Mode coupling chatter suppression for robotic machining using semi-active magnetorheological elastomers absorber

Mechanical Systems and Signal Processing 117 (2019) 221–237

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Mechanical Systems and Signal Processing journal homepage: www.elsevier.com/locate/ymssp

Mode coupling chatter suppression for robotic machining using semi-active magnetorheological elastomers absorber Lei Yuan a, Shuaishuai Sun a, Zengxi Pan a,⇑, Donghong Ding b, Orm Gienke a, Weihua Li a a b

University of Wollongong, Australia Foshan University, China

a r t i c l e

i n f o

Article history: Received 2 April 2018 Received in revised form 24 May 2018 Accepted 27 July 2018

Keywords: Robotic machining Magnetorheological elastomer absorber Chatter Mode coupling Industrial robot

a b s t r a c t Chatter is one of the major barriers for robotic machining process. As the dominant vibration frequency of the chatter varies under different working conditions, Magnetorheological elastomers (MREs) whose stiffness is adjustable is an ideal device to be used for chatter control. This paper presents a new mode coupling chatter reduction scheme by assembling an MRE absorber on the spindle to absorb vibration with a specific frequency range. Firstly, a MRE absorber was designed and fabricated to suppress the target chatter according to the robot model and then a test was implemented to obtain the frequency shift property of the designed MRE absorber. Subsequently, robotic milling of an aluminium block using ABB IRB6660 robot was tested under various conditions to demonstrate the performance of the MRE absorber under different constant currents. After that, a semi-active controller was established to control the electrical current applied to the MRE absorber to trace the chatter frequency. The experimental results show that the semi-active MRE absorber performs better on the chatter reduction during robotic milling than passive absorbers. Ó 2018 Elsevier Ltd. All rights reserved.

1. Introduction Modern industrial robots offer flexibility, efficiency, low cost and safety, that have superseded many tiresome, repetitive and especially hazardous manual operations. Nowadays, industrial robots have been widely employed in various industrial applications, including welding, material handling, painting, assembly, machining, etc. [1–3]. In terms of machining applications, due to its high level of accuracy and contact force, CNC machine has been regarded as the backbone for the industrial use for a few decades. Despite this, exploring the potential of industrial robots for machining applications are still of interests. The main advantages of industrial robot compared to CNC machine are flexibility and low cost. However, the relatively low stiffness, which results in mode coupling chatter, is still the main barrier limiting the use of the articulated robot in machining applications [4–6]. Merritt [7] and Tlusty [8] identified two most powerful sources of self-excited vibration (or chatter): regenerative chatter and mode coupling chatter in the machining process. The regenerative chatter occurs during the subsequent processing on the rough surface after the previous cutting path [9]. During milling, the next tooth in cut collides with the wavy surface from the previous cut and generates a new wavy surface. The chip thickness and, hence, the cutting force vary due to the ⇑ Corresponding author. E-mail addresses: [email protected] (L. Yuan), [email protected] (S. Sun), [email protected] (Z. Pan), [email protected] (D. Ding), [email protected] (W. Li). https://doi.org/10.1016/j.ymssp.2018.07.051 0888-3270/Ó 2018 Elsevier Ltd. All rights reserved.

