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Research on Cutting Force Model of Triangular Blade for Ultrasonic Assisted Cutting Honeycomb Composites
Available online at www.sciencedirect.com
ScienceDirect Procedia CIRP 66 (2017) 159 – 163
1st Cirp Conference on Composite Materials Parts Manufacturing, cirp-ccmpm2017
Research on Cutting Force Model of Triangular Blade for Ultrasonic Assisted Cutting Honeycomb Composites X. P. Hu *, B. H. Yu, X. Y. Li, N. C. Chen Hangzhou Dianzi University, School of Mechanical Engineering, Hanghzou 310018, China * Corresponding author. Tel.:+0086-571-86915141; fax: +0086-571-86915141.E-mail [email protected]
Abstract The triangular blade is a primary tool for ultrasonic assisted cutting honeycomb composites. The machining parameters optimization for cutting force minimization, it is proven important for a better surface quality, higher machining efficiency and lower tool wear to be obtained. Based on the analysis of the ultrasonic assisted cutting of honeycomb composites and the triangular blade movement law, the cutting force theoretical model was established. The relationship between the cutting force and the machining parameters was expressed explicitly. The experiments of blade cutting of honeycomb composites with ultrasonic and non- ultrasonic assistance were executed by the control variable method. The effects of the cutting depth, the blade inclined angle and the deflection angle on the cutting force were verified, which were reflected by the cutting force theoretical model. The theoretical foundation was provided for further optimizing other process parameters during ultrasonic assisted machining, such as both the acoustic and tool structure parameters. ©©2017 Authors. Published by Elsevier B.V. This 2017The The Authors. Published by Elsevier B.V.is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility ofthe scientific committee of the 1st Cirp Conference on Composite Materials Parts Manufacturing. Peer-review under responsibility of the scientific committee of the 1st Cirp Conference on Composite Materials Parts Manufacturing Keywords: Cutting force model; Ultrasonic assisted cutting; Machining parameter; Triangular blade; Honeycomb composite
1. Introduction The honeycomb composite has been widely utilized in aerospace and other fields, due to excellent performance, such as in high specific strength, high specific rigidity, low density, corrosion resistance, impact resistance and good insulating properties. The honeycomb composite is typical hard-tomachining material. It has an axial uniform distribution of the hexagonal prism grid with orthotropic characteristics and the supportive matrix is full of short fibers. During the traditional NC (numerical control) high-speed milling [1], it is proven difficult for the composite to be stably fixed on the machine tool workbench and the milling constitutes a dusty operation. Certain problems during NC high-speed milling are prone to occur onto the machined surface, such as the fiber breakage, the matrix cracking and the grid collapse. These defects and damage highly reduce the mechanical properties of structural parts and consequently both the product safety performance and service lifetime are affected. With an aim towards these problems during high-speed milling, a new processing technology, called ultrasonic
assisted cutting, became apparent in recent years [2]. The problems during the traditional processing were solved to a certain extent. Certain corporations exist producing the NC machine integrated ultrasonic cutting process, such as the GFM, Creno and Dukane. They provide the optimal process solution for certain honeycomb composites. However the process solution varies along with the honeycomb composites of various mechanical properties in general. The manufacturers should understand the mechanism regarding the ultrasonic assisted cutting honeycomb composites in order for this new process to be improved. The cutting force is a most important physical quantity demonstrating the processing state. The cutting force affects the holding state of honeycomb composites, the machining surface quality and the tool life. Certain scholars studied the mechanical properties of honeycomb composites [3, 4] and the behavior impacted by an external force or energy [5, 6]. Liu presented a mechanistic model for the cutting force in RUM (rotary ultrasonic machining) of brittle materials [7]. Schulze determined the machining force for various parameters on the short glass fiber reinforced polyester [8].
2212-8271 © 2017 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the scientific committee of the 1st Cirp Conference on Composite Materials Parts Manufacturing doi:10.1016/j.procir.2017.03.283
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In contrast, any previous literature regarding both the cutting force and the machining parameters selection during the ultrasonic assisted cutting of honeycomb composites, scarcely exist. For lack of scientific theory, the machining parameters selection was generally obtained through a large number of experiments during the actual production, which was of high cost and time-consuming. The establishment of the process resource quickly and accurately is the bottleneck of popularizing this process technology in a wider scope. In this paper, based on the analysis of process technology and tool kinematics of ultrasonic cutting honeycomb composites with a triangular blade, the theoretical model of the ultrasonic assisted cutting force was established. The experiments were designed to be executed about cutting force with ultrasonic and non-ultrasonic assistance. The cutting force theoretical model was well demonstrated based on the experimental records. In addition, the effects of the cutting depth, the deflected angle and the inclined angle on the cutting force were analyzed through the experimental comparison. The research has a high significance on the mechanism of ultrasonic assisted cutting of honeycomb composites deep comprehension and the guide for the reasonable machining parameters selection.
