Investigation of Temperature Distribution and Residual Deformation in the Hardening Process of Gear Honing Matrix with Laser Heating

Transcription

1 International Journal of Mechanical & Mechatronics Engineering IJMME-IJENS Vol:17 No:05 9 Investigation of Temperature Distribution and Residual Deformation in the Hardening Process of Gear Honing Matrix with Laser Heating Guoxing Liang 1,a, Yang Han 2, b *, Kang Du 2,c, Donggang Liu 2,d, Zhili Li 3,e 1 College of Mechanical Engineer, Taiyuan University of Technology, Taiyuan , China 2 Shanxi Key Laboratory of Precision Machining, Taiyuan University of Technology, Taiyuan , China 3 Astronaut Center of China, State Key Laboratory of Space Medicine Fundamentals and Application. Beijing , China a liangguoxing@tyut.edu.cn, b hanyang0521@foxmail.com, c du_kang@126.com, d ldg @163.com, e li_zhili777@163.com Abstract-- Based on SYSWELD finite element code, Gauss heat source was chosen to describe the laser energy. A threedimensional finite element model for gear honing tool with laser brazing was created. The temperature distribution and strain field distribution of AISI 1045 steel gear honing tool were calculated and analyzed by different laser scanning path. The simulation results showed that the temperature of each node was basically the same when the heat source is sequentially loaded in the condition of the laser power is 300 W and the moving speed is 4 mm/s. The temperature gradient is large when the loaded path is arch. The strain trends of the two loading modes are the same. Experiment was carried out under the same condition as the simulation. The tooth profile and lead were measured after laser processing by gear detecting instrument. The experiment results are basically consistent with the simulation results. Index Term-- Strain field; laser brazing; temperature field; gear honing tool; finite element method 1 INTRODUCTION Honing wheel has been widely used in the field of precision machining gear workpieces [1]. Carbon boron nitride (CBN) gear honing wheel is a special gear which is bonded super-hard abrasive on the tooth profile with the process of physical or chemical methods [2]. The current preparation method for CBN honing wheel is mainly electroplating process, electroplated honing wheel is shown in Fig.1.The combination between abrasive grits and coating metal on the electroplated wheel is not chemical-metallurgy combination [3], as shown in Fig.1, and the grit is only embedded in the coating layer in a way of mechanical package, as shown in Fig.1 (c). Therefore the bonding force is not enough in honing process. Moreover, the localized deformation under the CBN grit is a critical factor to restraint high precision in machining gear workpiece due to low strength of the honing matrix, as shown in Fig.1 (d). When the contact force F is loaded on the grain between contact area, the localize deformation under the grain on the honing matrix become serious. High strength materials are usually adopted to eliminate or weak the deformation of the gear honing tool matrix. However, the higher costs will be induced in machining the honing matrix. Laser hardening process can improve mechanical properties to a sufficient strength with little deformation, which is an effective process for hardening honing matrix to ensure the precision of gear workpiece in the honing process. The main advantages of the laser hardening technology are the higher performance in 3D complex shapes with a minimum heat affected zone and poor distortions [4]. As a consequence of these merits, it is possible to reduce of even eliminate final finishing machining. Laser hardening is a high efficiency surface treatment. Therefore, the high temperature gradients, the thickness of hardened layer is usually between 0.8 and 1.5mm, which leads to a lower austenitization temperature and a less deformation generated in laser scanning [5]. It is an appropriate process for gear honing matrix hardening treatment. The principle barriers to widespread adoption of laser hardening in place of traditional technologies are tempering effects induced during multiple laser passes. In hardening the gear honing matrix with laser scanning, each tooth must be treated by multiple laser passes. Therefore, the temperature distribution and the residual thermal deformation will be a complex question, which limits the extent to employment in the real industrial manufacture [6]. Thermal deformation behavior in laser processing has been extensively studied [7,8], but most of the systematic studies were concerning with the plastic deformation in laser forming or bending applications. For numerical simulation, many literatures are focusing on the thermal distribution and residual deformation of the hardened workpiece in laser heat treatment. The model took into account of the effects of natural convection between material and air as well as radiation on the both internal and external of the workpiece, which made the results more reasonable. But their work lacked the experimental verifications [8]. Zhu et al. [9] investigated the tempering effect during the two pass spot continual induction hardening of AISI 1045 steel and found that the micro hardness distribution was strongly influenced by the overlapped width of the spot. In their paper, there are little contents to summarize the deformation after the laser heat treatment. Overall, most of the researcher work put the preference on the temperature distribution and residual deformation of simply geometrical workpiece, few reports can be found to

