Modeling and numerical simulation of chip formation in high speed machining of titanium alloy Ti6Al4V
Afaque Rafique Memon, Jun Zhang1, Riaz Hussain2
1
State Key Laboratory for manufacturing systems engineering, Xi’an Jiao tong University, Xi’an, Shaanxi, 7100049, China
[email protected] 2
Department of Mechanical Engineering
Mehran University of Engineering and Technology, Jamshoro Sindh Pakistan
Abstract:
This study develops simulation procedure to get extensive awareness into chip development technique for
high speed machining of Ti6Al4V using PCD (Polycrystalline Diamond) cutting tool. The simulation of high speed machining is accomplished with the aid of finite element analysis (FEA), in which the Johnson-Cook (JC) damage evolution model with a displacement failure criterion is adopted. The cutting speeds are selected ranging from 200 m/min to 5,000 m/min, and un-deformed chip thickness is fixed as 0.35 mm. The variables investigated include the temperature of the workpiece and frequency of chips in addition to the cutting force and stress. The results show that both the Temperature and frequency have positive correlations with the cutting speed. An important regularity for the transformation of chip morphology from serrated to unit at a critical cutting speed has been achieved, and the critical value for Ti6Al4V is about 5000 m/min. The research also finds the decrease in cutting force and temperature when the cutting velocity increases, while its fluctuant frequency and amplitude increase sharply and the influences of JC fracture constants (the five constants in J-C fracture model) on chip formation are investigated based on the finite element method.
1 INTRODUCTION With the recent development titanium compounds are exceptionally well known to use in the aviation, biomedical, automobile and petroleum enterprises as a result of their great quality to weight proportion and solid consumption resistance [1]. However, it is extremely hard to machine Ti6Al4V because of poor warm conductivity and high substance reactivity [2]. Siekmann (1955) identified that machining of titanium alloys is difficult, doesn’t matter the technique used to transform this metal into chips. The awful machinability of Ti6Al4V has driven numerous substantial organizations, such as (General Electric and Rolls-Royce) to put a great deal more in making new strategies to diminish machining cost (Ezugwu and Wang. 1997). Due to the unique properties of Ti6Al4V, especially for their poor thermal property, the chips produced are serrated chips even when the cutting speed is very low.
Sun et al. [3] tentatively assessed the dry turning of chip development of Ti6Al4V under various cutting velocities, depth of cut and feed rates. The reason behind the segmented chip development process was high frequency of the cyclic power. This frequency was observed to be corresponding cutting velocity which was inverse to the feed rate. Cotterell and byrne [4] also performed the same investigation using image study of saved video timeline. Umbrello [5] inspected the impact of cutting power, chip segmentation and chip morphology during conventional and rapid machining of Ti6Al4V in which three Johnson-Cook conditions with various arrangements of material constants were enacted. The good result can be accomplished for both (the primary cutting power and chip morphology) if the material parameters for the Johnson-Cook constitutive equation embraced are reasonable. Hosseini and Kazeminezhad [6] implemented a new and advanced constitutive model in FE method to investigate the material behavior during intense deformation. The new model was entirely based on the physical components that can anticipate all phases of stream stress advancement and also can illustrate the effects of strain and strain rate on stream stress advancement of material during serious plastic deformation which can be utilized as a part of simulation of rapid machining. Karpat [7] recommended different temperature-dependent stream softening settings which were evaluated by utilizing FE analysis. The outcomes were justified with the experimental results taken from the writing serves, stream softening started begin around 350-500°C consolidated with suitable softening parameters yields simulation results in good contract with the investigational measurements. The biggest challenge now is to conduct simulation for material like titanium alloys widely used in aerospace industry. Calamaz, et al [8] made a finite element simulation to check the effects of cutting velocity, feed rates and cutting force in the development of segmented chip for titanium alloys. Vijay Sekar, K.S and Kumar, M.P [10] made a simulation of titanium allow with the same models employed by [8] for flow stress model analyzing parameters like the chip morphology, stress, strain, temperature distribution, feed force and cutting force but the specimen was a tube and only the cutting speed was varied and [11] made a 3D thermo-mechanical simulation of milling process of Ti6Al4V alloy to analyze the stress distribution considering speed, feed and depth of cut. The other authors used the speed not more than 3000 m/min which is very less as compared to the velocity used in this research. High speed will reduce the time, material cost, temperature and cutting force when cutting the titanium alloy. In this study we perform modeling and simulation of chip production of titanium alloy with various cutting velocities ranging from 200 m/min to 5000 m/min keeping in mind to examine the situation involved during chip segmentation. 2D numerical model is created then the chip morphology and serrated degree are analyzed through the finite element simulation with different Johnson-Cook fracture constants. In addition, material fracture energy is used to reduce the mesh dependency and accomplish material degradation during cutting process.