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phase difference between the wave left by the previous tooth and the wave generated by the current one [9]. On the other hand, the term mode coupling means the vibration exists simultaneously in two or more directions coupled to each other. The mode coupling chatter happens even when the successive passes of the tool do not overlap [10]. Its vibration amplitude has no fixed direction as the tool follows an elliptical path related to the workpiece. For CNC machine, the conventional wisdom focuses on the regenerative chatter of the machining tools such as boring bar and milling cutter, since the mode coupling chatter seldom happens due to the large stiffness of the CNC machine. However, in robotic machining process, due to the low structure stiffness of the robot, it is observed that the entire robot structure can vibrate during relatively light machining process [11]. The impact of mode coupling chatter on robotic machining is a more complicated issue and thereby improving robotic machining stability has been an interest of research in recent years. Many researchers have applied the mode coupling theory to explain robotic machining chatter and guide controlling it using either passive or active compensation method. The passive strategy addresses the issue through changing the robot configuration, process behaviours, or system structure, including stiffness, damping, etc. The stiffness of industrial robots varies at different robot configurations and positions due to their serial articulated structure. By selecting the most optimal robot configuration and trajectory, less chatter was observed [12]. Other researchers focused on the suppression of the chatter occurrence by changing the system structure [13]. Recently, active chatter compensation, in particular force control based strategy has also been developed in robotic machining study. The chatter phenomenon arises due to large cutting force, so the cutting force would be adjusted to avoid chatter occurrence through various force sensing technologies and active control strategies [14,15]. However, passive strategies restrict the flexibility of the machining setup and active force control strategy mainly avoids the chatter by limiting the cutting force, which results in low productivity. To the best of our knowledge, there is no research on absorption or disruption of low-frequency mode coupling chatter for robotic machining process. Dynamic vibration absorbers (DVAs) is a conventional solution to suppress vibration/chatter of machines [16]. DAVs have been categorized into three groups: passive DVAs, active DVAs and semi-active DVAs [17], traditional passive DAVs composed of an oscillator, a spring element, and a damping element, they are simple, reliable and cost-effective. However, this kind of passive absorbers is limited to operate at a single excitation frequency due to its uncontrollable damping or stiffness. For robotic machining system, the working condition may change and induce chatter with variant dominant frequency. As a result, active controlled absorbers, which have a time-varying natural frequency through altering its stiffness, are ideal for robotic machining chatter suppression. Nevertheless, the complexity, high-cost and more energy consumption of active control system retard its practical applications [18]. Comparatively, semi-active DVAs, which can achieve comparable active absorption performance, are promising for chatter suppression. Currently, DAVs are tuned by mechanical structure or smart material. Compared to mechanical tuned DVAs [19], Magnetorheological Elastomers (MREs)-based DVAs have the advantages of short response time, simple structure, and easy control, and is a better semi-active absorption technology for many applications [20–22]. Yang et al. [23] presented a study on the MREs-based semi-active vibration absorber. The authors claimed that the proposed device achieved a better performance compared to classic passive dynamic vibration absorbers in terms of frequency-shift property and vibration absorption capacity. In addition, Sun et al. [24] developed a hybrid nonlinear MRE absorber which can vary its natural frequency and has a wider absorption bandwidth under each constant working scenario. The experimental results verified the proposed MRE absorber had a wider effective bandwidth than a linear absorber. Among all applications of the MREs-based semi-active vibration absorber, its application on chatter suppression for robotic machining has rarely been investigated. The objective of this research is to develop a semi-active vibration control system utilising MREs to achieve a more stable and more productive machining process. This paper is organised into five sections. Following this introduction, Section 2 presents the chatter analyses based on robot and process model. Section 3 presents the design and test of the MRE absorber. Section 4 demonstrates the effectiveness of the MRE absorber on chatter suppression, followed by a conclusion in Section 5. 2. Identification of chatter frequency based on robot model Generally, the frequency-shift property of MRE absorber determines the frequency range that chatter/vibration it can absorb. Thus, the first step is to investigate the frequency feature of chatter in robotic machining before designing MRE absorber. The results obtained in this section will be used to guide the design of the MRE absorber in the next section. 2.1. Robot model In this study, an ABB IRB 6660 machining robot was used for milling test. Compared to the conventional CNC machine, the industrial robot features a serial articulated structure. Traditionally, Denavit-Hartenberg (DH) model [25–27] is employed to analyze the robot forward and inverse kinematics. This model considers rigid links and flexible joints (revolute joints) that is sufficient for low-frequency vibration analysis. The DH model and parameters of ABB IRB 6660 were demonstrated in Fig. 1. Regarding DH-convention the forward kinematics can be derived from the Eq. (1):

Ai ðqi Þ ¼ T rz ðhi ÞT t ðai ; 0; di ÞT rz ðai Þ

ð1Þ

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223

Fig. 1. DH model of ABB IRB 6660 [28].

where qi means the joint angle of the robot. Eq. (1) defines forward kinematics of a mechanical structure between the neighbouring joints. For industrial robots such as ABB IRB6660, there are 6 revolute joints, as shown in Fig. 1. Eq. (1) takes values from each row in Fig. 1, and calculates the transformation from joint n-1 to joint n. By multiplying 6 of these relations, as in Eq. (1), we can calculate the complete forward kinematics of the robot, which defines the transformation from robot base to tool tip.

0T E ðqÞ ¼ 0T 1 ðq1 Þ . . . 5T 6 ðq6 Þ

ð2Þ

¼ A1 ðq1 Þ . . . A6 ðq6 Þ Employing the xE = f(q) [29] in forward kinematics, the analytical Jacobian can be calculated as:

2 @f

1

@q1

Jð q Þ ¼

@f ðqÞ 6 6 ¼ 6 ... 4 @q

@f m @q1

 ..

.