Fig. 1. Ultrasonic assisted cutting of honeycomb composite diagram
Following the attitude proper adjustment, the blade is moved into the honeycomb composite according to the programmed tool path and vibrates simultaneously at the ultrasonic frequency along the corresponding central axis. The former movement is controlled by the NC system, whereas the latter vibration is controlled by an acoustic system. The blade separates the cuttings from the work material of the honeycomb composites under the combination of these two movements.
2.2. Cutting process analysis based on kinematics 2. Ultrasonic assisted cutting process
2.1. Ultrasonic assisted cutting technology with triangular blades The triangular blade is a main tool type for the ultrasonic assisted cutting of honeycomb composites. It is mainly utilized during the rough machining of honeycomb structures, on the blanking and boundary trimming. As shown in Fig.1, in order for the plane P on a honeycomb composite to be machined, the triangular blade is driven according to the following steps. Firstly the blade is rotated at an angle ψ encircling the axis Z’ of tool coordinate system under the NC system control. Consequently, the blade is deflected at an angle α encircling the axis X’ retaining the corresponding neutral surface consistent with the plane P. In order for the honeycomb composite to be stably fixed on the worktable for the machining stability to be ensured, the blade is usually inclined encircling the axis Y’, forming the angle θ between the direction of the advancing speed and the blade central axis.
When the ultrasonic vibration with both the amplitude A and the frequency f affects the blade and the blade moves along the tool path with the speed ve and the inclined angleT, the blade displacement and velocity along the cutting direction are respectively: s
A sin 2πft cos θ vet
v 2πfA cos 2πft cos θ ve
(1)
(2) With various combinations of the cutting speed, the amplitude, the frequency and the inclined angle, two circumstances might exist: x ve t 2S fA cosT The blade speeds to the same direction with the ve throughout cutting, which indicates the blade contact with the work material all the time. It is a continuous cutting process. x ve 2S fA cosT The blade speeds to the opposite direction with the ve in a certain period of the ultrasonic cycle. It was interpreted that the blade gradually disengaged from the work material during this period. The periodic discontinuous cutting process was formed between the blade and the work material in this situation. This contact mode of the tool and the work material was expected during the ultrasonic assisted machining.
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was that it was the damage resistance, which the tool required to overcome in order for the cuttings to be separated from the work material of honeycomb composites. Under nonultrasonic machining, the blade cut the honeycomb composite at a constant speed of ve, whereas the force on the blade was the damage resistance of the honeycomb composite exactly. This was the cutting force with non-ultrasonic assistance. The honeycomb composite could be an equivalent to a continuous orthotropic material. During the interval T, the depth of blade machining honeycomb composite along cutting direction was ve T and the damage resistance to be overcome was: Fig. 2. Tool displacement and velocity in cutting direction
Fig. 2 illustrates the displacement and the velocity of the blade. At the t1 moment, the displacement was the maximum in an ultrasonic cycle and the velocity was 0. It was interpreted that the blade reached at the maximum displacement, which was the maximum depth blade penetration into the work material. From the t1 to the t2 the value of displacement decreased gradually and the velocity was always negative. It was interpreted that the blade disengaged from the maximum cutting depth of the work material and was gradually removed from the work material. At the t2 moment the displacement value changed from a gradual decrease to a gradual increase and the velocity increased gradually from 0. It was interpreted that the blade began to move towards the cutting direction and approximated the work material gradually after the t2 moment. The blade contacted the work material again until the t3, because the displacement at the t3 was equal to that at time t1. From the t3 to the t4, the displacement increased continuously till the t4 momentˈ whereas the velocity increased firstly and consequently decreased to 0. During this time, the blade engaged into cutting again and penetrated the newly he maximum depth until the t4. During an ultrasonic cycle of t1 to t4, the effective blade cutting duration was from t3 to t4, because the blade did not engage the work material from the t1 to the t3. Consequently, the actual cutting distance during an ultrasonic cycle is the following:
s(T )
³
t4
[ A sin(2S ft ) cos T vet ] ve T
(3) Apparently, during the same period of an ultrasonic cycle the blade cutting depth into the work material with ultrasonic assistance, was the same with the non-ultrasonic assistance, which all were the ve T . t1
3. Cutting force model in ultrasonic assisted cutting of honeycomb composites
3.1. The required force to perform cuttings The cutting force is an extrusion force on tool edges during the machining of honeycomb composites [9]. The meaning
W ' S ABCD W '
FL
a ve T p cos(M / 2) cos D
(4)
where, theW' refers to the shear stress of the cut plane on an equivalent solid material, the ap refers to the cutting depth, the Drefers to the deflected angle of the blade neutral surface and the Mrefers to the actual cutting angle.
