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Investigations of ultrasonic frequency effects on surface deformation in rotary ultrasonic roller burnishing Ti-6Al-4V
Investigations of ultrasonic frequency effects on surface deformation in rotary ultrasonic roller burnishing Ti-6Al-4V Jian Zhao, Zhanqiang Liu PII: DOI: Reference:
S0264-1275(16)30775-4 doi: 10.1016/j.matdes.2016.06.024 JMADE 1899
To appear in: Received date: Revised date: Accepted date:
20 April 2016 26 May 2016 7 June 2016
Please cite this article as: Jian Zhao, Zhanqiang Liu, Investigations of ultrasonic frequency effects on surface deformation in rotary ultrasonic roller burnishing Ti-6Al-4V, (2016), doi: 10.1016/j.matdes.2016.06.024
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ACCEPTED MANUSCRIPT Investigations of ultrasonic frequency effects on surface
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School of Mechanical Engineering, Shandong University, Jinan 250061, China
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Jian Zhao a,b, Zhanqiang Liu a,b,*
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deformation in rotary ultrasonic roller burnishing Ti-6Al-4V
Key Laboratory of High Efficiency and Clean Mechanical Manufacture, Ministry of Education, Shandong University, China
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*Corresponding author, Telephone: 86-531-88393206, Fax: 86-531-88392045 [email protected]
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Abstract
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Roller burnishing can be applied for surface quality improvement without chip generation in machining processes. A rotary roller burnishing assisted with ultrasonic vibration machining technology has been developed. The present work aims to investigate mechanism of deformation for the machined surface layer material under different vibration frequencies. Firstly, an analysis model and 2D finite element simulation model of rotary roller burnishing process with and without ultrasonic vibration were established. Secondly, the area of material happened plastic flow and the displacements of material at the free surface were analyzed. Thirdly, von Mises stress of being deformed material under different frequencies were presented. The residual stress on the free surface are discussed and the simulation result has a good agreement with experimental result. The micro-hardness at the machined surface are measured. The result shows that ultrasonic vibration can decrease the flow stress of material deformation. Finally, the effect of ultrasonic softening and ultrasonic enhancement with the variable vibration frequencies are discussed. The material deformation experiences a process from ultrasonic softening to ultrasonic enhancement in rotary ultrasonic roller burnishing compared to the material deformation in conventional rotary roller burnishing.
Key words: rotary ultrasonic roller burnishing; vibration frequency; plastic deformation; surface enhancement
1 Introduction Titanium alloys are famous for several inherent properties of material including high strength, high specific strength, and high thermal strength. They have been widely applied to engine compressor parts, structural parts of rockets and aircrafts [1-3]. However, with large chemical activity and low elastic modulus, titanium alloys are one of the typical difficult-to-machine materials.
ACCEPTED MANUSCRIPT Surface quality of material is an important factor in determining its service life. Severe plastic deformation without chip based on material plastic flow is being increasingly concerned to improve surface integrity. Especially, the application of relevant machining processes has been the subject of most studies in the field of aviation, automobile and military [4-6].
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Ultrasonic burnishing is an attractive finishing technique, which can obtain an increase in strength and hardness as well as a reduction in surface roughness. Ultrasonic burnishing superimposes 20 kHz to 30 kHz vibration-impacts on conventional burnishing process. Assistance of ultrasonic vibration in machining can reduce the burnishing force and improves tool life. Ultrasonic burnishing has a benefit in machining difficult-to-machine metal alloys [7-9], such as titanium alloys and Inconel alloys [10]. The effects of ultrasonic burnishing parameters on mechanical behaviors including residual stress, surface roughness, and micro-hardness of machined materials have been experimentally researched [7, 9, 11, 12]. The ultrasonic vibration helps to strengthen material through severe plastic deformation.
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Atanasiu [13] developed a quantitative computing formulas on the changes of parameters for metal materials during ultrasonic forming process. He described the stress-strain behavior with the rigid-viscoplastic model in the strong ultrasonic field. The research result of Atanasiu indicated that the yield strength of forming materials decreased exponentially with the increasing of ultrasonic strength. He had also researched on the influence of ultrasonic vibration on the friction coefficient between formed material and die. A simulation of deformation for single crystals with ultrasonic treatment was proposed by Blagoveshchenskii et al [14]. They found that the effect of the ultrasonic frequency on the deformation of a crystalline material is maximal. The reason is the fact that the time of formation of a closed loop coincides with the period of ultrasonic vibrations. Yang [11] studied the influence of superimposed ultrasonic vibration on surface asperities deformation and drew a conclusion that deformation of metal foil surface was approximately linear to the superimposed ultrasonic vibration amplitude and initial static stress. It was found that the sample dimensions had an influence on the ultrasonic softening effect. The ultrasonic softening effect was closely related to the ratio of the number of surface layer grains and total grains in the micro scale. Biswas and Alavi [15] investigated laser surface melting of Ti-6Al-4V alloy under the influence of ultrasonic vibration (20 kHz). It had been observed that the phenomenon of material refinement was due to the enhanced material plastic flow and cavitation caused by ultrasonic vibration. Patil et al [2] proposed a 2D finite element transient simulation method to study the effect of ultrasonic vibrations on machining. The results showed that the cutting force had a reduction in ultrasonic assisted turning over that in continuous turning. A decrease in cutting force by 17% was observed with the amplitude of vibration increasing from 10 μm to 20 μm. The average effective strain had 27% reduction during in ultrasonic assisted cutting as compared with that in continuous cutting. The reduction of effective strain leads to lesser strain hardening in ultrasonic assisted cutting, which results in the decreasing of cutting force. Bozdana [12] found that the ultrasonic vibration can reduce rolling force in the deep cold rolling. Shalvandi et.al [16] have a research on the stress relieving phenomenon based on ultrasonic vibration. The result shows that the amount of stress reduction is proportional to the ultrasonic intensity. The results of these researches shows that there is an acoustic softening to material deformation in ultrasonic vibration machining process. In this paper, the plastic flow of material in the surface layer will be analyzed in rotary
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ultrasonic roller burnishing. A theoretical model and a 2D finite element simulation model of plastic deformation are proposed. For verifying the accuracy of simulation model, experimental burnishing forces are compared with the simulated ones. The displacements of material in the free surface are discussed. Von Mises stresses are analyzed under different ultrasonic vibration frequencies. The effect of ultrasonic vibration is investigated. The general framework of this paper is shown in Fig. 1.
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Confirm research purpose Mechanism of material deformation in RURB Confirm variable
Simulation model
Theoretical model
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Experiment (CRRB and RURB)
Analysis of material property during machining process
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Analysis of material property after machining
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Ultrasonic frequency
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Research object: σr and HV
Research object: σm
Research object: Ac, Au, U1, U2
Summary the mechanism of material deformation in RURB
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Fig.1. General framework of this paper.
2 Experiments 2.1 Experimental equipment and material Milling test as a pretreatment was conducted on DAEWOOACE-V500 CNC-vertical machining center. Then, conventional rotary roller burnishing (CRRB) and rotary ultrasonic roller burnishing (RURB) processes were carried out on the same machine tool, respectively. A rotary ultrasonic burnishing tool was attached on the tool holder, which was connected with ultrasonic generator by a lead-electricity device. The non-contact lead-electricity device was used to realize the rotary ultrasonic machining. The workpiece was mounted on a dynamometer through a fixture. The dynamometer was clamped on the machine tool bed. The experimental setup is shown in Fig. 2 (a).
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Table 1 Mechanical properties of Ti-6Al-4V at room temperature.
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The flat-based burnishing tool with four rollers was employed. The structure and dimension of burnishing tool are shown in Fig.2 (b). The rollers were made of steel. The hardness of roller was 60 HRC. The diameter and length of roller were 4 mm and 10 mm, respectively. The accessible maximum burnishing depth of the burnishing tool was 0.4 mm. Ti-6Al-4V was chosen as workpiece material, whose mechanical properties was shown in Table 1.
Strength factor (MPa)
Tensile strength (MPa)
Surface hardness (HRC)
Hardening exponent
897
331
993-973
33-35
0.34
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workpiece fixture
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Yield stress (MPa)
Fig. 2. RURB experimental setup (a) and burnishing tool (b).