@f 1 @qn

3

7 .. 7 . 7 5

@f m @qn

m ¼ dimðxE Þ; n ¼ dimðqÞ; DxE ¼ JðqÞDq

ð3Þ

The Jacobian matrix can be employed to relate the small displacement of the robot tool tip due to the machining force [30]. 2.2. Robot-tool model The general robot-tool structure equation in task space is

½Mf€xg þ ½C fx_ g þ ½K fxg ¼ fF g

ð4Þ

where [M], [C] and [K] are six by six mass, damping and stiffness matrixes, respectively. fF g is the vector of external forces, which is machining force in this case. The vector fxg represents the task space Cartesian coordinates, which include 3 translational and 3 rotational degree of freedoms (DOFs). Pan et al. [31] and Gasparetto [32] explained that the damping matrix could be ignored due to its solely stability increasing effect in mode coupling analysis, only mass and stiffness matrix need to be identified through establishing robotic machining force model. Then, Eq. (5) can be simplified as:

½Mf€xg þ ½K fxg ¼ fF g

ð5Þ

On the other hand, the stiffness matrix could be represented in joint space as:

s ¼ K q Dq

ð6Þ

where s is the torque load on each joint and Kq is a six by six diagonal matrix with the joint stiffness values on its diagonal. The value of joint stiffness of the robot is presented in [33], as listed in Table 1. The mass matrix is related to robot rotational inertia in joint space as

h i1 M ¼ J ðqÞT Iq ðqÞ1 J ðqÞ

ð7Þ

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Table 1 The stiffness value (N/um) of each joint in ABB IRB6660. Axis

1

2

3

4

5

6

Value (N.m/Rad)

1.18  106

2.666  106

2.488  106

4.5  105

4.32  105

4.33  105

where Iq(q) is the robot rotational inertia in joint space. It could be derived from robot kinematic model by Newton–Euler method or Lagrangian method, if the rigid body inertia parameters are available. Detailed explanation can be found in [31]. Although in joint space the stiffness of each joint is independent to each other, the stiffness matrix transformed to Cartesian Space Stiffness K will have a coupled structure and its value depends on the current configuration of the robot, through the Jacobian matrix,

h i1 K ¼ JðqÞT K 1 q J ðqÞ

ð8Þ

The detailed model derivation process can be found in [1]. 2.3. Chatter analysis To analyse chatter frequency, the first step is to identify the base frequency of the robotic system. The base frequency of a mechanical structure is calculated without contemplating an external force, using the homogeneous solution of the characteristic equation

detð½K   ½Mk2 Þ ¼ 0

ð9Þ

where the k is the angular frequency which can be calculated given stiffness matrix [K] and mass matrix [M] at different robot configuration. Then, the natural frequency of robot f would be obtained by:

f ¼

k 2p

ð10Þ

according to the mathematical model above, once the robot configuration is determined by workpiece positions, six base frequencies can be obtained. Theoretically, the six frequency modes in 3D space that need to be considered in the machining operations. In the practice, the major chatter was observed along XY plane in this setup which was parallel to the machining table. Thus, it is only necessary to calculate the first three modes and their base frequencies. Fig. 2 shows the variation of the base frequency of the first three modes at a range of robot positions. It can be seen that all chatter frequencies are between 6.5 Hz and 20 Hz. In combination with the work space limit of the ABB IRB 6660 machining robot [34], the MRE would be designed to operate this frequency range for the best chatter reduction performance. This matches the results from Pan, et al. [31], which states the frequency of mode coupling chatter is around 10 to 20 Hz for a large sized ABB machining robot.

Fig. 2. ABB IRB6660 natural frequency of (a) the first mode (b) the second mode and (c) the third mode.

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3. Development and test of the MRE absorber According to the target frequency range based on the modelling of robotic machining process in the above section, an MRE based vibration absorber is designed, fabricated, and tested in this section. Details of the structural design, working principle and fabricating process are presented in the following subsections. 3.1. The structure and design of the laminated MRE absorber Currently, the MRE based adaptive tuned vibration absorber (ATVA) consists of four main parts: the dynamic mass, MRE layers, magnetic conductor and excitation coils [35]. The target of MRE absorber is that the chatter energy of the controlled objects would be largely transferred to the oscillator of the absorber through adjusting the natural frequency of the oscillator [17]. In this study, it is required to design the MRE absorber regarding features of robotic machining application including: (1) a low operation frequency range due to the chatter occurring in robotic machining is around 7 to 20 Hz. (2) A good vertical load capacity to support large mass oscillator. (3) A large stroke amplitude of oscillators to absorb energy as much as possible. To construct an ATVA which caters above features, a multi-layer MRE structure was regarded as an ideal solution due to the vertical support ability for a large mass, relatively low operation frequency and a relative larger stroke of the oscillator [36]. Fig. 3 demonstrates the flowchart of designing process of MRE absorber and Fig. 4 describes the conceptual design of the MRE absorber operating in shear mode. It can be seen that the four main parts of the ATVA are oscillator, laminated MRE pillar, magnetic conductor, and coil. The working principle of this device can be described as: the magnetic fields generated by the coil can be controlled by the applied current provided by an external direct current (DC) power. The modulus determines the stiffness of the ATVA such that any change in the MRE’s stiffness will vary the natural frequency of the ATVA. Thus, the natural frequency of the absorber can be corrected to match the excitation frequency by adjusting the current in the coil and thereby the chatter can be controlled quite significantly. To assess the principal design of the magnetic circuit, Fig. 4 also illustrates the schematic for the initial design of the vibration absorbers with four MRE sheets, as well as the magnetic closed loop circuit. In addition, the operation mode was selected as shear mode considering the target mode coupling chatter mainly occurs in the horizontal plane. To ensure the ATVA works by the shear mode, the smart spring elements (MRE pillar) were stuck on the oscillator and the mounting plate in vertical order. To transfer chatter energy to MRE absorber, the geometry of the MRE layer and other components of the MRE absorber needs to be designed to make the natural frequency of the absorber match the excitation frequency through the adjustment of the current input. With the calculated target frequency range in Section 2, the frequency range of the MRE absorber can be obtained according to Sun, et al. [36].

