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SN Applied Sciences

, 2:65 | Cite as

Design and optimization of multi-stage manufacturing process of stirling engine crankshaft

  • Mohsen Noorbakhsh
  • Hamid Reza MoradiEmail author
Research Article
  • 117 Downloads
Part of the following topical collections:
  1. 3. Engineering (general)

Abstract

Crankshafts are among the most important parts in internal combustion engines, of which stirling engine is a useful example. Manufacturing process of a crankshaft, is considered as a three-step forging process using preform, due to the complexity in geometry. The most challenging step of the multistage forging process is to avoid stress concentration and to create uniformity of strain by controlling metal flow. In the present study, the final part was achieved under three manufacturing processes namely: upsetting, hot and cold forging. The models used in each manufacturing process are designed by CATIA software. A finite element simulation on the basis of Cockcraft–Latham damage criterion was developed in DEFORM software. Using experiment design by Taguchi method, The optimization of manufacturing processes were carried out by MINITAB software in two steps, in which the optimization objectives are considered as force, damage and strain uniformity, and; input variables are taken as part-mold friction, pressing velocity and process temperature. In order to find the most effective parameter of each manufacturing process, analysis of variance was conducted on the results, in which, the most effective parameters in the upsetting, hot and cold forging processes were temperature, friction and temperature, respectively.

Keywords

Finite element method Optimization Manufacturing Design of experiment Stirling engine 

1 Introduction

In recent years, significant efforts have been made to develop some new methods including FE method (FEM) and intelligent control system to optimize upsetting process. Quan et al. [1] Sukjantha et al. [2], Nuasri et al. [3], Jeong et al. [4], and Quan et al. [5] analysed the influence of processing parameters on the upsetting process, predicted an optimum process condition, determined an optimal preform part and saved the secondary upsetting defect, respectively by FEM. Liu et al. [6] introduced a new computer-controlled upsetting system and solved the underfill defect in next hot forging.

The process parameters involved in hot forging and their role have been subject of investigation by [7, 8]. They can be clustered under the following main groups [9]:
  • Product geometry

  • Product material

  • Tooling

  • Machine

  • Process

  • Tool-work piece interface effects

Junjia et al. [10] and Xing et al. [11] investigated microstructure distribution and mechanical properties of boron alloy in hot forging. The complexity of global multi-objective optimization of every factor in the process is so high that several authors prefer to develop empirical expert systems to assist in the design phase [12, 13].

Eventually, some researchers [14, 15] proposed to use a sequential approximate optimization algorithm (SAO) to optimize forging process, using the time-consuming FEM simulation only to fit a meta-model of the process, by Polynomial regression or Kriging interpolation. The meta-model is used by the optimization algorithm that is evaluated by simulating the optimum with FEM.

In a study by Espadafor et al. [16] failure analysis of a generator crankshaft, using finite elemental simulations, have been conducted and the points of the crankshaft which have the maximum stress and are subjected to failure are identified. Chen et al. [17] in the field of crankshaft fatigue analysis, used the flexural fatigue test, the SAFL method, and statistical analysis to obtain fatigue limit. Çevik et al. [18] have evaluated the performance of a diesel engine crankshaft fatigue during its forging process. Ktari et al. [19] have conducted research on the fatigue failure of the crankshaft used in the train engine.

The aim of this study was to obtain the optimum values of process force parameters, part damage parameters and strain uniformity by conducting Taguchi method on the model in which the variables were determined to be part temperature, mold velocity and friction between part and mold. Meanwhile, the most effective parameters in each manufacturing process were also determined. `

2 Methodology: designing the part and mold

Since the geometry of mold cavity is obtained based on the design, it will be considered as the first step of manufacturing in the forging method. A precise and suitable design will result in cost savings, adequate quality of final part, waste reduction and mold life. In this study, firstly we intend to analyse and optimize the part’s geometry and the fixed-end crankshaft mold. In Figs. 1 and 2, the geometric design of one and both fixed-end part, and in Fig. 3 the final part map are shown, respectively. As shown in the figures, the part having a crank with a diameter much larger than the main axis of the crankshaft, which, as a result, make the material distribution in this part to be extremely unbalanced and, generating the final formation of this part can’t be achieved, therefore, using a preform is vital.
Fig. 1

