Controlling Flow Instability in Straight Spur Gear Forging Using Numerical Simulation and Response Surface Method

doi:10.1007/s40195-017-0669-1

Abstract

Abstract:

Workability domain without the onset of flow instability was developed by numerical simulation and response surface method (RSM) for complex-shaped straight spur gear forging. The processing map of AZ31B alloys was calculated from flow stress curves and then integrated with the finite element model to simulate the distribution of flow instability in the straight spur gear undergoing isothermal forging process. Occurrence of flow instability depends on forging temperature, punch velocity and billet reduction. Taking forging temperature and punch velocity as design variables, while billet reduction as response variable, RSM of workability domain was established. Analysis of variance indicates that forging temperature is the most significant factor determining the appearance of flow instability in the forged gear. Flow instability is easier to take place at lower temperatures of 250 and 300 °C in the early stage of forging but at higher temperatures of 350 and 400 °C in the later stage of forging, which is attributed to different deformation mechanisms and dynamic recrystallization behaviors at different temperatures or deformation levels. Meanwhile, increasing punch velocity further reduces the workability of the forged gear. Four different processing paths were chosen to carry out the gear forging trials. Visual observations and metallographic examinations demonstrate that the developed workability domain contributes to optimization of forging parameters.

Key words: Processing map, Finite element method, Response surface method, Straight spur gear, Magnesium alloy

Zhao-Yang Jin, Nan-Nan Li, Kai Yan, Jing-Xin Chen, Dong-Lai Wei, Zhen-Shan Cui. Controlling Flow Instability in Straight Spur Gear Forging Using Numerical Simulation and Response Surface Method[J]. Acta Metallurgica Sinica (English Letters), 2018, 31(1): 82-96.

Figures/Tables 24

Fig. 1 True stress-strain curves of AZ31B alloy during hot compression under conditions of a 300 °C, b 1 s-1

Fig. 2 Plot of \( \lg \sigma \) versus \( \lg \dot{\varepsilon } \) at strains of a 0.3, b 0.7

Fig. 3 Processing maps of AZ31B alloys at strains of a 0.2, b 0.4, c 0.6, d 0.8

Table 1 Geometric parameters of the straight spur gear

Module	Teeth number	Pressure angle (°)	Reference diameter (mm)	Addendum coefficient	Bore diameter (mm)
0.5812	15	14.5	8.7173	1.0	3.985 ± 0.01

Fig. 4 Designed die structure with divided flow mandrel and linkage demolding device. 1—thermocouple, 2—linkage, 3—billet, 4—toothed ejector, 5—lower bolster, 6—upper platen, 7—toothed punch, 8—cooling pipe, 9—heating rod, 10—female die, 11—spring, 12—lower platen

Fig. 5 Distribution of flow instability as forged at temperature of 320 °C and apparent average strain rate of 0.63 a simulated results, bexperimental results

Fig. 6 Variation of minimal instability parameter with reduction percent at temperature of 320 °C and apparent average strain rate of 0.63 s-1

Table 2 Design variables and their levels

Design variables	Levels
Design variables	- 1	- 1/2	- 1/3	0	1/3	1/2	1
T (°C)	250	287.5	300	325	350	362.5	400
V (mm/s)	0.10	0.33	0.40	0.55	0.70	0.78	1.00