8 > > > > > > > > <

1 2p

rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi   2 3 G0 þ36£l0 l1 b2 ðBg =lM l0 Þ ðdaÞ f A nmh

If the iron particles do not saturate f ¼ rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi   > 3 > G0 þ4£l0 l1 M2s ðadÞ A > 1 > > > 2 nmh p > > : If the iron particles saturate Table 2 listed the description of the parameters in Eq. (12) and b ¼

ð12Þ



lp  l1





lp þ 2l1  1, f ¼

Pn

1 j¼1 i3

 1:202, In practice,

two groups of parameters need to be calculated once the raw material and fabricating machinery were decided. Firstly, all

Fig. 3. The flowchart of designing process of MRE absorber.

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Fig. 4. The design conception and the working principle of MRE absorber.

Table 2 The parameters of MRE absorber. Group 1

Symbol

Description

1 2 3 4 5 6

G0 £

l0 lM l1 lp

The The The The The The

zero-field modulus volume fraction vacuum permeability of MRE relative permeability of MRE relative permeability of silicon rubber relative permeability of the particles

7 8 9 10

a d Bg Ms

The The The The

average radius of iron particle original particle distance magnetic flux density of the MRE saturation intensity of the particles

Group 2

Symbol

Description

1 2 3 4

A n m h

The The The The

contact area between MRE layer and the oscillator number of the layers mass of the steel oscillator thickness of the MRE layer

the parameters in the Table 2 are determined by the properties of the raw materials and the weight ratio of iron particles, silicon rubber and silicon oil. The weight ratio determines the zero-field modulus G0 in Eq. (12) to affect the initial frequency of the MRE absorber. Besides, the weight ratio also affects the width of the frequency range and the supporting capability of the MRE pillar. In the second group, serval geometrical dimensions (in Table 4) affect the operation frequency range as well. Combining Eq. (12) and the target frequency range of MRE absorber, all the components of the device are designed accordingly. All the components of the device were designed accordingly. 3.2. Prototyping of an MRE-based absorber MRE sheets were manufactured by three basic MRE materials: iron particles (C3518, Sigma- Aldrich Pty. Ltd), silicon rubber (Selleys Pty. Ltd) and silicon oil (Sigma-Aldrich Pty. Ltd) with the weight ratio of 70: 15: 15. Fig. 5 demonstrates the process of MRE fabrication: silicon rubber, silicon oil and iron particles were weighed and placed in a glass burette and then mixed thoroughly. The container was placed in a vacuum pump to vacuum the air bubbles from the mixture. Subsequently, the mixture was filled in a 1 mm thick mould and placed in a room at a stable ordinary temperature for seven days. In addition, the whole curing process was carried out without magnetic field to ensure an isotropic MRE structure.

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227

Fig. 5. The fabrication of MRE pillar.

Fig. 6. (a) The fabricated steel sheet, MRE sheet and the MRE pillar and (b) the structure of fabricated MRE absorber.

