Optimal Process Conditions for the Manufacture of Aluminum Alloy Bicycle Pedals

Abstract

Numerous forms and manufacturing methods of bicycle pedals exist in current markets. The purpose of this study was primarily to design an innovative forging die for a bicycle pedal company through a simulative analysis, using commercial finite element package software. A series of simulation analyses adopted workpiece temperature, mold temperature, forging speed, friction factor, and size of the mold as variables to evaluate the methods of lightweight in the bicycle pedal forging press. The study involved modifying professional bicycle pedal sizes. The effective strain, effective stress, and die radius load distribution of the pedals were analyzed under various forging conditions. Aluminum (A6061 and A7075) was used to analyze the simulative data. The optimal control parameters were subsequently obtained using the Taguchi methods and a genetic algorithm. The results of the simulation analyses indicated that the design of an experimental forging die can lower the deformation behavior of a bicycle pedal.

1. Introduction

Progress in precision forging technology, including low production costs and rapid production, has allowed for the intensive use of forging. Wang et al. [1] developed a practical compliance control method for hydraulic forging manipulators. A hybrid force-position control method was proposed and performed on a novel serial-parallel forging manipulator. Lu and Ou [2] used an improved approach to characterize press elastic behavior and to quantify the effect of press elasticity to forge complex three-dimensional (3D) shapes. Wang et al. [3] improved the two-stage extrusion process and related die designs of a forging company that currently manufactures a support shaft by using the traditional method. Narayanasamy et al. [4, 5] evaluated aspects of extrusion forging during cold upsetting by using a suitable die and aluminum alloy (H9-6063) solid cylinders that were subjected to various geometrical conditions. Zhao et al. [6] improved the microstructure and properties of hot isostatic pressed Ti-17 power compact through isothermal forging with preferable deformation parameters that were provided by a processing map.

Kazeminezhad and Hosseini [7] used a new constitutive model for severe plastic deformation to optimize groove pressing die design. Wu and Hsu [8] used the finite element method (FEM) and experimental models of flow under extrusion forging conditions to analyze forging deformation. Park et al. [9] used finite element (FE) analysis of multiple cross-sectional shape forging to analyze subsequent forging size errors. This study involved using A7075 and A6061 alloy. Bhushan et al. [10] studied the fabrication and microstructural investigations of AA7075-SiCpMMCs. A 7075 Al alloy was reinforced with 10 and 15 wt.% SiCp at 20–40 μm by using a stir casting process. Thipprakmas and Phanitwong [11] used the FEM to investigate the flange-forming mechanism and effects of upward and downward burr orientation flange-forming directions. Hino et al. [12] used a new simulation-based technique for the optimal design of a multistage forging process aimed at reducing the number of press-forming stages. Verleene et al. [13] studied the hardening stress train law to determine the AISI M2 cold forging tool steel. Chen et al. [14, 15] studied numerous bicycle pedal factors of forging and forming by using the FEM.

In this study, rigid-plastic finite element software was used to investigate the plastic deformation behavior of the aluminum alloy (A6061) and alloy (A7075) workpiece that are used to forge bicycle pedals. The results confirmed the suitability of the proposed design process, which allowed a bicycle pedal die to achieve perfect forging. The results of the simulation analyses of the experimental forging die revealed lower deformation behavior in the bicycle pedals.

2. Finite Element Method

Rigid-plastic FE DEFORM 3D software is widely used in forging, extrusion, pulling, rolling, stamping, upsetting, and other forming processes of precision metals. This software is composed of multiple modules. The primary structure can be divided into pretreatment modules, the simulation engine, postprocessor modules, and multifunction modules. DEFORM 3D also simulates plastic deformation to express plastic flow stress (flow stress). The flow stress equation can be written as

\bar{σ} = \bar{σ} (\bar{ε}, \dot{\bar{ε}} \cdot T),

(1)

where T is temperature, $\bar{ε}$ is the strain, and $\dot{\bar{ε}}$ is the strain rate. The location of the greatest damage and destruction of the value of the occurrence is determined by the accumulated energy.

The present analysis involved adopting the following assumptions: (1) the mold and die are both rigid bodies; (2) the aluminum alloy (A7075 and A6061) billet is a rigid-plastic material; and (3) the materials are isotropic and exhibit a homogeneous property. This study involved using the shear friction equation for FE analysis.