Table 3 Design variables and two simulated responses

No	Coded		Actual		Response variables
No	A	B	T (°C)	V (mm/s)	L ₁	L ₂
1	0.500	0.500	362.50	0.78	0.000	0.610
2	0.000	0.500	325.00	0.78	0.000	0.650
3	1.000	1.000	400.00	1.00	0.000	0.505
4	- 0.333	1.000	300.00	1.00	0.000	1.000
5	1.000	0.000	400.00	0.55	0.000	0.615
6	0.000	0.000	325.00	0.55	0.455	0.925
7	0.000	- 0.500	325.00	0.33	0.390	0.970
8	- 1.000	- 1.000	250.00	0.10	0.000	1.000
9	1.000	- 1.000	400.00	0.10	0.000	0.955
10	- 0.500	0.000	287.50	0.55	0.435	1.000
11	- 0.333	0.333	300.00	0.70	0.460	1.000
12	- 1.000	0.000	250.00	0.55	0.775	1.000
13	- 0.333	- 1.000	300.00	0.10	0.000	1.000
14	0.500	0.000	362.50	0.55	0.000	0.605
15	1.000	0.333	400.00	0.70	0.000	0.600
16	- 0.500	- 0.500	287.50	0.33	0.000	1.000
17	- 0.333	- 0.333	300.00	0.40	0.475	1.000
18	- 1.000	0.333	250.00	0.70	0.775	1.000
19	0.000	1.000	325.00	1.00	0.435	0.740
20	- 1.000	- 0.333	250.00	0.40	0.685	1.000
21	0.333	0.333	350.00	0.70	0.000	0.605
22	1.000	- 0.333	400.00	0.40	0.000	0.640
23	0.333	- 1.000	350.00	0.10	0.000	0.960
24	- 1.000	1.000	250.00	1.00	0.815	1.000
25	0.333	1.000	350.00	1.00	0.000	0.600
26	- 0.500	0.500	287.50	0.78	0.435	1.000
27	0.333	- 0.333	350.00	0.40	0.000	0.635
28	0.500	- 0.500	362.50	0.33	0.000	0.655
29	0.000	- 1.000	325.00	0.10	0.000	1.000

Fig. 7 Model summary statistics of L 2

Table 4 ANOVA for reduced cubic response surface of L 2

Source	Sum of squares	df	Mean square	F value	P value Prob. > F
Model	0.91	7	0.13	35.31	< 0.0001
A	0.34	1	0.34	92.48	< 0.0001
B	0.13	1	0.13	35.66	< 0.0001
AB	0.069	1	0.069	18.70	0.0003
A ²	0.001042	1	0.001042	0.28	0.6004
B ²	0.021	1	0.021	5.76	0.0258
AB ²	0.012	1	0.012	3.19	0.0885
A ³	0.10	1	0.10	27.43	< 0.0001
Residual	0.077	21	0.003684
Cor total	0.99	28

Fig. 8 Response surface model of L 2 a 3D plot, b 2D contour plot

Table 5 ANOVA for reduced cubic response surface of L 1

Source	Sum of squares	df	Mean square	F value	P value Prob. > F
Model	1.90	7	0.27	11.42	< 0.0001
A	1.03	1	1.03	43.26	< 0.0001
B	0.012	1	0.012	0.49	0.4913
AB	0.17	1	0.17	7.34	0.0131
A ²	0.10	1	0.10	4.35	0.0493
B ²	0.15	1	0.15	6.33	0.0200
A ² B	0.053	1	0.053	2.22	0.1509
AB ²	0.11	1	0.11	4.83	0.0394
Residual	0.50	21	0.024
Cor total	2.40	28

Fig. 9 Response surface model of L 1 a 3D plot, b 2D contour plot

Fig. 10 Workability domain for AZ31B straight spur gear forging

Fig. 11 Effects of deformation temperature and punch velocity on responses of L 1 and L 2

Fig. 12 2D cross section of 3D workability domain at punch velocity of a 0.1 mm/s, b 1 mm/s

Fig. 13 Photograph of forging equipments

Fig. 14 Photographs of the straight spur gear forged by four different processing paths as a P1, b P2, c P3, d P4

Fig. 15 Schematic diagram of observation sites

Fig. 16 Metallographic microstructure of the straight spur gear forged by P1 path at the positions of a S1, b S2, c S3

Fig. 17 Metallographic microstructure of the straight spur gear forged by P2 path at the sites of a S4, b S2, c S3

Fig. 18 Metallographic microstructure of the straight spur gear forged by P3 path at the sites of a S2, b S3

Fig. 19 Metallographic microstructure of the straight spur gear forged by P4 path at the sites of a S2, b S3

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