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Study on reducing edge effects by using assistant force in laser forming
Journal of Materials Processing Technology 227 (2016) 169–177
Contents lists available at ScienceDirect
Journal of Materials Processing Technology journal homepage: www.elsevier.com/locate/jmatprotec
Study on reducing edge effects by using assistant force in laser forming Yongjun Shi ∗ , Chen Zhang, Guidong Sun, Chuanxiu Li College of Mechanical & Electronic Engineering, China University of Petroleum, Qingdao, Shandong 266580, China
a r t i c l e
i n f o
Article history: Received 12 November 2014 Received in revised form 1 July 2015 Accepted 17 August 2015 Available online 21 August 2015 Keywords: Laser forming Edge effect Heating method Assistant force Metal plate
a b s t r a c t The laser forming process, in which a bending deformation of a metal plate is produced by nonuniform thermal stress coming from nonlinear laser-heating cycles, is a promising technology for the rapid production of metallic shaping components. In laser forming, except for the desirable bending deformation, the bending angle varies along the laser-heating line. This undesirable deformation, or edge effect, exists because the forming process is asymmetrical, which leads to the forming accuracy failing to reach the design requirement. To reduce the edge effect, a method with various assistant forces is proposed and the effects of these different forces on forming accuracy have been studied. The results show that the forming accuracy can be improved under the action of two unequal concentrated forces. The relative variation of the value of the bending angle decreases by about 80% compared with that of the pure laser forming when the proper external forces are chosen. The laser process parameters also play an important role in the bending angle variations under constant geometry, material, and assistant forces. The final shapes of a forming part may be controlled to a desirable accuracy by selecting the proper assistant forces and process parameters. © 2015 Elsevier B.V. All rights reserved.
1. Introduction The laser forming technique has its origins in oxyacetylene flame line heating for ship hull construction (Scully, 1987). Although the energy input of the two heat sources is different, the processes share similarities in temperature distribution, forming mechanism, path planning, etc. In laser forming, a metal plate is plastically deformed by nonuniform thermal stresses introduced into the local surface during the laser scanning and cooling process. This technology offers promise for the short production of metallic shaping components (Sistaninia et al., 2009). Its advantages are that 1. It requires no external forces and 2. Many hard and brittle materials can be processed. Its disadvantage lies in the fact that forming accuracy cannot usually reach the design requirements because of the elimination of stamping dies and presses. In the laser forming process, the bending angle was found to vary along the heating line, which was known as the edge effect (Magee et al., 1997). The influence of the edge effect on the service performance of a forming part must be taken into account in high-precision manufacturing.
∗ Corresponding author. E-mail address: [email protected] (Y. Shi). http://dx.doi.org/10.1016/j.jmatprotec.2015.08.018 0924-0136/© 2015 Elsevier B.V. All rights reserved.
There are mainly three kinds of forming mechanisms suggested to describe the deformation behavior in laser forming (Vollertson, 1994a): temperature gradient mechanism (TGM), buckling mechanism (BM), and upsetting mechanism (UM). The type of forming mechanism activated mainly depends on the process parameters for a given workpiece. Bao and Yao (2001) performed a numerical investigation to reveal the edge effect mechanism in BM-dominated processes. Two causes for the bending variation were found, one being that the temperature of the exit point is much higher than that of the entrance point and the other being the curved bending edge. Magee et al. (1997) analyzed the effects of laser process parameters and material properties on the edge effect. To reduce the edge effect, a method was proposed in which the heating velocity along the scanning line was varied. The results showed that the varying velocity can result in a sizable reduction of bending angle variation. Shi et al. (2013) discussed the edge effect under conditions of different laser process parameters. Their results indicated that the forming accuracy can be improved by increasing the laser beam power. Shi et al. (2011) showed that the geometry sizes of the plate have an important influence on the bending angle variation. The relative variation in the bending angle greatly decreases with an increase of the length, whereas it increases as the width or thickness increases. Jha et al. (2008) analyzed the edge effect in laser forming of AISI 304 stainless steel, demon-
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Fig. 1. Schematic of a conventional heating process with a laser beam.
strating that the proper laser parameters can assist in reducing the irregularity of the bending angle, with a combination of two of three optimal parameters or higher number of passes making it possible to control for the edge effect. Shen et al. (2010) proposed six varying velocity scanning schemes used to decrease the edge effect. The experimental results showed that this method of combining acceleration and deceleration can reduce the edge effect, and relative bending angle in an example from the literature varies from 16% for constant-speed heating to 5.6% by using this method. Hu et al. (2013) improved an analytical model presented by other researchers to predict the edge effect and proposed a new method by changing the constraint condition. The experimental results showed that the variation of the bending angle using the new method is smaller than that using the conventional method. Cheng et al. (2005) proposed an analytical model of the bending angle to predict the edge effect by modeling a moving-strip heat source over a finite-size plate, in which the pre-bending effect had been considered. The model-predicted trends showed good agreement with the experimental and simulation results. Furthermore, passive water cooling can reduce the difference between the entrance and exit temperatures of a laser-scanned sheet, which is helpful for decreasing the edge effect (Lambiase et al., 2013). It follows that laser process parameters, geometry size, and material properties are the important controlling parameters for reducing the edge effect. Despite the improvement made in previous research, the forming accuracy still needs to be raised further in industrial applications. In this work, a method in which different external loads are applied is presented to reduce the edge effect of a plate in laser forming. The effects of the magnitude of the force on forming accuracy have been examined to obtain the optimum value of the loads. Finally, the relationship between the laser process parameters and the edge effect is analyzed to better understand the causes of the inaccuracy produced.