In next stage, the cured MRE sheets and 1 mm thick low carbon steel sheet were cut into the designed shaped as shown in Fig. 6 (a). To fabricate the MRE pillar, three MRE and steel sheets were bonded together layer by layer with a cyanoacrylate glue (Loctite 480, Henkel AG & Co. KGaA). For a coil, 800 turns of 0.5 mm diameter copper wire were twined tightly around solenoids. A low carbon steel block was fabricated as the oscillator of the absorber and four steel columns were designed inside of the oscillator which would be covered by four non-magnetic supporters made from 2 mm thick plastic. The four multi-layered MRE pillars were bonded on the bottom of steel column after installing the excitation coils as shown in Fig. 6 (b). So far, the above section provides the whole process of the laminated MRE pillar as well as the entire MRE absorber from design to manufacturing which was based on the frequency range of mode coupling chatter during robotic machining process. 3.3. Experimental tests The identification of the frequency-shift property is essential and fundamental to analyse an MRE absorber. It demonstrates the valid frequency bandwidth of the MRE absorber. The MRE absorber was tested using the vibration platform and swept sinusoidal signals. Based on the measurement, the frequency-shift performance of the proposed absorber was evaluated.

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Fig. 7. The setup for testing frequency-shift property of the MRE absorber.

3.3.1. Transmissibility of the MRE absorber The presented absorber is a single-degree-of-freedom (SDOF) system and its transmissibility can be identified. According to Zhang and Li [37] and Sun, et al. [17], the transmissibility of the MRE absorber can be represented by magnitude and phase from the equation:

vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u u 1 þ ð2fkÞ2 T ¼ t 2 1  k2 þ ð2fkÞ2

u ¼ tan1

2fk3 1  k2 þ ð2fkÞ2

where f ¼ 2mcx , x0 ¼

qffiffiffi

k m

ð13Þ

ð14Þ

and k ¼ xx0 . Among above equations, c is the damping ratio, x is the external vibration frequency, the

lateral stiffness of the spring is k and the mass of oscillator is m. The transmissibility T reaches its peak value when resonance phenomenon appears and the phase difference between the oscillator and the mounting plate is p/2. In this case, the corresponding exciting frequency was the resonance frequency. 3.3.2. Experimental setup Fig. 7 demonstrates the experimental setup utilized to evaluate the performance of the absorber. An aluminium sheet was mounted on the two linear bearings, which were supported by the vibration platform. The mounting plate of the MRE absorber was directly fixed on the aluminium sheet. A shaker (VTS, Model No. VG 100-8) was excited by a harmonic signal generated by computer and amplified by a power amplifier (YE5871) via the DAQ board (LabVIEW PCI-6221, National Instruments Corporation). A DC power supply (Thurlby Thandar Instruments Ltd) was used to provide current to solenoid such that the amplitude and direction of the current could be controlled thus to change the strength and direction of the electromagnetic field. The lateral acceleration of the mounting plate and the oscillator were measured by two accelerometers which were installed on the surface of the two components. The acceleration signal generated by these accelerometers (CAYD-106) were then transferred to the computer via the DAQ board, while the signal collection, recording, and processing systems were developed using the LabVIEW program. In this program, there are two analog input channels were designed to measure the frequency of the MRE absorber from the two accelerometers and one analog output channel was used to control power amplifier to excite the shaker. In the test, the sweeping signal was set with a frequency range from 5 to 25 Hz to excite the shaker to drive the horizontal vibration platform. The frequency-shift performance of the MRE absorber is tested under the electric current from 0 to 2.0 A with a step of 0.2A. Then, the transmissibility of the MRE absorber was recorded and displayed directly on the computer. 3.3.3. Test results Fig. 8 (a) and (b) presents the transmissibility and phase of the device and the peak of the transmissibility line is the resonance frequency point. Based on that, Table 3 captures the natural frequency with respect to the currents and Fig. 8 (c) presents a fitted curve of the relationship between the natural frequency shift and the excitation current, the result indicates that the magnetic system is able to control the natural frequency of the absorber, as the current varies from 0 A to 2.0 A, the natural frequency of the MRE absorber increased from 6.8 Hz to 20 Hz. It is explained by the MR effect of MRE absorber that usually its stiffness and damping are increased with the increase of applied current. Moreover, the lowest natural frequency can be identified as low as 6.8 Hz which verifies that the laminated structure of the MRE absorber has a low natural frequency. In Table 3, the relative change in the natural frequency of this absorber is nearly 200% which demonstrates a great frequency bandwidth of the absorber. 4. Performance evaluation of the MRE absorber 4.1. Experimental setup A series of vibration experiments were conducted for robotic milling with an aluminium workpiece. The MRE absorber system was attached to the spindle that is held by an ABB IRB 6660 machining robot. A schematic diagram of

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Fig. 8. The testing results (a) the magnitude, (b) the phase and (c) The fitted curve of the frequency-current relationship.

