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Numerical analysis and experimental validation of conjunction gear via hot forging-upsetting finishing-radial extrusion
archives of civil and mechanical engineering 19 (2019) 391–404
Available online at www.sciencedirect.com
ScienceDirect journal homepage: http://www.elsevier.com/locate/acme
Original Research Article
Numerical analysis and experimental validation of conjunction gear via hot forging-upsetting finishing-radial extrusion Shilin Li a, Hongchao Ji a,b, Baoyu Wang a b
a,*
, Yanhong Mu a,*
School of Mechanical Engineering, University of Science and Technology Beijing, Beijing 100083, China College of Mechanical Engineering, North China University of Science and Technology, Tangshan 063210, China
article info
abstract
Article history:
The formation of hot forging-upsetting finishing-radial extrusion (HF-UF-RE) compound into
Received 16 July 2018
conjunction gears is an innovative process. This study describes the most existing
Accepted 25 November 2018
manufacturing methods of the conjunction gear. Simulation and experimental research
Available online
is conducted using this new method. First, a type of extrusion die is designed to form the
Keywords:
established to estimate the feasibility of formation process of this compound. This study
back taper. The finite element models of hot forging, finishing, and radial extrusion are then Conjunction gear
analyzes the law of metal flow in the process, the influence of the finishing parameters on
Upsetting finishing
the surface quality, and the distribution of stress and strain in extrusion. Metal flows from
Radial extrusion
the tooth tip to the tooth bottom during the finishing process. The finishing qualities of
Finishing parameter
different finishing parameters have been discussed. Local plastic deformation occurs at the
Die design
tooth bottom during radial extrusion. The gears formed by each process are consistent with the designed shapes and meet the application requirements of the conjunction gear. HF-UFRE is feasible for the formation process of conjunction gears. © 2018 Politechnika Wroclawska. Published by Elsevier B.V. All rights reserved.
1.
Introduction
Global vehicle production and sales reached 97.3 and 96.8 million vehicles, respectively, in 2017 [1]. Each vehicle includes four to five conjunction gears. Thus, the demand for conjunction gear could reach 400 million for new cars alone. The present manufacturing processes for conjunction gear include the following: (1) forging of no tooth gear billet then cut the tooth; (2) tooth ring and the main body of the conjunction gear are manufactured and linked through spline fit or welding; (3) integrated precision forging is applied on the conjunction gear.
Conjunction gear created from the first two methods involves the following problems: (1) Metal flow line is cut off. (2) Relief groove is needed for cutting tooth. (3) Welding quality is hard to guarantee, which greatly reduces teeth intensity. These problems can easily cause serious hidden danger in the running process of a vehicle, such as broken tooth or difficulty of engaging the gear [2]. Forged gear has the following advantages compared with traditional cutting gears [3–5]: (1) higher production efficiency, (2) higher dynamic properties,
* Corresponding authors. E-mail addresses: [email protected] (B. Wang), [email protected] (Y. Mu). https://doi.org/10.1016/j.acme.2018.11.006 1644-9665/© 2018 Politechnika Wroclawska. Published by Elsevier B.V. All rights reserved.
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(3) higher tooth strength because forging maintains the continuous flow line of the tooth, (4) higher material utilization, and (5) lower power dissipation. Considerable progress has been achieved in gear forging the research. OHGA et al. [6] proposed the idea of relief-axis and relief-hole on the basis of divided flow principle to forge gear; this contributed to tooth filling and reduced load formation. Choi and Choi [7] proposed a two-step compound forging process of the gear. This process effectively reduces final forging load. The accuracy of the forged spur gear is set nearly equal to that of the machining gear of the fourth and the fifth classes in the Korean industrial standard. Cai et al. [8] designed alternative die and chamfered punches. The alternative die is beneficial to the filling of the lower corner of the gear, whereas the chamfered punch helps reduce load formation by 64%. Hu et al. [9] proposed the rigid-parallelmotive flow mode and axial uniform flow mode. The rigidparallel-motive flow mode can effectively promote the filling ability of the tooth and reduce the sensitivity of the formation process to the distance of filling and friction. Chen et al. [10] studied the effect of grain size on tooth filling in the mini gearforging process. A small grain will result in improved filling ability but larger load. Sheu and Yu [11] studied the preforging process and die design of a product that features a solid spur gear and cylindrical cup features; they provided the foundation for the compound process design of the conjunction gear in the present study. Zhen et al. [12] optimized the hot forging process of the spiral bevel gear, wherein the tooth profile is formed in the pre-forging process. Elevated temperature in hot forging is attributed to increased dimensional error, including thermal deformation and elastic deformation of die and the forging [13]. Kang et al. [14] proposed a new method of machining die with first matching and reworking. The precision of the gear formed by this method was fourth-grade. Zuo et al. [15] studied the precision hot forging of involute cylindrical gear; he proposed a modified model of hot forging die and a model to predict load formation. Compared with hot forging, cold forging has higher dimensional accuracy. However, cold forging also has the disadvantage of higher forming force and a higher requirement to die. Therefore, cold forging is only suitable for small modules (1–4 mm) and small diameter gears [16]. The formation process of hot-cold compound, which combines the advantages of hot and cold formation, has recently become a focus of research [3]. Hot forging results in blank parts. The
dimension precision and surface quality of the product were enhanced by cold finishing [17]. Liu et al. [18] studied the cold forging and tooth profile correction methods of cylindrical gears and obtained gears with seventh-grade accuracy. Eyercioglu [19] proposed an ironing finishing method to enhance the surface quality of hot forged gear. The cold ironing finishing process of thick-walled cylinders was studied by Stone et al. [20]; they concluded that ironing finishing can improve the dimensional accuracy and surface quality of forged parts. Chang et al. [21] designed a single-tooth ironing die to study the influence of finishing parameters on tooth dimensions and surface quality. Zuo et al. [15] proposed a modified model of the ironing finishing tooth shape, wherein the elastic deformation of the forged gear and die are considered. Li et al. [17] proposed a type of compressing finishing process for hot forged gear, wherein the load formation, dimension, and surface roughness of finished gear are compared with the ironing finished ones. Owing to the particularity of a conjunction gear, the hot forging and finishing process can only result in straight teeth. The formation process of HF-UF-RE compound is proposed in this study to form a conjunction gear. Hot forging process is used to forming the gear blank. Upsetting finishing is adapted to improve the dimensional precision and surface quality of the locking face and profile surface. Finally, the conjunction gear is obtained by radial extrusion of back taper. Radial projection images of the teeth obtained from the HF-UF-RE process are shown in Fig. 1. Several scholars have studied forging process. Ji et al. [22]. studied the hot forging process by DEFORM-3D. The microstructural simulation of 21-4N during the hot forging process was carried out. Jin et al. [23] studied the cold orbital forging of component with deep and narrow groove. The cold orbital forging processes under three kinds of metal flow modes were analyzed by FE simulations and the mechanisms for forging defects of underfilling, folding and poor stress state of the tool are revealed. A new forging method for reducing process steps in automotive fasteners production has been proposed by Qin et al. [24]. FE simulation and forging experiment results confirmed feasibility of using this forging method. In this study, 3D FE models were established to study conjunction gear forging, finishing, and radial extrusion process. We examined the metal flow law of this process, the effect of finishing parameters on finishing dimensional precision, the forming law of the back taper extrusion process, and the demission of conjunction gear. Finally, the validation of the conjunction gear compound process was experimentally verified.
Fig. 1 – Radial projection image of the teeth.
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Fig. 2 – Conjunction gear dimension.
2.
Die design
2.1.
Hot forging die and upsetting finishing die design
The conjunction gear is a transmission part used in the automobile transmission and cooperating with the conjunction gear ring. The gear dimension and key parameters of selected conjunction gear are shown in Fig. 2 and Table 1, respectively. The diagram shows that the conjunction gear has two different characteristics distinct from ordinary gears. First, the end of the tooth is a symmetrical inclined plane with a certain angle different from the flat face of the common gear.
Table 1 – Main characteristics of conjunction gear. Number of tooth Normal module (mm) Pressure angle (8) Addendum circle diameter (mm) Root circle diameter (mm) back taper angle (8) Length of conjunction gear (mm)
33 2 20 68.8 63.8 3 5.8
The symmetric slope is called the locking surface, and the angle of the inclined planes is called the locking angle. The locking surface is designed to ensure that the conjunction gear and gear rings rotate synchronously and without impact. Moreover, the conjunction gear has two symmetrical tooth profiles, which are at a certain angle with the symmetrical planes called the back taper angle. Angle can prevent the vehicle from being out of gear when shifting. Therefore, the key and difficult point of this part is to form locking surface and back taper. Fig. 3 shows the dimensional difference of teeth during the HF-UF-RE process. The finished tooth is DL1 smaller than the hot forged ones in length, and the finished tooth is also thinner than the hot forged ones because of the existence of die clearance. After radial extrusion, the conjunction gear is DL2 longer than the finished ones in length. The back taper is also formed. Table 2 shows the tooth profile information formed by three processes. Metal fills die cavities during hot forging and finishing. Thus, the tooth shape of dies determines the shape of the hot forged gear and finished gear. The factors that affect the tooth shape of the finishing gear are the elastic deformations of the die and forging have little influence on the tooth shape of the finished gear. Thus, the tooth profile modification of the finishing die is neglected.
