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Theoretical calculation and experiment of the surface residual stress in the plane ultrasonic rolling
Journal of Manufacturing Processes 50 (2020) 573–580
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Journal of Manufacturing Processes journal homepage: www.elsevier.com/locate/manpro
Theoretical calculation and experiment of the surface residual stress in the plane ultrasonic rolling
T
Feng Jiaoa, Shuai-ling Lana,b, Bo Zhaoa,*, Yi Wanga a b
School of Mechanical and Power Engineering, Henan Polytechnic University, Jiaozuo Henan, 454003, China School of Mechanical and Automotive Engineering, Kaifeng University, Kaifeng Henan, 475004, China
ARTICLE INFO
ABSTRACT
Keywords: Plane ultrasonic rolling Residual stress Rolling force Contact area coefficient
The service life of the workpiece is largely determined by residual stress on the workpiece surface, which is the most important parameter of anti-fatigue. In order to study the characteristics of residual stress on workpiece surface, the theoretical model of residual stress on the surface of the single impact workpiece is established based on the elastoplastic theory. Subsequently, the relationship between the rolling depth and the rolling force in the plane ultrasonic rolling is established based on the Hertz contact theory, and the contact area coefficient is established to correct the theoretical model. Then, the plane ultrasonic rolling experiments are carried out to validate the model. The results exhibit that the rolling force linearly increases with the increase of rolling depth. The effect of step has a highest relationship with the contact area coefficient, moderate with the feed rate, and minor with the static force. With the increase in static force, the residual compressive stress increased as a whole. The residual compressive stress decrease with the increase in step and the feed rate has little influence on the residual stress. The results reveal that the modified theoretical model can improve the prediction accuracy of residual stress.
1. Introduction The fatigue life of the metallic components is largely determined by the surface residual stress [1–3]. At present, surface quenching, shot peening, laser intensification and supersonic particle bombardment are utilized to improve the surface residual stress [4,5]. Although the surface residual stress has been improved to a certain extent using the traditional techniques, the strengthen effect will be weaken due to the random impingement location, and the overlaps produced adjacent indentations under inappropriate process parameter [6,7]. With the development of ultrasonic technology, the ultrasonic rolling process (USRP) has been regarded as an outstanding technique to enhance the material surface residual compressive stress and maintain the interior invariant chemical composition of the material [8]. Wang et al. [9] found that the plastic deformation and residual stress of X80 steel after the USRP are calculated using finite element method, the error between simulation residual stress and measured on X80 steel surface was about 4.8 %. Zhao et al. [10] demonstrated that a uniformly distributed residual compressive stress on the surface of 304 Austenitic stainless steel was generated after the USRP using the finite element method, and a numerical simulation approach to investigate residual stress of the surface layer was presented. Mao et al. [11] explained that the
⁎
ultrasonic surface deep rolling could generate the compressive residual stress near the surface of Ti-6Al-4 V using the experimental method, and it also affect fatigue crack growth behavior by delaying the crack initiation and decelerating the crack propagation rate. Liu et al. [12] studied the surface characteristics of USRP by the finite element method, the results showed that the residual stress predicted from the FEM are in good agreement with the measurements, which can be used as a fast prediction tool for the design of process parameters. Zheng et al. [13] investigated the formation process of residual stress fields and distribution law of surface residual stress of 7050 aluminum alloy after 2D USRP, and the error of the FEM results reached about 10 % compared with experiments. Yang et al. [14] explored that the surface residual stress distribution of 2D21 aluminum alloy after USRP, and it was revealed that the fatigue life of materials increases by 7 times than that before ultrasonic rolling processing under the same stress condition. Zhang et al. [15] investigated the relationship between surface residual stress and fatigue limit, and found that the residual compressive stress and the fatigue limit increase significantly. From the above review, the residual compressive stress can effectively improve the service life of the workpiece. Therefore it is necessary to deeply research the residual stress after USRP. Till date, many scholars have used the finite element method to study the residual
Corresponding author. E-mail address: [email protected] (B. Zhao).
https://doi.org/10.1016/j.jmapro.2019.12.058 Received 27 July 2019; Received in revised form 26 December 2019; Accepted 30 December 2019 Available online 14 January 2020 1526-6125/ © 2019 Published by Elsevier Ltd on behalf of The Society of Manufacturing Engineers.
Journal of Manufacturing Processes 50 (2020) 573–580
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Fig. 1. Contact state between roller and plane.
stress after USRP. However, few references about theoretical model of the residual stress by USRP are available. Therefore, the theoretical model of residual stress on workpiece surface is established through combining the contact area coefficient with the residual stress on the surface of single impact workpiece. The results will be beneficial for the appropriate selection of the process parameters.
Fig. 2. Geometric contact model.
residual stress, a contact process of elastic-plastic between roller and plane should be investigated based on the contact mechanics [18]. According to the Hertz contact theory, as the roller contacts with the plane, there is an approximately circular pit and its radius is as same as roller on the surface of the workpiece. When the roller is removed, the radius of the pit increases due to elastic recovery. The specific contact process is shown in Fig. 3. When the material comes into yield, the residual stress is generated [19].
2. Theoretical model of single point impact residual stress The contact state between the roller and the plane is shown in Fig. 1 [16,17]. As shown in Fig. 1, a plastic deformation in the middle zone of the contact area and the contact stress is uniformly distributed. The rest of the contact zone is in the elastic deformation stage, and it is consistent with the Hertz stress distribution which gradually changes from the maximum contact to zero. The detailed expression is shown in Eq. (1).
2E * 2 a RT kRe
p (z ) =
z2
b 0
z z
y
where, σy is the single impact residual stress, σ´ is the unloading stress. According to the Hertz contact theory, the unloading process can be assumed to be an elastic process because the elastic recovery is not much. Based on the elastic half-space volume, the elastic recovery of the roller and plane is expressed in Eq. (7).
a (1)
b
+ E2 (1 where, E * = E1 (1 k is the function of the contact radius and the contact deformation; E1 and E2 are elastic modulus of roller and plane, respectively; μ1 and μ2 are Poisson’s ratios of roller and plane, respectively; Re is the yield strength of the material; RT is the radius of roller; a is the contact radius; b is the radial distance from the center of the contact area to the boundary point of elastic-plastic contact stress. By integrating Eq. (1) in the whole contact zone, the load F can be obtained. u22) ,
u12)
F=
a b
2E * 2 a RT
z 2 •2 zdz +
b 0
kRe•2 zdz
=
2E * 2 a R
b2
y
1 3
F = kR e 1 a2
1 3
2
kRT R e 2E *a
kRT R e 2E *a
2
9 16
FkRe 1
1 3
(
E *2
)
kRT Re 2 2E *a
•E
(8)
When the roller contacts with the workpiece, the surfaces will undergo the elastoplastic deformation. Compared with the plastic deformation, the elastic deformation is quite smaller and will rebound after the USRP. The displacement of elastic recovery is ignored, and only the plastic deformation is analyzed. The specific force analysis is shown in Fig. 4. F is the static force in Fig. 4; N is the pressure exerted by the workpiece on the roller; f is the friction force exerted by the workpiece on the roller; RT is the radius of the roller; θ and φ are the contact angle of the roller and the workpiece in the x–y plane and the x–z plane, respectively. According to the Hertz contact theory, the contact shape of the roller and workpiece is approximately spherical cap [20]. In order to obtain the pressure N acting on the roller in the contact zone, the contact area is divided into j discrete equally spaced units. The area of
(4)
In order to obtain the contact area, the geometric contact model is shown in Fig. 2. Therefore, the average contact stress between the roller and the plane is obtained as shown in Eq.5.