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2.2 Experimental procedures and measurements Firstly, the selected free surfaces of six groups of workpieces were milled in the pretreatment process. Each group had five samples to make sure the accurate of experimental results. The mean value of five measured results was taken as the final test result in one group of experiment. The dimensions of all samples were 40 mm×60 mm×35 mm uniformly. The milled free surfaces of five groups of workpieces were treated with RURB process. The rest group of workpiece was machined with CRRB process. The setting of relevant experimental parameters was listed in Table 2. Fig. 3 showed the movement of burnishing tool on the free surface of material. The movement of burnishing tool was a compound behavior including three independent movements. These movements included a rotary motion around spindle, a straight motion along the direction of feed, and a periodic vibration along spindle direction. v
burnished region roller
w
unburnished region milled area z y workpiece x
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Table 2
Feed
Cutting depth
Spindle speed
Amplitude of vibration
milling CRRB
\ \ 20 kHz 22 kHz 24 kHz 26 kHz 28 kHz
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50 mm/min 50 mm/min
0.1 mm 0.1 mm
500 r/min 500 r/min
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50 mm/min
0.1 mm
500 r/min
10 um
RURB
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Direction of vibration
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Machining
Frequency of vibration
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Pretreatment
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Experimental parameters.
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LK-G30 Laser displacement sensor was applied to measure the vibration of burnishing tool during the RURB process. Z-axis positioner was used to make sure the accurate of cutting depth in the experiment. The burnishing forces were measured by using the Kistler piezoelectric dynamometer (type 9129AA). The residual stress on the free surface was measured by the blind hole method. The measurement of micro-hardness on the free surface was accomplished in the nano-indentor.
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3 Finite element modeling
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The finite element modeling is developed to research the deformation behavior of material in the contact area between roller and workpiece material. Considering the periodic characteristic of ultrasonic vibration, the deformation behavior in one period is analyzed. The total simulation time for 3D RURB finite element model (FEM) will be too much and the essential operation is very little compared with the operation of the total model. The applied force imposed on the burnishing tool is uniform. Therefore, a 2D plastic strain FEM is preferable to analyze the behavior of material deformation in this work. The material deformation in burnishing process is a nonlinear problem. Abaqus software has the advantages of the solution of nonlinear problem. With the application of intelligent solver, it is easier in solving the nonlinear problem of converge. The Abaqus/Explicit module was chosen in this work. The diagonal mass element matrices and explicit integration rule were utilized to achieve the computational accuracy and efficiency [17].
3.1 Geometry, interactions and boundary conditions The burnishing roller was replaced by a semicircle plane of radius R=2 mm, which was considered as a rigid body. A rectangle was set as the workpiece. The top surface of workpiece was defined as free surface. The experimental burnishing depth was 0.1mm and the real contact length between roller and workpiece was 1.25 mm. The dimension of workpiece was 4 mm×1 mm. The schematic of the finite element model was shown in Fig. 4.
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The contact type between roller and workpiece is surface to surface contact (explicit). The mechanical constraint formulation was kinematic contact method. The friction coefficient of milled surface of workpiece was measured on UMT-2 tribometer with a ball-on-plate configuration at room temperature. The test mode of friction coefficient was set as linear reciprocating motion, which is similar with the motion of ultrasonic surface rolling process. The friction tests were conducted at a normal load of 10 N and sliding speed of 10 mm/s. The materials of ball and plate were 45 steel and Ti-6Al-4V, respectively. The friction coefficient between ball and plate were measured as ranging from 0.1 to 0.3. Considering the coexistence of rolling friction and sliding friction in rotary roller burnishing process, the friction coefficient was determined as 0.15 which was the mean value for the friction test results.
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The minimum critical value of ultrasonic vibration frequency is 20 kHz, which is 240 times larger than spindle speed 500r/min in the experiment. Therefore, the spindle speed can be ignored. To simulate the material deformation process in one period of time, three steps were combined. These steps were loading step, moving step and unloading step, respectively. The sampling frequency of output data was one fifth than ultrasonic vibration frequency. In addition to the top surface, displacements perpendicular to the boundaries were prohibited for other surfaces of workpiece. There was no constraint on the top surface. RP
Roller
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3.2 Material properties and meshing The mechanical properties of Ti-6Al-4V applied in the FEM were provided by the manufacturer. Young’s modulus was 110 GPa, Poisson’s ratio was 0.31, and Mass density was 4.43E-09. J-C model was applied to depict the material constitutive relation, which has been widely used to analyze the variation of material flow stress in large strain and large strain rate deformation process. The expression of J-C constitutive relation is given in equation (1). m T Tr = A+B 1 C ln 1 Tm Tr 0 n
(1)
ACCEPTED MANUSCRIPT where A is the yield strength of material, B is hardening modulus, C is strain rate sensitivity coefficient, n is hardening coefficient, m is thermal softening, ε is true stress,
is reference shear
is true strain rate, Tm is melt temperature, Tr is room temperature and T is working
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temperature. The values of relevant coefficients are shown in Table 3. Table 3 B/MPa 656
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Relevant coefficients in J-C model.
A/MPa 907
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strain rate,
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m 0.8
ε0 1
Tm /°C 1933
Tr /°C 20
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Suitable meshing is crucial to the accuracy of simulation result. We took the method of local mesh refinement at the workpiece material as shown in Fig. 4. It can be seen that double bias seed type mesh in the top and bottom edge of workpiece material was used. The seed type of two side edges was single bias. Four-nodal quadrilateral elements (type CPS4R) were used in the workpiece, while three-nodal triangular elements were used in the roller. The FE model consisted of 1471nodes and 1351elements.
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4.1 General assumptions
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4 Theoretical analysis
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Ultrasonic burnishing strengthens surface materials with cold working. In the surface deformation layer, the percentage of plastic deformation is much larger than that of elastic deformation. The analysis of the process of material plastic deformation is priority and the phenomenon of material elastic deformation is ignored for simplicity. The friction condition is not considered and the volume of machined material is assumed invariable. The material plastic deformation only exists in the processing area, which means little material flow toward the unmachined area. The type of ultrasonic vibration is simplified as a simple harmonic motion along one direction based on the experimental research as shown in Fig. 5.
(U,I)
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roller
z(t) Fig. 5. Harmonic vibration model.
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Ar1
af1
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coordinate system
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ap2
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Ar4
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The mode of motion of materials in the free surface is plastic flow in rotary ultrasonic roller burnishing (RURB) process. The plastic flow of materials is one basic reason to improve surface mechanical properties. Fig. 6 is a schematic illustration of materials plastic flow in the free surface. The top model and the bottom model in Fig. 6 can be used to explain the material plastic flow process without and with ultrasonic vibration-assisted, respectively. The dashed curve and the solid curve represent the beginning position and the final position of roller, respectively. The thick solid line means the free surface of workpiece. On account of the periodicity of ultrasonic vibration, the plastic flow of materials in a period of ultrasonic vibration is chosen to be analyzed. In order to compare materials plastic flow exactly, burnishing depth h takes the same value in both machining processes.
Au
F
A
G C
B
Au3
D Au5 A E C D E
Au4 H
h
workpiece B
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Fig. 6. Material plastic flow with and without ultrasonic vibration.
In the conventional rotary roller burnishing (CRRB) process, workpiece is stationary, while, roller feeds right-forward at a rate of vf, which is rotated at a unfixable rotational speed of ω, as shown in the top one of Fig. 6. In a period time of ultrasonic vibration, roller moves from point A to point B and only Ar3 zone happens materials plastic flow in this process. The materials of Ar3 zone flows to Ar2 and Ar4 zones. The materials in Ar4 zone exist in a way like built-up edge, which is very few compared with the materials in Ar2 zone. A coordinate system has been set, in which x-axis is located at the workpiece surface and y-axis goes through point D as shown in Fig. 6. According to the constant volume assumption, areas of these zones can be solved by integral method with equations (2), (3), and (4), respectively. A r1 A r 4
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dz
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dx
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R 2 z R h 1 AB 2 2 R 2 z R h 1 AB 2 2
dz
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A r 3 dz
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h
R 2 z R h 1 AB 2 2 R 2 z R h 1 AB 2
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dx
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Ar 2
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where ap1 is the dimensional change between unfinished surface and finished surface in rotary roller burnishing, af1 is the depth of plastic flow of material (ap1+ af1=h), R is the radius of roller, h means burnishing depth determined by experiment, |AB| is the distance that roller moves in a period time of ultrasonic vibration. |AB| can be calculated by equations (5) and (6) with the coordinate system in Fig. 7.
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Fig. 7. Linear velocity of roller.