Table 3 The frequency-current relationship. Current (A)

0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

Relative change

Natural frequency (Hz)

6.8

6.9

7

7.2

8.2

9.8

11.5

14.8

17.5

19

20

194%

the experimental setup is shown in Fig. 9 (a) and an experimental setup is shown in Fig. 9 (b) and (c) which illustrate the entire structure of the system combining the robot, spindle and MRE device. A three flutes endmill (R45 W – Regular, Suttontools, Ltd) was used and the spindle speed is set to 2400r/min in all the tests, more information is provided in Fig. 10 and Table 4 below. A force/torque sensor (ATI six-DOF) was included between the robot wrist and spindle mount to collect real-time machining force data for vibration analysis. An adjustable DC power supply was employed to provide power for MRE absorber. 4.2. Performance of the MRE absorber without control system Two group of cutting parameters were selected to conduct the evaluation experiment. The frequencies of mode coupling chatter under the two scenarios are around 12 and 18 Hz, respectively. Table 4 listed the detailed experimental setups of the

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Fig. 9. (a) Schematic diagram of the experimental setup, (b) experimental setup for robotic milling of aluminium samples and (c) A 3D model of MRE and robot system.

Fig. 10. The diagrammatic drawing of endmill.

Table 4 The experimental design of group A and B. Robot configuration Joint angle

Axis 1

Axis 2

Axis 3

Axis 4

Axis 5

Axis 6

Group A Group B

13.5° 12.2°

20.6° 58.9°

44.2° 25.2°

99.5° 111.2°

80.4° 52.6°

134.3° 122.2°

Index

Cutting speed (mm/s)

Depth of cut (mm)

Width o cut (mm)

Milling direction

Group A Group B

30 10

2 1

6 6

+X +X

Item

d1(mm)

l1(mm)

l2(mm)

d2(mm)

Z (No. of flute)

E1211000

10

72

22

10

3

Milling parameters

Information of endmill

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two scenarios including joint angles, cutting speed, the depth of cut, the width of cut, cutting direction, and the use of the MRE absorber. The milling test without MRE absorber was firstly conducted in every group to identify the chatter frequency and the PSD of those two tests were utilised as the original chatter occurrence for further comparison. To compare the performance of MRE absorber, other two cases were designed in each group to compare the magnitude of mode coupling chatter in the milling tests with MRE under attached and the optimal value which was calculated according to chatter frequency and the frequency-current relationship as shown in Fig. 8 (c). The test results including cutting force, chatter frequency and power spectral density (PSD) were recorded in Table 5 for analysis. Notably, the wavy surface left from the previous cut was cleaned before the next test to ensure the consistency of the results. In order to analyse the mode coupling chatter, the measured force signal was processed in both time and frequency domain using MATLAB. The severity of the chatter between various experiments is compared based on PSD value of the force signal after Fast Fourier Transform (FFT) process. The case 1 in group A as shown in Table 5, was the original robotic milling setup without the MRE absorber. As the FFT results shown in Fig. 11(a), the frequency of the mode coupling chatter was 12.21 Hz, the PSD was 25.38. Case 2 was

Table 5 The experimental results of group A and B. Index

Control method information

Chatter frequency (Hz)

Maximum PSD value

Group A

Case 1 Case 2 Case 3

Original milling without MRE absorber Passive control method without electric current Passive control method with an optimal current of 1.3A

12.21 12.79 11.39

25.38 11.98 2.481

Group B

Case 1 Case 2 Case 3

Original milling without MRE absorber Passive control method without electric current Passive control method with an optimal current of 1.55A

18.83 17.17 17.3

36.7 23.41 0.0334

Fig. 11. (a) The experimental results of group A and (b) group B.