Pm =
= kR e 1
1 3
3. The mechanical analysis in the plane ultrasonic rolling
(3)
kRT R e 2E *
(7)
It can be seen from Eq. (8) that the relationship between rolling depth and rolling force is established to obtain the parameter of force in the USRP.
(2)
Substituting Eq. (3) into Eq. (2), the Eq.(4) can be written as
F = kR e a2
9 FPm 16 E *2
Therefore, the theoretical model of single point impact residual stress can be obtained.
According to the continuous condition of contact stress, when z=b, Eq. (3) can be obtained.
kR e =
(6)
= Pm
2
(5)
It can be seen from Eq. (5) that the unknown parameters of k and a are solved using the finite element method, respectively. In order to establish the theoretical model of single point impact 574
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Fig. 3. Contact process between roller and plane.
F=
1 2 RT Pm (1 4 RT Pm h 0 1
cos 2 ) µ
2
µ (2
sin 2 )
h0 2RT
(19)
Because h0 is much less than 2RT, h0 is approximated to 0, μ is very 2RT small, and Pm is approximately the workpiece surface micro-hardness Hv [18,21], and Eq. (19) is simplified as follows.
F = RT Pm h 0 = RT Hvh 0
It can be seen from Eq. (20) that a linear relationship is presented between rolling depth and rolling force. Therefore, the rolling force is directly obtained by setting the corresponding rolling depth in USRP.
Fig. 4. Mechanical analysis.
each interval is much small, so the pressure Ni is assumed to be an approximately constant dN in the ith interval. The pressure acting on the roller can be calculated by the integrating over the contact zone.
N =
dN
4. Finite element analysis The contact model between roller and workpiece is simplified to a plane structure to improve the efficiency of the finite element simulation, as shown in Fig. 5. The roller and workpiece are set as target surface and contact surface, respectively. The mesh size is 0.01 mm, and the time step is 0.003 ms. The material is defined as Bilinear Isotropic [22]. The strain rate of 7075 aluminum alloy was added to the finite element model, and the detail relationship between stress and strain is given [23]. Their mechanical properties are shown in Table 1. The material of roller is the YG8 cemented carbide, and the reinforced material is the 7075 aluminum alloy, and its Vickers hardness 325Hv. Because the hardness of the YG8 is higher than that of 7075 aluminum alloy, the roller is regarded as rigid body. The result of finite element analysis is presented in Fig. 6. As shown in Fig. 6, the roller is superimposed with static force 80 N to 240 N, and the corresponding contact radius is calculated by the finite element method as shown in Fig. 7. According to Eq. (4), the relationship between rolling force and K is presented in Fig. 8. According to Figs. 7 and 8, the fitting function is established with respect to the influence of
(9)
where dN = Pm dA = Pm•(RT d )•(RT sin d ) = Pm•RT2 sin d d , Pm is the average surface stress in the contact zone. Then, the pressure N is decomposed along the axes. (10)
N = Nx + Ny + Nz Nx =
dN sin sin
Ny =
dN cos
=
=
Pm RT2
Pm R2
0
sin2 d
0
sin cos d
0
0
sin d
d
(11) (12) (13)
Nz = 0
where the minus sign means that Nx and Ny are opposite to the x and y axis, respectively. According to the Coulomb’s law, the forces of friction along the axis are calculated as follows.
f =
df
(14)
f = fx + fy
(15)
fx = µNy =
µPm RT2
fy = µNx =
µPm RT2
0
0
sin cos d sin2 d
0
d
(16)
sin d
(17)
0
where, df = µdN . df and dN are perpendicular, and μ is the friction coefficient between the roller and the workpiece. According to the relationship of the Newtonian law, the forces acting on the roller are balanced in the USRP, and the net force along the y axis is zero.
F + N y+ fy = 0
(20)
(18) Fig. 5. Diagram of indentation model.
Substituting Eqs. (12) and (17) into Eq. (18) 575
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Table 1 Mechanical performance parameters of material. Material
Density/(kg. m−3)
Modulus/GPa
Poisson Ratio /u
Tangent Modulus/MPa
Yield Stress/MPa
YG8 7075
14500 2600
600 70
0.21 0.3
/ 300
/ 450
Fig. 9. Contact process between the workpiece and the roller. Fig. 6. Result of finite element analysis.
correlations between calculation values and fitting values. Therefore, the fitting model of Eqs. (21) and (22) are appropriate. However, the difference between the residual stress calculated by Eq. (8) and that obtained by USRP. It is contributed to that the action of vibration is ignored. Therefore; the contact area coefficient is needed to establish to modify the model. 5. Model of contact area coefficient Fig. 9 presents the contact process between the workpiece and the roller. As is shown in Fig.9, L is the step length, b is the processing length. The contact model of roller and workpiece is shown in Fig. 10. The contact area coefficient w represents the value of actual contact area on per unit area between roller and workpiece surface. It can be seen from Fig. 10(b) that the trajectory K2 is sine curve in ultrasonic rolling, and the contact radius is a in Fig. 10(d). Therefore, the actual contact area Su is calculated.
Fig. 7. Relationship between force and contact radius.
SU = 2a•K2 = 2a•
1 + y (t )
(23)
The unit contact area Sc is calculated in Fig. 10(a) and (c). (24)
SC = L•K1 The contact area coefficient w is expressed in Eq. (25).
w=
=
rolling force on contact radius and K, as shown in Eqs. (21) and (22), respectively.
K=
0.12428e
F 104.70211
7.53391 + 8.29777e
F 1002.98703
(
2 0.26007
0.12428e
F 104.70211
) Lb
0
b v
1 + (2 fA) 2 cos2 (2 ft ) dt (25)
When the rolling force decrease, the step increase, and the feed rate increase, the contact area coefficient w is less than 1, which leads to intermittent processing. On the contrary, when w is larger than 1, the unit area acting on the workpiece surface is subjected to shock. According to Eq. (25), the response curves of different processing parameters to contact area coefficient were drawn from Figs. 11–13. As seen from Fig. 11, the contact area coefficient tended to increase with increase in static force. It could be detailed that with the increase of static force, the contact radius increases, which give rise to the increase of contact area coefficient. The influence of feed rate on contact area coefficient is presented in Fig. 12. It was concluded that the contact area coefficient decreases as the feed rate increases. The reason is that with the increase of feed rate, the length of actual contact trajectory K
Fig. 8. Relationship between force and K.
a = 0.26007
2a•K L•b
(21) (22)
By virtue of variance analysis and F tests, the regression of Eqs. (21) and (22) are demonstrated to be remarkable under the confidence level at 99.49 % and 99.99 %, respectively. It is shown that the strong 576
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Fig. 10. Contact model of roller and workpiece.