Fig. 2. Comparison of experimental and numerical results (for a plate size of 50 × 50 × 2 mm3 ).
scans because it can reduce production time. Natural air cooling is employed in this study. In the following analysis, because bending deformations toward the laser beam are needed for most industrial applications, cases in which the temperature gradient mechanism is dominant are researched by selecting proper parameters. Because laser forming is a thermal-mechanical coupling problem, it is very difficult to obtain an analytical solution. Vollertsen (1994b) proposed a twolayer model based on the temperature-gradient mechanism. Shen et al. (2006) presented an analytical model to estimate the bending angle based on a history-dependent incremental stress–strain relationship by considering plastic deformation. Lambiase (2012) developed an analytical model adopting a two-layer model to evaluate the bending angle based on the evaluation of thermal strain, which is suitable for TGM conditions and BM-to-TGM transition conditions. However, in none of these models is the effect of the plate edge on the bending angle considered. A three-dimensional finite-element model has been established to simulate the heating and deforming process (Shi et al., 2011). The nonlinear finiteelement software ANSYS is used in the numerical simulations of the laser forming. The structure analysis can be decoupled from the thermal analysis because the heat generated by plastic deformation
2. Numerical simulations and experimental verification A schematic of a conventional laser forming process, including a Cartesian coordinate system (X–Z), is shown in Fig. 1. Generally, one end of the plate is clamped and the other is kept free. Cooling of the heated plate is mainly accomplished through forced water cooling or forced natural air cooling. Natural air cooling has little influence on the material property compared with forced water cooling. Forced water cooling is usually used for multiple laser
Fig. 3. Variation of peak temperature reached on the top and bottom surfaces along the heating path.
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Fig. 4. Temperature profiles of the top surface when the laser beam moves (a) at the entering end and (b) at the exiting end.
of the plate can be neglected (Hu et al., 2001). The temperature dependences of the material properties are considered because the material properties vary with temperature. The material investigated in this work is the low-carbon steel DC01, and the physical and mechanical properties are obtained by using linear interpolation of data from Chen and Zhang (1985). A sharp temperature gradient exists near the zone irradiated by the laser owing to the short duration of heating. The same mesh model is used for the heat transfer and structural analysis. To obtain higher calculation accu-
racy, three-dimensional solid elements with eight nodes, SOLID70 and SOLID45, are employed for the thermal and structure analysis, respectively. A sparse director solver is adopted. The laser system used in the experiments is an HJ-3000CO2 laser operating in a continuous wave mode, with a maximum output power of 3 kW and a power density distribution of TEM00 . The plates are coated with graphite to increase the absorption of laser power. The deformation the sample is measured before and after heating by a laser placement sensor (LK-081CCD).
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Fig. 5. Y-direction plastic strain distributions (a) along the scanning path and (b) along observation lines 1–3.
The experimental and numerical results of the average bending angle variation are shown in Fig. 2; the values selected for the laser parameters are 750 W for the power, 30 mm/s for the velocity, and 6 mm for the spot diameter. From the figure, it can be seen that the experimental results are in reasonable agreement with the numerical results. 3. Analysis of edge effects Fig. 3 shows the peak temperature reached at both the top and bottom surfaces at different positions along heating line for a workpiece with dimensions of 50 mm by 50 mm by 2 mm subjected to a laser power of 750 W with a spot diameter of 6 mm and a scanning velocity of 20 mm/s. As can be seen, the peak temperature reached varies along the heating line owing to the asymmetry of the process. The peak temperature of the top and bottom surfaces is basically stable when the laser beam moves far away from the edges of the workpiece. The peak temperature of the entering edge is lower than that of the exiting end. The reason for this difference is that the heat input into the plate as the laser beam moves is continually flowing into the cold region ahead of the beam. In addition, the much higher peak temperature at the exiting end can be attributed to the reduced heat dissipation near the exit boundary. Fig. 4 shows the temperature profile of the top surface when the laser beam moves at the entering and exiting ends, respectively. The transient temperature distributions at the two edges are different. Apparently, the high-temperature zone of the exiting edge is larger than that of the entering end. The bending deformation mainly depends on the temperature distributions, and the different temperature distributions lead to the discrepancy between the final bending angles of the two heating positions. Fig. 5a shows the y-axis plastic strain distributions of the top and bottom surfaces along the scanning path. From the figure, it can be seen that the compressive strain of the top surface at the middle is obviously greater than that at the two edges, whereas the tensile strain of the bottom surface at the middle is obviously less than that at the two edges. The main reason for this difference is that the plastic strains rely on the restraining force of surrounding materials to a large extent when the heated area expands. This means that the bending deformations are different even if the temperature distributions at the two edges are the same. The y-axis plastic strain distributions of the top surface perpendicular to the scanning path are shown in Fig. 5b, where the positions of observation lines are indicated in Fig. 6. Plastic strain mainly exists in the
Fig. 6. Schematic diagram of the positions of observation lines 1–3.
laser-irradiated zone. The average value of the plastic strain along observation line 3 is far greater than that of the other lines. The nonuniform plastic strain distribution indicates that there exists a deviation of the bending angle because the bending deformation is mainly controlled by the plastic strain of the top surface. 4. Analysis of forming accuracy under various assistant forces 4.1. Uniform line load Guan et al. (2003) investigated the effects of pre-loads on the bending deformations of a plate. Their results showed that the final bending angles can increase by choosing proper values of loads. Generally, a uniform line load qF is applied on the free edge of the plate parallel to the clamped edge, as shown in Fig. 7. Fig. 8 shows the variations of bending angle along the x-axis with different loads for the case where the same laser process parameters and plate size as in the previous temperature analysis are employed. For convenient comparison, the variation of bending angle without any assistant force is also superimposed in this figure. It is observed that the trends of bending angle variation of the six cases are quite similar and that the average bending angle increases with the increase of the uniform line load. To estimate quantitatively the forming accuracy of the plate, a coefficient of relative variation in the bending angle is defined as ␣ = (˛max − ˛min )/˛ave , where ˛max denotes the maximal bending angle, ˛min the minimal
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Fig. 7. Schematic diagram of laser forming with the external force applied. Fig. 9. Schematic diagram of a method with two concentrated forces.