Fig. 3 – Dimensional difference of teeth during the HF-UF-RE process.
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Table 2 – Tooth profile information formed by three processes. Item
HF tooth UF tooth RE tooth
Number of tooth Normal module (mm) Pressure angle (8) Addendum circle diameter (mm) Root circle diameter (mm) Back taper angle (8) Length of conjunction gear (mm)
33 2 20 68.6 63.6 0 6.3
33 2 20 68.8 63.8 0 5.7
33 2 20 68.8 63.8 3 5.8
Many factors affect the shape of the hot forged gear. Thus, we must modify the shape of the die to obtain the ideal hot forged gear. The shape of the hot forging die is modified following the model to predict involute profile deflection in the hot precision forging of gears proposed by Zuo et al. [25]. This model includes four differences, namely, the thermal die expansion, the elastic die expansion, the thermal forged gear contraction, and the elastic workpiece recovery. Eq. (1) shows model formula [25,26], where fr(ri) and fu(ri) are the total deflections in the radial and circumferential direction, respectively. The modified involute of the hot forging die is shown in Fig. 4.
Fig. 4 – Modified involute.
8 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi d pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi d > > < r ¼ b 1 þ w2 þ f r ðriÞ b 1 þ w2 2 2 > > u ¼ warctan f u ðriÞ 180 : r u
2.2.
(1)
Extrusion die design
Given the existence of the back taper, the formed conjunction gear cannot be removed from the integral die along the axial direction as part of the hot forging and finishing process. To solve this problem, a type of multi-blade extrusion die (Fig. 5 (a)) is designed to form the back taper. Fig. 5(b) shows the segmenting position of each part. Theoretically, the extrusion die can be divided for every other tooth. However, the greater the amount of division, the worse the die life and the higher the manufacturing cost. Therefore, we divide the tooth die into three three-tooth dies along the diameter direction and 12 two-tooth dies. The tooth shape of the die is processed following the shape of a conjunction gear. To form the conjunction gear accurately, the toothed die must move along the radial direction simultaneously and accurately. A slide guide is designed to ensure the accurate movement of the tooth die. As shown in Fig. 5(c), the radial extrusion die is processed into prismatic ridges. The two sides of each blade and the groove of the pressure ring cooperate with each other to restrict the circumferential movement of the die. The outer side of the die is processed into an inclined plane. The die and the pressure ring come into contact by the inclined plane, thereby resulting in the conversion of pressure direction. The inclined surface of the die and the pressure ring are designed at 108 in opposite directions. This angle can ensure the smooth sliding of the extrusion die with sufficient radial pressure and without self-locking. The tool can also ensure that the contact consistently keeps surface contact, thereby helping to reduce the wear of the tooth die.
3.
FE model and experiment procedure
3.1.
Establishment of FE models
Forging simulation can significantly reduce cost and time by providing detailed information on the forging process before
Fig. 5 – Extrusion die of back taper: (a) structure diagram; (b) the distribution of tooth die; (c) sketch map of the coordination between the tooth die and pressure ring.
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Fig. 6 – 3D FE model: (a) hot forging; (b) upsetting finishing; (c) radial extrusion.
tool selection and process decisions being made in the workshop [27]. Thus, we must use FE simulation before actual trials [28]. The geometric model of the hot forging process is established by the Pro/Engineer (PRO/E) software system; the Deform-3D was applied to the FE simulation. Fig. 6(a) is a hot forging model composed of tooth die, top die, bottom die, and billet. The FE simulation of hot forging is based on the following assumptions [29]. Large plastic deformation is observed on the forging process, and the elastic deformation is negligible. Therefore, the billet can be considered a plastic body, while the tool can be considered a rigid body. In the process of deformation, the tetrahedron mesh is selected to divide the billet. Deform automatically redivides the grid when the cumulative maximum strain increment of the rolling piece is 0.7 to ensure that the software is sufficiently accurate without requiring excessive mesh repartitioning. A three-tooth model is simulated to save CPU processing time. The friction type is shear friction and the friction coefficient is assumed to be invariable during the forging process [12,15].
The friction force in the shear friction model is defined by Eq. (2): f s ¼ mk
(2)
fs is frictional stress, m is the friction coefficient and k is shear yield stress. The billet material is AISI-4120, which has high hardenability, no temper brittleness, good machinability and cold strain plasticity. Thus, this material is widely used in manufacturing gears and shafts. Fig. 7(a) shows the flow stress of materials at 25 8C [30], and Fig. 7(b)–(e) shows the flow stress of materials at 800–1100 8C [31]. Tables 3 and 4 present the hot forging simulation parameters and the main chemical composition of the material, respectively. Fig. 6(b) shows the finishing model consists of the top die, tooth die, and hot forged gear. Finishing parameters DL1 and c are important in the finishing process. The value of DL1 and c are selected from (0.4, 0.5, 0.6, 0.7) and (0.5, 0.1, 0.15) respectively. Based on the volume invariance theory in plastic form, the volume of the gear teeth is unchanged in the finishing process. However, considering the existence of die
Fig. 7 – Flow stress of AISI-4120 at different temperatures and strain rates: (a) 25 8C; (b) 800 8C; (c) 900 8C; (d) 1000 8C; (e) 1100 8C.
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Table 3 – Main parameters of hot forging simulation.
Table 7 – Main parameters of radial extrusion simulation.
Parameters
Parameters
Value
Top die velocity (mm/s) The initial temperature of the material (8C) The initial temperature of the die (8C) Environment temperature (8C) Heat transfer coefficient (N/s/mm/8C) Convection coefficient (N/s/mm/8C) Friction factor Mesh number for billet Billet material
600 1100 150 20 5 0.02 0.3 50000 AISI-4120
Table 4 – Chemical composition of AISI-4120 (mass fraction, %). C
Cr
0.34 1.10
Mn
Mo
Si
Ni
Cu
S
P
Fe
0.70
0.25
0.25
0.20
0.014
0.012
0.013
Balance
clearance c, some metals will flow through the gap. Thus, the tooth volume (V1) of the hot forged gear is slightly larger than the tooth volume (V2 = 38.10 mm3) of the finished gear. The tooth volume is affected by the dimensional parameters and finishing parameters. Therefore, some combinations of DL1 and c whose tooth volume is much smaller than the volume of the cavity V2 are discarded. The simulation parameters and process parameters are shown in Tables 5 and 8, respectively. Fig. 6(c) presents the FE model of the extrusion of back taper. A two-tooth die is selected for simulation. The vertical movement of the lower pressure ring is transformed into radial movement of the extrusion die. The radial movement is directly applied to the two-tooth die. Extrusion simulation parameters are shown in Table 7.
Table 5 – Main parameters of finishing simulation. Parameters
Value
Top die velocity (mm/s) Friction factor Mesh number for billet Refine ratio of the tooth Billet material
20 0.12 70000 0.1 AISI-4120
Table 6 – Main process parameters of finishing simulation. Group number Allowance Die Friction Tooth of length, clearance, coefficient volume, DL1 (mm) c (mm) V1 (mm3) 1 2 3 4 5 6 7 8 9 10
0.4 0.5 0.4 0.5 0.6 0.7 0.7 0.6 0.6 0.6
0.05 0.05 0.1 0.1 0.1 0.1 0.15 0.1 0.1 0.1
0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.08 0.2 0.3
39.8 40.51 38.12 38.80 39.48 40.26 38.27 39.48 39.48 39.48
Die velocity (mm/s) Friction factor Mesh number for billet Refine ratio of the tooth Billet material
3.2.
Value 2 0.12 50000 0.1 AISI-4120
Experiment procedure
The hot forging process is conducted on the 10,000 kN hot forging machine (FP-1000 hydraulic press made by Taiwan Jing Yong Precision Forging Co., Ltd.) [Fig. 8(a)]. The finishing and extrusion experiments are conducted on a 5000 kN hydraulic machine (Y27-500T four column hydraulic press made by Hebei Hong Kai Heavy Machine Tool Co., Ltd.) [Fig. 8 (c)]. The tools for hot forging, finishing, and extrusion tests are shown in Figs. 8(b), (d), and (e). The experiment was conducted in Shandong Da Wei Gear Co., Ltd. The die material is Cr12Mo1V1, the hardness is 60HRC after heat treatment, and the hot forging is lubricated by graphite water-based solution.