2 International Journal of Mechanical & Mechatronics Engineering IJMME-IJENS Vol:17 No:05 10 illustrate the mechanism of the complex geometrical workpiece such as gear honing matrix. In this paper, numerical simulation works for temperature distribution and residual deformation on the gear honing matrix have been calculated in SYSWELD software, the simulation results of temperature and deformation on each tooth of honing matrix are obtained after laser scanning in different scanning path. In the same condition of the simulation parameters, the experiments for laser scanning process have been conducted. 2 NUMERICAL SIMULATIONS 2.1 Model building and element meshing The parameters of the honing wheel are shown in Table I. The AISI 1045 steel was firstly supplied in an annealed condition of 34 (HRC) and the chemical composition of AISI 1045 steel is given in Table 2. The honing wheel belongs to the axisymmetric structure, and only the parts of the honing Items Normal modulus Number of teeth Fig. 1. The diagram of honing wheel Table I The geometric parameters of Gear-honing-tool Base Helix angle wheel are selected to load the Gaussian heat source in the finite element analysis of laser hardening, which can meet the analysis requirements. The model input in SYSWELD. is shown in Fig. 2. So far as the calculation precision and efficiency, an optimized mesh density for established model has been applied during the meshing step. The meshed model is shown in Fig. 3. Helix angle pressure angle on pitch circle Tooth width Value [ ]4[ ' ]34[ ' ] 15[ ] 20[ ] 30[mm] Table II The chemical composition of AISI 1045 steel ( wt %) C P Si Ca Mn Mo Ni Cr W Fe <0. Bal ance

3 International Journal of Mechanical & Mechatronics Engineering IJMME-IJENS Vol:17 No:05 11 Fig. 2. The model of Gear-honing-tool 2.2 Scanning path In the process of numerical simulation of the laser hardening to calculate the temperature field, the scanning methods of bow-shaped path and the sequential path are applied on the single tooth accordance with the actual scanning path and time. The height of tooth is about 7 mm, the Fig. 3. The diagram of meshing Gear-honing-tool spot diameter of the laser is 3 mm, and there are three trajectories in the tooth leader to obtain full of coverage tooth surface. The scanning paths are shown in Fig.4. Each tooth flank has three scanning tracks in total and the defocusing distance of heat source is 1.5 mm. Fig. 4. The scanning path of the moving heat source. bow-shaped path, sequential path. 2.3 Heat source Laser hardening belongs to heat transfer and the absorbed laser energy on material surface can be converted into heat result in high temperature rising in localized zone which reaches the phase transition temperature of the material. Then the energy transfers to internal material surrounding the heat zone. After laser scanning, the energy is unevenly and it is not an even distribution with a circular shape. After laser focusing, the laser energy is unevenly distributed in the circular area. For laser hardening, energy is loaded on the tooth profile. The flux can be described by the Gaussian mathematical model. The expression is as follows [10,11]: 2 3 r q r Pexp R R Where R is spot radius; r is the distance between the measurin g point and the center of heat source; P is laser power; η is abs (1) orption rate of material on the laser; q m is energy density of th e light source center. 2.4 Material thermo-physical properties The thermo-physical properties and mechanical properties of the honing matrix material are constantly changing with increasing temperature. If the thermal performance parameters and mechanical performance of the material are set at a room temperature, the calculation deviation will be increased. In order to improve the accuracy of calculation, linear interpolation is used to decrease the calculation deviation, which also solves the latent heat of the phase transition during the scanning process on the honing matrix. In all physical parameters, the density affected by the temperature is minimum. Therefore, it can be set as a constant of 7824 kg/m 3, thermo-physical parameters of AISI 1045 steel are shown in Table 3.

