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Optimization of residual stress field in ultrasonic assisted burnishing process
International Journal of Lightweight Materials and Manufacture xxx (xxxx) xxx
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Optimization of residual stress field in ultrasonic assisted burnishing process Reza Teimouri Faculty of Mechanical Engineering, University of Kashan, Kashan, Iran
a r t i c l e i n f o
a b s t r a c t
Article history: Received 30 March 2019 Received in revised form 25 April 2019 Accepted 27 April 2019 Available online xxx
Surface compressive residual stress and its penetration depth are of important characteristics of burnishing process. The higher values compressive residual stress in the surface of the treated sample can delay the fatigue crack initiation; also, the further penetration depth restricts fatigue crack propagation. However, achieving both of performance at same time needs careful selection of burnishing parameter. In the present study an optimization approach is made to maximize the value of surface compressive residual stress subjected to specified penetration depth. The analytical model of residual stress previously developed by the author is firstly modified with a cubic interval function and then used to find how the ultrasonic assisted burnishing factors i.e. static force, vibration amplitude, ball diameter and material influence the residual stress field distribution. Then the model was then incorporated with particle swarm optimization algorithm to find optimal parameter setting. Results showed that it isn't possible to maximize both the surface compressive residual stress and its penetration depth at same time. Furthermore, to have maximum value of compressive residual stress magnitude at the surface with the penetration depth of 0.5 mm, it is required to use tungsten carbide ball with 3 mm diameter; also, the static load and vibration amplitude should be selected at the values of 120 N and 14 mm. The compressive surface residual stress in optimized condition is about 110 MPa that is compatible well with the 98 MPa obtained by confirmatory experiment. Also, the maximum depth compressive residual stress for optimum condition measured by experiment is 0.7 mm while it is predicted 0.8 mm by analytical approach. © 2019 The Authors. Production and hosting by Elsevier B.V. on behalf of KeAi Communications Co., Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/bync-nd/4.0/).
Keywords: Ultrasonic burnishing Compressive residual stress field Particle swarm optimization
1. Introduction Ultrasonic surface treatment is a cold working process in which ball or roller shape tool are exerted to the work surface incorporating both the static and dynamic loads. Here, the static load is forced to the work surface by a static pressure caused by downward motion of the tool tip into work surface; also, the dynamic load is applied by series of overlapped vibration impacts. This treatment leads to an improvement of fatigue behavior caused by both the developed compressive residual stresses and plastic strains due to the cold working effect. Ultrasonic nanocrystalline surface modification, and ultrasonic surface rolling or burnishing [1e3] are two main alternatives of ultrasonic surface treatment process. In former, the contact
E-mail address: [email protected]. Peer review under responsibility of Editorial Board of International Journal of Lightweight Materials and Manufacture
condition between the tool tip and work surface is purely sliding which leads to the tool to be worn-out and increases the surface roughness; while in the latter, the burnishing ball rolls over the work surface that enhances the surface quality and significantly reduces the tool wear. Burnishing in presence of ultrasonic vibration is a surface mechanical treatment process that is used in the last stage of manufacturing process planning. The process causes achieving high quality surface finish and enhanced fatigue properties through inducing compressive residual stress in the surface layers. Depends to the processed material, the compressive residual stress depth obtained by burnishing is significantly higher than other surface treatment process such as shot peening [1]. The burnishing process is applicable for many engineering materials including metals [2e5], ceramics [6], polymers [7] and biomaterials [8]. Compressive residual stress field (CRSF) distributed in burnished part plays an important role in functionality of burnishing process. However, due to expensive and time consuming measurement of residual stress; analyzing effect of burnishing
https://doi.org/10.1016/j.ijlmm.2019.04.009 2588-8404/© 2019 The Authors. Production and hosting by Elsevier B.V. on behalf of KeAi Communications Co., Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
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parameters on this characteristic wasn't well understood. Limited study reported in the literatures regarding effect of burnishing parameters on CRSF through experimental measurements. Ting et al. [9] compared residual stress of as polished 40Cr steel with burnished sample. They revealed that surface residual stress of burnished sample is enhanced from 200 MPa to 846 MPa. Rodriguez et al. [10] reported that applying burnishing process with hydrostatic pressure of 20 MPa to turned samples changes the surface tensile residual stress with magnitude of 700 MPa to 800 MPa. Korzynski et al. [11] showed that performing burnishing process significantly enhances the state of residual stress after coating. Sachin et al. [12] applied burnishing process with cryogenic cooling to burnish the precipitated hardened stainless steel. Results revealed amount of compressive residual stress of burnished sample in presence of cryogenic cooling is significantly improved compared to MQL and dry condition. According to above reviewed papers, it is found that analyzing residual stress has been carried out in limited number of experiments due to costly and time consuming measurements. Hence, to solve this problem, finite element simulation has been applied for analyzing the residual state in burnishing process. In this case, Sayahi et al. [13] analyzed burnishing of Titanium alloy and found effect of static pressure and ball diameter on residual stress distribution. Mohammadi et al. [13] used FE simulation by ABAQUS software to study effect of static force, feed rate, ball diameter and pass number on residual stress distribution of Tie6Ale4V. Liu et al. [14] performed a FEA to study effect of ultrasonic surface burnishing factor on compressive residual stress field. They reported that to achieve desired value of residual stress and penetration depth, further values of static force and vibration amplitude as along with less value of spindle speed should be adopted. Even though, finite element simulation is effective method to precisely predict the performance measures the computational time by this method is quite long where it sometimes computational goes beyond one week [15]. Hence, analytical models are applicable way to understand the mechanics of residual stress distribution in a very short period of the time. In the previous work carried out by the author, the residual stress distribution of thin walled aluminum alloy has been modeled through an analytical approach [16]. However, the effect of process parameters on surface residual stress and the maxim penetration depth of compressive residual stress were not well analyzed. In the present study, firstly the developed analytical model of residual stress is modified to smooth type through applying a cubic function. Then effect of static force, vibration amplitude, ball diameter and its material on magnitude of residual stress in the surface and the maximum penetration depth of compressive residual stress are studied. Furthermore, the developed analytical model is used as objective function to be incorporated by particle swarm optimization for maximization of the surface compressive residual stress subjected to specified penetration depth. The analytical model of residual stress in author's previous work [16] ignored final relaxation stage. Hence, in the present study a relaxation based on a cubic model was developed to enhance the prediction accuracy of analytical model. On the other hand, for thin strip, due to relaxation of stress after unclamping, it is tough to maximize both the surface compressive residual stress and maximum depth simultaneously. Hence, in order to achieve desired residual stress value, it is required to solve a constrained optimization problem. Hence, in the present paper, the proposed objectives are considered.