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where v is burnishing velocity, vf is feed velocity, vs is linear velocity of spindle rotation, f is ultrasonic frequency, ws is angular velocity of spindle rotation, l is the length of roller, θ is the angle between the axis of roller and feed direction. In the rotary ultrasonic roller burnishing (RURB) process, roller moves through five points A、 C、D、E、and B in a sinusoidal trajectory. With the amplitude of ultrasonic vibration Av, the depth of materials plastic flow layer will increase, as seen in the bottom model of Fig.6. The material in Au5 zone is an extra part that happened plastic flow compare to conventional rotary roller burnishing process. Materials plastic flow in RURB can be expressed as equations (7) - (13).
A u 4 A u1
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ap 2
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R h A v R2 x 1 AB 4
xG
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dz dx
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R h A v R2 x 1 AB 4
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xF
R h R 2 x 1 AB 2
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dx
AB 4 R 2 Av2 3 AB A v 2
(9)
xH
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xG
R h A v R 2 x 1 AB 4
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Au 5 dx
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h
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(11)
(12)
x H R 2 Av R h 1 AB 4
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where ap2 is the dimensional change between unfinished surface and finished surface in rotary ultrasonic roller burnishing, af2 is the depth of plastic flow of material and ai is an increased depth of material plastic flow compared to conventional rotary roller burnishing process (ap2+ af2- ai =h and ai=Av), respectively. Where xF、xG、xH are abscissas of three points F、G、H, respectively.
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Material plastic flow rate of change η is introduced in equation (14) to have a further analysis to the effect of ultrasonic vibration on material plastic flow.
=
A u5 Au 3 Ar 3
(14)
5 Discussion 5.1 Area of plastic flow of material Experimental parameters in Table 2 are substituted into equations (1) to (14), then the area of plastic flow of material can be calculated. Fig. 8 shows the theoretical calculated area of plastic flow of material at different frequencies in RURB processes. The variation of these values appears full sine waves in the range of 360 degree. It is due to that circumferential velocity changes with the variation of θ from 0 to 360 degree as shown in Fig. 7. It can be seen that the mean value of Au3 (Ar3) decreases with the increase of ultrasonic vibration frequency. The reason is that the value of Au3 (Ar3)
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is decided by feed rate and the movement time of roller. Therefore, the vibration cycle decreases with the increase of vibration frequency. However, the mean value of Au5 increases with the increase of ultrasonic vibration frequency in Fig. 9. It is a result of the concerted action of ultrasonic vibration and feed rate. Ultrasonic vibration frequency has a more effect on Au5. Au5 is the increased area of plastic flow of material caused by ultrasonic vibration. Compared Fig. 8 with Fig. 9, the mean value of Au5 is larger than the value of Au3 (Ar3). The result can also be found in Fig. 12.
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Fig. 8. Au3 of plastic flow of material with different frequencies RURB and Ar3 in CRRB (Au3= Ar3).
Fig. 9. Au5 of increased plastic flow of material with different frequencies RURB.
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Fig. 10. Area of plastic flow of material (Au5+Au3) with different frequencies RURB.
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As shown in Fig. 10, the area of plastic flow of material changes in CRRB and RURB process, in which θ changes periodically. In the frequency range of 22 kHz to 28 kHz, the maximum value of the area of plastic flow of material occurs when θ=270°. While, the minimum value of it occurs when θ=90°. However, the results of ones are opposite completely under 20 kHz ultrasonic vibration. It is because that the area of plastic flow of material is subject to feed rate, too. Ultrasonic frequency has little effect on the depth of plastic flow layer of material. Because the change of ultrasonic frequency could not influence the burnishing depth. The burnishing depth is the main reason that influences the depth of plastic flow layer of material. But the ultrasonic frequency can increase the area of plastic flow of material at unit time, which would have a significant effect on grain refinement in the surface layer. It is because that the change of plastic flow of material at unit time has an effect on the material flow stress. The flow stress of material has an interaction with the property of surface layer grains based on the surface grain theory [18]. The dislocation tangling and pile-ups in the surface grains are fewer, hence the slip system movement is easier compared with the inner grains which reduces the deformation resistance of the material [11].
Fig. 11. Selection of path for surface deformation in FEM.
A path was established to analyze the free surface deformation of workpiece in FEM as shown
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In Fig. 12, the red lines show the rate of change η of plastic flow of material under different ultrasonic vibration frequencies comparing the ones in CRRB. The red solid line represents theoretical calculated values and the red dotted line represents simulation values. It can be seen that the assistance of ultrasonic vibration increases the area of plastic flow of material, which would cause the increase of the influence depth of residual compressive stress and grain refinement [13], which is the same as the effect of the change of burnishing depth. The maximum value that obtained under 28 kHz frequency is 7.67 times than the one in CRRB. There is an average 4.1% deviation between theoretical values and simulation values. It is within the allowable range. The friction between roller and workpiece is the main reason caused the deviation.
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The black lines show the area of plastic flow of material during one vibration cycle in RURB (θ=90°). The time of vibration cycle decreases with the increase of vibration frequency. However, the area of plastic flow of material is first decreased and then increased with the time of vibration cycle decreasing. So, it is obvious that the increase of ultrasonic vibration frequency can increase the area of plastic flow of material during the same time in RURB process.
Fig. 12. Rate of change and total area of plastic flow of material with different frequencies in RURB (θ=90°).
5.2 U1 and U2 displacements of material at free surface U1 is the displacement of material along the direction of feed. U1 in one ultrasonic vibration cycle in the load step was selected to analyze the deformation of material. Fig. 13 shows the U1 displacement of the material in the free surface in CRRB, while Fig. 14 to Fig. 18 show the one under different vibration frequencies in RURB. In Fig. 13, the direction of U1 of material in the free surface does not have variation during one vibration cycle. It means that the machined material in the free surface is subject to extrude from zero point to both sides throughout during one vibration cycle. The position of zero point of horizontal axis means the first contact point between roller and material, which is the point contacted the bottom of roller. However, with the assistance of ultrasonic vibration, both the direction and amplitude of U1 change during one vibration cycle as
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shown in Fig. 14 to Fig. 18. It can been seen that the U1 of material are central symmetric curves in Fig. 14 to Fig. 18. The U1 of material can be divided to two section. The material in the zone close to zero point are subject to extrusion to zero point, however, the material in the zone far from zero point are subject to extrusion to both sides. Compared the value of U1, it can be found that the maximum value appear when the load step time are 1/4 T or 3/4 T. Because the roller reached the maximum displacement position in the Z coordinate direction.
Fig. 14. Variation of U1 during one vibration cycle in RURB (20 kHz).
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Fig. 13. Variation of U1 during one vibration cycle in CRRB.
Fig. 15. Variation of U1 during one vibration cycle in RURB (22 kHz).
Fig. 16. Variation of U1 during one vibration cycle in RURB (24 kHz).
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Fig. 18. Variation of U1 during one vibration cycle in RURB (28 kHz).
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Fig. 17. Variation of U1 during one vibration cycle in RURB (26 kHz).
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Fig. 19. Comparison of U1 in one ultrasonic vibration cycle.
In Fig. 19, the black solid line represents the percent of deformation zone close to zero point in total deformation zone. The red dotted line represents the maximum of U1 during one ultrasonic vibration cycle under different frequencies. With the increase of ultrasonic frequency, the percent has a little decrease, except the one in 26 kHz. The percent in 26 kHz has a large decrease compared with the ones under other frequencies. The reason may be related to the nature of material. The maximum of U1 has a similar sinusoidal change with the increase of ultrasonic frequency. The range of change is 0.1 μm. The U2 displacement of material in the free surface during one vibration cycle in the load step is shown in Fig. 20 (CRRB) and Fig. 21 (20 kHz). The variation of U2 under ultrasonic frequencies are the same as each other because of the same of ultrasonic amplitude, so we chose the variation of U2 in 20 kHz as the case sample in Fig. 21. In Fig.20, the variation of U2 during one ultrasonic vibration is very small, which means that the U2 is continuously variable in CRRB. It means that the roller and workpiece always contact each other during the machining process. While, the variation of U2 is larger in Fig. 21, which means separation phenomenon happens between roller
ACCEPTED MANUSCRIPT and workpiece in RURB because of the assistance of ultrasonic vibration. When the load step time is 5E-5, the maximum values of U2 are 10.5 μm and 13.36 μm in CRRB and RURB process, respectively. This different value is the result of ultrasonic amplitude and elastic recovery of material.