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designed to test the MRE absorber without electric current during the same milling process. According to Table 3, the natural frequency of MRE absorber with 0A was 6.8 Hz, which does not match the frequency of mode coupling chatter in this case. The PSD values of case 2 was smaller than it in case 1, which indicates that the proposed MRE absorber reduced the chatter vibration to a certain degree, even the natural frequency of the MRE absorber and the frequency of mode coupling chatter do not totally match each other. To achieve the best chatter control performance, in case 3, the current was set to 1.3 A, which adjusts the natural frequency of MRE absorber to 12 Hz. The results in Fig. 11(a) clearly shows that the chatter was further restrained when the natural frequency of MRE matches the chatter frequency. Group B represents the same machining condition at a different robotic position/configuration, where the chatter frequency is around 18 Hz, as shown in case 1. Fig. 11(b) and Table 5 illustrate that the milling process became stable with an optimal current of MRE absorber setting to match robotic machining chatter frequency in case 3. The results could be explained and summarised here: 1. The experimental results show a certain level of reduction of low-frequency mode coupling chatter from two groups. Considering the original PSD of the mode coupling chatter in case 1 of each group, most of the chatter energy was absorbed by the proposed device. 2. Compared to case 2 in each group, the results in case 3 validate that the MRE absorber is most effective when its natural frequency matches the frequency of the chatter. if the natural frequency of the MRE absorber and the chatter frequency differs, the efficiency of MRE absorber decreases. 3. It is important to highlight that the chatter occurred at two different frequencies (around 12 Hz in group A and around 18 Hz in group B) due to the difference in robot configuration. It implies that the proposed device can absorb chatter with different vibration frequencies, which means the absorber can be always effective in the machining process under various milling conditions. 4.3. Performance of the MRE absorber with the developed controller As mentioned in Section 4.3, the results reveal that the MRE absorber only works effectively when its natural frequency matches the chatter frequency. Thus, a semi-active control system is established to trace the chatter frequency and make the adjustment on MRE current accordingly. 4.3.1. Control system setup The schematic diagram of the experimental setup is shown in Fig. 12 (a) and a detailed experimental setup is shown in Fig. 12 (b). Firstly, the proposed MRE absorber was attached to the spindle the same way as in Section 3.3. Then, an accelerometer was used to measure the vibration information and transmit to controller, the real-time frequency signals of the mode coupling chatter are recorded for the frequency adjustment. The interface connecting the accelerometer and power amplifier to the computer was supplied by a DAQ board (USB-6009, National Instruments Corporation, USA). The controller then calculates and generates a control signal to control the MRE absorber via a power amplifier. In addition, the LabVIEW based controller was utilized to gather and process the measured signals and provide a control signal for the power amplifier. The workflow of the controller is described in Fig. 12(c). The Short-time Fourier transform (STFT) control algorithm is utilized to convert the vibration information from a time-domain into a frequency-domain format to determine the dominant frequency f max [38,39]. The algorithm of STFT can be explained by following equations [40,41]: The time segment can be calculated by multiplying the signal S(t) by a window function h(t):

Ss ðtÞ ¼ SðtÞhðt  sÞ

ð15Þ

where the t and s are running time and fixed time, respectively. The Fourier transform for the adjusted signal can be obtained as:

1 Ss ðxÞ ¼ pffiffiffiffiffiffiffi 2p

Z

ejxt Sðt Þhðt  sÞdt

ð16Þ

Then, to obtain the frequency distribution in a time domain, the energy density of the modified signal at the fixed time s can be presented as:

2 Z 1 ejxt SðtÞhðt  sÞdt Pðs; xÞ ¼ jSx ðsÞj2 ¼ pffiffiffiffiffiffiffi 2p

ð17Þ

Thus, the instantaneous frequency at the time s is calculated by:

hxis ¼

Z

1 jSðsÞj

2

x

2 jSt ðxÞj dx

ð18Þ

In all the tests, the window length 100 and the sampling frequency 200 Hz. After identifying the dominant frequency, the desired current value for MRE absorber can be calculated by an equation which was obtained from the fitted curve of

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Fig. 12. (a) The schematic diagram of the experimental setup, (b) the experimental setup and (c) The workflow of the controller.

frequency-current relationship. Then, according to the current-signal relationship of the power amplifier, the control signal was output to the power amplifier to adjust the stiffness of the MRE absorber through varying current in real time. Table 6 presents the parameters of the experiment. Two groups of tests were designed using various cutting conditions, such as robot configuration, cutting speed and the depth of cut, to excite mode coupling chatter with two different frequencies. In addition, case 1 in each group was tested under passive control with 0A current as a comparison. Both case 2 in group C and group D were designed to verify the performance of the semi-active system. 4.3.2. Experimental results Based on the setup above, the performance of the MRE absorber with semi-active control system was tested in terms of the chatter occurrence identified from FFT and milled surface quality. It can be seen from Fig. 13 that the MRE absorber under semi-active control manifests a more stable machining process than those with passive control in the same cutting conditions. It demonstrates that mode coupling chatter occurred in the uncontrolled reference cases when the natural frequency Table 6 The experimental setup of group C and D. Robot configuration Joint angle

Axis 1

Axis 2

Axis 3

Axis 4

Axis 5

Axis 6

Group C Group D

14.7° 12.2°

12.5° 58.9°

46.2° 25.2°

100.7° 111.2°

79.9° 52.6°

136.4° 122.2°

Index

Cutting speed (mm/s)

Depth of cut (mm)

Width of cut (mm)

Milling direction

Group C Group D

20 10

3 1

6 6

+X +X

Milling parameters

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Fig. 13. (a) The experimental results of group C and (b) group D.

Table 7 The experimental results of group C and D. Index

Control method

Frequency (Hz)

PSD value

Reduction percentage

Group C

Case 1 Case 2

Passive control system (0A) Semi-active control system

12.22 12.5

14.41 2.033

85.89%

Group D

Case 1 Case 2

Passive control system (0A) Semi-active control system

17.17 18.31

23.41 0.125

99.47%

Fig. 14. The machined surface of (a) case 1 and (b) case 2 in group C.