Fig. 8. Variations of bending angle along the scanning direction with and without external forces.
bending angle, and ˛ave the average bending angle. The relative variation ␣ in the bending angle increases as the uniform line load increases. Remarkably, the forming inaccuracy cannot be reduced by applications of a uniform line load. 4.2. Two equal concentrated forces Inhomogeneity of the restraining force is one of the main causes of bending angle variation based on the previous analysis. The restraining forces at two edges are smaller than that of the others. To raise the forming accuracy, we propose a method in which two equal concentrated forces are applied to enhance the deformation of the two edges. The concentrated forces F1 and F2 are located at the two ends of the free edge parallel to the fixed edge, as shown in Fig. 9. Fig. 10 shows the variations of bending angle along the scanning direction with various concentrated forces. The trends of the curves are roughly the same. The bending angles for the five cases level off first and then gradually increase. The bending angle of the exiting edge is obviously greater than that of the starting edge. The differences between the bending angles of exiting and starting edges further increase compared with that of pure laser forming
Fig. 10. Variations of bending angle along the scanning direction under two equal forces.
(see Fig. 8) when the assistant forces are applied mainly because the high-temperature zone is more prone to deform under external loads since the yield stress of the material decreases quickly as the temperature rises. From the preceding analysis, we see that the temperature of the exiting end is far greater than that of the entering end. This leads to an increase in the relative variation value of bending angle, ␣ , from 2.112% to 3.057% when the concentrated forces F1 and F2 vary from 5 to 25 N. 4.3. Two unequal concentrated forces Based on the above research, the forming accuracy cannot be raised when the two concentrated forces are equal. In view of the different temperature and bending angles at the two ends, two unequal concentrated forces are employed. A larger force is applied at the entering end and a smaller one is applied at the exiting end. Keeping the force F1 unchanged (F1 = 10 N), the variation of bending angle along the heating direction with the various forces F2 is shown in Fig. 11. It is observed that the trends of the six curves of bending angle variation are quite different. The bending angle at the exiting end gradually decreases relative to that of the entering end as the force F2 is reduced. The relative variation value of the bending angle, ␣ , decreases quickly, reaches a minimum at F2 = 2 N,
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Fig. 12. Time history of plastic strains at the exit point of the heating path when F2 = 2 and 10 N, respectively (with F1 = 10 N). Fig. 11. Variations of bending angle along the scanning direction with various values for force F2 (with F1 = 10 N).
and then slightly increases when the force F2 varies from 10 N to zero. The relative variation value ␣ when F2 = 2 N decreases by about 80% compared with that of pure laser forming. Therefore, the final geometry of the workpiece may be controlled to an acceptable degree of accuracy by application of proper external forces. Fig. 12 shows the time history of plastic strain at the exit point of the heating line when F2 is equal to 10 and 2 N, respectively. The plastic strains change dramatically when the laser beam moves at the exit point, and then they change steadily during the cooling stage. The x-direction and z-direction plastic strains slowly increase and the y-direction tensile plastic strain is changed gradually into
a compressive state after ∼3 s. According to the assumption of constant volume in plasticity, the plastic strains in all three directions must always sum to zero at any given time. The y-direction compressive plastic strain when F2 = 2 N is less than that when F2 = 10 N. It is well known that the bending angle is mainly controlled by the y-direction plastic strain. Thus, the bending deformation can be changed by variation of the external force. 5. Effect of process parameters on forming accuracy The bending deformation when the geometry and material of a plate are given mainly depends on the following laser process parameters: the laser power, the scanning velocity, and the spot diameter. From the above analysis, we know that the relative vari-
Fig. 13. Variation of bending angle along the x-axis with different values of power (with scanning velocity = 20 mm/s, spot diameter = 6 mm, F1 = 10 N, and F2 = 2 N).
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Fig. 14. Variation of bending angle along the x-axis with different scanning velocities (with power = 750 W, spot diameter = 6 mm, F1 = 10 N, and F2 = 2 N).
Fig. 15. Variation of bending angle along the x-axis with different spot diameters (with power = 750 W, scanning velocity = 20 mm/s, F1 = 10 N, and F2 = 2 N).
ation value of the bending angle, ␣ , is minimal when F1 = 10 N and F2 = 2 N. We need to know whether high forming accuracy can be achieved under the condition of constant assistant force when the laser process parameters change. Several simulations were per-
formed on a plate of 50 × 50 × 2 mm3 in size to analyze the effect of the process parameters on the edge effect when assistant forces are applied. Fig. 13 shows the curves of bending angle variation along the x-axis at three different power levels. Although high accuracy
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Fig. 16. Temperature distributions along the y-axis direction with different process parameters.