3. Taguchi Method and Genetic Algorithm

The Taguchi method, a well-known robust design technique, provides comprehensive understanding of the individual and combined effects of various design parameters based on a minimal number of experimental trials. Its aim is to establish parameter settings that achieve a robust product that is unaffected by unavoidable variations in external noise. Depending on the characteristics involved, various S/N ratios can be used: “lower is better” (LB), “nominal is best” (NB), or “higher is better” (HB). William and Creveling [16] and Belavendram [17] adopted the S/N ratio to describe the LB characteristics of the forging process of bicycle pedals. The equation can be expressed as

S / N = - 10 \log [\frac{1}{n} \sum_{i = 1}^{n} y_{i}^{2}],

(2)

where n is the number of simulation repetitions under the same design parameters, y_i indicates the measured results, and i indicates the number of design parameters in the Taguchi orthogonal array (OA).

The nonlinear modeling capability of a combination of artificial neural networks and genetic algorithms, as well as the overall optimization ability of the decision-making system, was used. The “enhanced learning” strategy can be used to optimize the link weights of the neural network. Learning can be strengthened for the training samples that do not contain the target output values. The model can still be used for measurements to assess optimization and prediction of the output layer. Therefore, genetic algorithm neural networks were used in this study.

4. Numerical Simulation

4.1. 3D Structure Design

Figure 1 presents the finite element model of a professional bicycle pedal forging mold. Figure 2 presents meshed models of the 6061 and 7075 aluminum alloy billet and die before, during, and after the forging process.

Figure 1:

Finite element model of bicycle pedals forging process.

Figure 2:

It presents meshed models of the 7075 and 6061 aluminum alloy billet and die before, during, and after the forging process: (a) before the forming process, (b) during the forming process, and (c) after the forming process.

4.2. Factor Selection

The Taguchi experimental trials in this study involved adopting a designed mold and die for the bicycle pedal. Table 1 presents the five design factors, each with four levels, that were specified for the bicycle pedal. Accordingly, the experimental trials were arranged in an L₁₆(4⁵) orthogonal array matrix. The design factors in the bicycle pedal (Table 1) included the following: Factor A, workpiece temperature; Factor B, die temperature; Factor C, forging speed; Factor D, friction factor; and Factor E, dimension of the die.

Table 1:

Design parameters and levels for the A7075 and A6061 bicycle pedal forming.

Symbol	Parameters	Level 1	Level 2	Level 3	Level 4

A	Workpiece temperature (°C)	20	150	300	450
B	Die temperature (°C)	20	150	300	450
C	Forging speed (mm/sec)	30	40	50	60
D	Friction factor	0.25	0.4	0.6	0.8
E	Dimension of die (mm)	29	30	31	32

5. Results and Discussion

Tables 2 and 3 list the multiquality characteristics: the effective stress weight was 40%; the effective strain weight was 30%; and the die load weight was 30%. Because the effective stress has larger effect for the forging forming. The factors included effective stress and die load, supporting the LB rationale. The effective strain supports the HB rationale.

Table 2:

Overall evaluation criteria (OEC) for the A6061.

Criteria description	Worst value	Best value	QC	Rel. wt. (%)

Effective stress (MPa)	400	80	≪ S	40%
Effective stain	7	12	B ≫	30%
Die load (kN)	2800	350	≪ S	30%

Table 3:

Overall evaluation criteria (OEC) for the A7075.

Criteria description	Worst value	Best value	QC	Rel. wt. (%)

Effective stress (MPa)	1000	150	≪ S	40%
Effective stain	7	13	B ≫	30%
Die load (kN)	8100	1000	≪ S	30%

Tables 4 and 5 present the S/N responses for the forging of the bicycle pedals. Tables 6 and 7 present the corresponding factor response data. Following the principles of the Taguchi method, a high S/N ratio was assumed to indicate high product quality. Therefore, Tables 8 and 9 present the following optimal parameter settings for bicycle pedal forging: (1) aluminum alloy A6061: A1 workpiece temperature, 20°C; B1 die temperature, 20°C; C3 forging speed, 50 mm/s; D4 friction factor, 0.8; and E2 dimension of the die, 30 mm, and (2) aluminum alloy A7075: A1 workpiece temperature, 20°C; B4 die temperature, 450°C; C4 forging speed, 60 mm/s; D4 friction factor, 0.8; and E2 dimension of the die, 30 mm.