Fig. 3. Angle on the blade edge
The relationship among the cutting angle M, the blade edge angle Jand the inclined angleTis presented in Fig.3, whereas the following equation could be obtained:
M
J
tan sin T 2 2 Therefore the damage resistance is represented as:
tan
FL
W ' ve T
a p 1 tan 2 (J )sin 2 T 2 cos D
(5)
(6)
3.2. Cutting force model with ultrasonic assistance As aforementioned, during the interval of vibration period T the blade penetration depth into the work material with ultrasonic assistance was the same as that with the nonultrasonic assistance. In order for the cuttings of the width ve T to be formed, the same works were required in these two processing technology types. The cutting force was constant during the cutting with nonultrasonic assistance. Also it was equal to the damage resistance. The work performed by the cutting force was calculated as follows: W FL ve T (7)
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The cutting force was not a constant value during the ultrasonic assisted cutting. In the interval from t1 to t3, the blade did not engage the work material; consequently the force on the work material was zero. In the period of t3 to t4, the blade penetrated the work material with a speed from v t3 up to a maximum and subsequently dropped to 0.
Table 1. HDL-1-1.83-48 mechanical properties L-shear W-shear T-compress material Strength Strength Modulus Strength Modulus (Mpa) (Mpa) (Mpa) (Mpa) (Mpa) HDL-1-1.83-48 1.54 1.07 36 0.58 19
According to the impulse theorem, the extrusion pressure between the blade and the work material was the maximum when the relative velocity between the former reached the highest value. In extremely the average cutting force F during a vibration period was valued with the maximum pressure and it could be calculated by the following: 2 J 2 ve 1 a p 1 tan ( 2 )sin T (8) F W ' ve cos D f A2S f cos T ve Also, the following equation could be obtained further: F F FL
4.2. Experiment on cutting force
W ' ve
2 J 2 A2S f cos T 1 a p 1 tan ( 2 )sin T f cos D A2S f cos T ve
(9)
4. Honeycomb composite cutting experiment
4.1. Experimental platform Fig. 4 presents the developed experimental platform of the honeycomb composite cutting. The ultrasonic system including the energy transducer, the horn and the triangular blade was installed on a specialized clamp jig. Both the inclined and deflected angles could easily be set by the fixed position adjustment. The honeycomb composite utilized in the experiment was the HDL-1-1.83-48, whereas the corresponding mechanical properties are presented in Table 1. It was attached on the Kistler-9257A dynamometer with a double sided adhesive tape. The dynamometer was installed on the workbench of the platform which moved along the Y axis of the platform.
1. Acoustic system 6. Dynoware 2. Clamp jig 7. Charge amplifier 3. Honeycomb composite 8. Data acquisition card 4. Dynamometer 9. Ultrasonic generator 5. Workbench Fig. 4. Experimental platform
According to equation (8), the cutting force with ultrasonic assistance was not only related with the ultrasonic characteristics of amplitude A and frequency f, whereas it was also related to the machining parameters, such as speed, cutting depth, deflected and inclined angles. Additionally, it was associated with the blade structure, such as the blade edge angle. The experiment was designed to focus on the machining parameters effects on the cutting force and the corresponding effects on the cutting force changes under an ultrasonic and a non-ultrasonic assistance. Due to the experimental platform limitation, the blade cutting direction was assumed being along the Y axis and the workbench moved in the speed of approximately 10m/mm. Such parameters as the cutting depth, the deflected angle and the inclined angle were selected as the affecting factors on the cutting force and each factor demonstrates 4 different levels. The experiment was repeated 5 times with each group of machining parameters. The average values were considered as the three components of cutting force. The results of experiment are recorded in Table 2. Table 2. Experimental results of cutting force in honeycomb composite with non-ultrasonic with ultrasonic T ap D (damage resistance) No. (mm) F F'x F'y F'z F' °) °) Fx Fy Fz (N) (N) (N) (N) (N) (N) (N) (N) 1
40
15
15
3.8 15.4 4.8 16.6 1.7
5.1
2.4
5.8
2
40
15
20
4.8 18.8 5.3 20.1 2.4
6.4
2.7
7.2
3
40
15
25
5.6 19.1 5.8 20.7 2.8
7.8
3.2
8.7
4
40
15
30
6.4 20.3 6.5 22.3 3.2
8.3
3.6
9.3
5
80
15
20
4.2 21.2 5.9 22.4 2.1
8.6
3.2
9.2
6
70
15
20
5.1 19.4 5.6 20.8 2.4
6.5
2.7
7.3
7
60
15
20
5.8 18.1 4.7 19.6 2.8
5.9
2.4
6.9
8
50
15
20
6.5 15.4 4.1 17.2 3.6
5.1
1.9
6.5
9
40
9
20
3.5 14.1 3.3 14.9 1.5
5.4
2.1
6
10 40
12
20
4.4 16.9 4.8 18.1 2.1
5.9
2.8
6.7
11 40
15
20
5.2 19.8 5.9 21.3 2.6
6.8
3
7.7
12 40
18
20
7.1 22.5 7.4 24.7 3.4
9.8
3.9 10.7
5. Theoretical verification analysis based on experimentation According to equation (6), the damage resistance of honeycomb composites increases as the cutting depth, declined and inclined angles increase. The cutting depth is proportional to the damage resistance among these three machining parameters; consequently it has the highest damage resistance effect. According to the experimental data, it was
X.P. Hu et al. / Procedia CIRP 66 (2017) 159 – 163
apparent in Fig. 5, as the cutting depth varied from 9mm to 18mm, the damage resistance was almost doubled, which increased from 14.9N to 24.7N.