Fixed-end crankshaft final part map

Fig. 2

The cantilever crankshaft final part map

Fig. 3

Fixed-end crankshaft final geometric model

The process of designing the part and mold are shown in Fig. 4.
Fig. 4

Flowchart of Forging mold designing steps

Forging part is usually designed based on machining part and, various parameters of this design modification, are such as adding gradients to the walls, corner radius etc. the mechanical properties of the part based on standard conditions are given in Table 1.
Table 1

Mechanical properties of 30CrNiMo -(vcn200)—for parts with a diameter of 40–100 mm

VCN 200 alloy

E (GPa)

Hardness H (RC)

Ultimate tensile strength Sut (MPa)

Yield strength SY (MPa)

 

212

41

1400

950

2.1 Separation level place

Separation level is a line which separates the two upper and lower sides of the mold and is shown as a separation line at the pleated canal in the forged part.

In this study, the supposed part is a crankshaft and the separation level of cantilever crank is shown in Fig. 5.
Fig. 5

Dotted lines showing the crossing point of separation line

2.2 Dimensional consideration for machining

According to DIN7523 standard [20], the maximum machining rate depending on the type and dimension of cantilever and fixed-end parts is considered to be 5.4 mm. The part is made of heat-treating steel and has a length of 5.465 mm.

2.3 Mold wall gradient

Mold wall gradient facilitates the removal of the part from the inside of forging mold cavity. Regarding that the part is brought to the center when it cools down, the inner wall of the part needs more gradient than the outer wall.

According to the DIN7523 standard [20], the external gradient of 5.4° and internal gradient of 6° are considered for both parts.

2.4 The radius of corners and edges

The sharp corners result in stress concentration and also hampering in the flow of materials during the forging process. Therefore, the corners of the part are considered to be rounded in order to facilitate the flow of materials, reduce forging force and energy, reduce friction and prolong forging mold’s life. Values of radiuses are proposed from Ref. [21], based on maximum altitude and with the help of the following relations.
$$ r = \frac{1}{10} \cdot h\quad h < 100\;{\text{mm}} $$
(1)
$$ r = \frac{1}{20} \cdot h\quad 250\;{\text{mm}} > h > 100\;{\text{mm}} $$
(2)

In which, h is the height of the part.

In the Considered part, the maximum height is 161 mm (crank length), so:
$$ {\text{r}} = \frac{1}{20} \cdot {\text{h}} = \frac{1}{20} \times 161 = 8 \cdot 05\;{\text{mm}} $$

Due to the presence of radius in some of outer corners of the crankshaft, the same value as 2 mm is used to design the mold, otherwise the radius of the outer edges is 8 mm.

In Fig. 6, in addition to applying the angle of gradient, the radius of corners and edges is also considered.
Fig. 6

Adding edges and corners radius

2.5 Burr design

There are many relations to design the dimensions of the canal and the burr hole. In this study, the relation used by Brochanov and Rebelski [22] has been used to design the canal and burr cavity.
$$ {\text{t}} = 0 \cdot 015\sqrt {A_{w} } $$
(3)

In the above-mentioned equation, Aw is the cross-sectional area of forged part (mm2) in the separation line and t is the burr thickness (mm).

Timensions of burr canal are shown in Fig. 7. The relations described in Ref. [20] have been used to design the burr enclosure.
$$ {\text{T}}_{\text{g}} = 1 \cdot 6{\text{T}}_{f} $$
(4)
$$ r = T_{f} $$
(5)
$$ R = T_{g} $$
(6)
$$ \to A_{w} = 27677 \cdot 875 $$
Fig. 7

Burr placement enclosure

According to the Brochanov and Rebelski, \( \frac{w}{t} \) for a part’s cross section in the previous section is equal to 3.66. As a result, using interpolation technique, the values of Wg and Tg from Table 5-4 of [20] are 33 and 5, respectively.
$$ {\text{t}} = 2 \cdot 89 \approx 3 $$
$$ \frac{{W_{f} }}{{T_{f} }} = 3 \cdot 66 \Rightarrow W_{f} = 10 \cdot 98 \simeq 11 $$

The value of \( A_{w} \) for fixed-end crankshaft is 28,175 mm2. According to Eq. 4, the burr thickness (t) is 2/92 = 3. As a result, W_g and T_g will be same as the values obtained for cantilever crankshaft.