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The displacement of material has a great effect on the strain rate of material in the deformation zone [19], especially the variation of U1, which will influence the yield strength of material in this zone. It may be the reason that causes the variation of burnishing force in RURB compared with the one in CRRB.
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Fig. 20. Variation of U2 during one vibration cycle in CRRB.
Fig. 21. Variation of U2 during one vibration cycle in RURB (20 kHz).
5.3 Analysis of stress behavior in CRRB and RURB process
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The assistance of vibration with appropriate ultrasonic strength can decrease burnishing force in RURB. The main burnishing force is the acting force component along the Z coordinate direction just as shown in Table 4. It means that ultrasonic vibration may has an effect on the deformation of material. In order to analysis the deformation of material under ultrasonic vibration, the state of von Mises stress at a point in the free surface is discussed. The chosen point is the first contact point between roller and material. The analysis stage of time begins in loading and ends in the time of the first contact point appearing yield in the first time, which is based on the deformation of material in CRRB. Fig. 22 to Fig. 26 show the variation of von Mises stress with load step time under different ultrasonic frequencies. The black dotted line means the real law of von Mises stress. It can be found that the variation of von Mises stress appears similar sine wave. The red solid line is a fitting curve. With ultrasonic frequency increases, the mean values of von Mises stress in the steady stage are 776.51 MPa, 806.81 MPa, 821.72 MPa, 851.83 MPa and 861.94 MPa, respectively, which are lower than the yield strength of the material Ti-6Al-4V. However, the mean value of von Mises stress is 889.07 MPa in CRRB in Fig. 27. The decrease of mean von Mises stress values in RURB are shown in Fig. 28 as compared to the one in CRRB. The mean value of von Mises stress increases with the increase of ultrasonic vibration frequency. The result indicates that appropriate ultrasonic vibration can decrease the yield stress of being deformed material, which agrees with the ultrasonic softening raised by Nicolae Atanasiu [6]. The result also has a good agreement with the variation of
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Measurements of burnishing force.
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261.57
168.52
197.43
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Fig. 23. Von Mises stress of the first contact point in 22 kHz RURB.
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Fig. 22. Von Mises stress of the first contact point in 20 kHz RURB.
Fig. 24. Von Mises stress of the first contact point in 24 kHz RURB.
Fig. 25. Von Mises stress of the first contact point in 26 kHz RURB.
Fig. 27. Von Mises stress of the first contact point in CRRB.
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Fig. 26. Von Mises stress of the first contact point in 28 kHz RURB.
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Fig. 28. Comparison of von Mises stresses in RURB.
5.4 Residual stress and micro-hardness on free surface The residual stress on the free surface after RURB treatment is shown in Fig. 29. The residual compressive stress values firstly increase and then decrease with the increase of ultrasonic vibration frequencies. The maximum of residual compressive stress on the free surface was obtained with 26 kHz RURB treatment. The value of residual compressive stress with 26 kHz treatment is 0.62 times of that obtained after CRRB. The stress result of FEM are good agreement with the experimental results. The maximum of deviation is 8.4% at 28 kHz RURB. Fig. 30 shows the micro-hardness values measured on the free surface with different ultrasonic frequencies machining. The micro-hardness measured with CRRB treatment is 362.1 HV. Therefore, there is a significant increase in surface micro-hardness after RURB as compared to CRRB. The main reason is caused by work hardening. The grain refinement is one of the main reasons of work hardening in burnishing process. And, the ultrasonic vibration has positive promotion on the grain refinement of material [21]. The result shows that the variation of ultrasonic frequency has a little effect on the hardness on the free surface.
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Fig. 29. Mean value of residual stress for the first contact point in RURB.
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Fig. 30. Mean value of micro-hardness on the free surface in RURB.
6 Conclusion
In the present work, the deformation of material under different ultrasonic frequencies has been simulated by a 2D model and described by a theoretical model. The result shows that deformation of material experiences from ultrasonic softening to ultrasonic enhancement. In the initial stage of material deformation, ultrasonic vibration decreases the flow stress of material caused the decrease of burnishing force. Then, roller burnishing assisted with ultrasonic vibration leads to the grain refinement at the surface layer, which is a main reason of ultrasonic enhancement. The following conclusions could be draw from the research: The assistance of ultrasonic vibration increases the area of plastic flow of material. The variation of these values appear full sine waves in the range of 360 degree. The maximum value that obtained under 28 kHz frequency is 7.67 times than the one in CRRB (θ=90°). There is an average 4.1% deviation between theoretical values and simulation values. It is obvious that the increase of ultrasonic vibration frequency can increase the amount of plastic flow of material during the same time in RURB process.
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With the analysis of U1 displacement, it can be found that the machined material in the free surface are subject to two types of extrusion from roller during one vibration cycle under different frequencies. However, the ones are only subject to extruded from zero to both sides in CRRB. The variation of U2 indicate that the assistance of ultrasonic vibration causes the discontinuous contact of roller and material in RURB. When the load step time is 5E-5, the maximum value of U2 is 10.5 μm and 13.36 μm in CRRB and RURB process respectively.
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The values of von Mises stress are obtained and analyzed. The mean values of von Mises stress with the increase of ultrasonic frequency are 776.51 MPa, 806.81 MPa, 821.72 MPa, 851.83 MPa and 861.94 MPa, respectively. The result indicates that appropriate ultrasonic vibration can decrease the yield stress of being deformed material. It means that the ultrasonic vibration has an ultrasonic softening effect on the deformation of material.
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With the increase of ultrasonic frequency, the residual stress on the free surface firstly increases and then decreases. The micro-hardness on the surface has an improvement in RURB compared to CRRB. However, the hardness on the free surface only has a little change with the variation of ultrasonic frequency.
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Considering the effect of ultrasonic softening and ultrasonic enhancement, the machining result in 26 kHz was better than those in other frequencies. An increasement in the frequency up -to 26 kHz would lead to the higher values of residual stresses. Above this threshhold, the residual stress would decrease. On the other hand, with the increasement of frequency, von Mises stress appeared an increasing tendency. However, the high von Mises stress was not conductive to the burnishing process. The frequency with 26 kHz would thus be the level off point for the frequency value.
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Acknowledgements
The authors would like to acknowledge the financial support from the National Natural Science Foundation of China (51425503, 51375272, and U1201245), and the Major Science and Technology Program of High-end CNC Machine Tools and Basic Manufacturing Equipment (2015ZX04005008 and 2014ZX04012014). This work was als o supported by grants from Taishan Scholar Foundation (TS20130922).
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ACCEPTED MANUSCRIPT [4] H. Basak, H.H. Goktas, Burnishing process on al-alloy and optimization of surface roughness and surface hardness by fuzzy logic, Mater. Des. 30(2009)1275-1281.
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[5] Y. Liu, X.H. Zhao, D.P. Wang, Determination of the plastic properties of materials treated by ultrasonic surface rolling process through instrumented indentation, Mater. Sci. Eng. A. 600(2014) 21-31.
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[6] S.L. Wei, H. Zhao, J.T. Jing, Investigation on three-dimensional surface roughness evaluation of engineering ceramic for rotary ultrasonic grinding machining, Appl. Surf. Sci. 357(2015)139-146.
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[7] J. Huuki, S.V. Laakso, Integrity of surfaces finished with ultrasonic burnishing, J. Eng. Manuf. 227(2013) 45-53.
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[8] H.B. Wang, G.L. Song, G.Y. Tang, Enhanced surface properties of austenitic stainless steel by electropulsing-assisted ultrasonic surface rolling process, Surf. Coat. Technol. 282(2015)149-154.
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[9] G.G. Gras, J.A. T. Rodriguez, R.J. Mesa, J.L. Fuentes, B.G. Calle, Experimental study of lateral pass width in conventional and vibrations-assisted ball burnishing , Int. J. Adv. Manuf. Tech. 1(2016)1-9.
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[10] J. Kumar, J.S. Khamba, S.K. Mohapatra, An investigation into the machining characteristics of titanium using ultrasonic machining, Int. J. Mach. Mach. Mater. 3(2008)143-161. [11] Y. Bai, M. Yang, The influence of superimposed ultrasonic vibration on surface asperities deformation, J. Mater. Process. Technol. 229(2016)367-374.