Fig. 11. Effect of static force on contact area coefficient.
Fig. 13. Effect of step on contact area coefficient.
Fig. 12. Effect of feed rate on contact area coefficient.
decreases, and the processing efficient was further improved. In Fig. 13, the step is remarkable sensitive to the contact area coefficient and the unit area increases with the increase of step. 6. Ultrasonic rolling experiment 6.1. Experiment setup Fig. 14. Ultrasonic rolling experiment.
The ultrasonic rolling experiments are carried out on vertical 577
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Table 2 the experiment parameters. Item
parameter −1
n/r. min v/mm. min−1 F/mm L/mm RT/mm f/KHz A0/um
3000 60, 80, 100, 120 120, 160, 200, 240 0.1, 0.2, 0.3, 0.4 4 30 3
Table 3 the experimental scheme and results. No
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
Fig. 15. Principle of ultrasonic rolling.
machining center VMC-850E. The experimental system is composed of the Kistler dynamometer (9257B) and self-design wireless transmission ultrasonic vibration assisted rolling system. The detailed experiment is shown in Fig. 14. The principle of ultrasonic rolling is shown in Fig. 15. The processing size of square is 60 mm × 60 mm. After the USRP, the residual stress σ is measured using the PROTO X-ray. The measurement direction of residual stress is presented in Fig. 9(a). The residual stress in y axis is used to evaluate the physical properties of the process quality. The basic principle of residual stress measurement is based on Bragg law, and the calculation formula is shown in Eq. (26).
2d•sin
Static force F/N
Feed Rate v/mm. min−1
Step L/mm
Residual Stress σ/(MPa)
Error coefficient σ/σy
Contact area coefficient w
120 160 200 240 120 160 200 240 120 160 200 240 120 160 200 240
60 80 100 120 80 60 120 100 100 120 60 80 120 100 80 60
0.1 0.2 0.3 0.4 0.3 0.4 0.1 0.2 0.4 0.3 0.2 0.1 0.2 0.1 0.4 0.3
−289 −293 −305 −319 −252 −273 −331 −358 −231 −263 −342 −386 −249 −298 −303 −365
0.77 0.69 0.64 0.62 0.67 0.64 0.70 0.69 0.62 0.62 0.72 0.75 0.66 0.70 0.64 0.71
26.5 10.5 5.8 3.7 6.6 7.0 14.5 8.9 4.0 4.7 14.5 22.3 6.6 16.8 5.4 9.9
(26)
= n•
The diffracted crystal spacing d is calculated by measuring the diffraction angle 2θ. The stress measurement formula is derived based on the elastoplastic theory, as shown in Eq. (27). (27)
= K •M E
where, K = 2(1 + ) cot 0 180 , M = ( sin2 ) , d is the spacing of the diffraction plane; n is reflection series; λ is the length of wave; K is the stress constant; M is the slope; 2θ is the diffraction angle measured values corresponding to the ψ angle. E and v are the elastic modulus and Poisson ration of the sample. θ0 is Bragg angle of diffraction angle. 30Kv was used for X-ray tube voltage, tube current is 25 mA, Cu is selected for X-ray target material, radiating surface area is 1 mm2. Sin2ψ are used to test method. The average of three measurements is taken as the result. (2 )
Fig. 16. Signal of rolling force under different rolling depths.
6.3. Results and analysis
6.2. Experiment parameters
6.3.1. Relationship between rolling force and depth The Fig. 16shows signals of rolling force F as the rolling depth h0 is 0.02 mm, 0.03 mm, 0.04 mm, 0.05 mm and 0.06 mm, respectively. The rolling force increases as the rolling depth increases. It is attributed to that when the rolling depth is small and the surface roughness is larger, the variation contact area between the roller and the surface leads to the fluctuation of rolling signals. It can be seen from Fig. 17 that the rolling force increases linearly with the increase of the rolling depth, which is consistent with the conclusions of the references [18,20]. Meanwhile, due to the original surface roughness of the workpiece, the contact area between the roller and workpiece surface becomes smaller. Therefore, the experiment values are smaller than the theoretical values, but the errors are within 10%.
When the contact state of roller and plane changes from the elastic deformation to elastic-plastic deformation, the value of K ranges from 1.466 to 3 [24]. Therefore, the rolling force from 80 N to 240 N is obtained in the elastic-plastic deformation by Eq. (22). To match the continuous processing, as is shown in Fig. 9(a), a reasonable step (L) is determined by the geometric relationship between roller and workpiece. It can be seen from Eq. (21) that the contact radius increases with the increase of the rolling force. In this paper, the contact radius is determined when the rolling depth is the minimum. The experiment parameters and scheme are shown in Tables 2 and 3.
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Fig. 20. Effect of static force on residual stress.
Fig. 17. Theoretical value vs experimental value of the rolling force.
Fig. 21. Effect of speed rate on residual stress.
Fig. 18. Relationship between w and correction coefficient. Table 4 the verification experiments. No
Static force F/N
Feed Rate v/mm. min−1
Step L/mm
1 2 3 4 5 6 7 8
120 120 160 160 200 200 240 240
60 120 80 100 100 120 120 100
0.4 0.1 0.3 0.4 0.4 0.2 0.3 0.3
Fig. 22. Effect of step on residual stress.
per unit area vary due to the feed rate and step. The larger the feed rate and step are, the smaller the contact area coefficient, and it lead to get closer to single point impact residual stress. (28)
0.00168w 2 + 3.38142e 5w 3
f (w ) = 0.52088 + 0.03036w
Therefore, the model of residual stress on surface after modification is shown in Eq. (29). In order to judge the model of residual stress, verification experiment is carried out in accordance with Table 4. The calculation values vs experiment values is presented in Fig. 19. It can be seen from Fig. 19 that the calculation values are close to experiment results. Therefore, the theoretical model has high precision.
Fig. 19. Calculation values vs experiment values.