3 Designing the crankshaft preform

The desired part, which is the crankshaft, has a crank arm with a height difference of about 50 mm on one side of the part compared to the other parts of the crankshaft, thus having a great deal of geometry complexity and a non-balanced material distribution, which itself complicates the design of the corresponding molds. On the other hand, in the crank arm, a flow distribution of about 4 times greater than the other parts is required for the complete filling of the mold, so the production of this part requires preform and middle mold.

Besides, due to its application, crankshafts should have high mechanical properties. Therefore, in crankshaft design, the last stage is cold forging, in order to achieve the final target properties with high precision.

In this study, according to the explanations of the crankshaft design cycles, in the previous chapter and the geometry of the crankshaft of a Stirling engine, before the final forging process, two preforms have been used to manufacture the crankshaft. The preform is made of ALSI_H_13, the first preform of upsetting process is designed to smoothing the metal flow in the forging part and the second preform of hot forging process is designed to provide easier formation to reduce the applied force. The preforms design is in reverse order, which means that we first design the second preform using the final shape of the part and then, we design the first preform based on the second one.

3.1 Hot forging process

Hot forging is performed in the range of 900–1100 °C for heat-treating steels (VCN 200). In order to design a preform for forging parts, various methods such as co-potential lines, response level method, neural network, mass distribution method, etc. can be used. Since the investigated part is crankshaft and is common in industry, the mass distribution method is used to design the preforms in this part.

The mass distribution method has been used to obtain an approximate form of preform in this design. In Fig. 8a, b, the chart related to the forging part is depicted.
Fig. 8

Forging part mass distribution diagram, A cantilever crankshaft, B fixed-end crankshaft

3.2 Upsetting process

This process is similar to the forging process, except that the press direction is along the length of the part and reduction of the length. In this process, the pressing movement is usually along the longest side of the part. Upsetting part is used when we want to apply a diagonal change in a section of the part.

In order to avoid buckling in the process of hot upsetting, relations (7) are used from Ref. [23]. In this relation, S represents the ratio of initial length to the initial diameter. The part value of s ≤ 3/2 can be formed in one step, otherwise, two or more steps are needed to produce a well part without buckling.
$$ \begin{aligned} & {\text{s}} = {\text{l}}_{0} /{\text{d}}_{0} \\ & s \le 2 \cdot 3\quad {\text{onestage}} \\ & s \le 4 \cdot 5\quad {\text{twostage}} \\ & s \le 8\quad {\text{threestage}} \\ \end{aligned} $$
(7)
For cantilever crankshaft, \( d_{0} = 80\;{\text{mm}} \) and \( l_{0} = 161\;{\text{mm}} \).
$$ s = 161/80 = 2 \cdot 0125 \le 2 \cdot 3 $$

So the number of upsetting steps is 1.

For fixed-end crankshaft, \( d_{0} = 90\;{\text{mm}} \) and \( l_{0} = 400\;{\text{mm}} \). With respect to relations (7), this preform is created in two stages of upsetting from the initial billet at each stage, 30 mm diameter change in work part is applied.
$$ s = 400/90 = 4 \cdot 44 \le 4 \cdot 5 $$

4 Finite element simulation

For checking preforms, numerical simulation of the forging process was performed by DEFORM 10 software. The mechanical properties of the part in the processes of upsetting and hot forging at the respective temperature are given in Table 2.
Table 2

Simulation parameters of the upsetting and hot forging processes using DEFORM software

30 CrNiMo8 mechanical properties

Process temperature °C

Heat transfer coefficient (w/m k)

Modulus of elasticity (GPa)

Poisson coefficient

Density (kg/dm3)