Fig. 5. Damage resistance changes
When the blade cut the honeycomb composites with the certain machining parameters, the cutting force during the ultrasonic assisted machining must be lower than the force with non-ultrasonic assistance, which could be inferred from equation (9). Therefore, the machining parameters effects on the ultrasonic cutting force were lower than the effects with non-ultrasonic machining. In other words, the cutting force sensitivity on the machining parameters was relatively weakened. According to the experimental data, Fig. 6 illustrated clearly the machining parameters effects on the ultrasonic cutting force and the non-ultrasonic cutting force. As the deflected angle changed, the cutting force changing range with non-ultrasonic assistance was 5.7N, whereas with ultrasonic assistance it was only 3.5N. Regarding the inclined angle, it ranged from 5.2N to 2.7N. Also, the cutting depth ranged from 9.8N to 4.7N.
Fig. 6. Contrast of machining parameters effects on cutting force
As presented in Table 2, the cutting force with ultrasonic assistance apparently decreased in the Y axis direction, which was the cutting direction. The cutting force component in this direction was the main factor for the blade edge to be made blunt. Therefore, it was visible that ultrasonic assisted machining could reduce the tool wear effectively.
6. Conclusions The cutting force theoretical model was established, based on the process technology and blade kinematics analysis during the ultrasonic assisted cutting of honeycomb composites. Also, the theoretical model rationality was verified well by the three machining parameters experimentation on the cutting force. The theoretical basis was provided for both the reasonable selection and optimization of the machining parameters for the ultrasonic assisted cutting of honeycomb composites with various mechanical properties. From the cutting force theoretical model, the ultrasonic vibration parameters had high effects on the ultrasonic cutting force. Further research in this aspect would be of high significance to the acoustic system design in the ultrasonic assisted cutting. The ideal vibration parameter determination of the acoustic system for honeycomb composites with various mechanical properties is regarded as the direction of our further research. Acknowledgements This research is supported by National Nature Science Fund Project of China: Research on Ultrasonic Machining Mechanism and Process Optimization for Aramid Fiber Honeycomb Material (No.51475130). References [1] H. Hocheng, Machining technology for composite materials-principles and practice, Woodhead Publishing Limited; 2012 [2] Florian Feucht, Jens Ketelaer, Alexander Wolff, Masahiko Mori, Makoto Fujishima, Lastest machining technologies of hard-to-cut materials by ultrasonic machined tool, Procedia CIRP 2014; 14: 148 -152 [3] Foo, C.C., G.B. Chai, L.K. Seah. Mechanical properties of Nomex material and Nomex honeycomb structure. Composite structures 2007;80(4): 588-594. [4] Alp Karakoc, Jouni Freund. Experimental studies on mechanical properties of cellular structures using Nomiex honeycomb core. Composite Structure 2012; 94:2017-2024. [5] Castanié, B. et al. Modelling of low-energy/low-velocity impact on Nomex honeycomb sandwich structures with metallic skins. International Journal of Impact Engineering 2008; 35(7): 620-634. [6] Gornet, L., S. Marguet, G. Marckmann. Modeling of Nomex® honeycomb cores, linear and nonlinear behaviors. Mechanics of advanced Materials and structures 2007; 14(8): 589-601. [7] D. F. Liu, W. L. Cong, J. J. Pei, Y. J. Tang. A cutting force model for rotary ultrasonic machining of brittle material. International Journal of Machine Tool & Manufacture 2012; 52:77-84. [8] V. Schulze, C. Bechke, R. Pabst. Specific machining forces and resultant force vectors for machining of reinforced plastics, CIRP Annals – Manufacturing Technology 2011; 60:69-72 [9] Y. W. Zhao, M. Shen, T. Li, H. Wang, Theory Study of Leather Cutting Force and Adsorption Force, Machine Tool ˂ Hydraulics 2012; 40(17):41-43.