4.
Results and discussions
4.1.
Hot forging process
Fig. 9 shows the load formation curve of the hot forging process and the billet shape of some important stages. The forging process can be mainly divided into three stages, including upsetting, cavity filling, and corner filling. The first stage is billet upsetting. In the beginning, only the top die, bottom die, and step surface of the die come in contact with the billet. Billet gradually shows a classical drum-shaped expansion under the press of top die, similar to upsetting deformation. Load formation is extremely small during his period. The second stage is cavity filling stage. The die cavity is separated into four sections by the billet according to the flow of metal. Based on the least flow resistance law of metal flow, the outer metal of billet mainly flows to the external step cavity and tooth cavity, and the core metal of the billet mainly flow to the upper and lower cylindrical cavity. The four sections are filled almost at the same time thereby avoiding partial stress concentration. The load formation increases compared with the first stage. The last stage is corner filling. Given the increase in the compressive displacement, the space of die cavities constantly decreases, and the free surface of the metal is rapidly reduced, thereby leading to rapidly increasing load formation as shown in Fig. 14(g). No fold occurs and fineshaped conjunction gear is obtained by the hot forging process. The load formation of hot forging simulation is 2750 kN. The load formation of hot forging experiment is 2600 kN. The load formation difference between the experiment and simulation is 5.77%. Fig. 10(a) displays the forged gear obtained by hot forging. The forged gear is well filled. The forging is cut along the center axis. The sand mill line cutting area is removed and inspected
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Table 8 – Results of finishing simulation. No. 1 2 3 4 5 6 7 8 9 10
The allowance of length, DL1 (mm)
Die clearance, c (mm)
Friction factor
Tooth volume, V1 (mm3)
0.4 0.5 0.4 0.5 0.6 0.7 0.7 0.6 0.6 0.6
0.05 0.05 0.1 0.1 0.1 0.1 0.15 0.1 0.1 0.1
0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.08 0.2 0.3
39.8 40.51 38.12 38.80 39.48 40.26 38.27 39.48 39.48 39.48
Back taper surface quality
Profile quality
Dedendum quality
Fig. 8 – Experiment equipment and tools: (a) 1000 tons hot forging equipment; (b) tools of hot forging; (c) 500 tons hydraulic press; (d) tools of upsetting finishing; and (e) tools of radial extrusion.
based on the test method of the national standard (China) for low department organization and defect etching GB226-91. Etching acid is 1:1 hydrochloric acid solution. Etching was conducted at 65–80 8C for 20 min. Then, the gear was rinsed with water after drying. Fig. 11(a) shows the metal streamline of AISI-4120 steel after hot forging. Fig. 11(b) is a metal streamline of hot forged gear obtained from a 2D finite element simulation with a quadrilateral mesh. The streamline of the important position of the gear is perpendicular to the gear axis. This process will help ensure that the gear will not easily break
under high speed and a complex loading environment [32]. The uniform and continuous metal streamline at all parts guarantee the overall mechanical properties of the gears. Fig. 12(a) shows a video measuring instrument (VMI) for measuring the hot forged gear. Fig. 12(b) is the tooth profile and tooth error (dimension difference between the forged tooth and objective tooth (Table 2 HF tooth)) along the involute profile. The negative value of tooth error indicates that the forged tooth is smaller than the objective one. The tooth errors are mostly in the range
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4.2.
Fig. 9 – Forming stages in the hot forging process of conjunction gear, where the first stage includes a, b, and c; the second stage includes d, e, and f; the last stage includes g.
0.05 to 0.025, and the largest tooth error occurs at the top of the tooth, which is approximately 0.14 mm. Oxidation caused by additional exposure to air may explain this phenomenon.
Finishing process
Fig. 13 presents the image of metal flow velocity in the process of finishing process (Group 6). The arrow shows the flow direction of the velocity and the color dedicated the value of the velocity. The locking surface touches the die first and metal fills the tooth profile near the locking surface when stroke is 0.1 mm. The upper die continues to push forward when stroke is 0.2–0.5 mm. Metal has two main flow directions, namely, the direction of tooth length to reduce the length of tooth and the normal locking surface to fill the die clearance. The height of the tooth reaches the designed value, and metal can only flow to the normal of the tooth profile when stroke is 0.6 mm. The metal flow velocity of the finished parts is almost zero. Deformation is very small during finishing, and the finishing effect cannot easily obtain an accurate conclusion by observing the shape of conjunction gear. The effect of the finishing was checked by observing the contact region between the die and the hot forgings and the accumulation of metal at the root of the tooth. Fig. 14 shows the contact status between the hot forging and the die after the finishing process. Fig. 14(a) shows that no contact occurs before finishing; (b) shows only the tooth tip contacts with die, that is, only the tooth tip is finished; (c) shows the tooth part contacts the die, that is, the tooth parts are all refined and the finishing effect is best; and (d) shows the tooth parts and
Fig. 10 – Gear blank in different experimental stages: (a) hot forging gear; (b) upsetting finishing gear; (c) radial extrusion gear.
Fig. 11 – Metal flow line: (a) the experiment result; (b) FEM results.
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Fig. 12 – Tooth inspection: (a) video measuring instrument; (b) inspected tooth profile and tooth error.
Fig. 13 – Metal flow of finishing process (group 6).
Fig. 14 – The contact status between the forged gear and the finishing die: (a) before finishing, simulation-1; (b) after finishing, simulation-3; (c) after finishing, simulation-5; (d) after finishing, simulation-2.
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Fig. 15 – Inspected tooth profile and the tooth error (simulation-5).
dedendum contact the die. Considerable metal accumulation occurred at dedendum. Table 8 shows the simulation results of the finishing process. Simulations-1, 3, 4, and 7 have no complete contact between the tooth parts and the finishing die, which indicate that these tooth profiles have not achieved the finishing effect. Simulations-2, 5, 6, 8, 9, and 10 show complete contact between the tooth parts and the finishing die, which indicate that the tooth profiles and locking surfaces are all finished well. However, the volume of a tooth (simulation-2) is far greater than V2. After finishing, the root of the teeth will be heavily contacted the die causing too much metal accumulation at the dedendum. Simulation-9 shows more metal accumulation at the root than simulation-5, 6, 7, and 8. Therefore, simulation indicates that (c = 0.1, DL1 = 0.6) is the best combination of finishing parameter. Friction greatly affects metal flow. In the comparison of ironing and compressing finishing, Li et al. [17] found that friction influences the finishing quality and load formation of the ironing finishing, but it has little effect on the compressing finishing. Simulations-5, 6, 7, and 8 show that friction has little effect on upsetting finishing. Thus, upsetting finishing needs simple lubrication or no lubrication at all. The reduction of the phosphate/soap can effectively protect the environment and reduce costs. Fig. 10(c) shows the gear obtained by the finishing experiment. The locking surface of the finishing piece is well-formed and no metal accumulation occurs at the root. The tooth profile is also checked by VMI. Fig. 15 displays tooth profile and tooth error. The maximum tooth error is 0.046 mm that appears at the root. The tooth errors of other parts are approximately 0.01 mm. (1) The locking surface touches the die and is finished. (2) Only the tip profile of the forged gear touches the die and is finished. (3) The entire profile of the forged gear touches the die and is finished.
(4) Basically no metal accumulation at the root. (5) Slight metal accumulation at the root. (6) Large amount of metal accumulation at the root.
4.3.
Radial extrusion process
Fig. 16 shows the image of metal flow velocity in the process of radial extrusion. When the extruding displacement is 0.1 mm, the bottom parts of the surface (2) and (3) initially come in contact the die leading metals flowing, and the flowing direction is mainly toward dedendum. When the extruding displacement is 0.2 mm, the metal of surfaces (2) and (3) begin to flow toward addendum. Surfaces (1) and (4) begin to contact the die. When the extruding displacement is 0.4 mm, addendums of teeth begin to contact die and the addendums are compressed in the radial direction. The metal of the tooth tip moves along the tooth length direction and the moving speed is almost equal. Thus, the movement of the tooth tip can be regarded as rigid shift. When the extruding displacement is 0.54 mm, the extrusion is completed. The metal of most parts of the tooth no longer flow. However, the metal of tooth tip retains a rigid shift trend because of the push of the die. The extrusion process of the three-tooth die is similar. The difference is the contact orders between the six surfaces of the three-tooth die and the conjunction gear. The finishing effects of the two-tooth die and the three-tooth die are basically the same. After the extrusion is completed, the excess metal is concentrated at the dedendum. The conjunction gear moves approximately 0.3 mm along the direction of the tooth length. The profile of the tooth tip remains intact. Fig. 17 displays the effective strain distribution of the tooth in the process of the radial extrusion process. In the beginning, the contact area of the die and the tooth part is small, the extrusion speed of the die is slow, and the strain is very small. When the extruding displacement is 0.4 mm, the four side surfaces all contact the die, the addendum of the tooth also
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Fig. 16 – Metal flow of the radial extrusion.