900–1150

33.7

139

0.3

7.80

The coefficient of friction between the work piece and mold is 0.25 for upsetting process, 0.7 for hot forging and 0.12 for cold forging. In Table 2, the mechanical properties of the part in hot processes are depicted. For a precise control of the formation conditions, regarding that the process is isothermal, the press velocity was considered to be 1 mm/s. Tetrahedral element type was used to mesh the parts considering Fig. 9 in this research, the maximum force of the process and the effective tension at one point were chosen for examination of the convergence of the simulation results (sensitivity to mesh), and according to the examination, the degree of meshing was considered to be 35,000.
Fig. 9

Meshing condition of cantilever crankshaft for upsetting (upsetting) process

5 Fracture theory

The intended fracture theory, with regards to using the finite element software DEFORM, is Cockcraft–Latham theory [24]. The critical damage parameter is calculated according to the Cockcraft–Latham relation, from the following equation:
$$ {\text{C}} = \int\limits_{{}}^{{\bar{\varepsilon }}} {\frac{{\sigma^{*} }}{{\bar{\sigma }}}\partial \bar{\sigma }} $$
(8)
In this relation, \( \sigma^{*} \) is the maximum main tensile stress of the material, \( \bar{\sigma } \) is the effective tension during the process and \( \bar{\varepsilon } \) is the fracture strain. Since, most of the processes for manufacturing of desired crankshaft, are considered as hot processes, the Johnson–cook model is chosen for calculation in the software. This model is shown in the following equation.
$$ \bar{\sigma } = \left( {{\text{A}} + {\text{B}}\bar{\varepsilon }^{n} } \right)\left( {1 + {\text{C}}\ln \left( {\frac{{\dot{\bar{\varepsilon }}}}{{\dot{\bar{\varepsilon }}_{0} }}} \right)} \right)\left( {\frac{{\dot{\bar{\varepsilon }}}}{{\dot{\bar{\varepsilon }}_{0} }}} \right)^{\alpha } \left( {{\text{D}} - {\text{ET}}^{{\varvec{*}m}} } \right) $$
(9)
The parameters A, B, C, \( {\text{D}}_{0} \), E, α and m are constant values of the model and are different depending on the type of material. The parameters \( {\text{T}}^{*} \) and D in the Johnson–Cook model are calculated by the following relations, respectively.
$$ {\text{T}}^{*} = \frac{{\left( {{\text{T}} - {\text{T}}_{\text{room}} } \right)}}{{\left( {{\text{T}}_{\text{melt}} - {\text{T}}_{\text{room}} } \right)}} $$
$$ {\text{D}} = {\text{D}}_{0} {\text{expk}}\left( {{\text{T}} - {\text{T}}_{b} } \right)^{\beta } $$
The constant values of equations for VCN200 alloy are presented in Table 3.
Table 3

The constant values of VCN 200 alloy

Parameter

Value

Parameter

Value

A

673

\( \alpha \)

0

B

1151

\( \beta \)

0

C

0.029

\( \dot{\bar{\varepsilon }}_{0} \)

1

\( {\text{D}}_{0} \)

1

\( {\text{T}}_{\text{room}} \)

20

E

1

\( {\text{T}}_{\text{melt}} \)

1527

n

0.31

\( {\text{T}}_{b} \)

0

m

0.49

K

0

By applying these values to the Johnson–Cook equation and simplifying it, the following equation is obtained for the alloy used in the crankshaft:
$$ \bar{\sigma } = 0 \cdot 2106\left( {673 + 1151^{ - 0 \cdot 31} } \right)\left( {1 + 0 \cdot 029{ \ln }\left( {\dot{\bar{\varepsilon }}} \right)} \right) $$
The parameter \( \sigma^{*} \) is equal to \( k\varepsilon^{n} \), where k and n for this alloy are 1240 and 0.61, respectively. By placing \( \bar{\sigma } \) and \( \sigma^{*} \) in Cockcraft–Latham, this integral is obtained:
$$ {\text{C}} = \mathop \smallint \limits_{ }^{{\bar{\varepsilon }}} \frac{{1240\varepsilon^{0 \cdot 61} }}{{\left( {673 + 1151\varepsilon^{0 \cdot 31} } \right)\left( {1 + 0 \cdot 029\ln \left( {\dot{\varepsilon }} \right)} \right)}} \partial \varepsilon $$

By placing the failure strain of VCN 200 alloy obtained from tensile test which were equal to 0.925, in the abovementioned integral, the damage parameter value is calculated as 0.74.