6.3.2. Experiment verification The model of correction coefficient is established based on Fig. 18, as shown in Eq. (28). As the contact area coefficient increases, the correctness coefficient increases. It is because that the times of impacts
R y
= kRe 1
1 3
kRT Re 2E *a
2
9 16
FkR e 1
1 3
(
E *2
)
kRT Re 2 2E *a
•E •f (w ) (29)
579
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6.3.3. Influence of processing parameters on residual stress The influences of processing parameters on residual stress are shown in Figs. 20 and 21. It can be seen from Fig. 20 that the residual stress is directly proportional to the static force. On the one hand, according to literature [10,25], as the static force increases, the energy of plastic strain is transmitted to the workpiece by roller increase, so that the grains are rearranged and the residual compressive stress is formed. On the other hand, according to Eqs. (21) and (23), with the increase of static force, the contact radius increases, which give rise to the increase of contact area coefficient. In other words, as the contact area coefficient increases, the times of shocks increase per unit area. The times of shock are positively correlated with the residual compressive stress [26,27]. Therefore, the residual compressive stress can be effectively increased by increasing the static force. The influence of feed rate on residual stress is presented in Fig. 21. It is concluded that as the feed rate increases, the residual compressive stress decreases. However, the residual compressive stress is insensitive to feed rate. The reason is that the feed rate is much lower than the ultrasonic frequency along the z direction in Fig. 9a. With the increase of feed rate, the length of actual contact trajectory K decreases, which lead to the decrease of the contact area coefficient. The influence of step on residual stress is illustrated in Fig. 22. It can be seen that as the step increases, the residual compressive stress decreases. It can be detailed by the fact that the impact times per unit area decreases with the increase of step, which give rise to the significant decrease of residual compressive stress.
Acknowledgement The authors gratefully acknowledge the support of the National Natural Science Foundation of China through Grants No. U1604255. References [1] Lu LX, Sun J, Li L, et al. Study on surface characteristics of 7050-T7451 aluminum alloy by ultrasonic surface rolling process. Int J Adv Manuf Technol 2016;87(9–12):1–7. [2] Zhuang W, Liu Q, Djugum R, et al. Deep surface rolling for fatigue life enhancement of laser clad aircraft aluminum alloy. Appl Surf Sci 2014;320(320):558–62. [3] Zulan R. Experimental Study on high-cycle fatigue life enhancement of shot-peening Al alloy. Hot Work Technol 2016:134–6. [4] Wang H, Song G, Tang G. Enhanced surface properties of austenitic stainless steel by electro pulsing-assisted ultrasonic surface rolling process. Surf Coat Technol 2015;282(51):149–54. [5] Liu Y, Zhao X, Wang D. Effective FE model to predict surface layer characteristics of ultrasonic surface rolling with experimental validation. Mater Sci Technol 2014;30(6):627–36. [6] Dai K, Shaw L. Comparison between shot peening and surface Nano-crystallization and hardening process. Mater Sci Eng 2007;463(1–2):46–53. [7] Liu Y, Wang LJ, Wang DP. Finite element modeling of ultrasonic surface rolling process. J Mater Process Technol 2011;211(116):2016–113. [8] Chen LQ, Xiang B, Ren XC, et al. Influence of surface ultrasonic rolling process parameters on surface condition of axle steel sued on high speed train. China Surf Eng 2014;27(5):1–7. [9] Wang BY, Yin Y, Hou ZB, et al. Finite element modeling of residual stress field on X80 steel after ultrasonic surface rolling process. Mater Mech Eng 2015;39(9):80–3. [10] Zhao YC, Wen CB. Simulation of 3D residual stress field of ultrasonic surface rolling by dynamic finite element analysis. J Mech Strength 2017;39(4):875–81. [11] Mao MD, Zhang XC. Stability of residual stress in ultrasonic surface deep rolling treated Ti-6Al-4V alloy under cyclic loading. Appl Mech Mater 2017;853(4):173–7. [12] Liu Y, Zhao X, Wang D, et al. Effective FE model to predict surface layer characteristics of ultrasonic surface rolling with experiment validation. Mater Sci Technol 2014;30(6):627–36. [13] Zheng JX, Jiang SX. Residual stress field in the process of 2D ultrasonic rolling 7075 aluminum alloy. Surf Technol 2017;12(12):265–9. [14] Yang W, Liu P, Xu L, et al. Research on fatigue property experiments of 2D12 aluminum alloy by ultrasonic rolling processing. Light Alloy Fabrication Technol 2015;43(10):61–3. [15] Zhang F, Shang G, Xu C. Effect of surface ultrasonic rolling processing on fatigue properties of AISI304 Austenite stainless steel. Hot Work Technol 2017;46(16):136–40. [16] Evseev DG, Medvedev BM, Grigoriyan GG. Modification of the elastic-plastic model for the contact of rough surfaces. Wear 1991;150:79–88. [17] Yu WP, Blanchard JP. An elastic-plastic indentation model and its solutions. J Mater Res 1996;11(9):2358–67. [18] Johnson KL. Contact Mechanics. England: The University of Cambridge; 1985. [19] Yuan RF. Measurement and calculation of residual stress. Hunan: Hunan university press; 1987. [20] Zhao J, Wang B, Liu ZQ. The investigation into burnishing force, burnishing depth and surface morphology in rotary ultrasonic burnishing. Acta Armamentarium 2016;37(4):696–704. [21] Huang SQ, Chao GB, Peng M, et al. Experimental calculating the surface roughness of SUS304 steel produced by the vibratory ball burnishing process. J Chengdu Univ Sci Technol 1990;51(3):1–8. [22] Zhu YB. Study on extrusion process and deformation behavior of 7075 aluminum alloy. Master thesis. Nanchang University; 2017. [23] Wu YF, Li SH, Hou B, et al. Dynamic flow stress characteristics and constitutive model of aluminum 7075-T651. Chin J Nonferrous Met 2013;23(3):658–65. [24] Guan CP, Jin HP. Calculation analysis for elastic-plastic contact between ball and plane. 2014. p. 5–8. (08). [25] Xu HY, Huang YY, Cui FK. A model for surface residual stress of ultrasonic rolling extrusion bearing ring. J Plast Eng 2018;25(5):205–11. [26] Kong ZY. Research on ultrasonic rolling hardening of gear. Master thesis. Dalian: University of Technology; 2014. [27] Li J, Ling X, Zhou J. Finite element simulation of residual stress field induced by ultrasonic impact treatment. J Aeronautical Mater 2012;32(1):84–8.
7. Conclusions The relationship between rolling force and rolling depth is investigated, and the theoretical model of residual stress on workpiece surface is established by combining the single point impact theory with the correction coefficient. Based on the above results, the following conclusions can be obtained: (1) The theoretical model of residual stress on the surface is established based on the elastoplastic theory. It could improve the prediction accuracy, and the error is within 5 %. (2) The rolling force increases linearly with the increase of rolling depth, and it increases by 41 N as the rolling depth increases each 0.01 mm. (3) As the static force increases, the contact area coefficient increase slightly, but the influences of feed rate and step on the contact area coefficient are opposite. (4) The residual compressive stress increases linearly with the increase of static force, and decreases with the increase of step and feed rate. Declaration of Competing Interest We declare that we have no financial and personal relationships with other people or organizations that can inappropriately influence our work, there is no professional or other personal interest of any nature or kind in any product, service or company that could be construed as influencing the position presented in, or the review of theoretical calculation and experiment of the surface residual stress in the plane ultrasonic rolling.