2. Analytical model The residual stress is a plane stress that is varied through the depth of the processed specimens. According to the work previously published by the author [16], the induced stress can be calculated by the difference between the devitoric plastic stress and elastic stress as expressed in Eq. (1).
srx ¼ sry ¼
1 p si sei 3
(1) p
where sr is the transition stress due to each impact, si and sei are the effective plastic and elastic stress respectively. The plastic stress is calculated by equation (2) according to combined isotropicekinematic hardening material model.
spi ¼ sy þ Q 1 exp bεpi
þ
C
g
p 1 exp gεi
(2)
where, Q and b are the materials parameters for isotropic hardening; also, C and g are the parameters related to kinematic hardening terms. Table 1 shows the material constants for combined isotopicekinematic hardening model. Also εip is the equivalent plastic strain that has linear relationship with equivalent elastic strain according to equations (3) and (4): p
εi ¼
e εi e εy þ j εi εs
εei < εy εei > εy
(3)
8 > > > > > r s þ r dp > > j ¼ ps > > > > r e þ r de > > > > 1 > > 2 > s F > > r ¼ > p > 3psy > > > > > 1 < 1 r 4 d 2 r ¼ 2Rð p Af Þ p > 3sy > > > > > 1 > > > 3FR 3 > > r se ¼ > > 4E > eq > > > > >
1 > > D 5rp3 A2 f 2 5 > d > r ¼ > e > > 2 Eeq > :
(4)
where, F, A, R, f and r are the static force, vibration amplitude, ball radius and vibration frequency and ball density, respectively. J is the strain coefficient that is obtained by the ratio of plastic to elastic contact radius. Also, r sp , r dp , r se and r de are the radius of contact in plastic and elastic regime due to static and dynamic loads. sy is the yield stress and εy is the yield strain. Eeq is the equal elasticity modulus that is calculated by Eq. (5); and εei is the effective elastic strain that is calculated by Eq. (6). For further clarification, Fig. 1 demonstrates the geometry of contact.
1 w21 1 w22 1 ¼ þ Eeq E1 E2
(5)
Table 1 Combined isotropicekinematic material constitutive parameters for AA6061-T6 [16]. Material
sy (MPa)
Q (MPa) (MPa)
b
C (MPa)
g
AA6061-T6
209.2
38.9
21.1
3529.3
65.16
Please cite this article as: R. Teimouri, Optimization of residual stress field in ultrasonic assisted burnishing process, International Journal of Lightweight Materials and Manufacture, https://doi.org/10.1016/j.ijlmm.2019.04.009
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momentum and tensile force are released and causes redistribution of residual stress. Hence, the final residual stress distribution is:
Res Ind sRes x ðzÞ ¼ sy ðzÞ ¼ sx ðzÞ þ sMx ðzÞ þ sFx
(11)
Fig. 1. A schematic illustration of elastic-plastic indentation of elastic sphere and elastic-plastic semi-finite body.
E1, E2 and w1 and w2 are the elastic modulus and Poisson ratios of workpiece and ball, respectively.
εei ¼
sei
(6)
E1
sei is the effective Von-Mises elastic stress that is calculated by following equations.
sei ¼
sex
sey
2
þ
sey
sez
pffiffiffi 2
2
2 2 1
þ
sez
sex
(7)
where, sx, sy and sz are the principal contact stresses that can be determined as follows:
8 ðt > > > > > Fx ¼ sInd x ðzÞwdz > > > > > 0 > > > > > ðt > > > t 0 > > > > > > F > > sF ¼ x > > > x A > > > > M t > > : sMx ðzÞ ¼ x z I 2
(12)
By clarification of residual stress field distribution, the typical form of residual stress can be modified by an interval function:
8 1 ! 1 > z z2 > e e 1 re > > 1þ 2 þ s ðzÞ ¼ sy ðzÞ ¼ P0 ð1 þ wÞ 1 tan > < x re 2 z re
(8)
> > > z2 e > > : sz ðzÞ ¼ P0 ð1 þ 2 Þ re
In Eq. (8), z is the through depth coordinate and P0 is the maximum contact pressure at the center of contact that can be calculated for static and dynamic loading according to Eq. (9). Also, re is the maximum elastic radius of contact that is calculated for static and dynamic loading by Eq. (4).
P0 ¼
8 > > > > > 1 > s > < P0 ¼
6FEeq 2 p R2
!13
> > i1 > > 4h d 3 2 2 5 > > 5 P ¼ rp E A f eq > 0 : p
(9)
However, the value of sr is the stress trapped in the workpiece due to on contact. When the process is finished, the relaxation occurs to satisfy the self-equilibrium condition. Hence, the induced stress after relaxation in the entire burnishing field is: Ind sInd x ¼ sy ¼
1þw r s 1w x
(10)
Another relaxation occurs when the thin strip is completely with thickness of t and width of w unclamped and released from clamping. In such condition, two source of stress due to bending
sRS
8 smax ssurf zmax z 1 s max > > zmax smax > > > > 2 3 > < 2 z zmax 1 ¼ z0 zmax > 6 7 > > smax 4( > 2 )2 5 > > > z zmax : 1 z0 zmax
z zmax (13) z > zmax
where the ssurf is the value of residual stress in the surface of the sample where the depth is zero; also, smax is the maximum value of compressive residual stress occurs at the depth of zmax. Furthermore, z0 is the depth where compressive residual stress reaches to zero. Fig. 2 clarifies the typical residual stress distribution curve through the depth of sample. 3. Experiments Burnishing experiments were carried out on 3 mm 50 mm 100 mm aluminum 6061-T6 made samples. The specimens were clamped on a force dynamometer which attached to the CNC machine table and then subjected to burnishing in squared area with dimension of 50 mm 50 mm. Ultrasonic apparatus including ultrasonic transducer, booster and horn was
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Fig. 2. Typical illustration residual stress field and its elements in burnishing process.
designed and fabricated to transfer the high-frequency vibration from ultrasonic power supply to the ball type strike. Modal analysis has been carried out to obtain the exact dimension of ultrasonic horn to assure its resonance frequency is within the range of ultrasonic transducer. According to the analysis, the vibration frequency was set to 20,180 Hz. The experimental setup has been shown in Fig. 3. During the process, the forming force in axial and transverse directions were measured through a 3-componenets force dynamometer KISTLER 9257B. The dynamometer is mounted on machine table and the specimens are clamped with dynamometer. In order to perform the process with different vibration amplitude, the power percentage is varied by regulating the input voltage and amplitude is measured by means of AEC-5502A-17 eddy current sensor.
In order to measure the residual stress, an X-ray diffraction (XRD) machine StressTech has been utilized. The XRD machine setup and its calibration for residual stress measurement of aluminum and copper were partially different. The Cr and Cu tubes were utilized for stress measurement of aluminum and copper, respectively; both the tubes were operating at 27 kV and 5 mA. The peaks were observed at angle of 139.6 for aluminum and 146 for copper. The measurement has been carried out under number of 11 tilt angles (i.e. 0 , ±18.4 , ±26.6 , ±33.2 , ±39.2 and ±45 ) to provide required data for construction of linear regression function Since, in the present work, the residual stress was modeled taking into account plane stress condition, the stress values only on 0 rotation angle was considered in order to achieve the consistency between the results of experiment and the analytical model. In order to measure through depth residual stress distribution, electro polishing has been carried out to remove surface layers without inducing additional stress. The area subjected to electro polishing was about 3 cm2 and different electrolytes and parameters were used for aluminum and copper. For aluminum alloy the electropolishing has been carried out with an electrolyte solution composed by 96% acetic acid and 4% perchloric acid; the cell voltage was fixed on 50 V and the machining time for achieving 0.1 mm material removal was 12 min. Furthermore, for electropolishing of copper, an electrolyte comprising 500 ml distilled water, 500 ml ethanol and 250 ml phosphoric acid was utilized; the polishing time and voltage for 0.1 mm material removal were fixed on 5 min and 30 V, respectively. The purpose of experimentations is to confirm the results derived by analytical model and optimization. Here, number of two experiments has been performed and their through depth residual stress distribution were measured. The first experiment is done for verification of analytical model under random parameter setting i.e. static force of 100 N, vibration amplitude of 10 mm and 6 mm tungsten carbide ball. Also, the second experiment has been conducted to confirm the results of optimization approach. 4. Results and discussion 4.1. Verification of optimal results In order to verify the results derived by analytical model, an experiment with operating condition of 100 N static force, 10 mm vibration amplitude and 6 mm tungsten carbide ball has been carried out and the residual stress distribution of the processed sample has been measured. Fig. 4 represents the comparison of residual stress distribution along the thickness direction obtained by both approaches. it is clear from the figure that the surface
Fig. 3. Experimental setup including g ultrasonic burnishing tool, power supply, CNC machine, dynamometer and workpiece.