can be obtained when the laser power is 750 W, the forming error rises with the increasing laser power. The largest bending angle is located at the middle when the laser power is 900 W, whereas the smallest bending angle is located at the middle when the laser power is 600 W. Fig. 14 shows the variations of bending angle along the x-axis with different scanning velocities. The relative variation values of bending angle, ␣ , are 1.480%, 0.382%, and 2.444% when the scanning velocities are 15, 20, and 25 mm/s, respectively. The variations of bending angle along the scanning direction with different spot diameters are shown in Fig. 15. The largest relative variation value is found when the spot diameter is 8 mm, whereas the smallest relative variation value is found when the spot diameter is 6 mm. From these three figures, it can be seen that the curves for laser power = 900 W, scanning velocity = 15 mm/s, and spot diameter = 4 mm all rise first and then drop. Conversely, the curves for laser power = 600 W, scanning velocity = 25 mm/s, and spot diameter = 8 mm all drop first and then rise. Fig. 16 shows the temperature distributions along the y-axis direction with the same parameters as in Figs. 13–15. Interestingly, it is observed that the temperature for the cases of laser power = 900 W, scanning velocity = 15 mm/s, and spot diameter = 4 mm is greater than that for the cases where ␣ is 0.382%, whereas the temperature for the cases of laser power = 600 W, scanning velocity = 25 mm/s, and spot diameter = 8 mm is less than that for the cases where ␣ is 0.382%. It follows that the bending angle variation is closely related to the temperature distribution. The thermal expansion of heated zone increases with the increase of the heat input energy. The bigger plastic strain occurs at the middle owing to the bigger geometric constraint. To control the forming accuracy, the two forces F1 and F2 should be increased if the curve of the bending angle variation is convex, and they should be reduced if the curve of the bending angle variation is concave. Consequently, the assistant force should be determined on the basis of the laser process parameters under constant geometry and material.
6. Conclusions In this paper, an analysis of the temperature and y-axis plastic strain distribution is performed to demonstrate the cause of the edge effect. On this basis, a method in which two concentrated forces are applied is introduced to improve geometrical accuracy. The results indicate that the forming accuracy cannot be improved
by using two equal concentrated forces, whereas the relative variation value of the bending angle, ␣ , decreases when two unequal concentrated forces are applied. The relative variation value ␣ when F1 = 10 N and F2 = 2 N decreases by about 80% compared with that of pure laser forming. The effects of the laser power, scanning velocity, and spot diameter on the edge effect have been discussed when external forces are kept constant. It is found that the forming accuracy is closely related to the temperature distribution. Therefore, the effects of the process parameters should be considered when determining the value of the assistant force. Acknowledgments It is gratefully acknowledged that the work presented in this paper was supported by the National Natural Science Foundation of China (No. 51175515), the Fundamental Research Funds for Central Universities (No. 13CX02029A), and Shandong Province Science and Technology Development Plans, China (No. 2011GGX10329). References Bao, J., Yao, Y.L., 2001. Analysis and prediction of edge effects in laser bending. J. Manuf. Sci. Eng. 123, 53–61. Chen, C., Zhang, Y., 1985. Welding Thermal Simulation Technology (in Chinese). China Machine Press, Beijing. Guan, Y., Sun, S., Zhao, G., Luan, Y., 2003. Finite element modeling of laser bending of pre-loaded sheet metals. J. Mater. Process. Technol. 142, 400–407. Hu, Z., Labudovic, M., Wang, H., Kovacevic, R., 2001. Computer simulation and experimental investigation of sheet metal bending using laser beam scanning. Int. J. Mach. Tools Manuf. 41, 589–607. Hu, J., Xu, H., Dang, D., 2013. Modeling and reducing edge effects in laser bending. J. Mater. Process. Technol. 213, 1989–1996. Jha, G.C., Nath, A.K., Roy, S.K., 2008. Study of edge effect and multi-curvature in laser bending of AISI 304 stainless steel. J. Mater. Process. Technol. 197, 434–438. Lambiase, F., 2012. An analytical model for evaluation of bending angle in laser forming of metal sheets. J. Mater. Eng. Perform. 21, 2044–2052. Lambiase, F., Di Ilio, A., Paoletti, A., 2013. An experimental investigation on passive water cooling in laser forming process. Int. J. Adv. Manuf. Technol. 64, 829–840. Magee, J., Watkins, K.G., Steen, W.M., Calder, N., Sidhu, J., Kirby, J., 1997. Edge effects in laser forming. Proceedings of the LANE’97 In: Laser Assisted Net Shape Engineering 2, Meisenbach Bamberg, Vol. 2, pp. 399–408. Cheng, P., Yao, Y., Liu, C., et al., 2005. Analysis and prediction of size effect on laser forming of sheet metal. J. Manuf. Processes 7, 28–41. Scully, K., 1987. Laser line heating. J. Ship Prod. 3, 237–246. Shen, H., Hu, J., Yao, Z., 2010. Analysis and control of edge effects in laser bending. Opt. Lasers Eng. 48, 305–315. Shen, H., Shi, Y., Yao, Z., Hu, J., 2006. An analytical model for estimating deformation in laser forming. Comput. Mater. Sci. 37, 593–598.
Y. Shi et al. / Journal of Materials Processing Technology 227 (2016) 169–177 Shi, Y., Hu, J., Dong, C., 2011. Analysis of the geometric effect on the forming accuracy in laser forming. Proc. Inst. Mech. Eng., Part B: J. Eng. Manuf. 225, 1792–1800. Shi, Y., Yi, P., Hu, J., 2013. Effects of process parameters on forming accuracy for the case of a laser formed metal plate. Lasers Eng. 26, 295–310. Sistaninia, M., Sistaninia, M., Moeanodini, H., 2009. Laser forming of plates using rotating and dithering beams. Comput. Mater. Sci. 45, 480–488.
