# Analysis of the Design of the Single-Cylinder Steam Engine of the Grasshopper Beam by Henry Muncaster

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Operation of the Machine

#### 2.2. Analysis from the Mechanical Engineering Point of View

- Pre-processing;
- Assignment of materials;
- Application of contacts;
- Boundary conditions;
- Discretization.

#### 2.2.1. Pre-Processing

- Pump: The function of this element is to compress the fluid (water vapor) before it enters the boiler. Since the variation in the pressure of the fluid will depend on the speed of rotation of the machine, this pump has been suppressed and only the stresses in the pump piston will be analyzed.
- Intake and regulation system: The speed regulator has a dynamic functionality as it will rotate at a speed proportional to that of the crankshaft and this will create more or less centrifugal force, so it would make more sense to analyze this component within a dynamic analysis. Similarly, the entry of steam through the intake housing, in which the flow control valve is located, will be eliminated from the analysis to simplify the model, since this could be analyzed separately simply by applying a pressure load on the contours of the elements through which the fluid passes.
- Union elements: Many fixing elements have been suppressed and replaced by contact relationships of the ‘bonded’ type, that is, by welded unions. This type of contact establishes that the nodes of the meshes of the elements whose surfaces are in contact will not have relative movement between them on these surfaces. Given that in most cases, welded joints have a higher resistance than bolted joints, this simplification will make sense. This can be achieved as long as the von Mises stresses (which will be used as the failure criterion by comparing them with the yield strength) in the joint areas are far from failure (safety factor greater than unity). This will ensure that the tension in these zones continues to work in safe conditions and there is no plasticization in the joints. That is to say, if the welded joint resulted in a stress lower than the yield strength, the stress that would occur in the case of a bolted joint would be slightly higher. In Figure 5, the simplified model is shown.

#### 2.2.2. Assignment of Materials

#### 2.2.3. Application of Contacts

- ‘Separation’ type: This is the most common contact between two elements. In this type of contact, the relative movement between the nodes of the elements in contact is allowed, but with a coefficient of friction (which will be that of the materials). Apart from that, the coefficient of friction depends on other parameters, such as the surface finish of the surfaces in contact, temperature, surface roughness, etc. To simplify, a coefficient of 0.25 was applied between surfaces without lubrication, and a coefficient of 0.1 between surfaces with lubrication, for example, in bearings.
- ‘Bonded’ type: In this type of contact, relative movement between nodes is not allowed; that is, it behaves as if the elements in contact were welded.
- ‘Symmetric/Unsymmetric contact’ penetration type: In the case of symmetric penetration, the nodes of a mesh cannot penetrate the nodes of the adjacent mesh, and in the case of the asymmetric type, the penetration of nodes in adjacent meshes in contact is allowed.

#### 2.2.4. Boundary Conditions

#### 2.2.5. Discretization

#### 2.2.6. Critical Positions

#### 2.2.7. Modal Analysis

#### 2.2.8. Linear Static Analysis

#### Determination of the Strain Envelope

#### Analysis Execution

## 3. Results and Discussion

#### 3.1. Critical Position: Lower Dead Center

#### 3.1.1. Modal Analysis

#### 3.1.2. Linear Static Analysis

#### 3.2. Critical Position: Upper Dead Center

#### 3.2.1. Modal Analysis

#### 3.2.2. Linear Static Analysis

#### 3.3. Discussion of the Results

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 13.**Axonometric views of the critical positions: lower dead center (

**left**) and upper dead center (

**right**).

**Figure 14.**Pressure loads at the lower dead center position: front view (

**left**) and axonometric view (

**right**).

Material | Young’s Modulus (MPa) | Poisson Coefficient | Density (Kg/m^{3}) | Yield Strength (MPa) |
---|---|---|---|---|

Carbon Steel | 200,000 | 0.290 | 7850 | 350.00 |

Stainless Steel | 193,000 | 0.300 | 8000 | 250.00 |

Cast Iron | 120,500 | 0.300 | 7150 | 758.00 |

Brass | 109,600 | 0.331 | 8470 | 103.40 |

Cast bronze | 109,600 | 0.335 | 8870 | 128.00 |

Nylon | 2930 | 0.350 | 1130 | 82.75 |

Element Size (mm) | Von Mises Stress (MPa) | Relative Error (%) | Iteration |
---|---|---|---|

1.5 | 175.5 | 0 | |

1 | 208.1 | 18.58 | 1 |

0.5 | 239.4 | 15.04 | 2 |

0.4 | 257 | 7.35 | 3 |

Element Size (mm) | Von Mises Stress (MPa) | Relative Error (%) | Iteration |
---|---|---|---|

2 | 54.9 | 0 | |

1.5 | 217.8 | 296.64 | 1 |

0.75 | 233.4 | 7.16 | 2 |

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© 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Rojas-Sola, J.I.; Gutiérrez-Antúnez, J.F.
Analysis of the Design of the Single-Cylinder Steam Engine of the Grasshopper Beam by Henry Muncaster. *Machines* **2023**, *11*, 703.
https://doi.org/10.3390/machines11070703

**AMA Style**

Rojas-Sola JI, Gutiérrez-Antúnez JF.
Analysis of the Design of the Single-Cylinder Steam Engine of the Grasshopper Beam by Henry Muncaster. *Machines*. 2023; 11(7):703.
https://doi.org/10.3390/machines11070703

**Chicago/Turabian Style**

Rojas-Sola, José Ignacio, and José Francisco Gutiérrez-Antúnez.
2023. "Analysis of the Design of the Single-Cylinder Steam Engine of the Grasshopper Beam by Henry Muncaster" *Machines* 11, no. 7: 703.
https://doi.org/10.3390/machines11070703