Fig. 4. Comparison of residual stress distribution derived from analytical model with that measured through experiment.
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residual stress that is predicted by analytical model is about 64 MPa; while the measured value is 58 MPa. The prediction error is 13% that is quite accurate compared to results derived by finite element studies developed in other literatures [13,14]. Also, the maximum value of residual stress occurs at the depth derived by analytical model is 113 MPa while the value measured through experiment is 134 MPa. The prediction error for this term is less than 15%. Also, it is clear from the figure, in both the approaches, the maximum depth of compressive residual is about 0.7 and 0.8 mm. From the obtained results, it can be inferred that the residual stress distribution derived from analytical model is consistent well with those measured through experiments. Hence, the analytical model can be effectively used to analyze effect of ultrasonic burnishing parameters on distribution of residual stress and find optimum parameter setting. For further analysis of consistency of the results, surface and maximum values of compressive residual stress for copper, titanium and steel which were obtained by experiments have been compared with the values derived from analytical model. The experimental residual stress values of copper samples has been used by a previous work carried out by author [16]; also the values for steel and titanium have been extracted from the works carried out by Liu et al. [17] and Pyoun et al. [18]. Table 2, demonstrates the comparison results along with prediction error. It is clear from the table that the values of prediction error of surface residual stress for copper, steel and titanium are 12%, 15% and 8%, respectively. Furthermore, the error values of maximum residual stress for copper, steel and titanium are 17%, 9% and 14%, respectively. The results of Table 2 confirm that the developed analytical model is consistent well for prediction of residual stress for different types of material. In other word, the model is adjustable not for specific type of material but for different material with various hardening behaviors. 4.2. Parametric influence In order to study effect of parameters on residual stress distribution, the target parameter is varied through its range while other
5
factors are kept constant at a given value. The devoted range for static force is 50, 100 and 150 N, for vibration amplitude is 5, 10 and 15 mm, for ball material is tungsten carbide, steel and silicon nitride and for ball diameter is 3, 6 and 9 mm. The elastic properties of different ball material have been presented in Table 3. Figs. 5 and 6 present effect of process parameters on residual stress distribution. It is clear from Fig. 5aec as well as 6a, 6b and 6c, that as the static force, vibration amplitude and ball diameter are increased, the value of surface compressive residual stress decreases; however, the maximum depth is increased. When the aforementioned parameters increase, the induced stress is distributed in further depth. This condition causes an increase in the bending momentum and its corresponding tensile stress after releasing from clamp. By summation of thee type stresses with induced stress, the value of compressive residual stress at the surface is decreased. On the other hand, the maximum depth of compressive residual stress increases by increasing the static force, vibration amplitude and ball diameter. In physical point of view, during indentation action of the ball into the tool, the plastic stress in plane direction is completely tensile; by increasing the aforementioned parameters, the amount of tensile plastic and relevant deformation band are also increased. In such condition, the residual stress that is difference between plastic and elastic tends to tensile values. Hence, the amount of compressive residual stress is decreased but it is distributed in wider and deeper dimensions. About the ball material, it is clear from Figs. 5d and 6d, that this parameter isn't a significant factor regarding residual stress distribution. On one hand, due to further density and tungsten carbide ball, the compressive induced stress and distributed depth caused by this material is significantly higher than that of steel and silicon nitride. On the other hand, the tensile stress after unclamping for tungsten carbide is also higher than other balls. However, summation these stresses result in the effect of ball material on magnitude residual stress distribution is being insignificant. It is worth notifying the effect of ball material on maximum compressive residual stress depth is completely significant where the tungsten carbide ball causes significant enhancement of the depth.
Table 2 Comparison of the results of residual stress measured by experiment and those derived from analytical model. Material
Copper [16]
Steel [17]
Titanium [18]
Condition
F ¼ 100 N A ¼ 10 mm D ¼ 6 mm WC ball F ¼ 200 N A ¼ 6 mm D ¼ 15 mm Steel ball F ¼ 20 N A ¼ 14 mm D ¼ 2.4 mm WC ball
Surface compressive residual stress
Maximum compressive residual stress
Measured
Predicted
Measured
Predicted
78
68
153
127
733
623
916
833
300
276
688
591
Table 3 Elastic properties of ball material. Ball material
Density (kg/m3)
Modulus of elasticity (GPa)
Poisson ratio
Tungsten carbide (WC) Silicon nitride (Si3N4) Steel (St)
15,600 2300 7800
600 230 210
0.22 0.27 0.3
Please cite this article as: R. Teimouri, Optimization of residual stress field in ultrasonic assisted burnishing process, International Journal of Lightweight Materials and Manufacture, https://doi.org/10.1016/j.ijlmm.2019.04.009
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Fig. 5. Residual stress distribution under different values of (a) static force (b) vibration amplitude (c) ball diameter (d) ball material.
Fig. 6. Effect of process factors on surface compressive residual stress and maximum depth of compressive residual stress (a) static force (b) vibration amplitude (c) ball diameter (d) ball material.
The density and elasticity modulus of tungsten carbide ball are significantly higher than those of steel and silicon nitride. For this reason, the contact pressure and corresponding elastic and plastic
stresses caused by this ball are higher. This characteristic causes increase in elastic and plastic deformation depths that lead to distribution of residual stress in further area.
Please cite this article as: R. Teimouri, Optimization of residual stress field in ultrasonic assisted burnishing process, International Journal of Lightweight Materials and Manufacture, https://doi.org/10.1016/j.ijlmm.2019.04.009
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increasing one of them, the other one is decreased subsequently. Hence, to have desired values of both at a same time, it is required to perform optimization. In this section a constrained optimization method is performed to maximize the surface residual stress with respect to desired value of maximum depth. Here the optimization is performed by use of particle swarm optimization (PSO) algorithm. Particle swarm optimization is an evolutionary search algorithm that uses population based stochastic method to find the global optima [17]. PSO is similar to GA to some extent during its evolutionary motion; both of them are initialized with a random population and then find the optimum by updating the generation. However, unlike GA, operator such as mutation and crossover cannot be found in the PSO. Hence, this difference makes implementation simpler and shortens execution time. It is reported b different author that the PSO is a completely suitable algorithm for multi-objective optimization of manufacturing process problems [18e20]. The step by step optimization of PSO is presented as follows; also, further detail about the algorithm implementation and mathematical equations can be found in a work by Rao [17]. The objective function is maximization of surface residual stress value; also, constrain is the maximum depth of compressive residual stress that is 0.8 mm. In other word, the PSO algorithm searches to find the solution causes maximum residual stress; if the solution satisfies the maximum depth of 0.8 mm, it will be accepted. Otherwise, the algorithm updates the results with new solution to find most suitable one. The flowchart of algorithm for this optimization technique has been presented in Fig. 7. In this algorithm the stop condition was set to 200 iterations. For more clarification, Table 4 remarks the optimization aim and relevant criterion. It is inferred from Table 4 that the maximum depth of compressive residual stress for the optimization was set to 0.8 mm. This value has been selected based on previous works [16,21], and the depth reported by Liu et al. [15]. For implementation of PSO algorithm, number of 200 particles was considered in a swarm; also, the initial velocity of zero and
Fig. 7. Flowchart of modified PSO algorithm for constrained optimization problem.