4 temperature( ) International Journal of Mechanical & Mechatronics Engineering IJMME-IJENS Vol:17 No:05 12 Specific heat capacity (j kg -1 k -1 ) Table III Thermo-physical of the 45 steel [12,13] Coefficient of expansion(10-6 K - 1 ) Thermal conductivity (W m -1 k-1 ) Elastic Modulus (GPa) Yield Strength (MPa) Boundary condition The temperature distribution of boundary conditions should meet the requirements of following rules: (1) The heat flux density q will be input on the gear honing tooth profile instead of energy; (2) Convective heat transfer is generated between the surface of work piece and air in contact with it; (3) The surface heat of the gear honing tooth will radiate to environment. The parameters in the calculation are set as: the heat transfer coefficient of honing wheel surface is 12.5 W/m 2, the ambient temperature is 20 ; process parameters: the heat source power is 300 W, the speed of moving heat source is 4 mm/s. 3 Discussion and analysis of results 3.1 The temperature distribution (1) The temperature distribution in the bow-shaped path scanning process are shown in Fig. 5 and the temperature distribution in sequential path scanning process are shown in Fig. 6.

5 International Journal of Mechanical & Mechatronics Engineering IJMME-IJENS Vol:17 No:05 13 (c) Fig. 5. Process diagram of temperature changes with bow-shaped Path Loading on honing matrix. 8s, 25s, (c) 40s, (d) the temperature changes with bowshaped path at different nodes. (d) (c) Fig. 6. Process diagram of temperature changes with sequential hardening Honing wheel. 8s, 25s, (c) 40s, (d) the temperature changes with sequential path at different nodes. Compared with the temperature of each node under the two scanning paths, it can be concluded that the temperatures of the nodes on the scanning trajectory are affected by the former scanning path. The maximum temperature of the heat source center is as higher as 30 ~ 40 than that of former scanning track, but the total temperature trend of each node is almost the same. When the heat source moves to the node or (d) closing the node, the temperature rises rapidly. When the heat source moves out of the heated node, the temperature decreases sharply due to the instant heat conduction. When laser is scanning on the tooth profile in the way of bow-shaped path, the heat source moves to the end of the first hardening seam and then transfers to the second hardening seam, that is the end of the first hardening seam and the

6 International Journal of Mechanical & Mechatronics Engineering IJMME-IJENS Vol:17 No:05 14 starting point of the second hardening seam are located at the same end face of the honing wheel based tooth, heat input is focused. At the same time, because the proportion of convection heat transfer between honing wheel and the surrounding air is relatively big, heat dissipation is slowly, it is bound to cause distribution gradient of the temperature field is large. The starting point of the second hardening seam and the starting point of the third hardening seam are located at the other end of the honing wheel base, and the energy input is also very concentrated. However, the proportion of convective heat transfer between the honing wheel and the surrounding air is smaller, transferring into internal of the honing wheel body, heat dissipation is faster, the temperature distribution gradient is relatively smaller. When laser is scanning on tooth profile in the way of sequential path, the heat source moves along three trajectories in the same direction and the scanning position is different. At the beginning and end of the two hardening seams, there is no heat source input. Therefore, the temperature of each node is tending to the similar situation after the heat source moves out. The temperature distribution of the tooth profile is relatively uniform. In order to present the difference of temperature distribution on the tooth profile in two scanning paths, the maximum temperature of the heat source at the addendum, pitch circle and the dedendum are compared along the scanning time, as is shown in Fig. 7. It can be seen in Fig. 7 that the node temperature difference between tow loading paths is very small. The general tendency is that the node temperature closing to the end of the path is higher than that of closing to the starting point. The heat dissipation near to the root of the tooth is faster, but because it is located near the third scanning trial, it is the node temperature that is finally subjected to that of the heat source. Thus, regardless of the bow-shaped loading path or the sequential loading path, the temperature of the node near to the dedendum is the highest. The node temperature at addendum is first consist with a heat source temperature, although the temperature of the node is affected by the second Fig. 7. Comparison of two loading path node temperatures. scanning path and the last path, the temperature is the lowest due to its long time of heat dissipation. On account of the special position (the node position at the mid trace), the periods of loading and the heat dissipation are the intermediate value compared to that of the time at the addendum and the dedendum in laser scanning process. 3.2 Strain distribution As the strain simulation conditions, the temperature results after laser scanning are employed to calculate the deformation field in the different scanning path and the deformation results are shown in Fig. 8. Fig. 8. Sequential path and bow-shaped path honing wheel matrix flank deformation field. sequential path, bow-shaped path.