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[12] A.T. Bozdana, N.N. Z. Gindy, H. Li, Deep cold rolling with ultrasonic vibrations－a new mechanical surface enhancement technique, Int. J. Mach. Tool. Manu. 45(2005)713-718. [13] N. Atanasiu. Metal forming in the ultrasonic field, Adv. Technol. Plast. 2 (1984)799-804. [14] V.V. Blagoveshchenskii, I.G. Panin. Effect of Ultrasound on Deformation of Crystalline Materials, Phys. N. A. 53(10) (2011)2112-2116. [15] S. Biswas, S.H. Alavi, S.P. Harimkar, Laser surface melting of Ti–6Al–4V under the influence of ultrasonic vibrations, J. Mater. Lett. 159(2015)470-473. [16] M. Shalvandi, Y. Hojjat, A. Abdullah et al. Influence of ultrasonic stress relief on stainless steel 316 specimens: A comparison with thermal stress relief, Mater. Des. 46 (2013) 713–723. [17] Y. Liu, L.J. Wang, D.P. Wang, Finite element modeling of ultrasonic surface rolling process, J. Mater. Process. Technol. 211(2011)106-2113. [18] F. Vollertsen, D. Biermann, H.N. Hansen, I.S. Jawahir, K. Kuman, Size effects in manufacturing of metallic components. CIRP Ann. Manuf. Technol. 58(2009) 566–587.
ACCEPTED MANUSCRIPT [19] B. Wu, L.J. Zhang, J.X. Zhang, R. Murakami, Y.S. Pyoun, An investigation of ultrasonic nanocrystal surface modification machining process by numerical simulation, Adv. in Eng. Softw. 83(2015)59-69.
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[20] F. Ahmadi, M. Farzin, M. Mandegari, Effect of grain size on ultrasonic softening of pure aluminum, Ultra. 63(2015)111-117.
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[21] J.A.T. Rodriguez, G.G. Gras, G. Dessein, F. Carrillo, J. Alexis, J.J. Peiro, N. Aubazac, Effects of a ball-burnishing process assisted by vibrations in G10380 steel specimens, Int. J. Adv. Manuf. Tech. 81(9) (2015)1757-1765.
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RP
R=2mm Roller x
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workpiece
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Graphical abstract
grain refinement
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z
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v roller Av Surface w G A u4 Au1 C B Au3 H h af2 Au F Au2 Au5D A E workpiece A C D E B Area of material plastic deformation in rotary ultrasonic roller burnishing
ACCEPTED MANUSCRIPT Highlights The material deformation behavior during rotary ultrasonic roller burnishing Ti-6Al-4V via two distinct stages: ultrasonic softening and enhancement.
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An analysis model and 2D finite element simulation model for surface deformation are
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proposed based on ultrasonic roller burnishing process kinematic analysis.
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Our findings may have general implications in the exploring rotary ultrasonic roller burnishing mechanism and presenting cost-effective machining technology as well as
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machined surface enhancement methodology.
S0264-1275(16)30775-4 doi: 10.1016/j.matdes.2016.06.024 JMADE 1899
To appear in: Received date: Revised date: Accepted date:
20 April 2016 26 May 2016 7 June 2016
Please cite this article as: Jian Zhao, Zhanqiang Liu, Investigations of ultrasonic frequency effects on surface deformation in rotary ultrasonic roller burnishing Ti-6Al-4V, (2016), doi: 10.1016/j.matdes.2016.06.024
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
ACCEPTED MANUSCRIPT Investigations of ultrasonic frequency effects on surface
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School of Mechanical Engineering, Shandong University, Jinan 250061, China
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a
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Jian Zhao a,b, Zhanqiang Liu a,b,*
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deformation in rotary ultrasonic roller burnishing Ti-6Al-4V
Key Laboratory of High Efficiency and Clean Mechanical Manufacture, Ministry of Education, Shandong University, China
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*Corresponding author, Telephone: 86-531-88393206, Fax: 86-531-88392045 [email protected]
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Abstract
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Roller burnishing can be applied for surface quality improvement without chip generation in machining processes. A rotary roller burnishing assisted with ultrasonic vibration machining technology has been developed. The present work aims to investigate mechanism of deformation for the machined surface layer material under different vibration frequencies. Firstly, an analysis model and 2D finite element simulation model of rotary roller burnishing process with and without ultrasonic vibration were established. Secondly, the area of material happened plastic flow and the displacements of material at the free surface were analyzed. Thirdly, von Mises stress of being deformed material under different frequencies were presented. The residual stress on the free surface are discussed and the simulation result has a good agreement with experimental result. The micro-hardness at the machined surface are measured. The result shows that ultrasonic vibration can decrease the flow stress of material deformation. Finally, the effect of ultrasonic softening and ultrasonic enhancement with the variable vibration frequencies are discussed. The material deformation experiences a process from ultrasonic softening to ultrasonic enhancement in rotary ultrasonic roller burnishing compared to the material deformation in conventional rotary roller burnishing.
Key words: rotary ultrasonic roller burnishing; vibration frequency; plastic deformation; surface enhancement
1 Introduction Titanium alloys are famous for several inherent properties of material including high strength, high specific strength, and high thermal strength. They have been widely applied to engine compressor parts, structural parts of rockets and aircrafts [1-3]. However, with large chemical activity and low elastic modulus, titanium alloys are one of the typical difficult-to-machine materials.
ACCEPTED MANUSCRIPT Surface quality of material is an important factor in determining its service life. Severe plastic deformation without chip based on material plastic flow is being increasingly concerned to improve surface integrity. Especially, the application of relevant machining processes has been the subject of most studies in the field of aviation, automobile and military [4-6].
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Ultrasonic burnishing is an attractive finishing technique, which can obtain an increase in strength and hardness as well as a reduction in surface roughness. Ultrasonic burnishing superimposes 20 kHz to 30 kHz vibration-impacts on conventional burnishing process. Assistance of ultrasonic vibration in machining can reduce the burnishing force and improves tool life. Ultrasonic burnishing has a benefit in machining difficult-to-machine metal alloys [7-9], such as titanium alloys and Inconel alloys [10]. The effects of ultrasonic burnishing parameters on mechanical behaviors including residual stress, surface roughness, and micro-hardness of machined materials have been experimentally researched [7, 9, 11, 12]. The ultrasonic vibration helps to strengthen material through severe plastic deformation.
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Atanasiu [13] developed a quantitative computing formulas on the changes of parameters for metal materials during ultrasonic forming process. He described the stress-strain behavior with the rigid-viscoplastic model in the strong ultrasonic field. The research result of Atanasiu indicated that the yield strength of forming materials decreased exponentially with the increasing of ultrasonic strength. He had also researched on the influence of ultrasonic vibration on the friction coefficient between formed material and die. A simulation of deformation for single crystals with ultrasonic treatment was proposed by Blagoveshchenskii et al [14]. They found that the effect of the ultrasonic frequency on the deformation of a crystalline material is maximal. The reason is the fact that the time of formation of a closed loop coincides with the period of ultrasonic vibrations. Yang [11] studied the influence of superimposed ultrasonic vibration on surface asperities deformation and drew a conclusion that deformation of metal foil surface was approximately linear to the superimposed ultrasonic vibration amplitude and initial static stress. It was found that the sample dimensions had an influence on the ultrasonic softening effect. The ultrasonic softening effect was closely related to the ratio of the number of surface layer grains and total grains in the micro scale. Biswas and Alavi [15] investigated laser surface melting of Ti-6Al-4V alloy under the influence of ultrasonic vibration (20 kHz). It had been observed that the phenomenon of material refinement was due to the enhanced material plastic flow and cavitation caused by ultrasonic vibration. Patil et al [2] proposed a 2D finite element transient simulation method to study the effect of ultrasonic vibrations on machining. The results showed that the cutting force had a reduction in ultrasonic assisted turning over that in continuous turning. A decrease in cutting force by 17% was observed with the amplitude of vibration increasing from 10 μm to 20 μm. The average effective strain had 27% reduction during in ultrasonic assisted cutting as compared with that in continuous cutting. The reduction of effective strain leads to lesser strain hardening in ultrasonic assisted cutting, which results in the decreasing of cutting force. Bozdana [12] found that the ultrasonic vibration can reduce rolling force in the deep cold rolling. Shalvandi et.al [16] have a research on the stress relieving phenomenon based on ultrasonic vibration. The result shows that the amount of stress reduction is proportional to the ultrasonic intensity. The results of these researches shows that there is an acoustic softening to material deformation in ultrasonic vibration machining process. In this paper, the plastic flow of material in the surface layer will be analyzed in rotary
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ultrasonic roller burnishing. A theoretical model and a 2D finite element simulation model of plastic deformation are proposed. For verifying the accuracy of simulation model, experimental burnishing forces are compared with the simulated ones. The displacements of material in the free surface are discussed. Von Mises stresses are analyzed under different ultrasonic vibration frequencies. The effect of ultrasonic vibration is investigated. The general framework of this paper is shown in Fig. 1.