6 Verification

Based on the aforementioned method, a FEM simulation was developed in which, the results were compared with the study of Danno et al. [22]. In their research, the geometry was taken as Fig. 10, its simulation was performed using DEFORM-2D with the coefficient of friction, the press velocity and the cushion force as 0.12, 0.1 mm/s and 17 KN, respectively.
Fig. 10

The shape and dimensions of work piece

In Fig. 11a the simulation contours of paper for the first step of forging are demonstrated, the performed simulation results are shown in Fig. 11b and the results comparison are demonstrated in Table 4.
Fig. 11

The simulation results of the first stage of the manufacturing process and the results of the damage parameter

Table 4

Comparison of the results of the present study and article

 

Danno et al. work [22]

This study

The effective strain of the first step of forging

1.87 (mm/mm)

1.77 (mm/mm)

The effective strain of the second step of forging

1.77 (mm/mm)

1.68 (mm/mm)

Damage parameter

0.453

0.429

7 Optimization

Since, one of the effective parameters in crankshaft fracture is strain concentration during formation, it’s possible to reduce the probability of fracture in the part by improving the strain distribution.

Therefore, optimization process has been performed to achieve the lowest strain concentration in the final forging part. Optimization process is done in two steps. In the first step, the goal is to find the optimal levels of input parameters and also determine the most effective input on the strain uniformity in each process. The design of experiment was done using Minitab software and Taguchi method. The optimization has been applied on a three-stage forging of fixed-end crankshaft that involves upsetting process, hot and cold forging. Input parameters of the software are considered for all three parameters of press velocity, friction coefficient and the work piece temperature. Strain uniformity, damage parameter, and process force are also considered as output parameters of processes.

The analysis of ANOVA’s variance and GLM method are used to find the most effective input parameters in each process. In this research, the strain uniformity is obtained by calculating the standard deviation of the strain parameter of all the elements extracted from the software.

In the second step, optimization was performed to estimate the best conditions of the processes to acquire the lowest uniformity of strain in the final part. According to the results obtained from the initial optimization, the most effective parameter for the strain uniformity of each process is chosen. These parameters are inputs of the second stage of optimization and the uniformity of strain in the final part, is considered the output of this optimization.

8 Results and discussion

As mentioned above, the MINITAB software and Taguchi test design are used to optimize the temperature, press velocity and friction parameters. In Table 5, the experiments and output values for upsetting process are represented. To obtain the strain uniformity, standard deviation of all the effective strains belonging to all part’s elements without considering the burr, has been calculated.
Table 5

Taguchi experiment design and the test results designed for the upsetting process

Experiment no.

Parameter 1 friction

Parameter 2 velocity

Parameter 3 Temp

Output parameter

Strain uniformity

Output parameter

Damage parameter

Output parameter

Process force

1

0.2

1

900

0.552

0.186

104,000

2

0.2

2

950

0.318

0.20

115,000

3

0.2

4

1050

0.356

0.2104

128,300

4

0.25

1

950

0.217

0.18

100,000

5

0.25

2

1050

0.316

0.222

95,600

6

0.25

4

900

0.436

0.20

121,000

7

0.3

1

1050

0.213

0.218

84,000

8

0.3

2

900

0.315

0.205

131,000

9

0.3

4

950

0.449

0.185

113,000

In Figs. 12, 13 and 14, the normalized signal-to- noise diagrams relative to the mean value of vertical axis representing the coefficient of influence, designed for investigating the effect of each of temperature, press and friction inputs, respectively, on force, damage parameter and strain uniformity outputs are depicted.
Fig. 12

Normalized signal-to-noise of velocity parameter in the upsetting process

Fig. 13

Normalized signal to noise of friction parameter in upsetting process

Fig. 14

Normalized signal to noise of temperature parameter in upsetting process

In Figs. 12, 13 and 14, the maximum strain uniformity and minimum force and damage are optimization objectives which are obtained by comparing the resulted optimal values of response level in friction of 0.25 (second level), press velocity (1 mm/s), and 1050 °C (third level).