Table 4:

S/N ratio for the A6061 bicycle pedal.

Experiment	A	B	C	D	E	Averages	S/N ratio

Case 01	1	1	1	1	1	37.69	−31.525
Case 02	1	2	2	2	2	23.64	−27.473
Case 03	1	3	3	3	3	30.21	−29.604
Case 04	1	4	4	4	4	26.26	−28.386
Case 05	2	1	2	3	4	43.89	−32.848
Case 06	2	2	1	4	3	54.92	−34.795
Case 07	2	3	4	1	2	51.08	−34.166
Case 08	2	4	3	2	1	57.53	−35.198
Case 09	3	1	3	4	2	37.17	−31.404
Case 10	3	2	4	3	2	68.17	−36.672
Case 11	3	3	1	2	4	75.14	−37.518
Case 12	3	4	2	1	3	68.57	−36.723
Case 13	4	1	4	2	3	85.34	−38.624
Case 14	4	2	3	1	4	73.75	−37.356
Case 15	4	3	2	4	1	77.26	−37.76
Case 16	4	4	1	3	2	89.57	−39.044

The total average						56.26	−34.318

Table 5:

S/N ratio for the A7075 bicycle pedal.

Experiment	A	B	C	D	E	Averages	S/N ratio

Case 01	1	1	1	1	1	28.70	−29.158
Case 02	1	2	2	2	2	29.08	−29.272
Case 03	1	3	3	3	3	27.63	−28.828
Case 04	1	4	4	4	4	17.35	−24.786
Case 05	2	1	2	3	4	47.86	−33.600
Case 06	2	2	1	4	3	37.20	−31.411
Case 07	2	3	4	1	2	40.03	−32.048
Case 08	2	4	3	2	1	44.20	−32.909
Case 09	3	1	3	4	2	60.81	−35.680
Case 10	3	2	4	3	2	62.14	−35.868
Case 11	3	3	1	2	4	78.51	−37.899
Case 12	3	4	2	1	3	69.31	−36.816
Case 13	4	1	4	2	3	73.30	−37.303
Case 14	4	2	3	1	4	80.18	−38.082
Case 15	4	3	2	4	1	81.15	−38.186
Case 16	4	4	1	3	2	71.30	−37.062

The total average						53.05	−33.682

Table 6:

Factor response table for the A6061 S/N ratio.

Experiment	A	B	C	D	E

Level 1	−29.247	−33.60	−35.72	−34.942	−35.289
Level 2	−34.252	−34.074	−33.701	−34.703	−33.022
Level 3	−35.579	−34.762	−33.39	−34.542	−34.936
Level 4	−38.196	−34.838	−34.462	−33.086	−34.072
Effects	8.949	1.238	2.33	1.856	2.267
Ranks	1	5	2	4	3

Table 7:

Factor response table for the A7075 S/N ratio.

Experiment	A	B	C	D	E

Level 1	−28.011	−33.935	−33.883	−34.026	−34.030
Level 2	−32.492	−33.658	−34.469	−34.346	−33.516
Level 3	−36.566	−34.240	−33.875	−33.84	−33.59
Level 4	−37.658	−32.894	−32.501	−32.516	−33.592
Effects	9.647	1.346	1.968	1.83	0.514
Ranks	1	4	2	3	5

Table 8:

Factor response table for the A6061 multiquality characteristics.

Experiment	A	B	C	D	E

Level 1	29.449	51.022	64.33	57.772	60.162
Level 2	51.854	55.119	53.34	60.412	50.364
Level 3	62.262	58.422	49.665	57.959	59.759
Level 4	81.48	60.482	57.712	48.902	54.76
Effects	51.981	9.46	14.665	11.51	9.798
Ranks	1	5	2	3	4

Table 9:

Factor response table for the A7075 multiquality characteristics.