Start
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Confirm research purpose Mechanism of material deformation in RURB Confirm variable
Simulation model
Theoretical model
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Experiment (CRRB and RURB)
Analysis of material property during machining process
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Analysis of material property after machining
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Ultrasonic frequency
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Research object: σr and HV
Research object: σm
Research object: Ac, Au, U1, U2
Summary the mechanism of material deformation in RURB
End
Fig.1. General framework of this paper.
2 Experiments 2.1 Experimental equipment and material Milling test as a pretreatment was conducted on DAEWOOACE-V500 CNC-vertical machining center. Then, conventional rotary roller burnishing (CRRB) and rotary ultrasonic roller burnishing (RURB) processes were carried out on the same machine tool, respectively. A rotary ultrasonic burnishing tool was attached on the tool holder, which was connected with ultrasonic generator by a lead-electricity device. The non-contact lead-electricity device was used to realize the rotary ultrasonic machining. The workpiece was mounted on a dynamometer through a fixture. The dynamometer was clamped on the machine tool bed. The experimental setup is shown in Fig. 2 (a).
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Table 1 Mechanical properties of Ti-6Al-4V at room temperature.
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The flat-based burnishing tool with four rollers was employed. The structure and dimension of burnishing tool are shown in Fig.2 (b). The rollers were made of steel. The hardness of roller was 60 HRC. The diameter and length of roller were 4 mm and 10 mm, respectively. The accessible maximum burnishing depth of the burnishing tool was 0.4 mm. Ti-6Al-4V was chosen as workpiece material, whose mechanical properties was shown in Table 1.
Strength factor (MPa)
Tensile strength (MPa)
Surface hardness (HRC)
Hardening exponent
897
331
993-973
33-35
0.34
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Yield stress (MPa)
Fig. 2. RURB experimental setup (a) and burnishing tool (b).
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2.2 Experimental procedures and measurements Firstly, the selected free surfaces of six groups of workpieces were milled in the pretreatment process. Each group had five samples to make sure the accurate of experimental results. The mean value of five measured results was taken as the final test result in one group of experiment. The dimensions of all samples were 40 mm×60 mm×35 mm uniformly. The milled free surfaces of five groups of workpieces were treated with RURB process. The rest group of workpiece was machined with CRRB process. The setting of relevant experimental parameters was listed in Table 2. Fig. 3 showed the movement of burnishing tool on the free surface of material. The movement of burnishing tool was a compound behavior including three independent movements. These movements included a rotary motion around spindle, a straight motion along the direction of feed, and a periodic vibration along spindle direction. v
burnished region roller
w
unburnished region milled area z y workpiece x
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Table 2
Feed
Cutting depth
Spindle speed
Amplitude of vibration
milling CRRB
\ \ 20 kHz 22 kHz 24 kHz 26 kHz 28 kHz
\ \
50 mm/min 50 mm/min
0.1 mm 0.1 mm
500 r/min 500 r/min
\ \
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50 mm/min
0.1 mm
500 r/min
10 um
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Frequency of vibration
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Pretreatment
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Experimental parameters.
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LK-G30 Laser displacement sensor was applied to measure the vibration of burnishing tool during the RURB process. Z-axis positioner was used to make sure the accurate of cutting depth in the experiment. The burnishing forces were measured by using the Kistler piezoelectric dynamometer (type 9129AA). The residual stress on the free surface was measured by the blind hole method. The measurement of micro-hardness on the free surface was accomplished in the nano-indentor.
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3 Finite element modeling
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The finite element modeling is developed to research the deformation behavior of material in the contact area between roller and workpiece material. Considering the periodic characteristic of ultrasonic vibration, the deformation behavior in one period is analyzed. The total simulation time for 3D RURB finite element model (FEM) will be too much and the essential operation is very little compared with the operation of the total model. The applied force imposed on the burnishing tool is uniform. Therefore, a 2D plastic strain FEM is preferable to analyze the behavior of material deformation in this work. The material deformation in burnishing process is a nonlinear problem. Abaqus software has the advantages of the solution of nonlinear problem. With the application of intelligent solver, it is easier in solving the nonlinear problem of converge. The Abaqus/Explicit module was chosen in this work. The diagonal mass element matrices and explicit integration rule were utilized to achieve the computational accuracy and efficiency [17].
3.1 Geometry, interactions and boundary conditions The burnishing roller was replaced by a semicircle plane of radius R=2 mm, which was considered as a rigid body. A rectangle was set as the workpiece. The top surface of workpiece was defined as free surface. The experimental burnishing depth was 0.1mm and the real contact length between roller and workpiece was 1.25 mm. The dimension of workpiece was 4 mm×1 mm. The schematic of the finite element model was shown in Fig. 4.
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The contact type between roller and workpiece is surface to surface contact (explicit). The mechanical constraint formulation was kinematic contact method. The friction coefficient of milled surface of workpiece was measured on UMT-2 tribometer with a ball-on-plate configuration at room temperature. The test mode of friction coefficient was set as linear reciprocating motion, which is similar with the motion of ultrasonic surface rolling process. The friction tests were conducted at a normal load of 10 N and sliding speed of 10 mm/s. The materials of ball and plate were 45 steel and Ti-6Al-4V, respectively. The friction coefficient between ball and plate were measured as ranging from 0.1 to 0.3. Considering the coexistence of rolling friction and sliding friction in rotary roller burnishing process, the friction coefficient was determined as 0.15 which was the mean value for the friction test results.
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The minimum critical value of ultrasonic vibration frequency is 20 kHz, which is 240 times larger than spindle speed 500r/min in the experiment. Therefore, the spindle speed can be ignored. To simulate the material deformation process in one period of time, three steps were combined. These steps were loading step, moving step and unloading step, respectively. The sampling frequency of output data was one fifth than ultrasonic vibration frequency. In addition to the top surface, displacements perpendicular to the boundaries were prohibited for other surfaces of workpiece. There was no constraint on the top surface. RP
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3.2 Material properties and meshing The mechanical properties of Ti-6Al-4V applied in the FEM were provided by the manufacturer. Young’s modulus was 110 GPa, Poisson’s ratio was 0.31, and Mass density was 4.43E-09. J-C model was applied to depict the material constitutive relation, which has been widely used to analyze the variation of material flow stress in large strain and large strain rate deformation process. The expression of J-C constitutive relation is given in equation (1). m T Tr = A+B 1 C ln 1 Tm Tr 0 n
(1)
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is reference shear
is true strain rate, Tm is melt temperature, Tr is room temperature and T is working
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temperature. The values of relevant coefficients are shown in Table 3. Table 3 B/MPa 656
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A/MPa 907
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ε0 1
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Tr /°C 20
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Suitable meshing is crucial to the accuracy of simulation result. We took the method of local mesh refinement at the workpiece material as shown in Fig. 4. It can be seen that double bias seed type mesh in the top and bottom edge of workpiece material was used. The seed type of two side edges was single bias. Four-nodal quadrilateral elements (type CPS4R) were used in the workpiece, while three-nodal triangular elements were used in the roller. The FE model consisted of 1471nodes and 1351elements.
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Ultrasonic burnishing strengthens surface materials with cold working. In the surface deformation layer, the percentage of plastic deformation is much larger than that of elastic deformation. The analysis of the process of material plastic deformation is priority and the phenomenon of material elastic deformation is ignored for simplicity. The friction condition is not considered and the volume of machined material is assumed invariable. The material plastic deformation only exists in the processing area, which means little material flow toward the unmachined area. The type of ultrasonic vibration is simplified as a simple harmonic motion along one direction based on the experimental research as shown in Fig. 5.
(U,I)
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The mode of motion of materials in the free surface is plastic flow in rotary ultrasonic roller burnishing (RURB) process. The plastic flow of materials is one basic reason to improve surface mechanical properties. Fig. 6 is a schematic illustration of materials plastic flow in the free surface. The top model and the bottom model in Fig. 6 can be used to explain the material plastic flow process without and with ultrasonic vibration-assisted, respectively. The dashed curve and the solid curve represent the beginning position and the final position of roller, respectively. The thick solid line means the free surface of workpiece. On account of the periodicity of ultrasonic vibration, the plastic flow of materials in a period of ultrasonic vibration is chosen to be analyzed. In order to compare materials plastic flow exactly, burnishing depth h takes the same value in both machining processes.