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Vollertson, F., 1994a. Mechanisms and models for laser forming. Laser Assisted Net Shape Engineering In: Meisenbach Bamberg, Proceedings of the LANE’94, Vol. 1, pp. 345–359. Vollertsen, F., 1994b. An analytical model for laser bending. Lasers Eng. 2, 261–276.
Contents lists available at ScienceDirect
Journal of Materials Processing Technology journal homepage: www.elsevier.com/locate/jmatprotec
Study on reducing edge effects by using assistant force in laser forming Yongjun Shi ∗ , Chen Zhang, Guidong Sun, Chuanxiu Li College of Mechanical & Electronic Engineering, China University of Petroleum, Qingdao, Shandong 266580, China
a r t i c l e
i n f o
Article history: Received 12 November 2014 Received in revised form 1 July 2015 Accepted 17 August 2015 Available online 21 August 2015 Keywords: Laser forming Edge effect Heating method Assistant force Metal plate
a b s t r a c t The laser forming process, in which a bending deformation of a metal plate is produced by nonuniform thermal stress coming from nonlinear laser-heating cycles, is a promising technology for the rapid production of metallic shaping components. In laser forming, except for the desirable bending deformation, the bending angle varies along the laser-heating line. This undesirable deformation, or edge effect, exists because the forming process is asymmetrical, which leads to the forming accuracy failing to reach the design requirement. To reduce the edge effect, a method with various assistant forces is proposed and the effects of these different forces on forming accuracy have been studied. The results show that the forming accuracy can be improved under the action of two unequal concentrated forces. The relative variation of the value of the bending angle decreases by about 80% compared with that of the pure laser forming when the proper external forces are chosen. The laser process parameters also play an important role in the bending angle variations under constant geometry, material, and assistant forces. The final shapes of a forming part may be controlled to a desirable accuracy by selecting the proper assistant forces and process parameters. © 2015 Elsevier B.V. All rights reserved.
1. Introduction The laser forming technique has its origins in oxyacetylene flame line heating for ship hull construction (Scully, 1987). Although the energy input of the two heat sources is different, the processes share similarities in temperature distribution, forming mechanism, path planning, etc. In laser forming, a metal plate is plastically deformed by nonuniform thermal stresses introduced into the local surface during the laser scanning and cooling process. This technology offers promise for the short production of metallic shaping components (Sistaninia et al., 2009). Its advantages are that 1. It requires no external forces and 2. Many hard and brittle materials can be processed. Its disadvantage lies in the fact that forming accuracy cannot usually reach the design requirements because of the elimination of stamping dies and presses. In the laser forming process, the bending angle was found to vary along the heating line, which was known as the edge effect (Magee et al., 1997). The influence of the edge effect on the service performance of a forming part must be taken into account in high-precision manufacturing.
∗ Corresponding author. E-mail address: [email protected] (Y. Shi). http://dx.doi.org/10.1016/j.jmatprotec.2015.08.018 0924-0136/© 2015 Elsevier B.V. All rights reserved.
There are mainly three kinds of forming mechanisms suggested to describe the deformation behavior in laser forming (Vollertson, 1994a): temperature gradient mechanism (TGM), buckling mechanism (BM), and upsetting mechanism (UM). The type of forming mechanism activated mainly depends on the process parameters for a given workpiece. Bao and Yao (2001) performed a numerical investigation to reveal the edge effect mechanism in BM-dominated processes. Two causes for the bending variation were found, one being that the temperature of the exit point is much higher than that of the entrance point and the other being the curved bending edge. Magee et al. (1997) analyzed the effects of laser process parameters and material properties on the edge effect. To reduce the edge effect, a method was proposed in which the heating velocity along the scanning line was varied. The results showed that the varying velocity can result in a sizable reduction of bending angle variation. Shi et al. (2013) discussed the edge effect under conditions of different laser process parameters. Their results indicated that the forming accuracy can be improved by increasing the laser beam power. Shi et al. (2011) showed that the geometry sizes of the plate have an important influence on the bending angle variation. The relative variation in the bending angle greatly decreases with an increase of the length, whereas it increases as the width or thickness increases. Jha et al. (2008) analyzed the edge effect in laser forming of AISI 304 stainless steel, demon-
170
Y. Shi et al. / Journal of Materials Processing Technology 227 (2016) 169–177
Fig. 1. Schematic of a conventional heating process with a laser beam.
strating that the proper laser parameters can assist in reducing the irregularity of the bending angle, with a combination of two of three optimal parameters or higher number of passes making it possible to control for the edge effect. Shen et al. (2010) proposed six varying velocity scanning schemes used to decrease the edge effect. The experimental results showed that this method of combining acceleration and deceleration can reduce the edge effect, and relative bending angle in an example from the literature varies from 16% for constant-speed heating to 5.6% by using this method. Hu et al. (2013) improved an analytical model presented by other researchers to predict the edge effect and proposed a new method by changing the constraint condition. The experimental results showed that the variation of the bending angle using the new method is smaller than that using the conventional method. Cheng et al. (2005) proposed an analytical model of the bending angle to predict the edge effect by modeling a moving-strip heat source over a finite-size plate, in which the pre-bending effect had been considered. The model-predicted trends showed good agreement with the experimental and simulation results. Furthermore, passive water cooling can reduce the difference between the entrance and exit temperatures of a laser-scanned sheet, which is helpful for decreasing the edge effect (Lambiase et al., 2013). It follows that laser process parameters, geometry size, and material properties are the important controlling parameters for reducing the edge effect. Despite the improvement made in previous research, the forming accuracy still needs to be raised further in industrial applications. In this work, a method in which different external loads are applied is presented to reduce the edge effect of a plate in laser forming. The effects of the magnitude of the force on forming accuracy have been examined to obtain the optimum value of the loads. Finally, the relationship between the laser process parameters and the edge effect is analyzed to better understand the causes of the inaccuracy produced.