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Theoretical calculation and experiment of the surface residual stress in the plane ultrasonic rolling
T
Feng Jiaoa, Shuai-ling Lana,b, Bo Zhaoa,*, Yi Wanga a b
School of Mechanical and Power Engineering, Henan Polytechnic University, Jiaozuo Henan, 454003, China School of Mechanical and Automotive Engineering, Kaifeng University, Kaifeng Henan, 475004, China
ARTICLE INFO
ABSTRACT
Keywords: Plane ultrasonic rolling Residual stress Rolling force Contact area coefficient
The service life of the workpiece is largely determined by residual stress on the workpiece surface, which is the most important parameter of anti-fatigue. In order to study the characteristics of residual stress on workpiece surface, the theoretical model of residual stress on the surface of the single impact workpiece is established based on the elastoplastic theory. Subsequently, the relationship between the rolling depth and the rolling force in the plane ultrasonic rolling is established based on the Hertz contact theory, and the contact area coefficient is established to correct the theoretical model. Then, the plane ultrasonic rolling experiments are carried out to validate the model. The results exhibit that the rolling force linearly increases with the increase of rolling depth. The effect of step has a highest relationship with the contact area coefficient, moderate with the feed rate, and minor with the static force. With the increase in static force, the residual compressive stress increased as a whole. The residual compressive stress decrease with the increase in step and the feed rate has little influence on the residual stress. The results reveal that the modified theoretical model can improve the prediction accuracy of residual stress.
1. Introduction The fatigue life of the metallic components is largely determined by the surface residual stress [1–3]. At present, surface quenching, shot peening, laser intensification and supersonic particle bombardment are utilized to improve the surface residual stress [4,5]. Although the surface residual stress has been improved to a certain extent using the traditional techniques, the strengthen effect will be weaken due to the random impingement location, and the overlaps produced adjacent indentations under inappropriate process parameter [6,7]. With the development of ultrasonic technology, the ultrasonic rolling process (USRP) has been regarded as an outstanding technique to enhance the material surface residual compressive stress and maintain the interior invariant chemical composition of the material [8]. Wang et al. [9] found that the plastic deformation and residual stress of X80 steel after the USRP are calculated using finite element method, the error between simulation residual stress and measured on X80 steel surface was about 4.8 %. Zhao et al. [10] demonstrated that a uniformly distributed residual compressive stress on the surface of 304 Austenitic stainless steel was generated after the USRP using the finite element method, and a numerical simulation approach to investigate residual stress of the surface layer was presented. Mao et al. [11] explained that the
⁎
ultrasonic surface deep rolling could generate the compressive residual stress near the surface of Ti-6Al-4 V using the experimental method, and it also affect fatigue crack growth behavior by delaying the crack initiation and decelerating the crack propagation rate. Liu et al. [12] studied the surface characteristics of USRP by the finite element method, the results showed that the residual stress predicted from the FEM are in good agreement with the measurements, which can be used as a fast prediction tool for the design of process parameters. Zheng et al. [13] investigated the formation process of residual stress fields and distribution law of surface residual stress of 7050 aluminum alloy after 2D USRP, and the error of the FEM results reached about 10 % compared with experiments. Yang et al. [14] explored that the surface residual stress distribution of 2D21 aluminum alloy after USRP, and it was revealed that the fatigue life of materials increases by 7 times than that before ultrasonic rolling processing under the same stress condition. Zhang et al. [15] investigated the relationship between surface residual stress and fatigue limit, and found that the residual compressive stress and the fatigue limit increase significantly. From the above review, the residual compressive stress can effectively improve the service life of the workpiece. Therefore it is necessary to deeply research the residual stress after USRP. Till date, many scholars have used the finite element method to study the residual
Corresponding author. E-mail address: [email protected] (B. Zhao).
https://doi.org/10.1016/j.jmapro.2019.12.058 Received 27 July 2019; Received in revised form 26 December 2019; Accepted 30 December 2019 Available online 14 January 2020 1526-6125/ © 2019 Published by Elsevier Ltd on behalf of The Society of Manufacturing Engineers.
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Fig. 1. Contact state between roller and plane.
stress after USRP. However, few references about theoretical model of the residual stress by USRP are available. Therefore, the theoretical model of residual stress on workpiece surface is established through combining the contact area coefficient with the residual stress on the surface of single impact workpiece. The results will be beneficial for the appropriate selection of the process parameters.
Fig. 2. Geometric contact model.
residual stress, a contact process of elastic-plastic between roller and plane should be investigated based on the contact mechanics [18]. According to the Hertz contact theory, as the roller contacts with the plane, there is an approximately circular pit and its radius is as same as roller on the surface of the workpiece. When the roller is removed, the radius of the pit increases due to elastic recovery. The specific contact process is shown in Fig. 3. When the material comes into yield, the residual stress is generated [19].
2. Theoretical model of single point impact residual stress The contact state between the roller and the plane is shown in Fig. 1 [16,17]. As shown in Fig. 1, a plastic deformation in the middle zone of the contact area and the contact stress is uniformly distributed. The rest of the contact zone is in the elastic deformation stage, and it is consistent with the Hertz stress distribution which gradually changes from the maximum contact to zero. The detailed expression is shown in Eq. (1).
2E * 2 a RT kRe
p (z ) =
z2
b 0
z z
y
where, σy is the single impact residual stress, σ´ is the unloading stress. According to the Hertz contact theory, the unloading process can be assumed to be an elastic process because the elastic recovery is not much. Based on the elastic half-space volume, the elastic recovery of the roller and plane is expressed in Eq. (7).
a (1)
b
+ E2 (1 where, E * = E1 (1 k is the function of the contact radius and the contact deformation; E1 and E2 are elastic modulus of roller and plane, respectively; μ1 and μ2 are Poisson’s ratios of roller and plane, respectively; Re is the yield strength of the material; RT is the radius of roller; a is the contact radius; b is the radial distance from the center of the contact area to the boundary point of elastic-plastic contact stress. By integrating Eq. (1) in the whole contact zone, the load F can be obtained. u22) ,
u12)
F=
a b
2E * 2 a RT
z 2 •2 zdz +
b 0
kRe•2 zdz
=
2E * 2 a R
b2
y
1 3
F = kR e 1 a2
1 3
2
kRT R e 2E *a
kRT R e 2E *a
2
9 16
FkRe 1
1 3
(
E *2
)
kRT Re 2 2E *a
•E
(8)
When the roller contacts with the workpiece, the surfaces will undergo the elastoplastic deformation. Compared with the plastic deformation, the elastic deformation is quite smaller and will rebound after the USRP. The displacement of elastic recovery is ignored, and only the plastic deformation is analyzed. The specific force analysis is shown in Fig. 4. F is the static force in Fig. 4; N is the pressure exerted by the workpiece on the roller; f is the friction force exerted by the workpiece on the roller; RT is the radius of the roller; θ and φ are the contact angle of the roller and the workpiece in the x–y plane and the x–z plane, respectively. According to the Hertz contact theory, the contact shape of the roller and workpiece is approximately spherical cap [20]. In order to obtain the pressure N acting on the roller in the contact zone, the contact area is divided into j discrete equally spaced units. The area of
(4)
In order to obtain the contact area, the geometric contact model is shown in Fig. 2. Therefore, the average contact stress between the roller and the plane is obtained as shown in Eq.5.