4.3. Optimization According to graphs shown in Figs. 5 and 6, it can be inferred that it isn't possible to increase the surface compressive residual stress and the maximum depth at a same time. It means that by
Fig. 8. Comparison of residual stress distribution derived from analytical model and confirmatory experiment.
Table 4 Optimization criteria for maximizing the surface residual stress subjected to a specified depth. Objectives
Criterion
Remarks
sRes(z ¼ 0) z0, sRes(z0) ¼ 0
Maximize Up to 0.8 mm 50e150 N 5e15 mm 3e9 mm Tungsten carbide, steel and silicon nitride
Residual stress at the depth of zero The depth that is expected for burnishing process The optimization limit for input variables
Static force Vibration amplitude Ball diameter Ball material
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Table 5 Obtained optimal setting along with residual stress magnitude and depth which were obtained from analytical model and confirmatory experiment and corresponding error values. Optimum setting
F ¼ 120 N A ¼ 14 mm D ¼ 3 mm WC ball
ssurf (MPa)
smax (MPa)
zmax (mm)
z0 (mm)
Analytical
Experiment
Analytical
Experiment
Analytical
Experiment
Analytical
Experiment
110 Error
98 12.2%
132 Error
151 12.5%
0.2 Error
0.2 0%
0.8 Error
0.7 14.3%
learning rate of 2 has been adopted. The algorithm has been implemented and the most optimal solution for maximizing the surface residual stress has been obtained and presented in Table 4. It is seen from Table 4 that the 3 mm tungsten carbide ball along with static force of 120 N and 14 mm vibration amplitude is the most optimal solution that causes achieving the surface residual stress of 110 N where the maximum depth is 0.8 mm. In order to investigate to find the consistency of the optimum result, a confirmatory experiment with the obtained optimal solution has been carried out and the residual stress distribution of the fabricated sample has been measured through XRD method. The optimum residual stress distributions derived from analytical approach as well as those measured through experimental measurement have been presented in Fig. 8. According to the figure, it is clear that the results derived from optimization approach are consistent well with experiments. Also, Table 5 summarizes the comparison between measured and predicted values of residual stress components at optimum processing condition. From this table, it is seen that the value of surface residual stress predicted by analytical study is 110 MPa where the experimental value is 98 MPa. Also, the maximum magnitude of compressive residual stress is 132 MPa while the value for experimental measurement is 151 MPa. Furthermore, for both approaches the maximum value of compressive residual stress occurs at the depth of 0.2 mm. It is worth notifying that the maximum depth of compressive residual stress obtained by analytical approach is 0.8 mm; while the depth measured by experiment is 0.7 mm. The results confirm that analytical and proposed optimization approach is consistent well to be used as effective tool for investigation and optimization of ultrasonic assisted ball burnishing process.
5. Conclusion In the present study an attempt was made to optimize the residual stress field distribution. Here, the analytical model of residual stress in author's previous work [16] has been incorporated with particle swarm optimization algorithm to maximize the surface residual stress subjected to maximum compressive residual stress depth of 0.8 mm. Obtained results can be summarized as follows: The improved analytical model of residual stress using cubic interval function (that is not previously considered in previous work) is consistent well with the experimental measurement. The mean prediction error of residual stress in surface layers are less than 13%, while the maximum compressive residual stress at the depth of 0.3 mm is modeled with error value of 15%. As the vibration amplitude and ball diameter are increases, the magnitude of surface residual stress and the maximum depth decreases due to increase of tensile plastic stresses; while, the maximum depth of compressive residual stress are increases due to increase of deformation area. Furthermore, the ball
material and static force aren't effective parameters influencing the residual stress distribution. It is found from the results that it is not possible to increase the surface compressive residual stress value and maximum depth at same time by controlling a factor. Hence, optimization is required to achieve best parameter setting. Optimization results revealed that the setting of 3 mm tungsten carbide ball along with 120 N static force and 15 mm vibration amplitude is an optimal parameter setting causes 110 MPa compressive residual stress at the surface as well as 0.8 mm depth where the CRS exists. The obtained optimal results from analytical approach and PSO algorithm was compatible with residual stress distribution according to the magnitude and the depth where the prediction error in all items were less than 15%.
Conflict of interest The authors declare that there is no conflicts of interest. Appendix A. Supplementary data Supplementary data to this article can be found online at https://doi.org/10.1016/j.ijlmm.2019.04.009. References [1] Z.Y. Liu, C.H. Fu, M.P. Sealy, Y. Zhao, Y.B. Guo, Benchmark burnishing with Almen strip for surface integrity, Proc. Manuf. 10 (2017 Jan 1) 456e466. [2] M.H. El-Axir, An investigation into roller burnishing, Int. J. Mach. Tool Manuf. 40 (11) (2000 Sep 1) 1603e1617. [3] A. Sequera, C.H. Fu, Y.B. Guo, X.T. Wei, Surface integrity of inconel 718 by ball burnishing, J. Mater. Eng. Perform. 23 (9) (2014 Sep 1) 3347e3353. [4] G.D. Revankar, R. Shetty, S.S. Rao, V.N. Gaitonde, Analysis of surface roughness and hardness in ball burnishing of titanium alloy, Measurement 58 (2014 Dec 1) 256e268. [5] L. Jinlong, L. Hongyun, Effect of surface burnishing on texture and corrosion behavior of 2024 aluminum alloy, Surf. Coat. Technol. 235 (2013 Nov 25) 513e520. [6] C. Ionescu, V. Hoeck, O.N. Crandell, K. Sari c, Burnishing versus smoothing in ceramic surface finishing: a SEM study, Archaeometry 57 (1) (2015 Feb) 18e26. [7] K.O. Low, K.J. Wong, Influence of ball burnishing on surface quality and tribological characteristics of polymers under dry sliding conditions, Tribol. Int. 44 (2) (2011 Feb 1) 144e153. [8] S. Yang, D. Umbrello, O.W. Dillon Jr., D.A. Puleo, I.S. Jawahir, Cryogenic cooling effect on surface and subsurface microstructural modifications in burnishing of CoeCreMo biomaterial, J. Mater. Process. Technol. 217 (2015 Mar 1) 211e221. [9] W. Ting, W. Dongpo, L. Gang, G. Baoming, S. Ningxia, Investigations on the nanocrystallization of 40Cr using ultrasonic surface rolling processing, Appl. Surf. Sci. 255 (5) (2008 Dec 30) 1824e1829. [10] A. Rodríguez, L.L. de Lacalle, A. Celaya, A. Lamikiz, J. Albizuri, Surface improvement of shafts by the deep ball-burnishing technique, Surf. Coat. Technol. 206 (11e12) (2012 Feb 15) 2817e2824. [11] M. Korzynski, A. Pacana, J. Cwanek, Fatigue strength of chromium coated elements and possibility of its improvement with slide diamond burnishing, Surf. Coat. Technol. 203 (12) (2009 Mar 15) 1670e1676. [12] B. Sachin, S. Narendranath, D. Chakradhar, Effect of cryogenic diamond burnishing on residual stress and microhardness of 17-4 PH stainless steel, Mater. Today Proc. 5 (9) (2018 Jan 1) 18393e18399.