Experiment	A	B	C	D	E

Level 1	25.689	52.667	53.927	54.555	54.047
Level 2	42.322	52.15	56.849	56.272	50.305
Level 3	67.692	56.83	53.205	52.232	51.86
Level 4	76.482	50.54	48.205	49.127	55.974
Effects	50.793	6.29	8.644	7.145	5.669
Ranks	1	4	2	3	5

Tables 10 and 11 present the variance of bicycle pedal forging. We analyzed the results of the experimental trials by using the analysis of variance (ANOVA) statistical method. Confidence and significance are highly critical for control factors. Aluminum alloys A7075 and A6061 used all factor levels at 99.99% confidence.

Table 10:

Analysis of variance (ANOVA) results for the bicycle pedal A6061 forming.

Factors	Sum of squares	DOF	Variance	F-ratio	Probability	Confidence	* Significant

Workpiece temperature	11282.071	3	3760.69	601.371	1.19E–16	99.99%	Yes
Die temperature	409.894	3	136.631	21.861	6.64E–06	99.99%	Yes
Forging speed	954.05	3	318.016	50.882	2.1E–08	99.99%	Yes
Friction factor	612.429	3	204.143	32.662	4.71E–07	99.99%	Yes
Dimension of die	515.843	3	171.947	27.511	1.49E–06	99.99%	Yes
Other/error	0	16	0

Total	13774.289	31

Note: at least 99% confidence.

Table 11:

Analysis of variance (ANOVA) results for the bicycle pedal A7075 forming.

Factors	Sum of squares	DOF	Variance	F-ratio	Probability	Confidence	* Significant

Workpiece temperature	13017.06	3	4339.02	1378.312	1.62E–19	99.99%	Yes
Die temperature	172.359	3	57.453	18.25	2.04E–05	99.99%	Yes
Forging speed	309.665	3	103.221	32.788	4.59E–07	99.99%	Yes
Friction factor	229.634	3	76.544	24.314	3.36E–06	99.99%	Yes
Dimension of die	148.011	3	49.337	15.672	5.07E–05	99.99%	Yes
Other/error	0.004	16	0

Total	13876.736	31

Note: at least 99% confidence.

Figures 3, 4, 5, 6, 7, and 8 depict the effective strain, effective stress, and die load distribution of bicycle pedals fabricated based on a perfect design, using (1) aluminum alloy A6061 (A1B1C3D4E2) and (2) aluminum alloy A7075 (A1B4C4D4E2). These results indicated the ideal specifications of the mold and die of the new design, with an (1) aluminum alloy A6061 effective strain of 10.5 mm/mm, effective stress of 864 MPa, and mold and die load of 8160 kN and (2) aluminum alloy A7075 effective strain of 11.1 mm/mm, effective stress of 1460 MPa, and mold and die load of 10,900 kN.

Figure 3:

Distribution of effective strain of 6061 aluminum alloy bicycle pedal.

Figure 4:

Distribution of effective stress of 6061 aluminum alloy bicycle pedal.

Figure 5:

Y load of 6061 aluminum alloy bicycle pedal forming.

Figure 6:

Distribution of effective strain of 7075 aluminum alloy bicycle pedal.

Figure 7:

Distribution of effective stress of 7075 aluminum alloy bicycle pedal.

Figure 8:

Y load of 7075 aluminum alloy bicycle pedal forming.

Nonlinear modeling capability of a combination of artificial neural networks and genetic algorithm, the overall optimization ability of decision-making system, is used. Tables 12 and 13 list effective stresses by using a genetic algorithm that verified the Taguchi method numerical analysis. The average prediction errors were 6.52% and 2.59% for the A6061 aluminum alloy and the A7075 aluminum alloy, respectively.

Table 12:

6061 aluminium alloy genetic algorithm verifies form.

Case	Workpiece temperature	Die temperature	Forging speed	Friction factor	Dimension of die	Effective stress	Predict effective stress	Error %

Case 01	20	20	30	0.25	29	359	342	4.7%
Case 02	20	150	40	0.4	30	378	354	6.3%
Case 03	20	300	50	0.6	31	358	322	10%
Case 04	20	450	60	08	32	362	384	5.7%
Case 05	150	20	40	0.6	32	254	278	8.6%
Case 06	150	150	30	0.8	31	239	198	17.2%
Case 07	150	300	60	0.25	30	254	215	15.4%
Case 08	150	450	50	0.4	29	259	230	11.2%
Case 09	300	20	50	0.8	30	168	164	2.4%
Case 10	300	150	60	0.6	29	171	180	5%
Case 11	300	300	30	0.4	32	156	150	3.8%
Case 12	300	450	40	0.25	31	173	164	5.2%
Case 13	450	20	60	0.4	31	87.6	85	3%
Case 14	450	150	50	0.25	32	127	124	2.4%
Case 15	450	300	40	0.8	29	99.4	98	1.4%
Case 16	450	450	30	0.6	30	97	95	2%

Average								6.52%

Table 13:

7075 aluminium alloy genetic algorithm verifies form.