Pm =
= kR e 1
1 3
3. The mechanical analysis in the plane ultrasonic rolling
(3)
kRT R e 2E *
(7)
It can be seen from Eq. (8) that the relationship between rolling depth and rolling force is established to obtain the parameter of force in the USRP.
(2)
Substituting Eq. (3) into Eq. (2), the Eq.(4) can be written as
F = kR e a2
9 FPm 16 E *2
Therefore, the theoretical model of single point impact residual stress can be obtained.
According to the continuous condition of contact stress, when z=b, Eq. (3) can be obtained.
kR e =
(6)
= Pm
2
(5)
It can be seen from Eq. (5) that the unknown parameters of k and a are solved using the finite element method, respectively. In order to establish the theoretical model of single point impact 574
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Fig. 3. Contact process between roller and plane.
F=
1 2 RT Pm (1 4 RT Pm h 0 1
cos 2 ) µ
2
µ (2
sin 2 )
h0 2RT
(19)
Because h0 is much less than 2RT, h0 is approximated to 0, μ is very 2RT small, and Pm is approximately the workpiece surface micro-hardness Hv [18,21], and Eq. (19) is simplified as follows.
F = RT Pm h 0 = RT Hvh 0
It can be seen from Eq. (20) that a linear relationship is presented between rolling depth and rolling force. Therefore, the rolling force is directly obtained by setting the corresponding rolling depth in USRP.
Fig. 4. Mechanical analysis.
each interval is much small, so the pressure Ni is assumed to be an approximately constant dN in the ith interval. The pressure acting on the roller can be calculated by the integrating over the contact zone.
N =
dN
4. Finite element analysis The contact model between roller and workpiece is simplified to a plane structure to improve the efficiency of the finite element simulation, as shown in Fig. 5. The roller and workpiece are set as target surface and contact surface, respectively. The mesh size is 0.01 mm, and the time step is 0.003 ms. The material is defined as Bilinear Isotropic [22]. The strain rate of 7075 aluminum alloy was added to the finite element model, and the detail relationship between stress and strain is given [23]. Their mechanical properties are shown in Table 1. The material of roller is the YG8 cemented carbide, and the reinforced material is the 7075 aluminum alloy, and its Vickers hardness 325Hv. Because the hardness of the YG8 is higher than that of 7075 aluminum alloy, the roller is regarded as rigid body. The result of finite element analysis is presented in Fig. 6. As shown in Fig. 6, the roller is superimposed with static force 80 N to 240 N, and the corresponding contact radius is calculated by the finite element method as shown in Fig. 7. According to Eq. (4), the relationship between rolling force and K is presented in Fig. 8. According to Figs. 7 and 8, the fitting function is established with respect to the influence of
(9)
where dN = Pm dA = Pm•(RT d )•(RT sin d ) = Pm•RT2 sin d d , Pm is the average surface stress in the contact zone. Then, the pressure N is decomposed along the axes. (10)
N = Nx + Ny + Nz Nx =
dN sin sin
Ny =
dN cos
=
=
Pm RT2
Pm R2
0
sin2 d
0
sin cos d
0
0
sin d
d
(11) (12) (13)
Nz = 0
where the minus sign means that Nx and Ny are opposite to the x and y axis, respectively. According to the Coulomb’s law, the forces of friction along the axis are calculated as follows.
f =
df
(14)
f = fx + fy
(15)
fx = µNy =
µPm RT2
fy = µNx =
µPm RT2
0
0
sin cos d sin2 d
0
d
(16)
sin d
(17)
0
where, df = µdN . df and dN are perpendicular, and μ is the friction coefficient between the roller and the workpiece. According to the relationship of the Newtonian law, the forces acting on the roller are balanced in the USRP, and the net force along the y axis is zero.
F + N y+ fy = 0
(20)
(18) Fig. 5. Diagram of indentation model.
Substituting Eqs. (12) and (17) into Eq. (18) 575
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Table 1 Mechanical performance parameters of material. Material
Density/(kg. m−3)
Modulus/GPa
Poisson Ratio /u
Tangent Modulus/MPa
Yield Stress/MPa
YG8 7075
14500 2600
600 70
0.21 0.3
/ 300
/ 450
Fig. 9. Contact process between the workpiece and the roller. Fig. 6. Result of finite element analysis.
correlations between calculation values and fitting values. Therefore, the fitting model of Eqs. (21) and (22) are appropriate. However, the difference between the residual stress calculated by Eq. (8) and that obtained by USRP. It is contributed to that the action of vibration is ignored. Therefore; the contact area coefficient is needed to establish to modify the model. 5. Model of contact area coefficient Fig. 9 presents the contact process between the workpiece and the roller. As is shown in Fig.9, L is the step length, b is the processing length. The contact model of roller and workpiece is shown in Fig. 10. The contact area coefficient w represents the value of actual contact area on per unit area between roller and workpiece surface. It can be seen from Fig. 10(b) that the trajectory K2 is sine curve in ultrasonic rolling, and the contact radius is a in Fig. 10(d). Therefore, the actual contact area Su is calculated.
Fig. 7. Relationship between force and contact radius.
SU = 2a•K2 = 2a•
1 + y (t )
(23)
The unit contact area Sc is calculated in Fig. 10(a) and (c). (24)
SC = L•K1 The contact area coefficient w is expressed in Eq. (25).
w=
=
rolling force on contact radius and K, as shown in Eqs. (21) and (22), respectively.
K=
0.12428e
F 104.70211
7.53391 + 8.29777e
F 1002.98703
(
2 0.26007
0.12428e
F 104.70211
) Lb
0
b v
1 + (2 fA) 2 cos2 (2 ft ) dt (25)
When the rolling force decrease, the step increase, and the feed rate increase, the contact area coefficient w is less than 1, which leads to intermittent processing. On the contrary, when w is larger than 1, the unit area acting on the workpiece surface is subjected to shock. According to Eq. (25), the response curves of different processing parameters to contact area coefficient were drawn from Figs. 11–13. As seen from Fig. 11, the contact area coefficient tended to increase with increase in static force. It could be detailed that with the increase of static force, the contact radius increases, which give rise to the increase of contact area coefficient. The influence of feed rate on contact area coefficient is presented in Fig. 12. It was concluded that the contact area coefficient decreases as the feed rate increases. The reason is that with the increase of feed rate, the length of actual contact trajectory K
Fig. 8. Relationship between force and K.
a = 0.26007
2a•K L•b
(21) (22)
By virtue of variance analysis and F tests, the regression of Eqs. (21) and (22) are demonstrated to be remarkable under the confidence level at 99.49 % and 99.99 %, respectively. It is shown that the strong 576
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Fig. 10. Contact model of roller and workpiece.