2 FINITE ELEMENT METHOD AND MODELING PROCEDURE To enhance physical conception of fragmented chip formation and friction properties during the cutting of titanium alloy Ti6Al4V, the commercial software Abaqus/Explicit was used. Finite element analysis (FEA) is just a new but most useable method in engineering and mathematics. The method has huge application and extensive use in the thermal, structural and industrial analysis areas. The FE method is comprised 3 major phases: (1) pre-processing, (2) solution, and (3) postprocessing. In this paper a two dimensional orthogonal cutting model was established as shown in fig 1. This model was built up by utilizing the (CPE4RT) planar quadrilateral continuum elements, which were reasonable for the coupled
temperature-displacement/explicit analysis. Cutting tool is considered as rigid body and its rake and flank angles are 15° and 10° respectively. The cutting tool edge radius is 0.03mm which is designed to reduce the mesh distortion problem [12]. The cutting velocity V ranges from 200 to 5000 m/min and is parallel to the workpiece as shown in fig 1.
Figure 1. Finite element model for orthogonal cutting including mesh properties
The workpiece is fixed in the bottom for any movement during the cutting process. The thickness of zone A and zone B (uncut chip) was set to 0.35 mm during entire study and 0.1 mm for comparison. To optimize the better outcomes, workpiece geometry is partitioned into three distinct zones. In every zone the mesh has different qualities. The zone A will be a layer which will be evacuated by cutting and zone B, the middle layer of 0.005mm thick. The Zone A and Zone B parts relates to the machined surface as shown in fig 2. The purpose of this mesh setting is to encourage the segmented chip during machining of titanium alloys [13].
Zone A Zone B WORKPIECE
Zone C U1=U2=U3=UR1=UR2=UR3=0
L = 4mm Figure 2. Finite Element model including boundary conditions
2.1 Constitutive model material The constitutive material model of Ti6Al4V follows the JC model as expressed in eq. (1) [14]. 𝑚
̇
𝑛
𝑟 ) ] 𝜎 = [𝐴 + 𝐵𝜀 ] [1 + 𝐶𝑙𝑛 (𝜀𝜀̇ )] [1 − (𝑇𝑇−𝑇 −𝑇 𝑚
0
(1)
𝑟
This provides the acceptable explanation of the ways of metals and alloys since it considers a temperature dependent viscoplasticity, vast strains and high strain rates. The Johnson-Cook material parameters of the workpiece of Ti6Al4V can be found in table 1 [15], and the constants for J-C model for Ti6Al4V is given in table: 2 [16].