163
ScienceDirect Procedia CIRP 66 (2017) 159 – 163
1st Cirp Conference on Composite Materials Parts Manufacturing, cirp-ccmpm2017
Research on Cutting Force Model of Triangular Blade for Ultrasonic Assisted Cutting Honeycomb Composites X. P. Hu *, B. H. Yu, X. Y. Li, N. C. Chen Hangzhou Dianzi University, School of Mechanical Engineering, Hanghzou 310018, China * Corresponding author. Tel.:+0086-571-86915141; fax: +0086-571-86915141.E-mail [email protected]
Abstract The triangular blade is a primary tool for ultrasonic assisted cutting honeycomb composites. The machining parameters optimization for cutting force minimization, it is proven important for a better surface quality, higher machining efficiency and lower tool wear to be obtained. Based on the analysis of the ultrasonic assisted cutting of honeycomb composites and the triangular blade movement law, the cutting force theoretical model was established. The relationship between the cutting force and the machining parameters was expressed explicitly. The experiments of blade cutting of honeycomb composites with ultrasonic and non- ultrasonic assistance were executed by the control variable method. The effects of the cutting depth, the blade inclined angle and the deflection angle on the cutting force were verified, which were reflected by the cutting force theoretical model. The theoretical foundation was provided for further optimizing other process parameters during ultrasonic assisted machining, such as both the acoustic and tool structure parameters. ©©2017 Authors. Published by Elsevier B.V. This 2017The The Authors. Published by Elsevier B.V.is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility ofthe scientific committee of the 1st Cirp Conference on Composite Materials Parts Manufacturing. Peer-review under responsibility of the scientific committee of the 1st Cirp Conference on Composite Materials Parts Manufacturing Keywords: Cutting force model; Ultrasonic assisted cutting; Machining parameter; Triangular blade; Honeycomb composite
1. Introduction The honeycomb composite has been widely utilized in aerospace and other fields, due to excellent performance, such as in high specific strength, high specific rigidity, low density, corrosion resistance, impact resistance and good insulating properties. The honeycomb composite is typical hard-tomachining material. It has an axial uniform distribution of the hexagonal prism grid with orthotropic characteristics and the supportive matrix is full of short fibers. During the traditional NC (numerical control) high-speed milling [1], it is proven difficult for the composite to be stably fixed on the machine tool workbench and the milling constitutes a dusty operation. Certain problems during NC high-speed milling are prone to occur onto the machined surface, such as the fiber breakage, the matrix cracking and the grid collapse. These defects and damage highly reduce the mechanical properties of structural parts and consequently both the product safety performance and service lifetime are affected. With an aim towards these problems during high-speed milling, a new processing technology, called ultrasonic
assisted cutting, became apparent in recent years [2]. The problems during the traditional processing were solved to a certain extent. Certain corporations exist producing the NC machine integrated ultrasonic cutting process, such as the GFM, Creno and Dukane. They provide the optimal process solution for certain honeycomb composites. However the process solution varies along with the honeycomb composites of various mechanical properties in general. The manufacturers should understand the mechanism regarding the ultrasonic assisted cutting honeycomb composites in order for this new process to be improved. The cutting force is a most important physical quantity demonstrating the processing state. The cutting force affects the holding state of honeycomb composites, the machining surface quality and the tool life. Certain scholars studied the mechanical properties of honeycomb composites [3, 4] and the behavior impacted by an external force or energy [5, 6]. Liu presented a mechanistic model for the cutting force in RUM (rotary ultrasonic machining) of brittle materials [7]. Schulze determined the machining force for various parameters on the short glass fiber reinforced polyester [8].
2212-8271 © 2017 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the scientific committee of the 1st Cirp Conference on Composite Materials Parts Manufacturing doi:10.1016/j.procir.2017.03.283
160
X.P. Hu et al. / Procedia CIRP 66 (2017) 159 – 163
In contrast, any previous literature regarding both the cutting force and the machining parameters selection during the ultrasonic assisted cutting of honeycomb composites, scarcely exist. For lack of scientific theory, the machining parameters selection was generally obtained through a large number of experiments during the actual production, which was of high cost and time-consuming. The establishment of the process resource quickly and accurately is the bottleneck of popularizing this process technology in a wider scope. In this paper, based on the analysis of process technology and tool kinematics of ultrasonic cutting honeycomb composites with a triangular blade, the theoretical model of the ultrasonic assisted cutting force was established. The experiments were designed to be executed about cutting force with ultrasonic and non-ultrasonic assistance. The cutting force theoretical model was well demonstrated based on the experimental records. In addition, the effects of the cutting depth, the deflected angle and the inclined angle on the cutting force were analyzed through the experimental comparison. The research has a high significance on the mechanism of ultrasonic assisted cutting of honeycomb composites deep comprehension and the guide for the reasonable machining parameters selection.