Please cite this article as: R. Teimouri, Optimization of residual stress field in ultrasonic assisted burnishing process, International Journal of Lightweight Materials and Manufacture, https://doi.org/10.1016/j.ijlmm.2019.04.009
R. Teimouri / International Journal of Lightweight Materials and Manufacture xxx (xxxx) xxx [13] M. Sayahi, S. Sghaier, H. Belhadjsalah, Finite element analysis of ball burnishing process: comparisons between numerical results and experiments, Int. J. Adv. Manuf. Technol. 67 (5e8) (2013 Jul 1) 1665e1673. [14] Y. Liu, L. Wang, D. Wang, Finite element modeling of ultrasonic surface rolling process, J. Mater. Process. Technol. 211 (12) (2011 Dec 1) 2106e2113. vesque, On the potential applications of a [15] H.Y. Miao, S. Larose, C. Perron, M. Le 3D random finite element model for the simulation of shot peening, Adv. Eng. Softw. 40 (10) (2009 Oct 1) 1023e1038. [16] R. Teimouri, S. Amini, M. Guagliano, Analytical modeling of ultrasonic surface burnishing process: evaluation of residual stress field distribution and strip deflection, Mater. Sci. Eng. A 747 (2019 Feb 18) 208e224. [17] Y. Liu, X. Zhao, D. Wang, Effective FE model to predict surface layer characteristics of ultrasonic surface rolling with experimental validation, Mater. Sci. Technol. 30 (6) (2014) 627e636.
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[18] Y.S. Pyoun, J.H. Park, C.M. Suh, A. Amanov, J.H. Kim, Friction and Wear Characteristics of SUS304 and SUS630 After Ultrasonic Nanocrystal Surface Modification, Advanced Materials Research, Trans Tech Publ, 2011, pp. 174e177. [19] S.S. Rao, Engineering Optimization: Theory and Practice, John Wiley & Sons, 2009 Jul 20. [20] C.P. Mohanty, S.S. Mahapatra, M.R. Singh, A particle swarm approach for multi-objective optimization of electrical discharge machining process, J. Intell. Manuf. 27 (6) (2016 Dec 1) 1171e1190. [21] V.N. Gaitonde, S.R. Karnik, Minimizing burr size in drilling using artificial neural network (ANN)-particle swarm optimization (PSO) approach, J. Intell. Manuf. 23 (5) (2012 Oct 1) 1783e1793.
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Optimization of residual stress field in ultrasonic assisted burnishing process Reza Teimouri Faculty of Mechanical Engineering, University of Kashan, Kashan, Iran
a r t i c l e i n f o
a b s t r a c t
Article history: Received 30 March 2019 Received in revised form 25 April 2019 Accepted 27 April 2019 Available online xxx
Surface compressive residual stress and its penetration depth are of important characteristics of burnishing process. The higher values compressive residual stress in the surface of the treated sample can delay the fatigue crack initiation; also, the further penetration depth restricts fatigue crack propagation. However, achieving both of performance at same time needs careful selection of burnishing parameter. In the present study an optimization approach is made to maximize the value of surface compressive residual stress subjected to specified penetration depth. The analytical model of residual stress previously developed by the author is firstly modified with a cubic interval function and then used to find how the ultrasonic assisted burnishing factors i.e. static force, vibration amplitude, ball diameter and material influence the residual stress field distribution. Then the model was then incorporated with particle swarm optimization algorithm to find optimal parameter setting. Results showed that it isn't possible to maximize both the surface compressive residual stress and its penetration depth at same time. Furthermore, to have maximum value of compressive residual stress magnitude at the surface with the penetration depth of 0.5 mm, it is required to use tungsten carbide ball with 3 mm diameter; also, the static load and vibration amplitude should be selected at the values of 120 N and 14 mm. The compressive surface residual stress in optimized condition is about 110 MPa that is compatible well with the 98 MPa obtained by confirmatory experiment. Also, the maximum depth compressive residual stress for optimum condition measured by experiment is 0.7 mm while it is predicted 0.8 mm by analytical approach. © 2019 The Authors. Production and hosting by Elsevier B.V. on behalf of KeAi Communications Co., Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/bync-nd/4.0/).
Keywords: Ultrasonic burnishing Compressive residual stress field Particle swarm optimization
1. Introduction Ultrasonic surface treatment is a cold working process in which ball or roller shape tool are exerted to the work surface incorporating both the static and dynamic loads. Here, the static load is forced to the work surface by a static pressure caused by downward motion of the tool tip into work surface; also, the dynamic load is applied by series of overlapped vibration impacts. This treatment leads to an improvement of fatigue behavior caused by both the developed compressive residual stresses and plastic strains due to the cold working effect. Ultrasonic nanocrystalline surface modification, and ultrasonic surface rolling or burnishing [1e3] are two main alternatives of ultrasonic surface treatment process. In former, the contact
E-mail address: [email protected]. Peer review under responsibility of Editorial Board of International Journal of Lightweight Materials and Manufacture
condition between the tool tip and work surface is purely sliding which leads to the tool to be worn-out and increases the surface roughness; while in the latter, the burnishing ball rolls over the work surface that enhances the surface quality and significantly reduces the tool wear. Burnishing in presence of ultrasonic vibration is a surface mechanical treatment process that is used in the last stage of manufacturing process planning. The process causes achieving high quality surface finish and enhanced fatigue properties through inducing compressive residual stress in the surface layers. Depends to the processed material, the compressive residual stress depth obtained by burnishing is significantly higher than other surface treatment process such as shot peening [1]. The burnishing process is applicable for many engineering materials including metals [2e5], ceramics [6], polymers [7] and biomaterials [8]. Compressive residual stress field (CRSF) distributed in burnished part plays an important role in functionality of burnishing process. However, due to expensive and time consuming measurement of residual stress; analyzing effect of burnishing
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parameters on this characteristic wasn't well understood. Limited study reported in the literatures regarding effect of burnishing parameters on CRSF through experimental measurements. Ting et al. [9] compared residual stress of as polished 40Cr steel with burnished sample. They revealed that surface residual stress of burnished sample is enhanced from 200 MPa to 846 MPa. Rodriguez et al. [10] reported that applying burnishing process with hydrostatic pressure of 20 MPa to turned samples changes the surface tensile residual stress with magnitude of 700 MPa to 800 MPa. Korzynski et al. [11] showed that performing burnishing process significantly enhances the state of residual stress after coating. Sachin et al. [12] applied burnishing process with cryogenic cooling to burnish the precipitated hardened stainless steel. Results revealed amount of compressive residual stress of burnished sample in presence of cryogenic cooling is significantly improved compared to MQL and dry condition. According to above reviewed papers, it is found that analyzing residual stress has been carried out in limited number of experiments due to costly and time consuming measurements. Hence, to solve this problem, finite element simulation has been applied for analyzing the residual state in burnishing process. In this case, Sayahi et al. [13] analyzed burnishing of Titanium alloy and found effect of static pressure and ball diameter on residual stress distribution. Mohammadi et al. [13] used FE simulation by ABAQUS software to study effect of static force, feed rate, ball diameter and pass number on residual stress distribution of Tie6Ale4V. Liu et al. [14] performed a FEA to study effect of ultrasonic surface burnishing factor on compressive residual stress field. They reported that to achieve desired value of residual stress and penetration depth, further values of static force and vibration amplitude as along with less value of spindle speed should be adopted. Even though, finite element simulation is effective method to precisely predict the performance measures the computational time by this method is quite long where it sometimes computational goes beyond one week [15]. Hence, analytical models are applicable way to understand the mechanics of residual stress distribution in a very short period of the time. In the previous work carried out by the author, the residual stress distribution of thin walled aluminum alloy has been modeled through an analytical approach [16]. However, the effect of process parameters on surface residual stress and the maxim penetration depth of compressive residual stress were not well analyzed. In the present study, firstly the developed analytical model of residual stress is modified to smooth type through applying a cubic function. Then effect of static force, vibration amplitude, ball diameter and its material on magnitude of residual stress in the surface and the maximum penetration depth of compressive residual stress are studied. Furthermore, the developed analytical model is used as objective function to be incorporated by particle swarm optimization for maximization of the surface compressive residual stress subjected to specified penetration depth. The analytical model of residual stress in author's previous work [16] ignored final relaxation stage. Hence, in the present study a relaxation based on a cubic model was developed to enhance the prediction accuracy of analytical model. On the other hand, for thin strip, due to relaxation of stress after unclamping, it is tough to maximize both the surface compressive residual stress and maximum depth simultaneously. Hence, in order to achieve desired residual stress value, it is required to solve a constrained optimization problem. Hence, in the present paper, the proposed objectives are considered.