Table1. Johnson Cook parameters of Ti6Al4V [15] A (MPa)
B (MPa)
n
C
m
950
331
0.387
1.1
0.02
2.2 Chip separation criterion For various programming and materials, the constitutive model way with element damage is different. According to the classical cumulative damage law, the fracture model is established and expressed by eq. (2), in which the JC fracture model has been developed [17]. 𝑤=∑
∆𝜀
(2)
𝜀𝑓
̇
𝑟 ] 𝜀𝑓 = [𝐷1 + 𝐷2 𝑒𝑥𝑝(𝐷3 𝑃𝜎)] [1 + 𝐷4 𝑙𝑛 𝜀𝜀̇ ] [1 + 𝐷5 𝑇𝑇−𝑇 𝑚 −𝑇𝑟
(3)
0
Where P is the average of three normal stresses. The ratio 𝑃𝜎 is reffered to as sress triaxiality. The parameters𝐷1 , 𝐷2 , 𝐷3 , 𝐷4 , and 𝐷5 are experimental data from (table 2).
Table 2. The constants for Johnson Cook material model for Ti6Al4V [16] D1
D2
D3
D4
D5
-0.09
0.25
-0.5
0.014
3.87
To simulate the damage evolution during high speed machining, an energy failure criterion is used in this research [18].
3. FINITE ELEMENT SIMULATION RESULT The chip development morphologies with high cutting speeds ranging from 200 to 5000 m/min is shown in fig 3, in which the distributions of equivalent plastic strain (PEEQ) can also be seen. As the cutting velocity increases, the chip serration is increased until the chip morphology evolving to unit at the cutting speed of 5,000 m/min. It can be seen that the highest strain in the PEEQ distributions decreases from 5.920 to 3.102 with the increase of cutting speed from 200 to 5000 m/min. From fig.3. it can also be noticed that at the speed of 200 m/min the plastic strain is more serious, as the speed increases the material becomes more brittle and cause the discontinuous chips. The mechanism to this result is that the material property changes from plastic to brittle under higher cutting speed [19]. This mechanism also explains why the chip evolves from continuous to serrate until it is fractured completely.
Figure 3. Variation in chip segments under different cutting speeds
Fig.4 shows the speed and temperature graph, which explains that increasing of the cutting speed from 200 to 5000 m/min cause the decrease in temperature from 1173 °C to 1045 °C due to the segmented chip at maximum speed. It can be seen that the fluctuation occurs due to the cyclic generation of the shear band in the serrated chips during high speed machining.
Figure 4. Cutting Temperature during high speed cutting on different cutting velocities The average cutting force variation under different cutting velocities has been analyzed as shown in fig.5. It can be deduced that the cutting force decreases with the increase of cutting speed. It is a good advantage of decreasing the cutting force in high speed machining when the cutting speed is high.
Fig.5. Average cutting force under various cutting speeds
3.1 comparison with other researchers The numerical results obtained from simulation in this research and compared with experimental results gathered from [20]. Fig.6 shows that the experimental cutting force is higher than the simulation results. Wang [20] used the cutting speed up to 3000 m/min and un-deformed chip thickness 0.1 mm. To validate the result, simulation were designed based on 0.1 mm undeformed chip thickness and speed up to 3000 m/min. In this research the maximum cutting speed of 5000 m/min is used to observe the cutting force. By comparing both results up to 3000 m/min. It is observed that the experimental cutting force is higher than that of simulation cutting force, the main reason is that the cutting tool has some radius on its edge in the simulation process where as the sharp edge tip cutting tool were used in the experiment.
Average cutting force (N)
Cutting Speed (m/min) Figure 6, Comparison cutting force under different cutting speeds [20]
4. CONCLUSION It has been seen that the machining is an important and complex process still in development; the machining simulation provides better understanding and help the industries and universities to find a proper state of the phenomena involved. Among all the morphology of chip and the effect of cutting parameters were observed. Some concluding’s are: The increasing of cutting speed cause the chip serrated degree increases until it tends to one in which the chip is become fragmented. For the orthogonal cutting process of titanium alloys the critical turning point of chip from serrated to segment is near 5000 m/min. The serrated chip frequency has positive connection with the cutting speed. When the chip morphology becomes unity, the serrated frequency could not be used to describe the geometric characteristic of chip.
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