7 International Journal of Mechanical & Mechatronics Engineering IJMME-IJENS Vol:17 No:05 15 In Fig. 8, the maximum deformation area of the tooth profile surface is located at the position away from the both ends of the honing tooth which is approximate 3 mm, and the deformation area is relatively large. The largest deformation with a 0.58 µm localizes at the pitch line. Integrated strain in the middle of the tooth profile is about 0.36 µm. in the middle of the addendum position, the integrated strain is about 0.26 µm. The total nodal strain at the position of the dedendum in the middle tooth is the smallest, which is about 0.21 µm. In Fig. 8, the maximum deformation area of the tooth profile is located at the position away from the region of the end face of the matrix which is 3 mm, and the area of maximum strain is smaller. The maximum area mainly accumulates near to the both ends of the dedendum and the pitch line, the strain is about 0.49 µm; the integrated strain in the middle of the tooth profile is about 0.32 µm. In the middle of the tooth root, the integrated strain is the smallest, which is about 0.17 µm; at the top of the tooth, the node strain is about 0.22 µm. Assuming that D BG (x i, y i, z i) is a pre-deformation coordinate value of the node, D AG (x j, y j, z j) is the coordinate value on the deformed nodes, where i and j are the node numbers. Corresponding to the relative displacement of all nodes, the tendency of the deformation on tooth profile can be visually shown in space. It is that the comprehensive relative deformation of each node: G x x y y 2 z z 2 j 2 i j i j i F (2) The coordinate values of all deformed and non-deformed nodes are mined from the tooth profile of tooth top. Those of value at section line and dedendum can be modeled to disclose the laws of deformation tendency. At the position of a 5 um away from the end face and the cross section of the honing wheel, coordinate values of deformed and non-deformed nodes have been acquired. The respective deformation tendency on the tooth profile at three positions is obtained, as shown in Fig. 9. Fig. 9. The deformation trend of the tooth flank of the base of the sequential path and bow-shaped path. the deformation trend of the honing wheel matrix flank of the sequential path, the deformation trend of honing wheel matrix flank of the bow-shaped path. In Fig. 9, the nodal is less affected by the confinement of the matrix at the two ends of the gear tooth profile near to