Fig. 1. Ultrasonic assisted cutting of honeycomb composite diagram
Following the attitude proper adjustment, the blade is moved into the honeycomb composite according to the programmed tool path and vibrates simultaneously at the ultrasonic frequency along the corresponding central axis. The former movement is controlled by the NC system, whereas the latter vibration is controlled by an acoustic system. The blade separates the cuttings from the work material of the honeycomb composites under the combination of these two movements.
2.2. Cutting process analysis based on kinematics 2. Ultrasonic assisted cutting process
2.1. Ultrasonic assisted cutting technology with triangular blades The triangular blade is a main tool type for the ultrasonic assisted cutting of honeycomb composites. It is mainly utilized during the rough machining of honeycomb structures, on the blanking and boundary trimming. As shown in Fig.1, in order for the plane P on a honeycomb composite to be machined, the triangular blade is driven according to the following steps. Firstly the blade is rotated at an angle ψ encircling the axis Z’ of tool coordinate system under the NC system control. Consequently, the blade is deflected at an angle α encircling the axis X’ retaining the corresponding neutral surface consistent with the plane P. In order for the honeycomb composite to be stably fixed on the worktable for the machining stability to be ensured, the blade is usually inclined encircling the axis Y’, forming the angle θ between the direction of the advancing speed and the blade central axis.
When the ultrasonic vibration with both the amplitude A and the frequency f affects the blade and the blade moves along the tool path with the speed ve and the inclined angleT, the blade displacement and velocity along the cutting direction are respectively: s
A sin 2πft cos θ vet
v 2πfA cos 2πft cos θ ve
(1)
(2) With various combinations of the cutting speed, the amplitude, the frequency and the inclined angle, two circumstances might exist: x ve t 2S fA cosT The blade speeds to the same direction with the ve throughout cutting, which indicates the blade contact with the work material all the time. It is a continuous cutting process. x ve 2S fA cosT The blade speeds to the opposite direction with the ve in a certain period of the ultrasonic cycle. It was interpreted that the blade gradually disengaged from the work material during this period. The periodic discontinuous cutting process was formed between the blade and the work material in this situation. This contact mode of the tool and the work material was expected during the ultrasonic assisted machining.
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was that it was the damage resistance, which the tool required to overcome in order for the cuttings to be separated from the work material of honeycomb composites. Under nonultrasonic machining, the blade cut the honeycomb composite at a constant speed of ve, whereas the force on the blade was the damage resistance of the honeycomb composite exactly. This was the cutting force with non-ultrasonic assistance. The honeycomb composite could be an equivalent to a continuous orthotropic material. During the interval T, the depth of blade machining honeycomb composite along cutting direction was ve T and the damage resistance to be overcome was: Fig. 2. Tool displacement and velocity in cutting direction
Fig. 2 illustrates the displacement and the velocity of the blade. At the t1 moment, the displacement was the maximum in an ultrasonic cycle and the velocity was 0. It was interpreted that the blade reached at the maximum displacement, which was the maximum depth blade penetration into the work material. From the t1 to the t2 the value of displacement decreased gradually and the velocity was always negative. It was interpreted that the blade disengaged from the maximum cutting depth of the work material and was gradually removed from the work material. At the t2 moment the displacement value changed from a gradual decrease to a gradual increase and the velocity increased gradually from 0. It was interpreted that the blade began to move towards the cutting direction and approximated the work material gradually after the t2 moment. The blade contacted the work material again until the t3, because the displacement at the t3 was equal to that at time t1. From the t3 to the t4, the displacement increased continuously till the t4 momentˈ whereas the velocity increased firstly and consequently decreased to 0. During this time, the blade engaged into cutting again and penetrated the newly he maximum depth until the t4. During an ultrasonic cycle of t1 to t4, the effective blade cutting duration was from t3 to t4, because the blade did not engage the work material from the t1 to the t3. Consequently, the actual cutting distance during an ultrasonic cycle is the following:
s(T )
³
t4
[ A sin(2S ft ) cos T vet ] ve T
(3) Apparently, during the same period of an ultrasonic cycle the blade cutting depth into the work material with ultrasonic assistance, was the same with the non-ultrasonic assistance, which all were the ve T . t1
3. Cutting force model in ultrasonic assisted cutting of honeycomb composites
3.1. The required force to perform cuttings The cutting force is an extrusion force on tool edges during the machining of honeycomb composites [9]. The meaning
W ' S ABCD W '
FL
a ve T p cos(M / 2) cos D
(4)
where, theW' refers to the shear stress of the cut plane on an equivalent solid material, the ap refers to the cutting depth, the Drefers to the deflected angle of the blade neutral surface and the Mrefers to the actual cutting angle.