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Fig. 6. Material plastic flow with and without ultrasonic vibration.
In the conventional rotary roller burnishing (CRRB) process, workpiece is stationary, while, roller feeds right-forward at a rate of vf, which is rotated at a unfixable rotational speed of ω, as shown in the top one of Fig. 6. In a period time of ultrasonic vibration, roller moves from point A to point B and only Ar3 zone happens materials plastic flow in this process. The materials of Ar3 zone flows to Ar2 and Ar4 zones. The materials in Ar4 zone exist in a way like built-up edge, which is very few compared with the materials in Ar2 zone. A coordinate system has been set, in which x-axis is located at the workpiece surface and y-axis goes through point D as shown in Fig. 6. According to the constant volume assumption, areas of these zones can be solved by integral method with equations (2), (3), and (4), respectively. A r1 A r 4
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A r 3 dz
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(3)
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where ap1 is the dimensional change between unfinished surface and finished surface in rotary roller burnishing, af1 is the depth of plastic flow of material (ap1+ af1=h), R is the radius of roller, h means burnishing depth determined by experiment, |AB| is the distance that roller moves in a period time of ultrasonic vibration. |AB| can be calculated by equations (5) and (6) with the coordinate system in Fig. 7.
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where v is burnishing velocity, vf is feed velocity, vs is linear velocity of spindle rotation, f is ultrasonic frequency, ws is angular velocity of spindle rotation, l is the length of roller, θ is the angle between the axis of roller and feed direction. In the rotary ultrasonic roller burnishing (RURB) process, roller moves through five points A、 C、D、E、and B in a sinusoidal trajectory. With the amplitude of ultrasonic vibration Av, the depth of materials plastic flow layer will increase, as seen in the bottom model of Fig.6. The material in Au5 zone is an extra part that happened plastic flow compare to conventional rotary roller burnishing process. Materials plastic flow in RURB can be expressed as equations (7) - (13).
A u 4 A u1
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where ap2 is the dimensional change between unfinished surface and finished surface in rotary ultrasonic roller burnishing, af2 is the depth of plastic flow of material and ai is an increased depth of material plastic flow compared to conventional rotary roller burnishing process (ap2+ af2- ai =h and ai=Av), respectively. Where xF、xG、xH are abscissas of three points F、G、H, respectively.
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Material plastic flow rate of change η is introduced in equation (14) to have a further analysis to the effect of ultrasonic vibration on material plastic flow.
=
A u5 Au 3 Ar 3
(14)
5 Discussion 5.1 Area of plastic flow of material Experimental parameters in Table 2 are substituted into equations (1) to (14), then the area of plastic flow of material can be calculated. Fig. 8 shows the theoretical calculated area of plastic flow of material at different frequencies in RURB processes. The variation of these values appears full sine waves in the range of 360 degree. It is due to that circumferential velocity changes with the variation of θ from 0 to 360 degree as shown in Fig. 7. It can be seen that the mean value of Au3 (Ar3) decreases with the increase of ultrasonic vibration frequency. The reason is that the value of Au3 (Ar3)
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is decided by feed rate and the movement time of roller. Therefore, the vibration cycle decreases with the increase of vibration frequency. However, the mean value of Au5 increases with the increase of ultrasonic vibration frequency in Fig. 9. It is a result of the concerted action of ultrasonic vibration and feed rate. Ultrasonic vibration frequency has a more effect on Au5. Au5 is the increased area of plastic flow of material caused by ultrasonic vibration. Compared Fig. 8 with Fig. 9, the mean value of Au5 is larger than the value of Au3 (Ar3). The result can also be found in Fig. 12.
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Fig. 8. Au3 of plastic flow of material with different frequencies RURB and Ar3 in CRRB (Au3= Ar3).
Fig. 9. Au5 of increased plastic flow of material with different frequencies RURB.
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Fig. 10. Area of plastic flow of material (Au5+Au3) with different frequencies RURB.
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As shown in Fig. 10, the area of plastic flow of material changes in CRRB and RURB process, in which θ changes periodically. In the frequency range of 22 kHz to 28 kHz, the maximum value of the area of plastic flow of material occurs when θ=270°. While, the minimum value of it occurs when θ=90°. However, the results of ones are opposite completely under 20 kHz ultrasonic vibration. It is because that the area of plastic flow of material is subject to feed rate, too. Ultrasonic frequency has little effect on the depth of plastic flow layer of material. Because the change of ultrasonic frequency could not influence the burnishing depth. The burnishing depth is the main reason that influences the depth of plastic flow layer of material. But the ultrasonic frequency can increase the area of plastic flow of material at unit time, which would have a significant effect on grain refinement in the surface layer. It is because that the change of plastic flow of material at unit time has an effect on the material flow stress. The flow stress of material has an interaction with the property of surface layer grains based on the surface grain theory [18]. The dislocation tangling and pile-ups in the surface grains are fewer, hence the slip system movement is easier compared with the inner grains which reduces the deformation resistance of the material [11].
Fig. 11. Selection of path for surface deformation in FEM.
A path was established to analyze the free surface deformation of workpiece in FEM as shown
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In Fig. 12, the red lines show the rate of change η of plastic flow of material under different ultrasonic vibration frequencies comparing the ones in CRRB. The red solid line represents theoretical calculated values and the red dotted line represents simulation values. It can be seen that the assistance of ultrasonic vibration increases the area of plastic flow of material, which would cause the increase of the influence depth of residual compressive stress and grain refinement [13], which is the same as the effect of the change of burnishing depth. The maximum value that obtained under 28 kHz frequency is 7.67 times than the one in CRRB. There is an average 4.1% deviation between theoretical values and simulation values. It is within the allowable range. The friction between roller and workpiece is the main reason caused the deviation.
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The black lines show the area of plastic flow of material during one vibration cycle in RURB (θ=90°). The time of vibration cycle decreases with the increase of vibration frequency. However, the area of plastic flow of material is first decreased and then increased with the time of vibration cycle decreasing. So, it is obvious that the increase of ultrasonic vibration frequency can increase the area of plastic flow of material during the same time in RURB process.
Fig. 12. Rate of change and total area of plastic flow of material with different frequencies in RURB (θ=90°).
5.2 U1 and U2 displacements of material at free surface U1 is the displacement of material along the direction of feed. U1 in one ultrasonic vibration cycle in the load step was selected to analyze the deformation of material. Fig. 13 shows the U1 displacement of the material in the free surface in CRRB, while Fig. 14 to Fig. 18 show the one under different vibration frequencies in RURB. In Fig. 13, the direction of U1 of material in the free surface does not have variation during one vibration cycle. It means that the machined material in the free surface is subject to extrude from zero point to both sides throughout during one vibration cycle. The position of zero point of horizontal axis means the first contact point between roller and material, which is the point contacted the bottom of roller. However, with the assistance of ultrasonic vibration, both the direction and amplitude of U1 change during one vibration cycle as
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shown in Fig. 14 to Fig. 18. It can been seen that the U1 of material are central symmetric curves in Fig. 14 to Fig. 18. The U1 of material can be divided to two section. The material in the zone close to zero point are subject to extrusion to zero point, however, the material in the zone far from zero point are subject to extrusion to both sides. Compared the value of U1, it can be found that the maximum value appear when the load step time are 1/4 T or 3/4 T. Because the roller reached the maximum displacement position in the Z coordinate direction.
Fig. 14. Variation of U1 during one vibration cycle in RURB (20 kHz).
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Fig. 13. Variation of U1 during one vibration cycle in CRRB.
Fig. 15. Variation of U1 during one vibration cycle in RURB (22 kHz).
Fig. 16. Variation of U1 during one vibration cycle in RURB (24 kHz).
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Fig. 18. Variation of U1 during one vibration cycle in RURB (28 kHz).
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Fig. 17. Variation of U1 during one vibration cycle in RURB (26 kHz).
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Fig. 19. Comparison of U1 in one ultrasonic vibration cycle.