To find the most effective parameter, as shown in Fig. 15, analysis of ANOVA’s variance has been used and the most effective parameter in upsetting process was obtained as temperature parameter.
Fig. 15

The table of variance analysis of upsetting process’s strain uniformity

Table 6 shows the experimental design and simulation results of the hot forging process.
Table 6

Taguchi experiment design and test results designed for hot forging process

Experiment no

Parameter 1

Friction

Parameter 2

Velocity

Parameter 3

Temp

Output parameter

Strain Distribution

Output parameter

Damage parameter

Output parameter

Process Force

1

0.3

1

900

0.781

0.488

422,000

2

0.3

2

950

0.691

0.51

361,000

3

0.3

4

1050

0.678

0.68

328,000

4

0.5

1

950

0.763

0.49

542,000

5

0.5

2

1050

0.721

0.81

311,000

6

0.5

4

900

0.756

0.84

583,000

7

0.7

1

1050

0.785

0.78

378,000

8

0.7

2

900

0.823

0.85

645,000

9

0.7

4

950

0.897

0.62

514,000

In Figs. 16, 17 and 18, the normalized signal to noise diagram for investigating the effect of input parameters on the outputs of hot forging process is shown.
Fig. 16

Normalized signal to noise diagram of velocity parameter in hot forging process

Fig. 17

Normalized signal to noise diagram of friction parameter in hot forging process

Fig. 18

Normalized signal to noise diagram of temp parameter in hot forging process

Regarding the output diagrams, the optimal response level of hot forging has been obtained as friction 0.3, mold velocity 2 mm/s and the work piece temp 1050 °C. It should be noted that in the diagram of Fig. 17, considering the different behaviour of the two outputs of strain uniformity and damage, in order to optimize the process while the whole part remains unaffected, the strain uniformity parameter is more important in terms of design and has a greater effect on choosing the relative optimal response level.

In Table 7, the design of the test related to the cold forging process is shown, which has been designed in accordance with the 9 previous tests for optimization.
Table 7

Results of experiments designed in the cold forging process

Experiment No

Parameter 1

Friction

Parameter 2

Velocity

Parameter 3

Temp

Output parameter

Strain Distribution

Output parameter

Damage Parameter

Output Parameter process force

1

0.08

1

350

0.8072

0.89

60,200

2

0.08

2

400

0.81

0.33

62,400

3

0.08

4

450

0.83

0.22

67,500

4

0.12

1

400

0.88

0.78

69,500

5

0.12

2

450

0.77

0.54

72,900

6

0.12

4

350

0.8017

0.3

78,700

7

0.16

1

450

0.7571

0.43

69,200

8

0.16

2

350

0.7356

0.34

90,100

9

0.16

4

400

0.8718

0.17

99,000

The investigation results of the parameters effects on the simulation outputs are shown in Figs. 19, 20 and 21.
Fig. 19

Normalized signal to noise diagram of velocity parameter in cold forging process

Fig. 20

Normalized signal to noise diagram of friction parameter in cold forging process

Fig. 21

Normalized signal to noise diagram of temperature parameter in cold forging process

As mentioned in the previous section, due to the greater importance of strain uniformity over damage in the two parameters of friction and velocity, this factor is taken into account for setting the optimal parameter therefore, the optimal response level for cold forging process is obtain as friction 0.16, press velocity 2 mm/s and work piece temperature 450 °C.

The variance analysis is used to determine the most effective parameter in accordance with the upsetting process, which is obtained as friction and temperature parameters in hot and cold forging process, respectively.

In the second step of optimization, according to the results obtained from the initial optimization, the most effective parameter in each process is considered as the variable parameter and the other two parameters are constantly equal to the related optimal response level values. In this step, all three processes are simulated sequentially and the strain uniformity of the final part is calculated after the three stages of manufacturing and based on this optimal parameter, the overall response level, which represents the overall optimal response considering all three manufacturing processes, is obtained.