8 International Journal of Mechanical & Mechatronics Engineering IJMME-IJENS Vol:17 No:05 16 the honing wheel, and the deformation of the tooth is larger; in the middle cross section, the nodal is affected greatly by the constraint of the matrix, and the deformation of the tooth is smaller. At the end of the honing wheel 2 µm and the middle section respectively, the coordinates are digged from deformation and non-deformation, the corresponding deformation trend of tooth position at three positions is shown in Fig. 9. From the Fig. 9, it can be seen that the comprehensive deformation of the tooth profile of the honing wheel base mainly occurs at ends of the honing wheel with the bow path scanning, and the maximum deformation amount can reach 0.53 µm; the deformation in the middle of the tooth profile is large, about 0.36 µm. Among them, the deformation of the tooth root position is the smallest along the tooth direction, and the pitch line position is the largest along the tooth direction, and the addendum is centered along the tooth orientation. The main reason is that the effect that the gear profile is subject to the constraint of the matrix is large and the deformation is smaller in the tooth root position; and in addition to the deformation of the node in the pitch line position under the temperature condition, the nodes in the pitch line are also affected by the deformation of the nodal at the addendum and dedendum; the nodal at the top of the tooth are affected by the constraint of the matrix, and the minimum deformation is due to the position node offset a part of the deformation by the tooth root and nodal position node. Through analyzing the deformation of the tooth profile surface in different loading paths, it can be seen that the surface strain contour distribution on the tooth profile of the honing matrix is relatively similar in two scanning path during the simulation work. the maximum strain region is generated at both ends around the honing matrix. The composite strain of tooth orientation at the dedendum is the smallest, the composition strain of tooth orientation at the pitch line is largest, the composition strain at addendum is at the middle of the two values. For the strain of the gear, the strain is the largest in the section of the wheel base, near the pitch line, the minimum strain at the root, and the center of the addendum; For the strain of the gear, the largest strain is in the cross section of the honing matrix closing the pitch line, the smallest strain is at the position of the tooth root, and the tooth top position is at the center; at the end of the scanning, the strain at the root position is the largest, the pitch line is middle, and the tooth tip position is minimum; at the beginning of the scanning, the pitch line position is the largest, the addendum position is minimum, and the root position is middle. But on the whole honing matrix, the thermal strain after scanning in two ways is compared. The thermal strain on the surface of the tooth profile after the bow loading is greater than the thermal strain on the surface of the tooth profile after sequential loading. As analyzing the thermal deformation of the tooth profile of the wheel matrix, it is not cooled down to room temperature of a 20. If the time for the convective heat dissipation between the substrate and the air is further extended in calculating work, the deformation results will be reduced during calculating temperature field. 3.3 Comparison of simulation results with measurement results Under the same conditions of laser scanning and simulation parameter, the bow shaped path and the sequential path of a single tooth surface using laser scanning are carried out, honing wheel machining and detecting equipment are shown in Fig. 10, In order to realize the laser brazing on both sides of the honing wheel surface, it is necessary to select the appropriate laser affected zone, as shown in Fig. 10, laser brazing machine for honing matrix is shown in Fig. 10. and the tooth profile and the tooth lead are measured by the gear measuring center and the equipment are shown in Fig. 10 (c). The measurement results are shown in Fig. 11. (c) Fig. 10. The equipment of the experiment and detection. the laser affected zone in the honing wheel, the laser brazing machine, (c) gear measuring center.

9 International Journal of Mechanical & Mechatronics Engineering IJMME-IJENS Vol:17 No:05 17 (c) (d) Fig. 11. Deviation of tooth profile and tooth lead under two scanning paths. the profile deviation after bow path scanning, The profile deviation after sequential path scanning, (c) the lead deviation after bow path scanning, (d) the lead deviation after sequential path scanning. In Fig. 11, 11, the right tooth profile is the laser scanning side, and the left tooth face is the non-scanning side of the same tooth. As can be seen from the diagram, in the two scanning paths, the right tooth flank deviation is relative to the other teeth, the deformation is relatively large, and the left tooth surface is slightly prominent in the middle, but not obvious. Compared with the two kinds of scanning paths, it can be seen that the difference of the tooth profile deviation of the bow scan and the sequential scan is not obvious, and they are in the same precision grade. The deformation of the tooth profile is close to the simulation result, but not in an order of magnitude. The reason is that during the simulation calculation, the temperature is calculated as the load condition of the strain field and is not cooled to room temperature. Therefore, the simulation results of the tooth deformation is much larger than the experimental results. For the tooth alignment deviation, as shown in Fig. 11 (c), 11 (d), it can be seen obviously from the figure that the tooth deformation occurs in the middle of the tooth surface of the honing wheel. When the bow-shaped is scanned, the right side of the tooth appears concave, the left side of the tooth surface appears convex; in the sequential scanning, the right tooth surface has the same concave phenomenon, and the left tooth surface is not deformed obviously. Compared with the two kinds of scanning paths, it can be seen that the tooth direction deviation is larger by the arcuate path scanning, and the tooth direction deviation of the honing wheel base is small after scanning with the sequential path, and the non-scanning side of the same tooth almost does not have deformation of the tooth orientation. 4 CONCLUSION According to the studies of the laser hardening simulation work and experiments, the conclusion have been obtained as following: (1) When the sequential loading path is employed in hardening process, the temperature on each node appears approximately similar and its gradient performs a smooth contour. When the heat source is loaded with a bow-shaped path, there is an abrupt temperature gradient on the tooth profile and it is hard to control the temperature under this condition (2) No matter what mode of path is, the nodes at the two ends of the gear tooth profile are slightly affected by the matrix constraint near the honing wheel, and the deformations of the tooth are serious; in the mid-section, the nodes are affected greatly due to the constraint provided by the matrix, therefore the deformation of the tooth become smaller. (3) With the bow-shaped path in laser scanning, there is a larger deviation on the tooth profile. Comparing to the bowshaped path, the smaller deviation has been found on the tooth profile in the sequential path scanning, and the non-scanningside tooth have good precision.