Fig. 17 – Effective strain distribution of the radial extrusion.
begins to contact the dedendum of the die. The addendum of the tooth is compressed and has a weak strain. At the end of the extrusion, the four side surfaces, the addendum, and the dedendum contact the die. This process indicates intense deformation. The back taper extrusion is a partial deformation process, and the deformation of the teeth mainly occurs in the latter half of extrusion. The biggest effective strain appeared in the fillet of the dedendum at the end of extrusion at approximately 1.5. We can also see the contact order between the tooth part and the die is side surfaces (2) (3), side surfaces (1) (4), addendum, and dedendum. The diagram shows that basically no deformation occurs at the tip of the tooth. The rigid translation of the conjunction gear is also verified. Fig. 18 shows the effective stress distribution of the tooth in extruding back taper. The contact order between die and tooth is also the side surfaces (2) (3), side surfaces (1) (4), addendum, and dedendum. At the beginning of extrusion, the four side
surfaces of the tooth touch the die. Effective stress is very small. The addendum the tooth begins to compress when extruded to 0.4 mm. The contact area of the tooth and die increases sharply, the free flow area of the metal decreases, and the metal deformation resistance increases. At the end of the extrusion, the tooth has the largest contact area with the die and the effective stress reaches the maximum value of about 881 MPa, mainly concentrating on the bottom of the conjunction gear. Fig. 10(c) shows a conjunction gear obtained from compound formation process. This gear is a spline with an inverted cone; thus, it cannot be directly measured by VMI. Fig. 19 shows a type of high-precision 3D scanner used to measure the part. After calibration, the accuracy of the scanner can reach 0.01 mm. The part model obtained from the scanning is compared with the design model by Geomagic Qualify. Fig. 20 (a) shows the error comparison of the conjunction gear
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Fig. 18 – Effective stress distribution of the radial extrusion.
Fig. 19 – High-precision 3D scanner.
obtained by simulation. It can be seen that the tooth profile errors of the conjunction gear are all within the range of 0.02 mm. During the extrusion process, the conjunction gear extends about 0.1 mm along the axial direction. Fig. 20(b)
shows the tooth error of the conjunction gear obtained by experiment. It is obvious that the errors of the two sides of the teeth are the smallest in the range of 0.06 mm. The error of addendum and dedendum are 0.1 mm and 0.3 mm respectively. The length of the tooth will lengthen about 0.1 mm. The experimental errors at addendum and dedendum are much larger than the simulated values. The reason is that there are errors of addendum and dedendum due to the influence of the two previous processes. But the experimental error is within the scope of application. The result of experiment and simulation error is consistent basically, which reflects the correctness of finite element simulation. The teeth formed by the two-and three-tooth die were also checked. Thus, no obvious difference was observed on tooth error indicating such that it is feasible to separate the toothed die per two and three teeth. This situation is significant in improving the die life and reducing the cost of die manufacturing. The experiment also found parts with incomplete forming of back taper, parts with good forming of back taper, but the height of the tooth was much smaller than the theoretical value. Extrusion failure and excessive extrusion may explain the former problem. Therefore, the moving of the extrusion die must be controlled strictly, which is essential to forming the back taper.
Fig. 20 – The tooth error comparison: (a) result of simulation and (b) result of experiment.
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5.
Summery and conclusions [3]
From the work carried out in FE simulations, HF-UF-RE experiment and sample parts analysis the following conclusions may be drawn:
[4]
[5]
1. A radial extrusion die is designed to form the back taper. The extrusion die is divided into multiple parts along the radial direction to ensure smooth reduction of the tooth die after a back taper formed. The design of oblique plane contact reduces the wear of die in the entire process. The design of track ensures the accurate sliding of the tooth dies. The experiment shows that the formation quality of the back taper is high, and the shift of the die is accurate and stable. 2. The profile of the forging die is calculated on the basis of the profile modification model of Zuo et al. [25]. The conjunction gear formed by the modified die meet the design requirements. The experimental results show that the hot forgings are filled fully and without folding and its metal flow line is reasonable. Experiments show that hot forging can be used for preform of conjunction gear. 3. Simulation analysis and experimental verification indicate that the upsetting finishing can enhance the dimension accuracy and surface quality of hot forged gear. The upsetting finishing is a type of partial metal deformation, and the finishing sequence is from the tooth tip to the tooth bottom. Finishing parameters have little effect on tooth length and the quality of locking surface but have great influence on the finishing effect of the profile. The best finishing effect is obtained when the finishing parameter combination is c = 0.1, DL1 = 0.6. 4. Local plastic deformation of the tooth bottom and the rigid shift of the tooth tip occurs during extrusion. The shift distance is approximately 0.3 mm. The feasibility of forming the back taper by the designed radial extrusion die is experimentally verified. The conjunction gears obtained by HF-UF-RE compound process meet the requirement of the application and its tooth error within the allowable range. The simulation and experiment show the feasibility of forming a conjunction gear through the HF-UF-RE compound process.
[6]
[7] [8] [9]
[10] [11]
[12]
[13]
[14]
[15]
[16]
[17]
[18]
Funding
[19]
This work is supported by the National Natural Science Foundation of China (Grant No. 51875036). This work is also supported by the National Natural Science Foundation of China (Grant No. 51375042).
[20]
references
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[23] [1] Oica, 2017. http://www.oica.net/statement-delivered-by-oicapresident-matthias-wissmann-at-the-oica-pressconference-in-geneva-on-march-7-2018/. [2] H. Xia, Y. Dong, Z. Huang, Application of precision forging technology in gear industry, in: 2005 (Xi'an) Symposium on
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Gear Materials and Heat Treatment Technology Development Seminar, 2005, 204–218. T. Dean, The net-shape forming of gears, Mater. Des. 21 (2000) 271–278. L. Berviller, R. Bigot, P. Martin, Technological information concerning the integrated design of ‘‘net-shape’’ forged parts, Int. J. Adv. Manuf. Technol. 31 (2006) 247–257. S. Yang, Mathematical model of a helical gear with asymmetric involute teeth and its analysis, Int. J. Adv. Manuf. Technol. 26 (2005) 448–456. K. Ohga, K. Kondo, T. Jitsunari, Research on precision die forging utilizing divided flow, Bull. Jpn. Soc. Mech. Eng. 209 (1982) 1836–1842. J. Choi, Y. Choi, Precision forging of spur gears with inside relief, Int. J. Mach. Tools Manuf. 39 (1999) 1575–1588. J. Cai, T. Dean, Z. Hu, Alternative die designs in net-shape forging of gears, J. Mater. Process. Technol. 150 (2004) 48–55. C. Hu, Q. Liu, Y. Liu, Q. Wang, Analysis of metal flow and technology improvement on gear forging, Chin. J. Mech. Eng. 5 (2008) 186–190. C. Chen, Grain-size effect on the forging formability of mini gears, Int. J. Adv. Manuf. Technol. 79 (2015) 863–871. J. Sheu, C. Yu, Preform and forging process designs based on geometrical features using 2D and 3D FEM simulations, Int. J. Adv. Manuf. Technol. 44 (2009) 244–254. Z. Gao, J. Li, X. Deng, J. Yang, F. Chen, A. Xu, L. Li, Research on gear tooth forming control in the closed die hot forging of spiral bevel gear, Int. J. Adv. Manuf. Technol. 94 (2018) 2993– 3004. M.H. Sadeghi, T. Dean, Analysis of dimensional accuracy of precision forged axisymmetric components, Proc. Inst. Mech. Eng. B: J. Eng. Manuf. 205 (1991) 171–178. J. Kang, K. Lee, J. Je, S. Kang, Spur gear forging tool manufacturing method considering elastic deformation due to shrink fitting, J. Mater. Process. Technol. 187–188 (2017) 14– 18. B. Zuo, The key technology on precision forming process by hot forging and cold ironing of cylindrical spur gears. Ph.D. Thesis. University of Science and Technology, Beijing, 2015. J. Choi, Y. Choi, S. Tak, The forging of helical gears (II): comparisons of the forging processes, Int. J. Mech. Sci. 41 (1999) 725–739. Z. Li, B. Wang, W. Ma, L. Yang, Comparison of ironing finishing and compressing finishing as post-forging for netshape manufacturing, Int. J. Adv. Manuf. Technol. 86 (2016) 3333–3343. H. Liu, Q. Xi, Y. Huo, H. Sun, X. Zhang, Y. Li, B. Liu, J. Chen, Numerical simulation to mold modification of cold precision forging of spur gear, J. Xi'an Jiaotong Univ. 11 (2004) 1186– 1190. O. Eyercioglu, Developments and performance analyses of precision forged spur gear, Ph.D. Thesis, The University of Birmingham, 1995. E.R.H. Stone, J. Cai, Z. Hu, T. Dean, An exercise in cold ironing as the post-forging operation for net-shape manufacture, J. Mater. Process. Technol. 135 (2003) 278–283. Y. Chang, Z. Hu, B. Kang, T. Dean, A study of cold ironing as a post-process for net-shape manufacture, Int. J. Mach. Tools Manuf. 42 (2002) 945–952. H. Ji, X. Huang, C. Ma, et al., Predicting the microstructure of a valve head during the hot forging of steel 21-4N, Metals 8 (6) (2018) 391. Q. Jin, X. Han, L. Hua, et al., Process optimization method for cold orbital forging of component with deep and narrow groove, J. Manuf. Process. 33 (2018) 161–174. S. Chen, Y. Qin, J.G. Chen, et al., A forging method for reducing process steps in the forming of automotive fasteners, Int. J. Mech. Sci. 137 (2018) 1–14.