Fig. 2. Comparison of experimental and numerical results (for a plate size of 50 × 50 × 2 mm3 ).
scans because it can reduce production time. Natural air cooling is employed in this study. In the following analysis, because bending deformations toward the laser beam are needed for most industrial applications, cases in which the temperature gradient mechanism is dominant are researched by selecting proper parameters. Because laser forming is a thermal-mechanical coupling problem, it is very difficult to obtain an analytical solution. Vollertsen (1994b) proposed a twolayer model based on the temperature-gradient mechanism. Shen et al. (2006) presented an analytical model to estimate the bending angle based on a history-dependent incremental stress–strain relationship by considering plastic deformation. Lambiase (2012) developed an analytical model adopting a two-layer model to evaluate the bending angle based on the evaluation of thermal strain, which is suitable for TGM conditions and BM-to-TGM transition conditions. However, in none of these models is the effect of the plate edge on the bending angle considered. A three-dimensional finite-element model has been established to simulate the heating and deforming process (Shi et al., 2011). The nonlinear finiteelement software ANSYS is used in the numerical simulations of the laser forming. The structure analysis can be decoupled from the thermal analysis because the heat generated by plastic deformation
2. Numerical simulations and experimental verification A schematic of a conventional laser forming process, including a Cartesian coordinate system (X–Z), is shown in Fig. 1. Generally, one end of the plate is clamped and the other is kept free. Cooling of the heated plate is mainly accomplished through forced water cooling or forced natural air cooling. Natural air cooling has little influence on the material property compared with forced water cooling. Forced water cooling is usually used for multiple laser
Fig. 3. Variation of peak temperature reached on the top and bottom surfaces along the heating path.
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Fig. 4. Temperature profiles of the top surface when the laser beam moves (a) at the entering end and (b) at the exiting end.
of the plate can be neglected (Hu et al., 2001). The temperature dependences of the material properties are considered because the material properties vary with temperature. The material investigated in this work is the low-carbon steel DC01, and the physical and mechanical properties are obtained by using linear interpolation of data from Chen and Zhang (1985). A sharp temperature gradient exists near the zone irradiated by the laser owing to the short duration of heating. The same mesh model is used for the heat transfer and structural analysis. To obtain higher calculation accu-
racy, three-dimensional solid elements with eight nodes, SOLID70 and SOLID45, are employed for the thermal and structure analysis, respectively. A sparse director solver is adopted. The laser system used in the experiments is an HJ-3000CO2 laser operating in a continuous wave mode, with a maximum output power of 3 kW and a power density distribution of TEM00 . The plates are coated with graphite to increase the absorption of laser power. The deformation the sample is measured before and after heating by a laser placement sensor (LK-081CCD).
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Fig. 5. Y-direction plastic strain distributions (a) along the scanning path and (b) along observation lines 1–3.
The experimental and numerical results of the average bending angle variation are shown in Fig. 2; the values selected for the laser parameters are 750 W for the power, 30 mm/s for the velocity, and 6 mm for the spot diameter. From the figure, it can be seen that the experimental results are in reasonable agreement with the numerical results. 3. Analysis of edge effects Fig. 3 shows the peak temperature reached at both the top and bottom surfaces at different positions along heating line for a workpiece with dimensions of 50 mm by 50 mm by 2 mm subjected to a laser power of 750 W with a spot diameter of 6 mm and a scanning velocity of 20 mm/s. As can be seen, the peak temperature reached varies along the heating line owing to the asymmetry of the process. The peak temperature of the top and bottom surfaces is basically stable when the laser beam moves far away from the edges of the workpiece. The peak temperature of the entering edge is lower than that of the exiting end. The reason for this difference is that the heat input into the plate as the laser beam moves is continually flowing into the cold region ahead of the beam. In addition, the much higher peak temperature at the exiting end can be attributed to the reduced heat dissipation near the exit boundary. Fig. 4 shows the temperature profile of the top surface when the laser beam moves at the entering and exiting ends, respectively. The transient temperature distributions at the two edges are different. Apparently, the high-temperature zone of the exiting edge is larger than that of the entering end. The bending deformation mainly depends on the temperature distributions, and the different temperature distributions lead to the discrepancy between the final bending angles of the two heating positions. Fig. 5a shows the y-axis plastic strain distributions of the top and bottom surfaces along the scanning path. From the figure, it can be seen that the compressive strain of the top surface at the middle is obviously greater than that at the two edges, whereas the tensile strain of the bottom surface at the middle is obviously less than that at the two edges. The main reason for this difference is that the plastic strains rely on the restraining force of surrounding materials to a large extent when the heated area expands. This means that the bending deformations are different even if the temperature distributions at the two edges are the same. The y-axis plastic strain distributions of the top surface perpendicular to the scanning path are shown in Fig. 5b, where the positions of observation lines are indicated in Fig. 6. Plastic strain mainly exists in the
Fig. 6. Schematic diagram of the positions of observation lines 1–3.