10 International Journal of Mechanical & Mechatronics Engineering IJMME-IJENS Vol:17 No:05 18 ACKNOWLEDGEMENTS The authors would like to acknowledge the support provided by the National Natural Science Foundation of China (grant No ). REFERENCES [1] LI Wenbin, LIANG Guoxing, YA Gang, LV Ming. Distribution characteristics of point discharge effect in the process of electroplating cbn gear-honing-tool. IET Conference Publications, v 2009, n 556 CP, 2009, International Technology and Innovation Conference 2009, ITIC [2] LUE Meihao. Present situation and development of precision machining technology of automobile cylindrical gears in our country, J. Mechanical Science and Technology for Aerospace Engineering, , [3] ZHANG Mandong, Lv Ming, Yang Shengqiang. Theoretical research on tooth profile modification with electroplated CBN hard honing wheels. Source: Key Engineering Materials, vol , p , 2008 [4] LIANG Guoxing, LV Ming, LI Wenbin, et al. Basic process research on laser brazing film CBN on the gear-honing-tool, J. New Technology & New Process, 2012, (1):53-56 [5] D. Couedel, P Pogeon, P. Lemasson etc. 2D-heat transfer modelling within limited regions using moving sources: application to electron beam welding, J. International Journal of Heat and Mass Transfer, 2003, vol (46): [6] LIANG Guoxing, Theoretical analysis and process study on brazing metallic-membrane-plating CBN on external honer by the method of laser-scan-heat, D. Taiyuan University of Technology, 2005 [7] Poprawe R. Tailored Light 2 - Laser Application Technology. Berlin, Germany.:Springer; [8] Shokouhmand, H, Ghaffari, S., Thermal analysis of moving induction heating of a hollow cylinder with subsequent spray cooling: effect of velocity, initial position of coil, and geometry. Appl. Math. Model. 36, [9] S. X Zhu, Z. Wang, X. P Qin, H. J Mao, K Gao. Theoretical and experimental analysis of two-pass spot continual induction hardening of AISI 1045 steel, International Journal of Fatigue, 68 (2014) [10] CHENG Jiuhuang, CHEN Li, YU Yousheng. Advance in research of welding heat source model, J. Welding Technology, 2004, 33(1):13-15 [11] W.S.Chang, S.J.Na. A study on the prediction of the laser weld shape with varying heat source equations and the thermal distortion of a small structure in micro-joining, J. Journal of Materials Processing Technology. 2002, vol(120): [12] ZHANG Jiarong, ZHAO Tingyuan. Handbook of thermos-physical properties of commonly used engineering materials, M. Beijing, New Times Press, [13] American Society for Metal, Metals Handbook, Welding and Brazing (eight edition), M. Beijing, China Machine Press