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[25] B. Zuo, B. Wang, Z. Li, N. Li, J. Lin, An investigation of involute and lead deflection in hot precision forging of gears, Int. J. Adv. Manuf. Technol. 88 (2017) 3017–3030. [26] P. Wu, Investigation on combined forming process by hot forging and cold rolling for conjunction gear blanks, M.D. Thesis, University of Science and Technology, Beijing, 2016. [27] S. Khalilpourazary, A. Dadvand, T. Azdast, M. Sadeghi, Design and manufacturing of a straight bevel gear in hot precision forging process using finite volume method and CAD/CAE technology, Int. J. Adv. Manuf. Technol. 56 (2011) 87–95. [28] M. Skunca, P. Skakun, Z. Keran, L. Sidjanin, M. Math, Relations between numerical simulation and experiment in closed die forging of a gear, J. Mater. Process. Technol. 177 (2006) 256–260.
[29] H. Ji, J. Liu, B. Wang, Z. Zhang, T. Zhang, Z. Hu, Numerical analysis and experiment on cross wedge rolling and forging for engine valves, J. Mater. Process. Technol. 221 (2015) 233– 242. [30] X. Deng, L. Hua, X. Han, Y. Song, Numerical and experimental investigation of cold rotary forging of a 20CrMnTi alloy spur bevel gear, Mater. Des. 32 (2011) 1376–1389. [31] M. Zou, W. Xu, P. Wang, Prediction of high temperature flow stress for AISI 4120 steel during hot compression, Appl. Mech. Mater. 233 (2012) 339–342. [32] H. Ji, J. Liu, B. Wang, X. Fu, W. Xiao, Z. Hu, A new method for manufacturing hollow valves via cross wedge rolling and forging: numerical analysis and experiment validation, J. Mater. Process. Technol. 240 (2017) 1–11.
Available online at www.sciencedirect.com
ScienceDirect journal homepage: http://www.elsevier.com/locate/acme
Original Research Article
Numerical analysis and experimental validation of conjunction gear via hot forging-upsetting finishing-radial extrusion Shilin Li a, Hongchao Ji a,b, Baoyu Wang a b
a,*
, Yanhong Mu a,*
School of Mechanical Engineering, University of Science and Technology Beijing, Beijing 100083, China College of Mechanical Engineering, North China University of Science and Technology, Tangshan 063210, China
article info
abstract
Article history:
The formation of hot forging-upsetting finishing-radial extrusion (HF-UF-RE) compound into
Received 16 July 2018
conjunction gears is an innovative process. This study describes the most existing
Accepted 25 November 2018
manufacturing methods of the conjunction gear. Simulation and experimental research
Available online
is conducted using this new method. First, a type of extrusion die is designed to form the
Keywords:
established to estimate the feasibility of formation process of this compound. This study
back taper. The finite element models of hot forging, finishing, and radial extrusion are then Conjunction gear
analyzes the law of metal flow in the process, the influence of the finishing parameters on
Upsetting finishing
the surface quality, and the distribution of stress and strain in extrusion. Metal flows from
Radial extrusion
the tooth tip to the tooth bottom during the finishing process. The finishing qualities of
Finishing parameter
different finishing parameters have been discussed. Local plastic deformation occurs at the
Die design
tooth bottom during radial extrusion. The gears formed by each process are consistent with the designed shapes and meet the application requirements of the conjunction gear. HF-UFRE is feasible for the formation process of conjunction gears. © 2018 Politechnika Wroclawska. Published by Elsevier B.V. All rights reserved.
1.
Introduction
Global vehicle production and sales reached 97.3 and 96.8 million vehicles, respectively, in 2017 [1]. Each vehicle includes four to five conjunction gears. Thus, the demand for conjunction gear could reach 400 million for new cars alone. The present manufacturing processes for conjunction gear include the following: (1) forging of no tooth gear billet then cut the tooth; (2) tooth ring and the main body of the conjunction gear are manufactured and linked through spline fit or welding; (3) integrated precision forging is applied on the conjunction gear.
Conjunction gear created from the first two methods involves the following problems: (1) Metal flow line is cut off. (2) Relief groove is needed for cutting tooth. (3) Welding quality is hard to guarantee, which greatly reduces teeth intensity. These problems can easily cause serious hidden danger in the running process of a vehicle, such as broken tooth or difficulty of engaging the gear [2]. Forged gear has the following advantages compared with traditional cutting gears [3–5]: (1) higher production efficiency, (2) higher dynamic properties,
* Corresponding authors. E-mail addresses: [email protected] (B. Wang), [email protected] (Y. Mu). https://doi.org/10.1016/j.acme.2018.11.006 1644-9665/© 2018 Politechnika Wroclawska. Published by Elsevier B.V. All rights reserved.
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(3) higher tooth strength because forging maintains the continuous flow line of the tooth, (4) higher material utilization, and (5) lower power dissipation. Considerable progress has been achieved in gear forging the research. OHGA et al. [6] proposed the idea of relief-axis and relief-hole on the basis of divided flow principle to forge gear; this contributed to tooth filling and reduced load formation. Choi and Choi [7] proposed a two-step compound forging process of the gear. This process effectively reduces final forging load. The accuracy of the forged spur gear is set nearly equal to that of the machining gear of the fourth and the fifth classes in the Korean industrial standard. Cai et al. [8] designed alternative die and chamfered punches. The alternative die is beneficial to the filling of the lower corner of the gear, whereas the chamfered punch helps reduce load formation by 64%. Hu et al. [9] proposed the rigid-parallelmotive flow mode and axial uniform flow mode. The rigidparallel-motive flow mode can effectively promote the filling ability of the tooth and reduce the sensitivity of the formation process to the distance of filling and friction. Chen et al. [10] studied the effect of grain size on tooth filling in the mini gearforging process. A small grain will result in improved filling ability but larger load. Sheu and Yu [11] studied the preforging process and die design of a product that features a solid spur gear and cylindrical cup features; they provided the foundation for the compound process design of the conjunction gear in the present study. Zhen et al. [12] optimized the hot forging process of the spiral bevel gear, wherein the tooth profile is formed in the pre-forging process. Elevated temperature in hot forging is attributed to increased dimensional error, including thermal deformation and elastic deformation of die and the forging [13]. Kang et al. [14] proposed a new method of machining die with first matching and reworking. The precision of the gear formed by this method was fourth-grade. Zuo et al. [15] studied the precision hot forging of involute cylindrical gear; he proposed a modified model of hot forging die and a model to predict load formation. Compared with hot forging, cold forging has higher dimensional accuracy. However, cold forging also has the disadvantage of higher forming force and a higher requirement to die. Therefore, cold forging is only suitable for small modules (1–4 mm) and small diameter gears [16]. The formation process of hot-cold compound, which combines the advantages of hot and cold formation, has recently become a focus of research [3]. Hot forging results in blank parts. The
dimension precision and surface quality of the product were enhanced by cold finishing [17]. Liu et al. [18] studied the cold forging and tooth profile correction methods of cylindrical gears and obtained gears with seventh-grade accuracy. Eyercioglu [19] proposed an ironing finishing method to enhance the surface quality of hot forged gear. The cold ironing finishing process of thick-walled cylinders was studied by Stone et al. [20]; they concluded that ironing finishing can improve the dimensional accuracy and surface quality of forged parts. Chang et al. [21] designed a single-tooth ironing die to study the influence of finishing parameters on tooth dimensions and surface quality. Zuo et al. [15] proposed a modified model of the ironing finishing tooth shape, wherein the elastic deformation of the forged gear and die are considered. Li et al. [17] proposed a type of compressing finishing process for hot forged gear, wherein the load formation, dimension, and surface roughness of finished gear are compared with the ironing finished ones. Owing to the particularity of a conjunction gear, the hot forging and finishing process can only result in straight teeth. The formation process of HF-UF-RE compound is proposed in this study to form a conjunction gear. Hot forging process is used to forming the gear blank. Upsetting finishing is adapted to improve the dimensional precision and surface quality of the locking face and profile surface. Finally, the conjunction gear is obtained by radial extrusion of back taper. Radial projection images of the teeth obtained from the HF-UF-RE process are shown in Fig. 1. Several scholars have studied forging process. Ji et al. [22]. studied the hot forging process by DEFORM-3D. The microstructural simulation of 21-4N during the hot forging process was carried out. Jin et al. [23] studied the cold orbital forging of component with deep and narrow groove. The cold orbital forging processes under three kinds of metal flow modes were analyzed by FE simulations and the mechanisms for forging defects of underfilling, folding and poor stress state of the tool are revealed. A new forging method for reducing process steps in automotive fasteners production has been proposed by Qin et al. [24]. FE simulation and forging experiment results confirmed feasibility of using this forging method. In this study, 3D FE models were established to study conjunction gear forging, finishing, and radial extrusion process. We examined the metal flow law of this process, the effect of finishing parameters on finishing dimensional precision, the forming law of the back taper extrusion process, and the demission of conjunction gear. Finally, the validation of the conjunction gear compound process was experimentally verified.