Case	Workpiece temperature	Die temperature	Forging speed	Friction factor	Size of mold	Effective stress	Predict effective stress	Error %

Case 01	20	20	30	0.25	29	864	844	2.3%
Case 02	20	150	40	0.4	30	864	850	1.6%
Case 03	20	300	50	0.6	31	864	848	1.9%
Case 04	20	450	60	08	32	863	859	0.5%
Case 05	150	20	40	0.6	32	629	580	7.8%
Case 06	150	150	30	0.8	31	691	648	6.3%
Case 07	150	300	60	0.25	30	694	669	3.6%
Case 08	150	450	50	0.4	29	641	597	6.9%
Case 09	300	20	50	0.8	30	393	395	0.5%
Case 10	300	150	60	0.6	29	384	377	1.8%
Case 11	300	300	30	0.4	32	384	389	1.3%
Case 12	300	450	40	0.25	31	385	376	2.3%
Case 13	450	20	60	0.4	31	202	198	2%
Case 14	450	150	50	0.25	32	193	189	2.1%
Case 15	450	300	40	0.8	29	193	197	2%
Case 16	450	450	30	0.6	30	184	180	2.2%

Average								2.59%

6. Experimental Design and Discussion of Bicycle Pedal

Figure 9 illustrates the tie bicycle pedal design. The finished product attained high strength and precision when the die was fabricated using this high-precision design. Figure 10 displays the die steel pushing of the bicycle pedal forming apparatus. Figure 11 illustrates the billet of the bicycle pedal forming apparatus, composed of A6061 materials. Figures 12 and 13 present the upper die and lower die of the bicycle pedal forming apparatus. Figure 14 presents the assembled die of the bicycle pedal forming apparatus. Figure 15 presents the A6061 product of the bicycle pedal forming apparatus. The experimental processing of the die combination entails appropriate assembly and spray lubricants in the die. The billet was heated to 500°C by using a high-temperature furnace. Table 14 predicts the significant dimensions of the bicycle pedal product. In addition to the 7 ± 0.05 mm dimension has small error, the other measured dimensions to be eligibility for bicycle pedal product.

Table 14:

Measurement of significant dimension into bicycle pedal product.

Number	Design dimensions (mm)	Measurement dimensions (mm)	Detect eligible

1	61 ± 0.1	61.06	o
2	55 ± 0.1	54.94	o
3	7 ± 0.05	7.10	x
4	42 ± 0.1	42.08	o
5	55.5 ± 0.1	55.48	o

Figure 9:

Die dimension design into bicycle pedal forming.

Figure 10:

Pushing of bicycle pedal forming.

Figure 11:

Billet of bicycle pedal forming.

Figure 12:

Upper die of bicycle pedal forming.

Figure 13:

Down die of bicycle pedal forming.

Figure 14:

Assemble die of bicycle pedal forming.

Figure 15:

Product of A6061 bicycle pedal forming.

7. Conclusions

This study involved using rigid-plastic finite element software to investigate the plastic deformation behavior of aluminum alloy (A6061) and alloy (A7075) workpiece used to forge bicycle pedals. The analysis results were as follows.

Confidence and significance were critical for all control factors (Factor A, workpiece temperature; Factor B, die temperature; Factor C, forging speed; Factor D, friction factor; and Factor E, dimension of the die).

Using a genetic algorithm verified the Taguchi method numerical analysis. The average prediction errors were 6.52% and 2.59% in A6061 aluminum alloy and A7075 aluminum alloy, respectively.

In experiment product, in addition to the 7 ± 0.05 mm dimension has small error, the other measured dimensions to be eligibility for bicycle pedal product. The results of simulation analyses indicated that the design of an experimental forging die can increase the strength and dimension precision of bicycle pedals.

Conflict of Interests

The authors declare that there is no conflict of interests regarding the publication of this paper.