2. Analytical model The residual stress is a plane stress that is varied through the depth of the processed specimens. According to the work previously published by the author [16], the induced stress can be calculated by the difference between the devitoric plastic stress and elastic stress as expressed in Eq. (1).
srx ¼ sry ¼
1 p si sei 3
(1) p
where sr is the transition stress due to each impact, si and sei are the effective plastic and elastic stress respectively. The plastic stress is calculated by equation (2) according to combined isotropicekinematic hardening material model.
spi ¼ sy þ Q 1 exp bεpi
þ
C
g
p 1 exp gεi
(2)
where, Q and b are the materials parameters for isotropic hardening; also, C and g are the parameters related to kinematic hardening terms. Table 1 shows the material constants for combined isotopicekinematic hardening model. Also εip is the equivalent plastic strain that has linear relationship with equivalent elastic strain according to equations (3) and (4): p
εi ¼
e εi e εy þ j εi εs
εei < εy εei > εy
(3)
8 > > > > > r s þ r dp > > j ¼ ps > > > > r e þ r de > > > > 1 > > 2 > s F > > r ¼ > p > 3psy > > > > > 1 < 1 r 4 d 2 r ¼ 2Rð p Af Þ p > 3sy > > > > > 1 > > > 3FR 3 > > r se ¼ > > 4E > eq > > > > >
1 > > D 5rp3 A2 f 2 5 > d > r ¼ > e > > 2 Eeq > :
(4)
where, F, A, R, f and r are the static force, vibration amplitude, ball radius and vibration frequency and ball density, respectively. J is the strain coefficient that is obtained by the ratio of plastic to elastic contact radius. Also, r sp , r dp , r se and r de are the radius of contact in plastic and elastic regime due to static and dynamic loads. sy is the yield stress and εy is the yield strain. Eeq is the equal elasticity modulus that is calculated by Eq. (5); and εei is the effective elastic strain that is calculated by Eq. (6). For further clarification, Fig. 1 demonstrates the geometry of contact.
1 w21 1 w22 1 ¼ þ Eeq E1 E2
(5)
Table 1 Combined isotropicekinematic material constitutive parameters for AA6061-T6 [16]. Material
sy (MPa)
Q (MPa) (MPa)
b
C (MPa)
g
AA6061-T6
209.2
38.9
21.1
3529.3
65.16
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momentum and tensile force are released and causes redistribution of residual stress. Hence, the final residual stress distribution is:
Res Ind sRes x ðzÞ ¼ sy ðzÞ ¼ sx ðzÞ þ sMx ðzÞ þ sFx
(11)
Fig. 1. A schematic illustration of elastic-plastic indentation of elastic sphere and elastic-plastic semi-finite body.
E1, E2 and w1 and w2 are the elastic modulus and Poisson ratios of workpiece and ball, respectively.
εei ¼
sei
(6)
E1
sei is the effective Von-Mises elastic stress that is calculated by following equations.
sei ¼
sex
sey
2
þ
sey
sez
pffiffiffi 2
2
2 2 1
þ
sez
sex
(7)
where, sx, sy and sz are the principal contact stresses that can be determined as follows:
8 ðt > > > > > Fx ¼ sInd x ðzÞwdz > > > > > 0 > > > > > ðt > > > t
(12)
By clarification of residual stress field distribution, the typical form of residual stress can be modified by an interval function:
8 1 ! 1 > z z2 > e e 1 re > > 1þ 2 þ s ðzÞ ¼ sy ðzÞ ¼ P0 ð1 þ wÞ 1 tan > < x re 2 z re
(8)
> > > z2 e > > : sz ðzÞ ¼ P0 ð1 þ 2 Þ re
In Eq. (8), z is the through depth coordinate and P0 is the maximum contact pressure at the center of contact that can be calculated for static and dynamic loading according to Eq. (9). Also, re is the maximum elastic radius of contact that is calculated for static and dynamic loading by Eq. (4).
P0 ¼
8 > > > > > 1 > s > < P0 ¼
6FEeq 2 p R2
!13
> > i1 > > 4h d 3 2 2 5 > > 5 P ¼ rp E A f eq > 0 : p
(9)
However, the value of sr is the stress trapped in the workpiece due to on contact. When the process is finished, the relaxation occurs to satisfy the self-equilibrium condition. Hence, the induced stress after relaxation in the entire burnishing field is: Ind sInd x ¼ sy ¼
1þw r s 1w x
(10)
Another relaxation occurs when the thin strip is completely with thickness of t and width of w unclamped and released from clamping. In such condition, two source of stress due to bending
sRS
8 smax ssurf zmax z 1 s max > > zmax smax > > > > 2 3 > < 2 z zmax 1 ¼ z0 zmax > 6 7 > > smax 4( > 2 )2 5 > > > z zmax : 1 z0 zmax
z zmax (13) z > zmax
where the ssurf is the value of residual stress in the surface of the sample where the depth is zero; also, smax is the maximum value of compressive residual stress occurs at the depth of zmax. Furthermore, z0 is the depth where compressive residual stress reaches to zero. Fig. 2 clarifies the typical residual stress distribution curve through the depth of sample. 3. Experiments Burnishing experiments were carried out on 3 mm 50 mm 100 mm aluminum 6061-T6 made samples. The specimens were clamped on a force dynamometer which attached to the CNC machine table and then subjected to burnishing in squared area with dimension of 50 mm 50 mm. Ultrasonic apparatus including ultrasonic transducer, booster and horn was
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Fig. 2. Typical illustration residual stress field and its elements in burnishing process.
designed and fabricated to transfer the high-frequency vibration from ultrasonic power supply to the ball type strike. Modal analysis has been carried out to obtain the exact dimension of ultrasonic horn to assure its resonance frequency is within the range of ultrasonic transducer. According to the analysis, the vibration frequency was set to 20,180 Hz. The experimental setup has been shown in Fig. 3. During the process, the forming force in axial and transverse directions were measured through a 3-componenets force dynamometer KISTLER 9257B. The dynamometer is mounted on machine table and the specimens are clamped with dynamometer. In order to perform the process with different vibration amplitude, the power percentage is varied by regulating the input voltage and amplitude is measured by means of AEC-5502A-17 eddy current sensor.