Fig. 1 – Radial projection image of the teeth.
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Fig. 2 – Conjunction gear dimension.
2.
Die design
2.1.
Hot forging die and upsetting finishing die design
The conjunction gear is a transmission part used in the automobile transmission and cooperating with the conjunction gear ring. The gear dimension and key parameters of selected conjunction gear are shown in Fig. 2 and Table 1, respectively. The diagram shows that the conjunction gear has two different characteristics distinct from ordinary gears. First, the end of the tooth is a symmetrical inclined plane with a certain angle different from the flat face of the common gear.
Table 1 – Main characteristics of conjunction gear. Number of tooth Normal module (mm) Pressure angle (8) Addendum circle diameter (mm) Root circle diameter (mm) back taper angle (8) Length of conjunction gear (mm)
33 2 20 68.8 63.8 3 5.8
The symmetric slope is called the locking surface, and the angle of the inclined planes is called the locking angle. The locking surface is designed to ensure that the conjunction gear and gear rings rotate synchronously and without impact. Moreover, the conjunction gear has two symmetrical tooth profiles, which are at a certain angle with the symmetrical planes called the back taper angle. Angle can prevent the vehicle from being out of gear when shifting. Therefore, the key and difficult point of this part is to form locking surface and back taper. Fig. 3 shows the dimensional difference of teeth during the HF-UF-RE process. The finished tooth is DL1 smaller than the hot forged ones in length, and the finished tooth is also thinner than the hot forged ones because of the existence of die clearance. After radial extrusion, the conjunction gear is DL2 longer than the finished ones in length. The back taper is also formed. Table 2 shows the tooth profile information formed by three processes. Metal fills die cavities during hot forging and finishing. Thus, the tooth shape of dies determines the shape of the hot forged gear and finished gear. The factors that affect the tooth shape of the finishing gear are the elastic deformations of the die and forging have little influence on the tooth shape of the finished gear. Thus, the tooth profile modification of the finishing die is neglected.
Fig. 3 – Dimensional difference of teeth during the HF-UF-RE process.
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Table 2 – Tooth profile information formed by three processes. Item
HF tooth UF tooth RE tooth
Number of tooth Normal module (mm) Pressure angle (8) Addendum circle diameter (mm) Root circle diameter (mm) Back taper angle (8) Length of conjunction gear (mm)
33 2 20 68.6 63.6 0 6.3
33 2 20 68.8 63.8 0 5.7
33 2 20 68.8 63.8 3 5.8
Many factors affect the shape of the hot forged gear. Thus, we must modify the shape of the die to obtain the ideal hot forged gear. The shape of the hot forging die is modified following the model to predict involute profile deflection in the hot precision forging of gears proposed by Zuo et al. [25]. This model includes four differences, namely, the thermal die expansion, the elastic die expansion, the thermal forged gear contraction, and the elastic workpiece recovery. Eq. (1) shows model formula [25,26], where fr(ri) and fu(ri) are the total deflections in the radial and circumferential direction, respectively. The modified involute of the hot forging die is shown in Fig. 4.
Fig. 4 – Modified involute.
8 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi d pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi d > > < r ¼ b 1 þ w2 þ f r ðriÞ b 1 þ w2 2 2 > > u ¼ warctan f u ðriÞ 180 : r u
2.2.
(1)
Extrusion die design
Given the existence of the back taper, the formed conjunction gear cannot be removed from the integral die along the axial direction as part of the hot forging and finishing process. To solve this problem, a type of multi-blade extrusion die (Fig. 5 (a)) is designed to form the back taper. Fig. 5(b) shows the segmenting position of each part. Theoretically, the extrusion die can be divided for every other tooth. However, the greater the amount of division, the worse the die life and the higher the manufacturing cost. Therefore, we divide the tooth die into three three-tooth dies along the diameter direction and 12 two-tooth dies. The tooth shape of the die is processed following the shape of a conjunction gear. To form the conjunction gear accurately, the toothed die must move along the radial direction simultaneously and accurately. A slide guide is designed to ensure the accurate movement of the tooth die. As shown in Fig. 5(c), the radial extrusion die is processed into prismatic ridges. The two sides of each blade and the groove of the pressure ring cooperate with each other to restrict the circumferential movement of the die. The outer side of the die is processed into an inclined plane. The die and the pressure ring come into contact by the inclined plane, thereby resulting in the conversion of pressure direction. The inclined surface of the die and the pressure ring are designed at 108 in opposite directions. This angle can ensure the smooth sliding of the extrusion die with sufficient radial pressure and without self-locking. The tool can also ensure that the contact consistently keeps surface contact, thereby helping to reduce the wear of the tooth die.
3.
FE model and experiment procedure
3.1.
Establishment of FE models
Forging simulation can significantly reduce cost and time by providing detailed information on the forging process before
Fig. 5 – Extrusion die of back taper: (a) structure diagram; (b) the distribution of tooth die; (c) sketch map of the coordination between the tooth die and pressure ring.
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Fig. 6 – 3D FE model: (a) hot forging; (b) upsetting finishing; (c) radial extrusion.
tool selection and process decisions being made in the workshop [27]. Thus, we must use FE simulation before actual trials [28]. The geometric model of the hot forging process is established by the Pro/Engineer (PRO/E) software system; the Deform-3D was applied to the FE simulation. Fig. 6(a) is a hot forging model composed of tooth die, top die, bottom die, and billet. The FE simulation of hot forging is based on the following assumptions [29]. Large plastic deformation is observed on the forging process, and the elastic deformation is negligible. Therefore, the billet can be considered a plastic body, while the tool can be considered a rigid body. In the process of deformation, the tetrahedron mesh is selected to divide the billet. Deform automatically redivides the grid when the cumulative maximum strain increment of the rolling piece is 0.7 to ensure that the software is sufficiently accurate without requiring excessive mesh repartitioning. A three-tooth model is simulated to save CPU processing time. The friction type is shear friction and the friction coefficient is assumed to be invariable during the forging process [12,15].
The friction force in the shear friction model is defined by Eq. (2): f s ¼ mk
(2)
fs is frictional stress, m is the friction coefficient and k is shear yield stress. The billet material is AISI-4120, which has high hardenability, no temper brittleness, good machinability and cold strain plasticity. Thus, this material is widely used in manufacturing gears and shafts. Fig. 7(a) shows the flow stress of materials at 25 8C [30], and Fig. 7(b)–(e) shows the flow stress of materials at 800–1100 8C [31]. Tables 3 and 4 present the hot forging simulation parameters and the main chemical composition of the material, respectively. Fig. 6(b) shows the finishing model consists of the top die, tooth die, and hot forged gear. Finishing parameters DL1 and c are important in the finishing process. The value of DL1 and c are selected from (0.4, 0.5, 0.6, 0.7) and (0.5, 0.1, 0.15) respectively. Based on the volume invariance theory in plastic form, the volume of the gear teeth is unchanged in the finishing process. However, considering the existence of die
Fig. 7 – Flow stress of AISI-4120 at different temperatures and strain rates: (a) 25 8C; (b) 800 8C; (c) 900 8C; (d) 1000 8C; (e) 1100 8C.