Fig. 3. Angle on the blade edge
The relationship among the cutting angle M, the blade edge angle Jand the inclined angleTis presented in Fig.3, whereas the following equation could be obtained:
M
J
tan sin T 2 2 Therefore the damage resistance is represented as:
tan
FL
W ' ve T
a p 1 tan 2 (J )sin 2 T 2 cos D
(5)
(6)
3.2. Cutting force model with ultrasonic assistance As aforementioned, during the interval of vibration period T the blade penetration depth into the work material with ultrasonic assistance was the same as that with the nonultrasonic assistance. In order for the cuttings of the width ve T to be formed, the same works were required in these two processing technology types. The cutting force was constant during the cutting with nonultrasonic assistance. Also it was equal to the damage resistance. The work performed by the cutting force was calculated as follows: W FL ve T (7)
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The cutting force was not a constant value during the ultrasonic assisted cutting. In the interval from t1 to t3, the blade did not engage the work material; consequently the force on the work material was zero. In the period of t3 to t4, the blade penetrated the work material with a speed from v t3 up to a maximum and subsequently dropped to 0.
Table 1. HDL-1-1.83-48 mechanical properties L-shear W-shear T-compress material Strength Strength Modulus Strength Modulus (Mpa) (Mpa) (Mpa) (Mpa) (Mpa) HDL-1-1.83-48 1.54 1.07 36 0.58 19
According to the impulse theorem, the extrusion pressure between the blade and the work material was the maximum when the relative velocity between the former reached the highest value. In extremely the average cutting force F during a vibration period was valued with the maximum pressure and it could be calculated by the following: 2 J 2 ve 1 a p 1 tan ( 2 )sin T (8) F W ' ve cos D f A2S f cos T ve Also, the following equation could be obtained further: F F FL
4.2. Experiment on cutting force
W ' ve
2 J 2 A2S f cos T 1 a p 1 tan ( 2 )sin T f cos D A2S f cos T ve
(9)
4. Honeycomb composite cutting experiment
4.1. Experimental platform Fig. 4 presents the developed experimental platform of the honeycomb composite cutting. The ultrasonic system including the energy transducer, the horn and the triangular blade was installed on a specialized clamp jig. Both the inclined and deflected angles could easily be set by the fixed position adjustment. The honeycomb composite utilized in the experiment was the HDL-1-1.83-48, whereas the corresponding mechanical properties are presented in Table 1. It was attached on the Kistler-9257A dynamometer with a double sided adhesive tape. The dynamometer was installed on the workbench of the platform which moved along the Y axis of the platform.
1. Acoustic system 6. Dynoware 2. Clamp jig 7. Charge amplifier 3. Honeycomb composite 8. Data acquisition card 4. Dynamometer 9. Ultrasonic generator 5. Workbench Fig. 4. Experimental platform
According to equation (8), the cutting force with ultrasonic assistance was not only related with the ultrasonic characteristics of amplitude A and frequency f, whereas it was also related to the machining parameters, such as speed, cutting depth, deflected and inclined angles. Additionally, it was associated with the blade structure, such as the blade edge angle. The experiment was designed to focus on the machining parameters effects on the cutting force and the corresponding effects on the cutting force changes under an ultrasonic and a non-ultrasonic assistance. Due to the experimental platform limitation, the blade cutting direction was assumed being along the Y axis and the workbench moved in the speed of approximately 10m/mm. Such parameters as the cutting depth, the deflected angle and the inclined angle were selected as the affecting factors on the cutting force and each factor demonstrates 4 different levels. The experiment was repeated 5 times with each group of machining parameters. The average values were considered as the three components of cutting force. The results of experiment are recorded in Table 2. Table 2. Experimental results of cutting force in honeycomb composite with non-ultrasonic with ultrasonic T ap D (damage resistance) No. (mm) F F'x F'y F'z F' °) °) Fx Fy Fz (N) (N) (N) (N) (N) (N) (N) (N) 1
40
15
15
3.8 15.4 4.8 16.6 1.7
5.1
2.4
5.8
2
40
15
20
4.8 18.8 5.3 20.1 2.4
6.4
2.7
7.2
3
40
15
25
5.6 19.1 5.8 20.7 2.8
7.8
3.2
8.7
4
40
15
30
6.4 20.3 6.5 22.3 3.2
8.3
3.6
9.3
5
80
15
20
4.2 21.2 5.9 22.4 2.1
8.6
3.2
9.2
6
70
15
20
5.1 19.4 5.6 20.8 2.4
6.5
2.7
7.3
7
60
15
20
5.8 18.1 4.7 19.6 2.8
5.9
2.4
6.9
8
50
15
20
6.5 15.4 4.1 17.2 3.6
5.1
1.9
6.5
9
40
9
20
3.5 14.1 3.3 14.9 1.5
5.4
2.1
6
10 40
12
20
4.4 16.9 4.8 18.1 2.1
5.9
2.8
6.7
11 40
15
20
5.2 19.8 5.9 21.3 2.6
6.8
3
7.7
12 40
18
20
7.1 22.5 7.4 24.7 3.4
9.8
3.9 10.7
5. Theoretical verification analysis based on experimentation According to equation (6), the damage resistance of honeycomb composites increases as the cutting depth, declined and inclined angles increase. The cutting depth is proportional to the damage resistance among these three machining parameters; consequently it has the highest damage resistance effect. According to the experimental data, it was
X.P. Hu et al. / Procedia CIRP 66 (2017) 159 – 163
apparent in Fig. 5, as the cutting depth varied from 9mm to 18mm, the damage resistance was almost doubled, which increased from 14.9N to 24.7N.