Footnotes

Acknowledgment

The authors gratefully acknowledge the financial support of the Ministry of Science and Technology of the Republic of China, Taiwan, under Grant no. NSC 100-2221-E-018-012.

References

Wang

Gao

, and Zhang

, “Adaptive compliance control of a hydraulic manipulator in free forging,” Proceedings of the Institution of Mechanical Engineers B: Journal of Engineering Manufacture, vol. 226, no. 2, pp. 279–289, 2012.

and Ou

, “Quantification of press elasticity in the forging of three-dimensional complex shapes,” Proceedings of the Institution of Mechanical Engineers B. Journal of Engineering Manufacture, vol. 226, no. 3, pp. 466–477, 2012.

Wang

G.-C.

Zhao

G.-Q.

Huang

X.-H.

, and Jia

Y.-X.

, “Analysis and design of a new manufacturing process for a support shaft using the finite element method,” Journal of Materials Processing Technology, vol. 121, no. 2–3, pp. 259–264, 2002.

Narayanasamy

Baskaran

, and Muralikrishna

, “Some studies on stresses and strains of aluminium alloy during extrusion-forging at room temperature,” Materials & Design, vol. 29, no. 8, pp. 1623–1632, 2008.

Narayanasamy

Baskaran

Arunachalam

, and Murali Krishna

, “An experimental investigation on barreling of aluminium alloy billets during extrusion forging using different lubricants,” Materials and Design, vol. 29, no. 10, pp. 2076–2088, 2008.

Zhao

Z. L.

Guo

H. Z.

Yao

Z. K.

Shi

Z. F.

Peng

X. N.

, and Qin

, “The microstructure and properties of ultra-fine grained Ti-17 powder compact improved through isothermal forging,” Journal of Materials Processing Technology, vol. 212, no. 7, pp. 1495–1500, 2012.

Kazeminezhad

and Hosseini

, “Optimum groove pressing die design to achieve desirable severely plastic deformed sheets,” Materials and Design, vol. 31, no. 1, pp. 94–103, 2010.

C.-Y.

and Hsu

Y.-C.

, “The influence of die shape on the flow deformation of extrusion forging,” Journal of Materials Processing Technology, vol. 124, no. 1–2, pp. 67–76, 2002.

Park

K. S.

VanTyne

C. J.

, and Moon

Y. H.

, “Process analysis of multistage forging by using finite element method,” Journal of Materials Processing Technology, vol. 187–188, pp. 586–590, 2007.

10.

Bhushan

R. K.

Kumar

, and Das

, “Fabrication and characterization of 7075 Al alloy reinforced with SiC particulates,” International Journal of Advanced Manufacturing Technology, vol. 65, pp. 611–624, 2013.

11.

Thipprakmas

and Phanitwong

, “Finite element analysis of flange-forming direction in the hole flanging process,” The International Journal of Advanced Manufacturing Technology, vol. 61, no. 5–8, pp. 609–620, 2012.

12.

Hino

Sasaki

Yoshida

, and Toropov

V. V.

, “A new algorithm for reduction of number of press-forming stages in forging processes using numerical optimization and FE simulation,” International Journal of Mechanical Sciences, vol. 50, no. 5, pp. 974–983, 2008.

13.

Verleene

Dubar

Dubois

Dubar

, and Oudin

, “Hardening behaviour law versus rigid perfectly plastic law: application to a cold forging tool steel,” International Journal of Plasticity, vol. 18, no. 8, pp. 997–1011, 2002.

14.

Chen

D.-C.

Nian

F.-L.

Shiu

J.-R.

, and Ku

W.-H.

, “Study of forging forming of 7075 aluminum alloy bicycle pedal,” Advanced Materials Research, vol. 579, pp. 101–108, 2012.

15.

Chen

D.-C.

Shiu

J.-R.

Nian

F.-L.

, and Chen

M.-R.

, “Analysis of forging forming of 6061 aluminum alloy bicycle pedal,” Applied Mechanics and Materials, vol. 271, no. 1, pp. 31–35, 2013.

16.

William

W. Y.

and Creveling

C. M.

, Engineering Methods for Robust Product Design, Addison-Wesley, Boston, Mass, USA, 1998.

17.

Belavendram

, Quality by Design, Prentice-Hall, New York, NY, USA, 1995.