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Table 3 – Main parameters of hot forging simulation.
Table 7 – Main parameters of radial extrusion simulation.
Parameters
Parameters
Value
Top die velocity (mm/s) The initial temperature of the material (8C) The initial temperature of the die (8C) Environment temperature (8C) Heat transfer coefficient (N/s/mm/8C) Convection coefficient (N/s/mm/8C) Friction factor Mesh number for billet Billet material
600 1100 150 20 5 0.02 0.3 50000 AISI-4120
Table 4 – Chemical composition of AISI-4120 (mass fraction, %). C
Cr
0.34 1.10
Mn
Mo
Si
Ni
Cu
S
P
Fe
0.70
0.25
0.25
0.20
0.014
0.012
0.013
Balance
clearance c, some metals will flow through the gap. Thus, the tooth volume (V1) of the hot forged gear is slightly larger than the tooth volume (V2 = 38.10 mm3) of the finished gear. The tooth volume is affected by the dimensional parameters and finishing parameters. Therefore, some combinations of DL1 and c whose tooth volume is much smaller than the volume of the cavity V2 are discarded. The simulation parameters and process parameters are shown in Tables 5 and 8, respectively. Fig. 6(c) presents the FE model of the extrusion of back taper. A two-tooth die is selected for simulation. The vertical movement of the lower pressure ring is transformed into radial movement of the extrusion die. The radial movement is directly applied to the two-tooth die. Extrusion simulation parameters are shown in Table 7.
Table 5 – Main parameters of finishing simulation. Parameters
Value
Top die velocity (mm/s) Friction factor Mesh number for billet Refine ratio of the tooth Billet material
20 0.12 70000 0.1 AISI-4120
Table 6 – Main process parameters of finishing simulation. Group number Allowance Die Friction Tooth of length, clearance, coefficient volume, DL1 (mm) c (mm) V1 (mm3) 1 2 3 4 5 6 7 8 9 10
0.4 0.5 0.4 0.5 0.6 0.7 0.7 0.6 0.6 0.6
0.05 0.05 0.1 0.1 0.1 0.1 0.15 0.1 0.1 0.1
0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.08 0.2 0.3
39.8 40.51 38.12 38.80 39.48 40.26 38.27 39.48 39.48 39.48
Die velocity (mm/s) Friction factor Mesh number for billet Refine ratio of the tooth Billet material
3.2.
Value 2 0.12 50000 0.1 AISI-4120
Experiment procedure
The hot forging process is conducted on the 10,000 kN hot forging machine (FP-1000 hydraulic press made by Taiwan Jing Yong Precision Forging Co., Ltd.) [Fig. 8(a)]. The finishing and extrusion experiments are conducted on a 5000 kN hydraulic machine (Y27-500T four column hydraulic press made by Hebei Hong Kai Heavy Machine Tool Co., Ltd.) [Fig. 8 (c)]. The tools for hot forging, finishing, and extrusion tests are shown in Figs. 8(b), (d), and (e). The experiment was conducted in Shandong Da Wei Gear Co., Ltd. The die material is Cr12Mo1V1, the hardness is 60HRC after heat treatment, and the hot forging is lubricated by graphite water-based solution.
4.
Results and discussions
4.1.
Hot forging process
Fig. 9 shows the load formation curve of the hot forging process and the billet shape of some important stages. The forging process can be mainly divided into three stages, including upsetting, cavity filling, and corner filling. The first stage is billet upsetting. In the beginning, only the top die, bottom die, and step surface of the die come in contact with the billet. Billet gradually shows a classical drum-shaped expansion under the press of top die, similar to upsetting deformation. Load formation is extremely small during his period. The second stage is cavity filling stage. The die cavity is separated into four sections by the billet according to the flow of metal. Based on the least flow resistance law of metal flow, the outer metal of billet mainly flows to the external step cavity and tooth cavity, and the core metal of the billet mainly flow to the upper and lower cylindrical cavity. The four sections are filled almost at the same time thereby avoiding partial stress concentration. The load formation increases compared with the first stage. The last stage is corner filling. Given the increase in the compressive displacement, the space of die cavities constantly decreases, and the free surface of the metal is rapidly reduced, thereby leading to rapidly increasing load formation as shown in Fig. 14(g). No fold occurs and fineshaped conjunction gear is obtained by the hot forging process. The load formation of hot forging simulation is 2750 kN. The load formation of hot forging experiment is 2600 kN. The load formation difference between the experiment and simulation is 5.77%. Fig. 10(a) displays the forged gear obtained by hot forging. The forged gear is well filled. The forging is cut along the center axis. The sand mill line cutting area is removed and inspected
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Table 8 – Results of finishing simulation. No. 1 2 3 4 5 6 7 8 9 10
The allowance of length, DL1 (mm)
Die clearance, c (mm)
Friction factor
Tooth volume, V1 (mm3)
0.4 0.5 0.4 0.5 0.6 0.7 0.7 0.6 0.6 0.6
0.05 0.05 0.1 0.1 0.1 0.1 0.15 0.1 0.1 0.1
0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.08 0.2 0.3
39.8 40.51 38.12 38.80 39.48 40.26 38.27 39.48 39.48 39.48
Back taper surface quality
Profile quality
Dedendum quality
Fig. 8 – Experiment equipment and tools: (a) 1000 tons hot forging equipment; (b) tools of hot forging; (c) 500 tons hydraulic press; (d) tools of upsetting finishing; and (e) tools of radial extrusion.
based on the test method of the national standard (China) for low department organization and defect etching GB226-91. Etching acid is 1:1 hydrochloric acid solution. Etching was conducted at 65–80 8C for 20 min. Then, the gear was rinsed with water after drying. Fig. 11(a) shows the metal streamline of AISI-4120 steel after hot forging. Fig. 11(b) is a metal streamline of hot forged gear obtained from a 2D finite element simulation with a quadrilateral mesh. The streamline of the important position of the gear is perpendicular to the gear axis. This process will help ensure that the gear will not easily break
under high speed and a complex loading environment [32]. The uniform and continuous metal streamline at all parts guarantee the overall mechanical properties of the gears. Fig. 12(a) shows a video measuring instrument (VMI) for measuring the hot forged gear. Fig. 12(b) is the tooth profile and tooth error (dimension difference between the forged tooth and objective tooth (Table 2 HF tooth)) along the involute profile. The negative value of tooth error indicates that the forged tooth is smaller than the objective one. The tooth errors are mostly in the range
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4.2.
Fig. 9 – Forming stages in the hot forging process of conjunction gear, where the first stage includes a, b, and c; the second stage includes d, e, and f; the last stage includes g.
0.05 to 0.025, and the largest tooth error occurs at the top of the tooth, which is approximately 0.14 mm. Oxidation caused by additional exposure to air may explain this phenomenon.
Finishing process
Fig. 13 presents the image of metal flow velocity in the process of finishing process (Group 6). The arrow shows the flow direction of the velocity and the color dedicated the value of the velocity. The locking surface touches the die first and metal fills the tooth profile near the locking surface when stroke is 0.1 mm. The upper die continues to push forward when stroke is 0.2–0.5 mm. Metal has two main flow directions, namely, the direction of tooth length to reduce the length of tooth and the normal locking surface to fill the die clearance. The height of the tooth reaches the designed value, and metal can only flow to the normal of the tooth profile when stroke is 0.6 mm. The metal flow velocity of the finished parts is almost zero. Deformation is very small during finishing, and the finishing effect cannot easily obtain an accurate conclusion by observing the shape of conjunction gear. The effect of the finishing was checked by observing the contact region between the die and the hot forgings and the accumulation of metal at the root of the tooth. Fig. 14 shows the contact status between the hot forging and the die after the finishing process. Fig. 14(a) shows that no contact occurs before finishing; (b) shows only the tooth tip contacts with die, that is, only the tooth tip is finished; (c) shows the tooth part contacts the die, that is, the tooth parts are all refined and the finishing effect is best; and (d) shows the tooth parts and
Fig. 10 – Gear blank in different experimental stages: (a) hot forging gear; (b) upsetting finishing gear; (c) radial extrusion gear.
Fig. 11 – Metal flow line: (a) the experiment result; (b) FEM results.
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Fig. 12 – Tooth inspection: (a) video measuring instrument; (b) inspected tooth profile and tooth error.
Fig. 13 – Metal flow of finishing process (group 6).
Fig. 14 – The contact status between the forged gear and the finishing die: (a) before finishing, simulation-1; (b) after finishing, simulation-3; (c) after finishing, simulation-5; (d) after finishing, simulation-2.