According to Table 8, the upsetting temperature of 900 °C, the friction of 0.3 between mold and work piece in hot forging process and cold forging process temperature of 350 °C are all obtained as overall optimal response level considering all three manufacturing processes.
Table 8

Designed tests and results obtained in strain uniformity optimization

Experiment no

Parameter 1

Part’s temp in upsetting process

Parameter 2

Friction in hot forging process

Parameter 3

Part temp in cold forging process

Output parameter

Strain uniformity

1

900

0.3

350

1.13,343

2

900

0.5

400

2.14457

3

900

0.7

450

3.17794

4

950

0.3

400

3.19653

5

950

0.5

450

3.19664

6

950

0.7

350

3.19609

7

1050

0.3

450

3.19697

8

1050

0.5

350

4.20845

9

1050

0.7

400

3.19966

The effective strain obtained from hot forging process of a fixed-end crankshaft and cold forging process of cantilever crankshaft, based on the optimum final values of temp, velocity and friction input parameters, are shown in Fig. 22a, b respectively.
Fig. 22

A Hot forging process of a fixed-end crankshaft, B Cold forging process of a cantilever crankshaft

Considering the simulation of all three manufacturing stages and the two models, it can be concluded that the strain is the same in most parts of the crankshaft, except the fillet region (the joint zone of axis and crank arm).

The force variations diagram for hot and cold forging process of cantilever and fixed end cranks are depicted in the Figs. 23 and 24.
Fig. 23

The cantilever crank force variations A Hot forging. B Cold forging

Fig. 24

Fixed-end crankshaft force variations A: Hot forging process B: Cold forging process

9 Conclusion

Due to the geometry of the model, the forging of Stirling engine crankshaft is designed in three stages, including two preforms and one final forging stage. The first preform of upsetting process is designed in order to smoothing the strain distribution in part, the second preform of hot forging process is intended to cause deformation, and the final cold forging process is applied to achieve the desired mechanical properties. The critical value of the damage parameter for 30CrNiMo8 alloy was calculated to be 0.74, using Cockcraft-Latham relation. The maximum damage values at each stages of forging, for designing processes of cantilever crank was 0.54, 0.59 and 0.6 and for fixed-end crank was 0.22, 0.55, 0.58, respectively; which indicates that the desired part remains undamaged and integrated.

Variation trends of input parameters versus objectives represent the following relations: in upsetting process, there is a reversal relation for velocity- strain uniformity and direct relation for both friction- strain uniformity and temperature- strain uniformity. In hot forging process, there can be seen a reversal relation for both velocity- damage and friction- strain uniformity and a direct relation for temperature- strain uniformity. In cold forging process, there is a direct relation for velocity- damage, friction- damage and temperature- damage.

Two optimization steps have been performed in which for the first step, the variable parameters were considered as: part temperature, mold velocity and friction between part and mold, and the objectives were taken as optimal value of process force parameters, part damage parameters and strain uniformity belonging to all part’s elements, using Taguchi method. The optimization results were obtained as follows:
  1. 1.

    The values of friction between part and mold, mold velocity and part temperature for upsetting process was equal to 0.25, 1 mm/s and 1050 °C, respectively.

     
  2. 2.

    The values of friction, mold velocity and part temperature for hot forging process was equal to 0.3, 2 mm/s and 1050 °C, respectively.

     
  3. 3.

    The values of friction, mold velocity and part temperature for cold forging process was equal to 0.16, 2 mm/s and 450 °C, respectively.

     

From F distribution and variance analysis, the most important factor and the most effective parameter for upsetting, hot and cold forging processes are obtained as: temperature, friction and part temperature, respectively.

Considering all three manufacturing processes simultaneously, and performing sequential simulation with the aim of maximizing the strain uniformity of the final part, the overall optimal response level of the part was obtained as the part temperature of 900 °C in upsetting process, friction of 0.3 in hot forging process and work piece temperature of 350 °C in cold forging process with final strain uniformity of 1.1334 (mm/mm).

Notes

Compliance with ethical standards

Conflict of interest

The authors declared that they have no conflict of interest.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringMalek Ashtar University of TechnologyTehranIran

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