laser-irradiated zone. The average value of the plastic strain along observation line 3 is far greater than that of the other lines. The nonuniform plastic strain distribution indicates that there exists a deviation of the bending angle because the bending deformation is mainly controlled by the plastic strain of the top surface. 4. Analysis of forming accuracy under various assistant forces 4.1. Uniform line load Guan et al. (2003) investigated the effects of pre-loads on the bending deformations of a plate. Their results showed that the final bending angles can increase by choosing proper values of loads. Generally, a uniform line load qF is applied on the free edge of the plate parallel to the clamped edge, as shown in Fig. 7. Fig. 8 shows the variations of bending angle along the x-axis with different loads for the case where the same laser process parameters and plate size as in the previous temperature analysis are employed. For convenient comparison, the variation of bending angle without any assistant force is also superimposed in this figure. It is observed that the trends of bending angle variation of the six cases are quite similar and that the average bending angle increases with the increase of the uniform line load. To estimate quantitatively the forming accuracy of the plate, a coefficient of relative variation in the bending angle is defined as ␣ = (˛max − ˛min )/˛ave , where ˛max denotes the maximal bending angle, ˛min the minimal
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Fig. 7. Schematic diagram of laser forming with the external force applied. Fig. 9. Schematic diagram of a method with two concentrated forces.
Fig. 8. Variations of bending angle along the scanning direction with and without external forces.
bending angle, and ˛ave the average bending angle. The relative variation ␣ in the bending angle increases as the uniform line load increases. Remarkably, the forming inaccuracy cannot be reduced by applications of a uniform line load. 4.2. Two equal concentrated forces Inhomogeneity of the restraining force is one of the main causes of bending angle variation based on the previous analysis. The restraining forces at two edges are smaller than that of the others. To raise the forming accuracy, we propose a method in which two equal concentrated forces are applied to enhance the deformation of the two edges. The concentrated forces F1 and F2 are located at the two ends of the free edge parallel to the fixed edge, as shown in Fig. 9. Fig. 10 shows the variations of bending angle along the scanning direction with various concentrated forces. The trends of the curves are roughly the same. The bending angles for the five cases level off first and then gradually increase. The bending angle of the exiting edge is obviously greater than that of the starting edge. The differences between the bending angles of exiting and starting edges further increase compared with that of pure laser forming
Fig. 10. Variations of bending angle along the scanning direction under two equal forces.
(see Fig. 8) when the assistant forces are applied mainly because the high-temperature zone is more prone to deform under external loads since the yield stress of the material decreases quickly as the temperature rises. From the preceding analysis, we see that the temperature of the exiting end is far greater than that of the entering end. This leads to an increase in the relative variation value of bending angle, ␣ , from 2.112% to 3.057% when the concentrated forces F1 and F2 vary from 5 to 25 N. 4.3. Two unequal concentrated forces Based on the above research, the forming accuracy cannot be raised when the two concentrated forces are equal. In view of the different temperature and bending angles at the two ends, two unequal concentrated forces are employed. A larger force is applied at the entering end and a smaller one is applied at the exiting end. Keeping the force F1 unchanged (F1 = 10 N), the variation of bending angle along the heating direction with the various forces F2 is shown in Fig. 11. It is observed that the trends of the six curves of bending angle variation are quite different. The bending angle at the exiting end gradually decreases relative to that of the entering end as the force F2 is reduced. The relative variation value of the bending angle, ␣ , decreases quickly, reaches a minimum at F2 = 2 N,
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Fig. 12. Time history of plastic strains at the exit point of the heating path when F2 = 2 and 10 N, respectively (with F1 = 10 N). Fig. 11. Variations of bending angle along the scanning direction with various values for force F2 (with F1 = 10 N).
and then slightly increases when the force F2 varies from 10 N to zero. The relative variation value ␣ when F2 = 2 N decreases by about 80% compared with that of pure laser forming. Therefore, the final geometry of the workpiece may be controlled to an acceptable degree of accuracy by application of proper external forces. Fig. 12 shows the time history of plastic strain at the exit point of the heating line when F2 is equal to 10 and 2 N, respectively. The plastic strains change dramatically when the laser beam moves at the exit point, and then they change steadily during the cooling stage. The x-direction and z-direction plastic strains slowly increase and the y-direction tensile plastic strain is changed gradually into
a compressive state after ∼3 s. According to the assumption of constant volume in plasticity, the plastic strains in all three directions must always sum to zero at any given time. The y-direction compressive plastic strain when F2 = 2 N is less than that when F2 = 10 N. It is well known that the bending angle is mainly controlled by the y-direction plastic strain. Thus, the bending deformation can be changed by variation of the external force. 5. Effect of process parameters on forming accuracy The bending deformation when the geometry and material of a plate are given mainly depends on the following laser process parameters: the laser power, the scanning velocity, and the spot diameter. From the above analysis, we know that the relative vari-
Fig. 13. Variation of bending angle along the x-axis with different values of power (with scanning velocity = 20 mm/s, spot diameter = 6 mm, F1 = 10 N, and F2 = 2 N).
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Fig. 14. Variation of bending angle along the x-axis with different scanning velocities (with power = 750 W, spot diameter = 6 mm, F1 = 10 N, and F2 = 2 N).
