the drilling tool significantly, and the working range in this study is not in the high-speed domain. The only limitation is the shorter drilling depth owing to the existence of the sensor, but the results obtained from the created experimental rig are still fundamental and contribute to advancing the knowledge of deep-hole drilling. Table 4 Comparison of roundness errors at different depths. Drilling depth (mm)
Roundness error ∆ (µm) With control Without control (control mode)
10
18.3
20
19.5
30
18.5
40
21.2
Error reduction (%)
12.1 (1st)
33.9
7.5 (1st + 2nd)
59.0
13.2 (1st)
32.3
7.9 (1st + 2nd)
59.5
13.1 (1st)
29.2
8.5 (1st + 2nd)
54.1
15.4 (1st)
27.4
11.2 (1st + 2nd)
47.2
50
23.3
17.5 (1st)
24.9
13.1 (1st + 2nd)
43.8
Fig. 12. Comparison of roundness errors.
Fig. 13. Percentage of roundness error reductions.
5. Future applications The solutions shown in this work can be used in applications in other processes or even fields with relevant features. The damper in this work is still an alien entity attached to the target. Making the damper part of the target structure would revolutionise its application. That is, a “structurisation” of the MR-fluid damper or a morphing of the target structure to embed the on-call damper can assist in some fields that still rely on alien tuned mass-damper inerters for vibration suppression. The online, on-call, quick-response, and low-cost advantages can then be harvested. However, this will not occur in a plug-and-play method. Significant research and time are needed, and limitations do exist. 6. Conclusions
roundness errors proved the value of the idea, damping mechanism, and proposed algorithms. The physical phenomenon of suppressing even the lowest two Eigen vibration modes can essentially elevate the already high manufacturing quality in the sense of “roundness”. This was definitely proven by this work. The concept and methodology proposed can be applied directly to BTA deep-hole drilling requirements with a rotating or stationary tool. For gun drilling, some adaptations are needed which require further research. The general significance of this work is on two levels: process and methodology. On the process level, the real-time precision suppression of undesirable modal vibration in a process as confronted in deep-hole drilling was shown in full. Any process that bears relevant features, i.e. cantilevered or weakly and/or peripherally supported beams, plates, shells, blades, etc., can derive ideas from this work. Possible applications include manufacturing and other industries such as crane, bridge (especially suspension bridges), aerial refuelling hoses/pipes (probe & drogue or flying boom), rotor blades of wind power generators, electricity post/transmission towers, and even kilns and chimneys. Process-specific dampers and a mechanism for attaching and actuating them to the identified nodes are needed. The solutions can follow a similar line of thought as that shown in this work. On the methodology level, this paper combined the minimum spillover objective function Jover based on the vibration principle with EFI and MAC to create a new methodology that achieves what all previous literature attempted, but with stronger ability in reducing the spillover effect. In addition, the proposed sensor (damper) position optimisation algorithm makes it possible to suppress multiple-order modes with fewer sensors and a damper. This greatly reduces the cost of technical implementation, which is of interest to various industries. References [1] X. Q. Zhang, G. L. Tnay, K. Liu, A. S. Kumar, Effect of apex offset inconsistency on hole straightness deviation in deep hole gun drilling of Inconel 718, Int. J. Mach. Tool Manuf. 125 (2018) 123-132. [2] I. M. Mehrabadi, M. Nouri, R. Madoliat, Investigating chatter vibration in deep drilling, including process damping and the gyroscopic effect, Int. J. Mach. Tool Manuf. 49 (2009) 939-946. [3] K. Matsuzaki, T. Ryu, A. Sueoka, K. Tsukamoto, Theoretical and experimental study on rifling mark generating phenomena in BTA deep
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Appendix A The Bouc-Wen model is extremely versatile and can exhibit a wide variety of hysteretic behaviour [28]. An applied force based on a shear model is given by M (A.1) where M and are the damping coefficient and hysteresis coefficient, respectively. The evolutionary variable z is governed by −| |||Z@ − ||Z (A.2)
By adjusting the parameters of the model (, and , one can control the shape of the hysteresis loops for the yielding element. To account for the dependence of the force on the electrical current q, M , and can be suggested as Eq. (A.3): MV MS q M V S q
(A.3)
where MV , MS , V , and V are constant values, and the resulting parameters as listed in Table 5 are obtained from identification experiments.
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Table 5 Identification results of Bouc-Wen model parameters. Parameters
Values
Parameters
Values
MV
168 (N·s-1/m)
220 (m-2)
MS V S
2820 (N·s-1/I·m) 0.16 (N/m) 3.9 (N/I·m)
#
225 (m-2) 37255 2
Acknowledgements: This work was supported by National Natural Science Foundation of China (Grant No. 51475367 and 51905421), Natural Science Foundation of Shaanxi province (Grant No. 2018JM5113) and Natural Science Foundation of Department of Education of Shaanxi Province of China (Grant No. 17JS093).
Highlights Real-time targeted suppression of drilling tool vibration modes is presented for improving the hole processing quality. An operable damper/sensor position optimization strategy was constructed to minimize the modal spillover. The presented idea may pave the way for elevating the quality of other manufacturing processes with similar weak stiffness features, such as long shaft tools or thin-wall workpieces.
In this paper, the contribution is on two levels, namely process and methodology. On the process level the real time, precision suppression of undesirable modal vibration in a process like that of deep hole drilling is shown in full. Any process that bears relevant features, i.e. cantilevered or weakly and/or peripherally supported beams, plates, shells, blades, etc., can derive ideas from this work. On the methodology level, this paper combines the minimum spillover objective function based on vibration principle with the effective independence method (EFI) and modal assurance criterion (MAC) to create a new methodology which achieves all those literatures are trying to do but with tougher ability in reducing the spillover effect. Besides, the proposed sensor (damper) position optimization algorithm makes it possible to suppress the multiple order modes with fewer sensors and a damper thus greatly reduce the cost of technical implementation which is definitely of interest to the industry.
We declare that we do not have any commercial or associative interest that represents a conflict of interest in connection with the work submitted