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of MRE absorber differs from the chatter frequency. As shown in Table 7, compared to the tests under passive control, the PSD value was significantly reduced from 85% in group C to nearly 100% in group D with the employment of the semiactive control system. In addition, group C and group D were proposed to test the performance of the system at different robot configurations, this difference proves that the proposed system can be used to suppress chatter in wider frequency range while the passive strategy cannot. It also reveals the MRE absorber with semi-active control system can reduce the mode coupling chatter arose under different cutting condition effectively. The advantage of this system is not only the remarkable chatter suppression, but also the operation simplicity and low cost. Once the system is set up, it can detect the chatter occurrence and adjust the stiffness of the MRE absorber to match the various chatter frequencies automatically. 4.3.3. Surface quantity investigation Upon evaluating the performance of MRE absorber by FFT based force analyses, the machined surface was photographed to compare the surface accuracy and roughness of the aluminium block. Compared to the finished surface without MRE absorber, a great surface improvement can be observed with the semi-active MRE system. For instance, Fig. 14 enumerates the machined surface of group C Fig. 14 (a) illustrates a very clear 12 Hz chatter marks were observed on the surface of case Table 8 The surface quality investigation. Group

Case

Mean surface deviation (mm)

Relative Improvement

C

1 2 1 2

0.2048 0.1352 0.1625 0.0825

33.98%

D

49.23%

Fig. 15. The PSD value caused by forced vibration (a) without mode coupling chatter, (b) with the mode coupling chatter around 17 Hz and (c) with the mode coupling chatter around 12 Hz.

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1, this can be explained as: the spindle travel speed is 20 mm/s, thus, the 12 Hz frequency chatter implies around 12 ridges can be counted identified in the length of 20 mm. Meanwhile, Fig. 14 (b) shows that the marks were barely observable in case 2. To further investigate the surface improvement by calculating the surface roughness, a series measurements using laser displacement sensor were carried out. The workpiece was placed on the workbench and a laser displacement sensor was attached on the robotic to measure the finished surface. The laser sensor was moved vertically to sweep the machined surface first and the obtained data was transferred to the software (scanCONTROL Configuration tools). Then, the most common one-dimensional roughness parameters Ra (arithmetic average value of filtered roughness profile) was used to evaluate the surface roughness as in (19).

Ra ¼

n 1X jy j n i¼1 i

ð19Þ

where yi is the vertical deviations of the roughness profile from the mean line and n is the number of recorded spots on the surface. Table 8 presents the calculated surface roughness, the negative impact of mode coupling chatter has been suppressed in those cases with proposed chatter absorption system. The surface improvement was confirmed from both visual and statistical approaches in this subsection and thereby the effectiveness of MRE absorber was proven. In addition, there are still visible marks on the workpiece surface in Fig. 14(b), which comes from the forced vibration between the teeth of the milling tool and the workpiece. Fig. 15 plots some results in our experiments with a broader bandwidth. In all three cases, the peak at 40 Hz is the forced vibration from tool tooth clash. Fig. 15 (a) illustrates the original setup with mode coupling chatter occurs at around 17 Hz. Fig. 15 (b) is the same machining condition under control of MRE absorber. It can be seen that the 17 Hz mode coupling chatter is compensated by the MRE, while the forced vibration at 40 Hz remains. Besides, Fig. 15 (c) shows the mode coupling chatter at a different robot pose, the frequency of mode coupling chatter, in this case, is around 12 Hz. So The frequency of forced vibration is always around 40 Hz irrelevant to the occurrence of mode coupling chatter as long as the spindle speed remains the same. The reason we focus on mode coupling chatter rather than other vibration is due to its sever damaging effects from large energy in low frequency large magnitude vibration. When mode coupling chatter happens, the entire robot starts shaking with large magnitude, which causes the damage of the tooling or even the robotic system [31]. 5. Conclusion This paper developed a semi-active chatter reduction method using MREs technology for robotic machining process. Firstly, based on the robot and machining process model analysis, an MRE absorber was designed, fabricated, and tested to cover the chatter frequency ranging 7–20 Hz successfully. Secondly, a series of experiments were conducted to identify the characteristics of the proposed device in actual robotic milling application. The PSD results reveal that if the natural frequency of the MRE absorber matches the target frequency of the robotic milling through adjusting the current value, the chatter would be absorbed by the MRE absorber most effectively. Finally, a semi-active control system was established to trace the chatter occurrence and vary the current for MRE absorber accordingly. The results based on FFT analyse demonstrate a great amount of chatter severity was absorbed with this semi-active control system. 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