Fig. 15. Variation of bending angle along the x-axis with different spot diameters (with power = 750 W, scanning velocity = 20 mm/s, F1 = 10 N, and F2 = 2 N).
ation value of the bending angle, ␣ , is minimal when F1 = 10 N and F2 = 2 N. We need to know whether high forming accuracy can be achieved under the condition of constant assistant force when the laser process parameters change. Several simulations were per-
formed on a plate of 50 × 50 × 2 mm3 in size to analyze the effect of the process parameters on the edge effect when assistant forces are applied. Fig. 13 shows the curves of bending angle variation along the x-axis at three different power levels. Although high accuracy
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Fig. 16. Temperature distributions along the y-axis direction with different process parameters.
can be obtained when the laser power is 750 W, the forming error rises with the increasing laser power. The largest bending angle is located at the middle when the laser power is 900 W, whereas the smallest bending angle is located at the middle when the laser power is 600 W. Fig. 14 shows the variations of bending angle along the x-axis with different scanning velocities. The relative variation values of bending angle, ␣ , are 1.480%, 0.382%, and 2.444% when the scanning velocities are 15, 20, and 25 mm/s, respectively. The variations of bending angle along the scanning direction with different spot diameters are shown in Fig. 15. The largest relative variation value is found when the spot diameter is 8 mm, whereas the smallest relative variation value is found when the spot diameter is 6 mm. From these three figures, it can be seen that the curves for laser power = 900 W, scanning velocity = 15 mm/s, and spot diameter = 4 mm all rise first and then drop. Conversely, the curves for laser power = 600 W, scanning velocity = 25 mm/s, and spot diameter = 8 mm all drop first and then rise. Fig. 16 shows the temperature distributions along the y-axis direction with the same parameters as in Figs. 13–15. Interestingly, it is observed that the temperature for the cases of laser power = 900 W, scanning velocity = 15 mm/s, and spot diameter = 4 mm is greater than that for the cases where ␣ is 0.382%, whereas the temperature for the cases of laser power = 600 W, scanning velocity = 25 mm/s, and spot diameter = 8 mm is less than that for the cases where ␣ is 0.382%. It follows that the bending angle variation is closely related to the temperature distribution. The thermal expansion of heated zone increases with the increase of the heat input energy. The bigger plastic strain occurs at the middle owing to the bigger geometric constraint. To control the forming accuracy, the two forces F1 and F2 should be increased if the curve of the bending angle variation is convex, and they should be reduced if the curve of the bending angle variation is concave. Consequently, the assistant force should be determined on the basis of the laser process parameters under constant geometry and material.
6. Conclusions In this paper, an analysis of the temperature and y-axis plastic strain distribution is performed to demonstrate the cause of the edge effect. On this basis, a method in which two concentrated forces are applied is introduced to improve geometrical accuracy. The results indicate that the forming accuracy cannot be improved
by using two equal concentrated forces, whereas the relative variation value of the bending angle, ␣ , decreases when two unequal concentrated forces are applied. The relative variation value ␣ when F1 = 10 N and F2 = 2 N decreases by about 80% compared with that of pure laser forming. The effects of the laser power, scanning velocity, and spot diameter on the edge effect have been discussed when external forces are kept constant. It is found that the forming accuracy is closely related to the temperature distribution. Therefore, the effects of the process parameters should be considered when determining the value of the assistant force. Acknowledgments It is gratefully acknowledged that the work presented in this paper was supported by the National Natural Science Foundation of China (No. 51175515), the Fundamental Research Funds for Central Universities (No. 13CX02029A), and Shandong Province Science and Technology Development Plans, China (No. 2011GGX10329). References Bao, J., Yao, Y.L., 2001. Analysis and prediction of edge effects in laser bending. J. Manuf. Sci. Eng. 123, 53–61. Chen, C., Zhang, Y., 1985. Welding Thermal Simulation Technology (in Chinese). China Machine Press, Beijing. Guan, Y., Sun, S., Zhao, G., Luan, Y., 2003. Finite element modeling of laser bending of pre-loaded sheet metals. J. Mater. Process. Technol. 142, 400–407. Hu, Z., Labudovic, M., Wang, H., Kovacevic, R., 2001. Computer simulation and experimental investigation of sheet metal bending using laser beam scanning. Int. J. Mach. Tools Manuf. 41, 589–607. Hu, J., Xu, H., Dang, D., 2013. Modeling and reducing edge effects in laser bending. J. Mater. Process. Technol. 213, 1989–1996. Jha, G.C., Nath, A.K., Roy, S.K., 2008. Study of edge effect and multi-curvature in laser bending of AISI 304 stainless steel. J. Mater. Process. Technol. 197, 434–438. Lambiase, F., 2012. An analytical model for evaluation of bending angle in laser forming of metal sheets. J. Mater. Eng. Perform. 21, 2044–2052. Lambiase, F., Di Ilio, A., Paoletti, A., 2013. An experimental investigation on passive water cooling in laser forming process. Int. J. Adv. Manuf. Technol. 64, 829–840. Magee, J., Watkins, K.G., Steen, W.M., Calder, N., Sidhu, J., Kirby, J., 1997. Edge effects in laser forming. Proceedings of the LANE’97 In: Laser Assisted Net Shape Engineering 2, Meisenbach Bamberg, Vol. 2, pp. 399–408. Cheng, P., Yao, Y., Liu, C., et al., 2005. Analysis and prediction of size effect on laser forming of sheet metal. J. Manuf. Processes 7, 28–41. Scully, K., 1987. Laser line heating. J. Ship Prod. 3, 237–246. Shen, H., Hu, J., Yao, Z., 2010. Analysis and control of edge effects in laser bending. Opt. Lasers Eng. 48, 305–315. Shen, H., Shi, Y., Yao, Z., Hu, J., 2006. An analytical model for estimating deformation in laser forming. Comput. Mater. Sci. 37, 593–598.
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