In Fig. 19, the black solid line represents the percent of deformation zone close to zero point in total deformation zone. The red dotted line represents the maximum of U1 during one ultrasonic vibration cycle under different frequencies. With the increase of ultrasonic frequency, the percent has a little decrease, except the one in 26 kHz. The percent in 26 kHz has a large decrease compared with the ones under other frequencies. The reason may be related to the nature of material. The maximum of U1 has a similar sinusoidal change with the increase of ultrasonic frequency. The range of change is 0.1 μm. The U2 displacement of material in the free surface during one vibration cycle in the load step is shown in Fig. 20 (CRRB) and Fig. 21 (20 kHz). The variation of U2 under ultrasonic frequencies are the same as each other because of the same of ultrasonic amplitude, so we chose the variation of U2 in 20 kHz as the case sample in Fig. 21. In Fig.20, the variation of U2 during one ultrasonic vibration is very small, which means that the U2 is continuously variable in CRRB. It means that the roller and workpiece always contact each other during the machining process. While, the variation of U2 is larger in Fig. 21, which means separation phenomenon happens between roller
ACCEPTED MANUSCRIPT and workpiece in RURB because of the assistance of ultrasonic vibration. When the load step time is 5E-5, the maximum values of U2 are 10.5 μm and 13.36 μm in CRRB and RURB process, respectively. This different value is the result of ultrasonic amplitude and elastic recovery of material.
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The displacement of material has a great effect on the strain rate of material in the deformation zone [19], especially the variation of U1, which will influence the yield strength of material in this zone. It may be the reason that causes the variation of burnishing force in RURB compared with the one in CRRB.
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Fig. 20. Variation of U2 during one vibration cycle in CRRB.
Fig. 21. Variation of U2 during one vibration cycle in RURB (20 kHz).
5.3 Analysis of stress behavior in CRRB and RURB process
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The assistance of vibration with appropriate ultrasonic strength can decrease burnishing force in RURB. The main burnishing force is the acting force component along the Z coordinate direction just as shown in Table 4. It means that ultrasonic vibration may has an effect on the deformation of material. In order to analysis the deformation of material under ultrasonic vibration, the state of von Mises stress at a point in the free surface is discussed. The chosen point is the first contact point between roller and material. The analysis stage of time begins in loading and ends in the time of the first contact point appearing yield in the first time, which is based on the deformation of material in CRRB. Fig. 22 to Fig. 26 show the variation of von Mises stress with load step time under different ultrasonic frequencies. The black dotted line means the real law of von Mises stress. It can be found that the variation of von Mises stress appears similar sine wave. The red solid line is a fitting curve. With ultrasonic frequency increases, the mean values of von Mises stress in the steady stage are 776.51 MPa, 806.81 MPa, 821.72 MPa, 851.83 MPa and 861.94 MPa, respectively, which are lower than the yield strength of the material Ti-6Al-4V. However, the mean value of von Mises stress is 889.07 MPa in CRRB in Fig. 27. The decrease of mean von Mises stress values in RURB are shown in Fig. 28 as compared to the one in CRRB. The mean value of von Mises stress increases with the increase of ultrasonic vibration frequency. The result indicates that appropriate ultrasonic vibration can decrease the yield stress of being deformed material, which agrees with the ultrasonic softening raised by Nicolae Atanasiu [6]. The result also has a good agreement with the variation of
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Measurements of burnishing force.
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Fig. 23. Von Mises stress of the first contact point in 22 kHz RURB.
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Fig. 22. Von Mises stress of the first contact point in 20 kHz RURB.
Fig. 24. Von Mises stress of the first contact point in 24 kHz RURB.
Fig. 25. Von Mises stress of the first contact point in 26 kHz RURB.
Fig. 27. Von Mises stress of the first contact point in CRRB.
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Fig. 26. Von Mises stress of the first contact point in 28 kHz RURB.
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Fig. 28. Comparison of von Mises stresses in RURB.
5.4 Residual stress and micro-hardness on free surface The residual stress on the free surface after RURB treatment is shown in Fig. 29. The residual compressive stress values firstly increase and then decrease with the increase of ultrasonic vibration frequencies. The maximum of residual compressive stress on the free surface was obtained with 26 kHz RURB treatment. The value of residual compressive stress with 26 kHz treatment is 0.62 times of that obtained after CRRB. The stress result of FEM are good agreement with the experimental results. The maximum of deviation is 8.4% at 28 kHz RURB. Fig. 30 shows the micro-hardness values measured on the free surface with different ultrasonic frequencies machining. The micro-hardness measured with CRRB treatment is 362.1 HV. Therefore, there is a significant increase in surface micro-hardness after RURB as compared to CRRB. The main reason is caused by work hardening. The grain refinement is one of the main reasons of work hardening in burnishing process. And, the ultrasonic vibration has positive promotion on the grain refinement of material [21]. The result shows that the variation of ultrasonic frequency has a little effect on the hardness on the free surface.
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Fig. 29. Mean value of residual stress for the first contact point in RURB.
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Fig. 30. Mean value of micro-hardness on the free surface in RURB.
6 Conclusion
In the present work, the deformation of material under different ultrasonic frequencies has been simulated by a 2D model and described by a theoretical model. The result shows that deformation of material experiences from ultrasonic softening to ultrasonic enhancement. In the initial stage of material deformation, ultrasonic vibration decreases the flow stress of material caused the decrease of burnishing force. Then, roller burnishing assisted with ultrasonic vibration leads to the grain refinement at the surface layer, which is a main reason of ultrasonic enhancement. The following conclusions could be draw from the research: The assistance of ultrasonic vibration increases the area of plastic flow of material. The variation of these values appear full sine waves in the range of 360 degree. The maximum value that obtained under 28 kHz frequency is 7.67 times than the one in CRRB (θ=90°). There is an average 4.1% deviation between theoretical values and simulation values. It is obvious that the increase of ultrasonic vibration frequency can increase the amount of plastic flow of material during the same time in RURB process.
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With the analysis of U1 displacement, it can be found that the machined material in the free surface are subject to two types of extrusion from roller during one vibration cycle under different frequencies. However, the ones are only subject to extruded from zero to both sides in CRRB. The variation of U2 indicate that the assistance of ultrasonic vibration causes the discontinuous contact of roller and material in RURB. When the load step time is 5E-5, the maximum value of U2 is 10.5 μm and 13.36 μm in CRRB and RURB process respectively.
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The values of von Mises stress are obtained and analyzed. The mean values of von Mises stress with the increase of ultrasonic frequency are 776.51 MPa, 806.81 MPa, 821.72 MPa, 851.83 MPa and 861.94 MPa, respectively. The result indicates that appropriate ultrasonic vibration can decrease the yield stress of being deformed material. It means that the ultrasonic vibration has an ultrasonic softening effect on the deformation of material.
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With the increase of ultrasonic frequency, the residual stress on the free surface firstly increases and then decreases. The micro-hardness on the surface has an improvement in RURB compared to CRRB. However, the hardness on the free surface only has a little change with the variation of ultrasonic frequency.
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Considering the effect of ultrasonic softening and ultrasonic enhancement, the machining result in 26 kHz was better than those in other frequencies. An increasement in the frequency up -to 26 kHz would lead to the higher values of residual stresses. Above this threshhold, the residual stress would decrease. On the other hand, with the increasement of frequency, von Mises stress appeared an increasing tendency. However, the high von Mises stress was not conductive to the burnishing process. The frequency with 26 kHz would thus be the level off point for the frequency value.
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Acknowledgements
The authors would like to acknowledge the financial support from the National Natural Science Foundation of China (51425503, 51375272, and U1201245), and the Major Science and Technology Program of High-end CNC Machine Tools and Basic Manufacturing Equipment (2015ZX04005008 and 2014ZX04012014). This work was als o supported by grants from Taishan Scholar Foundation (TS20130922).
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[5] Y. Liu, X.H. Zhao, D.P. Wang, Determination of the plastic properties of materials treated by ultrasonic surface rolling process through instrumented indentation, Mater. Sci. Eng. A. 600(2014) 21-31.
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RP
R=2mm Roller x
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Graphical abstract
grain refinement
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ap2
v roller Av Surface w G A u4 Au1 C B Au3 H h af2 Au F Au2 Au5D A E workpiece A C D E B Area of material plastic deformation in rotary ultrasonic roller burnishing
ACCEPTED MANUSCRIPT Highlights The material deformation behavior during rotary ultrasonic roller burnishing Ti-6Al-4V via two distinct stages: ultrasonic softening and enhancement.
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An analysis model and 2D finite element simulation model for surface deformation are
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proposed based on ultrasonic roller burnishing process kinematic analysis.
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Our findings may have general implications in the exploring rotary ultrasonic roller burnishing mechanism and presenting cost-effective machining technology as well as
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machined surface enhancement methodology.