Fig. 5. Damage resistance changes
When the blade cut the honeycomb composites with the certain machining parameters, the cutting force during the ultrasonic assisted machining must be lower than the force with non-ultrasonic assistance, which could be inferred from equation (9). Therefore, the machining parameters effects on the ultrasonic cutting force were lower than the effects with non-ultrasonic machining. In other words, the cutting force sensitivity on the machining parameters was relatively weakened. According to the experimental data, Fig. 6 illustrated clearly the machining parameters effects on the ultrasonic cutting force and the non-ultrasonic cutting force. As the deflected angle changed, the cutting force changing range with non-ultrasonic assistance was 5.7N, whereas with ultrasonic assistance it was only 3.5N. Regarding the inclined angle, it ranged from 5.2N to 2.7N. Also, the cutting depth ranged from 9.8N to 4.7N.
Fig. 6. Contrast of machining parameters effects on cutting force
As presented in Table 2, the cutting force with ultrasonic assistance apparently decreased in the Y axis direction, which was the cutting direction. The cutting force component in this direction was the main factor for the blade edge to be made blunt. Therefore, it was visible that ultrasonic assisted machining could reduce the tool wear effectively.
6. Conclusions The cutting force theoretical model was established, based on the process technology and blade kinematics analysis during the ultrasonic assisted cutting of honeycomb composites. Also, the theoretical model rationality was verified well by the three machining parameters experimentation on the cutting force. The theoretical basis was provided for both the reasonable selection and optimization of the machining parameters for the ultrasonic assisted cutting of honeycomb composites with various mechanical properties. From the cutting force theoretical model, the ultrasonic vibration parameters had high effects on the ultrasonic cutting force. Further research in this aspect would be of high significance to the acoustic system design in the ultrasonic assisted cutting. The ideal vibration parameter determination of the acoustic system for honeycomb composites with various mechanical properties is regarded as the direction of our further research. Acknowledgements This research is supported by National Nature Science Fund Project of China: Research on Ultrasonic Machining Mechanism and Process Optimization for Aramid Fiber Honeycomb Material (No.51475130). References [1] H. Hocheng, Machining technology for composite materials-principles and practice, Woodhead Publishing Limited; 2012 [2] Florian Feucht, Jens Ketelaer, Alexander Wolff, Masahiko Mori, Makoto Fujishima, Lastest machining technologies of hard-to-cut materials by ultrasonic machined tool, Procedia CIRP 2014; 14: 148 -152 [3] Foo, C.C., G.B. Chai, L.K. Seah. Mechanical properties of Nomex material and Nomex honeycomb structure. Composite structures 2007;80(4): 588-594. [4] Alp Karakoc, Jouni Freund. Experimental studies on mechanical properties of cellular structures using Nomiex honeycomb core. Composite Structure 2012; 94:2017-2024. [5] Castanié, B. et al. Modelling of low-energy/low-velocity impact on Nomex honeycomb sandwich structures with metallic skins. International Journal of Impact Engineering 2008; 35(7): 620-634. [6] Gornet, L., S. Marguet, G. Marckmann. Modeling of Nomex® honeycomb cores, linear and nonlinear behaviors. Mechanics of advanced Materials and structures 2007; 14(8): 589-601. [7] D. F. Liu, W. L. Cong, J. J. Pei, Y. J. Tang. A cutting force model for rotary ultrasonic machining of brittle material. International Journal of Machine Tool & Manufacture 2012; 52:77-84. [8] V. Schulze, C. Bechke, R. Pabst. Specific machining forces and resultant force vectors for machining of reinforced plastics, CIRP Annals – Manufacturing Technology 2011; 60:69-72 [9] Y. W. Zhao, M. Shen, T. Li, H. Wang, Theory Study of Leather Cutting Force and Adsorption Force, Machine Tool ˂ Hydraulics 2012; 40(17):41-43.
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