In order to measure the residual stress, an X-ray diffraction (XRD) machine StressTech has been utilized. The XRD machine setup and its calibration for residual stress measurement of aluminum and copper were partially different. The Cr and Cu tubes were utilized for stress measurement of aluminum and copper, respectively; both the tubes were operating at 27 kV and 5 mA. The peaks were observed at angle of 139.6 for aluminum and 146 for copper. The measurement has been carried out under number of 11 tilt angles (i.e. 0 , ±18.4 , ±26.6 , ±33.2 , ±39.2 and ±45 ) to provide required data for construction of linear regression function Since, in the present work, the residual stress was modeled taking into account plane stress condition, the stress values only on 0 rotation angle was considered in order to achieve the consistency between the results of experiment and the analytical model. In order to measure through depth residual stress distribution, electro polishing has been carried out to remove surface layers without inducing additional stress. The area subjected to electro polishing was about 3 cm2 and different electrolytes and parameters were used for aluminum and copper. For aluminum alloy the electropolishing has been carried out with an electrolyte solution composed by 96% acetic acid and 4% perchloric acid; the cell voltage was fixed on 50 V and the machining time for achieving 0.1 mm material removal was 12 min. Furthermore, for electropolishing of copper, an electrolyte comprising 500 ml distilled water, 500 ml ethanol and 250 ml phosphoric acid was utilized; the polishing time and voltage for 0.1 mm material removal were fixed on 5 min and 30 V, respectively. The purpose of experimentations is to confirm the results derived by analytical model and optimization. Here, number of two experiments has been performed and their through depth residual stress distribution were measured. The first experiment is done for verification of analytical model under random parameter setting i.e. static force of 100 N, vibration amplitude of 10 mm and 6 mm tungsten carbide ball. Also, the second experiment has been conducted to confirm the results of optimization approach. 4. Results and discussion 4.1. Verification of optimal results In order to verify the results derived by analytical model, an experiment with operating condition of 100 N static force, 10 mm vibration amplitude and 6 mm tungsten carbide ball has been carried out and the residual stress distribution of the processed sample has been measured. Fig. 4 represents the comparison of residual stress distribution along the thickness direction obtained by both approaches. it is clear from the figure that the surface
Fig. 3. Experimental setup including g ultrasonic burnishing tool, power supply, CNC machine, dynamometer and workpiece.
Fig. 4. Comparison of residual stress distribution derived from analytical model with that measured through experiment.
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residual stress that is predicted by analytical model is about 64 MPa; while the measured value is 58 MPa. The prediction error is 13% that is quite accurate compared to results derived by finite element studies developed in other literatures [13,14]. Also, the maximum value of residual stress occurs at the depth derived by analytical model is 113 MPa while the value measured through experiment is 134 MPa. The prediction error for this term is less than 15%. Also, it is clear from the figure, in both the approaches, the maximum depth of compressive residual is about 0.7 and 0.8 mm. From the obtained results, it can be inferred that the residual stress distribution derived from analytical model is consistent well with those measured through experiments. Hence, the analytical model can be effectively used to analyze effect of ultrasonic burnishing parameters on distribution of residual stress and find optimum parameter setting. For further analysis of consistency of the results, surface and maximum values of compressive residual stress for copper, titanium and steel which were obtained by experiments have been compared with the values derived from analytical model. The experimental residual stress values of copper samples has been used by a previous work carried out by author [16]; also the values for steel and titanium have been extracted from the works carried out by Liu et al. [17] and Pyoun et al. [18]. Table 2, demonstrates the comparison results along with prediction error. It is clear from the table that the values of prediction error of surface residual stress for copper, steel and titanium are 12%, 15% and 8%, respectively. Furthermore, the error values of maximum residual stress for copper, steel and titanium are 17%, 9% and 14%, respectively. The results of Table 2 confirm that the developed analytical model is consistent well for prediction of residual stress for different types of material. In other word, the model is adjustable not for specific type of material but for different material with various hardening behaviors. 4.2. Parametric influence In order to study effect of parameters on residual stress distribution, the target parameter is varied through its range while other
5
factors are kept constant at a given value. The devoted range for static force is 50, 100 and 150 N, for vibration amplitude is 5, 10 and 15 mm, for ball material is tungsten carbide, steel and silicon nitride and for ball diameter is 3, 6 and 9 mm. The elastic properties of different ball material have been presented in Table 3. Figs. 5 and 6 present effect of process parameters on residual stress distribution. It is clear from Fig. 5aec as well as 6a, 6b and 6c, that as the static force, vibration amplitude and ball diameter are increased, the value of surface compressive residual stress decreases; however, the maximum depth is increased. When the aforementioned parameters increase, the induced stress is distributed in further depth. This condition causes an increase in the bending momentum and its corresponding tensile stress after releasing from clamp. By summation of thee type stresses with induced stress, the value of compressive residual stress at the surface is decreased. On the other hand, the maximum depth of compressive residual stress increases by increasing the static force, vibration amplitude and ball diameter. In physical point of view, during indentation action of the ball into the tool, the plastic stress in plane direction is completely tensile; by increasing the aforementioned parameters, the amount of tensile plastic and relevant deformation band are also increased. In such condition, the residual stress that is difference between plastic and elastic tends to tensile values. Hence, the amount of compressive residual stress is decreased but it is distributed in wider and deeper dimensions. About the ball material, it is clear from Figs. 5d and 6d, that this parameter isn't a significant factor regarding residual stress distribution. On one hand, due to further density and tungsten carbide ball, the compressive induced stress and distributed depth caused by this material is significantly higher than that of steel and silicon nitride. On the other hand, the tensile stress after unclamping for tungsten carbide is also higher than other balls. However, summation these stresses result in the effect of ball material on magnitude residual stress distribution is being insignificant. It is worth notifying the effect of ball material on maximum compressive residual stress depth is completely significant where the tungsten carbide ball causes significant enhancement of the depth.
Table 2 Comparison of the results of residual stress measured by experiment and those derived from analytical model. Material
Copper [16]
Steel [17]
Titanium [18]
Condition
F ¼ 100 N A ¼ 10 mm D ¼ 6 mm WC ball F ¼ 200 N A ¼ 6 mm D ¼ 15 mm Steel ball F ¼ 20 N A ¼ 14 mm D ¼ 2.4 mm WC ball
Surface compressive residual stress
Maximum compressive residual stress
Measured
Predicted
Measured
Predicted
78
68
153
127
733
623
916
833
300
276
688
591
Table 3 Elastic properties of ball material. Ball material
Density (kg/m3)
Modulus of elasticity (GPa)
Poisson ratio
Tungsten carbide (WC) Silicon nitride (Si3N4) Steel (St)
15,600 2300 7800
600 230 210
0.22 0.27 0.3
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Fig. 5. Residual stress distribution under different values of (a) static force (b) vibration amplitude (c) ball diameter (d) ball material.