Fig. 11. Effect of static force on contact area coefficient.
Fig. 13. Effect of step on contact area coefficient.
Fig. 12. Effect of feed rate on contact area coefficient.
decreases, and the processing efficient was further improved. In Fig. 13, the step is remarkable sensitive to the contact area coefficient and the unit area increases with the increase of step. 6. Ultrasonic rolling experiment 6.1. Experiment setup Fig. 14. Ultrasonic rolling experiment.
The ultrasonic rolling experiments are carried out on vertical 577
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Table 2 the experiment parameters. Item
parameter −1
n/r. min v/mm. min−1 F/mm L/mm RT/mm f/KHz A0/um
3000 60, 80, 100, 120 120, 160, 200, 240 0.1, 0.2, 0.3, 0.4 4 30 3
Table 3 the experimental scheme and results. No
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
Fig. 15. Principle of ultrasonic rolling.
machining center VMC-850E. The experimental system is composed of the Kistler dynamometer (9257B) and self-design wireless transmission ultrasonic vibration assisted rolling system. The detailed experiment is shown in Fig. 14. The principle of ultrasonic rolling is shown in Fig. 15. The processing size of square is 60 mm × 60 mm. After the USRP, the residual stress σ is measured using the PROTO X-ray. The measurement direction of residual stress is presented in Fig. 9(a). The residual stress in y axis is used to evaluate the physical properties of the process quality. The basic principle of residual stress measurement is based on Bragg law, and the calculation formula is shown in Eq. (26).
2d•sin
Static force F/N
Feed Rate v/mm. min−1
Step L/mm
Residual Stress σ/(MPa)
Error coefficient σ/σy
Contact area coefficient w
120 160 200 240 120 160 200 240 120 160 200 240 120 160 200 240
60 80 100 120 80 60 120 100 100 120 60 80 120 100 80 60
0.1 0.2 0.3 0.4 0.3 0.4 0.1 0.2 0.4 0.3 0.2 0.1 0.2 0.1 0.4 0.3
−289 −293 −305 −319 −252 −273 −331 −358 −231 −263 −342 −386 −249 −298 −303 −365
0.77 0.69 0.64 0.62 0.67 0.64 0.70 0.69 0.62 0.62 0.72 0.75 0.66 0.70 0.64 0.71
26.5 10.5 5.8 3.7 6.6 7.0 14.5 8.9 4.0 4.7 14.5 22.3 6.6 16.8 5.4 9.9
(26)
= n•
The diffracted crystal spacing d is calculated by measuring the diffraction angle 2θ. The stress measurement formula is derived based on the elastoplastic theory, as shown in Eq. (27). (27)
= K •M E
where, K = 2(1 + ) cot 0 180 , M = ( sin2 ) , d is the spacing of the diffraction plane; n is reflection series; λ is the length of wave; K is the stress constant; M is the slope; 2θ is the diffraction angle measured values corresponding to the ψ angle. E and v are the elastic modulus and Poisson ration of the sample. θ0 is Bragg angle of diffraction angle. 30Kv was used for X-ray tube voltage, tube current is 25 mA, Cu is selected for X-ray target material, radiating surface area is 1 mm2. Sin2ψ are used to test method. The average of three measurements is taken as the result. (2 )
Fig. 16. Signal of rolling force under different rolling depths.
6.3. Results and analysis
6.2. Experiment parameters
6.3.1. Relationship between rolling force and depth The Fig. 16shows signals of rolling force F as the rolling depth h0 is 0.02 mm, 0.03 mm, 0.04 mm, 0.05 mm and 0.06 mm, respectively. The rolling force increases as the rolling depth increases. It is attributed to that when the rolling depth is small and the surface roughness is larger, the variation contact area between the roller and the surface leads to the fluctuation of rolling signals. It can be seen from Fig. 17 that the rolling force increases linearly with the increase of the rolling depth, which is consistent with the conclusions of the references [18,20]. Meanwhile, due to the original surface roughness of the workpiece, the contact area between the roller and workpiece surface becomes smaller. Therefore, the experiment values are smaller than the theoretical values, but the errors are within 10%.
When the contact state of roller and plane changes from the elastic deformation to elastic-plastic deformation, the value of K ranges from 1.466 to 3 [24]. Therefore, the rolling force from 80 N to 240 N is obtained in the elastic-plastic deformation by Eq. (22). To match the continuous processing, as is shown in Fig. 9(a), a reasonable step (L) is determined by the geometric relationship between roller and workpiece. It can be seen from Eq. (21) that the contact radius increases with the increase of the rolling force. In this paper, the contact radius is determined when the rolling depth is the minimum. The experiment parameters and scheme are shown in Tables 2 and 3.
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Fig. 20. Effect of static force on residual stress.
Fig. 17. Theoretical value vs experimental value of the rolling force.
Fig. 21. Effect of speed rate on residual stress.
Fig. 18. Relationship between w and correction coefficient. Table 4 the verification experiments. No
Static force F/N
Feed Rate v/mm. min−1
Step L/mm
1 2 3 4 5 6 7 8
120 120 160 160 200 200 240 240
60 120 80 100 100 120 120 100
0.4 0.1 0.3 0.4 0.4 0.2 0.3 0.3
Fig. 22. Effect of step on residual stress.
per unit area vary due to the feed rate and step. The larger the feed rate and step are, the smaller the contact area coefficient, and it lead to get closer to single point impact residual stress. (28)
0.00168w 2 + 3.38142e 5w 3
f (w ) = 0.52088 + 0.03036w
Therefore, the model of residual stress on surface after modification is shown in Eq. (29). In order to judge the model of residual stress, verification experiment is carried out in accordance with Table 4. The calculation values vs experiment values is presented in Fig. 19. It can be seen from Fig. 19 that the calculation values are close to experiment results. Therefore, the theoretical model has high precision.
Fig. 19. Calculation values vs experiment values.