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Fig. 15 – Inspected tooth profile and the tooth error (simulation-5).
dedendum contact the die. Considerable metal accumulation occurred at dedendum. Table 8 shows the simulation results of the finishing process. Simulations-1, 3, 4, and 7 have no complete contact between the tooth parts and the finishing die, which indicate that these tooth profiles have not achieved the finishing effect. Simulations-2, 5, 6, 8, 9, and 10 show complete contact between the tooth parts and the finishing die, which indicate that the tooth profiles and locking surfaces are all finished well. However, the volume of a tooth (simulation-2) is far greater than V2. After finishing, the root of the teeth will be heavily contacted the die causing too much metal accumulation at the dedendum. Simulation-9 shows more metal accumulation at the root than simulation-5, 6, 7, and 8. Therefore, simulation indicates that (c = 0.1, DL1 = 0.6) is the best combination of finishing parameter. Friction greatly affects metal flow. In the comparison of ironing and compressing finishing, Li et al. [17] found that friction influences the finishing quality and load formation of the ironing finishing, but it has little effect on the compressing finishing. Simulations-5, 6, 7, and 8 show that friction has little effect on upsetting finishing. Thus, upsetting finishing needs simple lubrication or no lubrication at all. The reduction of the phosphate/soap can effectively protect the environment and reduce costs. Fig. 10(c) shows the gear obtained by the finishing experiment. The locking surface of the finishing piece is well-formed and no metal accumulation occurs at the root. The tooth profile is also checked by VMI. Fig. 15 displays tooth profile and tooth error. The maximum tooth error is 0.046 mm that appears at the root. The tooth errors of other parts are approximately 0.01 mm. (1) The locking surface touches the die and is finished. (2) Only the tip profile of the forged gear touches the die and is finished. (3) The entire profile of the forged gear touches the die and is finished.
(4) Basically no metal accumulation at the root. (5) Slight metal accumulation at the root. (6) Large amount of metal accumulation at the root.
4.3.
Radial extrusion process
Fig. 16 shows the image of metal flow velocity in the process of radial extrusion. When the extruding displacement is 0.1 mm, the bottom parts of the surface (2) and (3) initially come in contact the die leading metals flowing, and the flowing direction is mainly toward dedendum. When the extruding displacement is 0.2 mm, the metal of surfaces (2) and (3) begin to flow toward addendum. Surfaces (1) and (4) begin to contact the die. When the extruding displacement is 0.4 mm, addendums of teeth begin to contact die and the addendums are compressed in the radial direction. The metal of the tooth tip moves along the tooth length direction and the moving speed is almost equal. Thus, the movement of the tooth tip can be regarded as rigid shift. When the extruding displacement is 0.54 mm, the extrusion is completed. The metal of most parts of the tooth no longer flow. However, the metal of tooth tip retains a rigid shift trend because of the push of the die. The extrusion process of the three-tooth die is similar. The difference is the contact orders between the six surfaces of the three-tooth die and the conjunction gear. The finishing effects of the two-tooth die and the three-tooth die are basically the same. After the extrusion is completed, the excess metal is concentrated at the dedendum. The conjunction gear moves approximately 0.3 mm along the direction of the tooth length. The profile of the tooth tip remains intact. Fig. 17 displays the effective strain distribution of the tooth in the process of the radial extrusion process. In the beginning, the contact area of the die and the tooth part is small, the extrusion speed of the die is slow, and the strain is very small. When the extruding displacement is 0.4 mm, the four side surfaces all contact the die, the addendum of the tooth also
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Fig. 16 – Metal flow of the radial extrusion.
Fig. 17 – Effective strain distribution of the radial extrusion.
begins to contact the dedendum of the die. The addendum of the tooth is compressed and has a weak strain. At the end of the extrusion, the four side surfaces, the addendum, and the dedendum contact the die. This process indicates intense deformation. The back taper extrusion is a partial deformation process, and the deformation of the teeth mainly occurs in the latter half of extrusion. The biggest effective strain appeared in the fillet of the dedendum at the end of extrusion at approximately 1.5. We can also see the contact order between the tooth part and the die is side surfaces (2) (3), side surfaces (1) (4), addendum, and dedendum. The diagram shows that basically no deformation occurs at the tip of the tooth. The rigid translation of the conjunction gear is also verified. Fig. 18 shows the effective stress distribution of the tooth in extruding back taper. The contact order between die and tooth is also the side surfaces (2) (3), side surfaces (1) (4), addendum, and dedendum. At the beginning of extrusion, the four side
surfaces of the tooth touch the die. Effective stress is very small. The addendum the tooth begins to compress when extruded to 0.4 mm. The contact area of the tooth and die increases sharply, the free flow area of the metal decreases, and the metal deformation resistance increases. At the end of the extrusion, the tooth has the largest contact area with the die and the effective stress reaches the maximum value of about 881 MPa, mainly concentrating on the bottom of the conjunction gear. Fig. 10(c) shows a conjunction gear obtained from compound formation process. This gear is a spline with an inverted cone; thus, it cannot be directly measured by VMI. Fig. 19 shows a type of high-precision 3D scanner used to measure the part. After calibration, the accuracy of the scanner can reach 0.01 mm. The part model obtained from the scanning is compared with the design model by Geomagic Qualify. Fig. 20 (a) shows the error comparison of the conjunction gear
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Fig. 18 – Effective stress distribution of the radial extrusion.
Fig. 19 – High-precision 3D scanner.
obtained by simulation. It can be seen that the tooth profile errors of the conjunction gear are all within the range of 0.02 mm. During the extrusion process, the conjunction gear extends about 0.1 mm along the axial direction. Fig. 20(b)
shows the tooth error of the conjunction gear obtained by experiment. It is obvious that the errors of the two sides of the teeth are the smallest in the range of 0.06 mm. The error of addendum and dedendum are 0.1 mm and 0.3 mm respectively. The length of the tooth will lengthen about 0.1 mm. The experimental errors at addendum and dedendum are much larger than the simulated values. The reason is that there are errors of addendum and dedendum due to the influence of the two previous processes. But the experimental error is within the scope of application. The result of experiment and simulation error is consistent basically, which reflects the correctness of finite element simulation. The teeth formed by the two-and three-tooth die were also checked. Thus, no obvious difference was observed on tooth error indicating such that it is feasible to separate the toothed die per two and three teeth. This situation is significant in improving the die life and reducing the cost of die manufacturing. The experiment also found parts with incomplete forming of back taper, parts with good forming of back taper, but the height of the tooth was much smaller than the theoretical value. Extrusion failure and excessive extrusion may explain the former problem. Therefore, the moving of the extrusion die must be controlled strictly, which is essential to forming the back taper.
Fig. 20 – The tooth error comparison: (a) result of simulation and (b) result of experiment.
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Summery and conclusions [3]
From the work carried out in FE simulations, HF-UF-RE experiment and sample parts analysis the following conclusions may be drawn:
[4]
[5]
1. A radial extrusion die is designed to form the back taper. The extrusion die is divided into multiple parts along the radial direction to ensure smooth reduction of the tooth die after a back taper formed. The design of oblique plane contact reduces the wear of die in the entire process. The design of track ensures the accurate sliding of the tooth dies. The experiment shows that the formation quality of the back taper is high, and the shift of the die is accurate and stable. 2. The profile of the forging die is calculated on the basis of the profile modification model of Zuo et al. [25]. The conjunction gear formed by the modified die meet the design requirements. The experimental results show that the hot forgings are filled fully and without folding and its metal flow line is reasonable. Experiments show that hot forging can be used for preform of conjunction gear. 3. Simulation analysis and experimental verification indicate that the upsetting finishing can enhance the dimension accuracy and surface quality of hot forged gear. The upsetting finishing is a type of partial metal deformation, and the finishing sequence is from the tooth tip to the tooth bottom. Finishing parameters have little effect on tooth length and the quality of locking surface but have great influence on the finishing effect of the profile. The best finishing effect is obtained when the finishing parameter combination is c = 0.1, DL1 = 0.6. 4. Local plastic deformation of the tooth bottom and the rigid shift of the tooth tip occurs during extrusion. The shift distance is approximately 0.3 mm. The feasibility of forming the back taper by the designed radial extrusion die is experimentally verified. The conjunction gears obtained by HF-UF-RE compound process meet the requirement of the application and its tooth error within the allowable range. The simulation and experiment show the feasibility of forming a conjunction gear through the HF-UF-RE compound process.
[6]
[7] [8] [9]
[10] [11]
[12]
[13]
[14]
[15]
[16]
[17]
[18]
Funding
[19]
This work is supported by the National Natural Science Foundation of China (Grant No. 51875036). This work is also supported by the National Natural Science Foundation of China (Grant No. 51375042).
[20]
references
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