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

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## 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.

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

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 S | Yield strength S |
---|---|---|---|---|

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.

### 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

In which, h is the height of the part.

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.

### 2.5 Burr design

In the above-mentioned equation, *A*_{w} is the cross-sectional area of forged part (mm^{2}) in the separation line and t is the burr thickness (mm).

The value of \( A_{w} \) for fixed-end crankshaft is 28,175 mm^{2}. 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.

### 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.

So the number of upsetting steps is 1.

## 4 Finite element simulation

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/dm |

900–1150 | 33.7 | 139 | 0.3 | 7.80 |

## 5 Fracture theory

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 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

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

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 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).

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 |

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.

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 |

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.

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 |

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).

## 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.

- 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.
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.
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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