6.3.2. Experiment verification The model of correction coefficient is established based on Fig. 18, as shown in Eq. (28). As the contact area coefficient increases, the correctness coefficient increases. It is because that the times of impacts
R y
= kRe 1
1 3
kRT Re 2E *a
2
9 16
FkR e 1
1 3
(
E *2
)
kRT Re 2 2E *a
•E •f (w ) (29)
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6.3.3. Influence of processing parameters on residual stress The influences of processing parameters on residual stress are shown in Figs. 20 and 21. It can be seen from Fig. 20 that the residual stress is directly proportional to the static force. On the one hand, according to literature [10,25], as the static force increases, the energy of plastic strain is transmitted to the workpiece by roller increase, so that the grains are rearranged and the residual compressive stress is formed. On the other hand, according to Eqs. (21) and (23), with the increase of static force, the contact radius increases, which give rise to the increase of contact area coefficient. In other words, as the contact area coefficient increases, the times of shocks increase per unit area. The times of shock are positively correlated with the residual compressive stress [26,27]. Therefore, the residual compressive stress can be effectively increased by increasing the static force. The influence of feed rate on residual stress is presented in Fig. 21. It is concluded that as the feed rate increases, the residual compressive stress decreases. However, the residual compressive stress is insensitive to feed rate. The reason is that the feed rate is much lower than the ultrasonic frequency along the z direction in Fig. 9a. With the increase of feed rate, the length of actual contact trajectory K decreases, which lead to the decrease of the contact area coefficient. The influence of step on residual stress is illustrated in Fig. 22. It can be seen that as the step increases, the residual compressive stress decreases. It can be detailed by the fact that the impact times per unit area decreases with the increase of step, which give rise to the significant decrease of residual compressive stress.
Acknowledgement The authors gratefully acknowledge the support of the National Natural Science Foundation of China through Grants No. U1604255. References [1] Lu LX, Sun J, Li L, et al. Study on surface characteristics of 7050-T7451 aluminum alloy by ultrasonic surface rolling process. Int J Adv Manuf Technol 2016;87(9–12):1–7. [2] Zhuang W, Liu Q, Djugum R, et al. Deep surface rolling for fatigue life enhancement of laser clad aircraft aluminum alloy. Appl Surf Sci 2014;320(320):558–62. [3] Zulan R. Experimental Study on high-cycle fatigue life enhancement of shot-peening Al alloy. Hot Work Technol 2016:134–6. [4] Wang H, Song G, Tang G. Enhanced surface properties of austenitic stainless steel by electro pulsing-assisted ultrasonic surface rolling process. Surf Coat Technol 2015;282(51):149–54. [5] Liu Y, Zhao X, Wang D. Effective FE model to predict surface layer characteristics of ultrasonic surface rolling with experimental validation. Mater Sci Technol 2014;30(6):627–36. [6] Dai K, Shaw L. Comparison between shot peening and surface Nano-crystallization and hardening process. Mater Sci Eng 2007;463(1–2):46–53. [7] Liu Y, Wang LJ, Wang DP. Finite element modeling of ultrasonic surface rolling process. J Mater Process Technol 2011;211(116):2016–113. [8] Chen LQ, Xiang B, Ren XC, et al. Influence of surface ultrasonic rolling process parameters on surface condition of axle steel sued on high speed train. China Surf Eng 2014;27(5):1–7. [9] Wang BY, Yin Y, Hou ZB, et al. Finite element modeling of residual stress field on X80 steel after ultrasonic surface rolling process. Mater Mech Eng 2015;39(9):80–3. [10] Zhao YC, Wen CB. Simulation of 3D residual stress field of ultrasonic surface rolling by dynamic finite element analysis. J Mech Strength 2017;39(4):875–81. [11] Mao MD, Zhang XC. Stability of residual stress in ultrasonic surface deep rolling treated Ti-6Al-4V alloy under cyclic loading. Appl Mech Mater 2017;853(4):173–7. [12] Liu Y, Zhao X, Wang D, et al. Effective FE model to predict surface layer characteristics of ultrasonic surface rolling with experiment validation. Mater Sci Technol 2014;30(6):627–36. [13] Zheng JX, Jiang SX. Residual stress field in the process of 2D ultrasonic rolling 7075 aluminum alloy. Surf Technol 2017;12(12):265–9. [14] Yang W, Liu P, Xu L, et al. Research on fatigue property experiments of 2D12 aluminum alloy by ultrasonic rolling processing. Light Alloy Fabrication Technol 2015;43(10):61–3. [15] Zhang F, Shang G, Xu C. Effect of surface ultrasonic rolling processing on fatigue properties of AISI304 Austenite stainless steel. Hot Work Technol 2017;46(16):136–40. [16] Evseev DG, Medvedev BM, Grigoriyan GG. Modification of the elastic-plastic model for the contact of rough surfaces. Wear 1991;150:79–88. [17] Yu WP, Blanchard JP. An elastic-plastic indentation model and its solutions. J Mater Res 1996;11(9):2358–67. [18] Johnson KL. Contact Mechanics. England: The University of Cambridge; 1985. [19] Yuan RF. Measurement and calculation of residual stress. Hunan: Hunan university press; 1987. [20] Zhao J, Wang B, Liu ZQ. The investigation into burnishing force, burnishing depth and surface morphology in rotary ultrasonic burnishing. Acta Armamentarium 2016;37(4):696–704. [21] Huang SQ, Chao GB, Peng M, et al. Experimental calculating the surface roughness of SUS304 steel produced by the vibratory ball burnishing process. J Chengdu Univ Sci Technol 1990;51(3):1–8. [22] Zhu YB. Study on extrusion process and deformation behavior of 7075 aluminum alloy. Master thesis. Nanchang University; 2017. [23] Wu YF, Li SH, Hou B, et al. Dynamic flow stress characteristics and constitutive model of aluminum 7075-T651. Chin J Nonferrous Met 2013;23(3):658–65. [24] Guan CP, Jin HP. Calculation analysis for elastic-plastic contact between ball and plane. 2014. p. 5–8. (08). [25] Xu HY, Huang YY, Cui FK. A model for surface residual stress of ultrasonic rolling extrusion bearing ring. J Plast Eng 2018;25(5):205–11. [26] Kong ZY. Research on ultrasonic rolling hardening of gear. Master thesis. Dalian: University of Technology; 2014. [27] Li J, Ling X, Zhou J. Finite element simulation of residual stress field induced by ultrasonic impact treatment. J Aeronautical Mater 2012;32(1):84–8.
7. Conclusions The relationship between rolling force and rolling depth is investigated, and the theoretical model of residual stress on workpiece surface is established by combining the single point impact theory with the correction coefficient. Based on the above results, the following conclusions can be obtained: (1) The theoretical model of residual stress on the surface is established based on the elastoplastic theory. It could improve the prediction accuracy, and the error is within 5 %. (2) The rolling force increases linearly with the increase of rolling depth, and it increases by 41 N as the rolling depth increases each 0.01 mm. (3) As the static force increases, the contact area coefficient increase slightly, but the influences of feed rate and step on the contact area coefficient are opposite. (4) The residual compressive stress increases linearly with the increase of static force, and decreases with the increase of step and feed rate. Declaration of Competing Interest We declare that we have no financial and personal relationships with other people or organizations that can inappropriately influence our work, there is no professional or other personal interest of any nature or kind in any product, service or company that could be construed as influencing the position presented in, or the review of theoretical calculation and experiment of the surface residual stress in the plane ultrasonic rolling.
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