Fig. 6. Effect of process factors on surface compressive residual stress and maximum depth of compressive residual stress (a) static force (b) vibration amplitude (c) ball diameter (d) ball material.
The density and elasticity modulus of tungsten carbide ball are significantly higher than those of steel and silicon nitride. For this reason, the contact pressure and corresponding elastic and plastic
stresses caused by this ball are higher. This characteristic causes increase in elastic and plastic deformation depths that lead to distribution of residual stress in further area.
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increasing one of them, the other one is decreased subsequently. Hence, to have desired values of both at a same time, it is required to perform optimization. In this section a constrained optimization method is performed to maximize the surface residual stress with respect to desired value of maximum depth. Here the optimization is performed by use of particle swarm optimization (PSO) algorithm. Particle swarm optimization is an evolutionary search algorithm that uses population based stochastic method to find the global optima [17]. PSO is similar to GA to some extent during its evolutionary motion; both of them are initialized with a random population and then find the optimum by updating the generation. However, unlike GA, operator such as mutation and crossover cannot be found in the PSO. Hence, this difference makes implementation simpler and shortens execution time. It is reported b different author that the PSO is a completely suitable algorithm for multi-objective optimization of manufacturing process problems [18e20]. The step by step optimization of PSO is presented as follows; also, further detail about the algorithm implementation and mathematical equations can be found in a work by Rao [17]. The objective function is maximization of surface residual stress value; also, constrain is the maximum depth of compressive residual stress that is 0.8 mm. In other word, the PSO algorithm searches to find the solution causes maximum residual stress; if the solution satisfies the maximum depth of 0.8 mm, it will be accepted. Otherwise, the algorithm updates the results with new solution to find most suitable one. The flowchart of algorithm for this optimization technique has been presented in Fig. 7. In this algorithm the stop condition was set to 200 iterations. For more clarification, Table 4 remarks the optimization aim and relevant criterion. It is inferred from Table 4 that the maximum depth of compressive residual stress for the optimization was set to 0.8 mm. This value has been selected based on previous works [16,21], and the depth reported by Liu et al. [15]. For implementation of PSO algorithm, number of 200 particles was considered in a swarm; also, the initial velocity of zero and
Fig. 7. Flowchart of modified PSO algorithm for constrained optimization problem.
4.3. Optimization According to graphs shown in Figs. 5 and 6, it can be inferred that it isn't possible to increase the surface compressive residual stress and the maximum depth at a same time. It means that by
Fig. 8. Comparison of residual stress distribution derived from analytical model and confirmatory experiment.
Table 4 Optimization criteria for maximizing the surface residual stress subjected to a specified depth. Objectives
Criterion
Remarks
sRes(z ¼ 0) z0, sRes(z0) ¼ 0
Maximize Up to 0.8 mm 50e150 N 5e15 mm 3e9 mm Tungsten carbide, steel and silicon nitride
Residual stress at the depth of zero The depth that is expected for burnishing process The optimization limit for input variables
Static force Vibration amplitude Ball diameter Ball material
Please cite this article as: R. Teimouri, Optimization of residual stress field in ultrasonic assisted burnishing process, International Journal of Lightweight Materials and Manufacture, https://doi.org/10.1016/j.ijlmm.2019.04.009
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R. Teimouri / International Journal of Lightweight Materials and Manufacture xxx (xxxx) xxx
Table 5 Obtained optimal setting along with residual stress magnitude and depth which were obtained from analytical model and confirmatory experiment and corresponding error values. Optimum setting
F ¼ 120 N A ¼ 14 mm D ¼ 3 mm WC ball
ssurf (MPa)
smax (MPa)
zmax (mm)
z0 (mm)
Analytical
Experiment
Analytical
Experiment
Analytical
Experiment
Analytical
Experiment
110 Error
98 12.2%
132 Error
151 12.5%
0.2 Error
0.2 0%
0.8 Error
0.7 14.3%
learning rate of 2 has been adopted. The algorithm has been implemented and the most optimal solution for maximizing the surface residual stress has been obtained and presented in Table 4. It is seen from Table 4 that the 3 mm tungsten carbide ball along with static force of 120 N and 14 mm vibration amplitude is the most optimal solution that causes achieving the surface residual stress of 110 N where the maximum depth is 0.8 mm. In order to investigate to find the consistency of the optimum result, a confirmatory experiment with the obtained optimal solution has been carried out and the residual stress distribution of the fabricated sample has been measured through XRD method. The optimum residual stress distributions derived from analytical approach as well as those measured through experimental measurement have been presented in Fig. 8. According to the figure, it is clear that the results derived from optimization approach are consistent well with experiments. Also, Table 5 summarizes the comparison between measured and predicted values of residual stress components at optimum processing condition. From this table, it is seen that the value of surface residual stress predicted by analytical study is 110 MPa where the experimental value is 98 MPa. Also, the maximum magnitude of compressive residual stress is 132 MPa while the value for experimental measurement is 151 MPa. Furthermore, for both approaches the maximum value of compressive residual stress occurs at the depth of 0.2 mm. It is worth notifying that the maximum depth of compressive residual stress obtained by analytical approach is 0.8 mm; while the depth measured by experiment is 0.7 mm. The results confirm that analytical and proposed optimization approach is consistent well to be used as effective tool for investigation and optimization of ultrasonic assisted ball burnishing process.
5. Conclusion In the present study an attempt was made to optimize the residual stress field distribution. Here, the analytical model of residual stress in author's previous work [16] has been incorporated with particle swarm optimization algorithm to maximize the surface residual stress subjected to maximum compressive residual stress depth of 0.8 mm. Obtained results can be summarized as follows: The improved analytical model of residual stress using cubic interval function (that is not previously considered in previous work) is consistent well with the experimental measurement. The mean prediction error of residual stress in surface layers are less than 13%, while the maximum compressive residual stress at the depth of 0.3 mm is modeled with error value of 15%. As the vibration amplitude and ball diameter are increases, the magnitude of surface residual stress and the maximum depth decreases due to increase of tensile plastic stresses; while, the maximum depth of compressive residual stress are increases due to increase of deformation area. Furthermore, the ball
material and static force aren't effective parameters influencing the residual stress distribution. It is found from the results that it is not possible to increase the surface compressive residual stress value and maximum depth at same time by controlling a factor. Hence, optimization is required to achieve best parameter setting. Optimization results revealed that the setting of 3 mm tungsten carbide ball along with 120 N static force and 15 mm vibration amplitude is an optimal parameter setting causes 110 MPa compressive residual stress at the surface as well as 0.8 mm depth where the CRS exists. The obtained optimal results from analytical approach and PSO algorithm was compatible with residual stress distribution according to the magnitude and the depth where the prediction error in all items were less than 15%.
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Please cite this article as: R. Teimouri, Optimization of residual stress field in ultrasonic assisted burnishing process, International Journal of Lightweight Materials and Manufacture, https://doi.org/10.1016/j.ijlmm.2019.04.009