# Study of Optimal Cam Design of Dual-Axle Spring-Loaded Camming Device

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## Abstract

**:**

## 1. Introduction

#### 1.1. Description of Protection Gears

#### 1.2. Properties of Dual-Axle Spring-Loaded Camming Device

#### 1.3. Analysis of the Current Dual-Axle Cam Design

#### 1.4. Possibilities of Dual-Axle Cam Design Improvement

## 2. Materials and Methods

#### 2.1. Stage I: Material Models and Initial Geometry Model

#### 2.2. Stage II: Virtual Modeling of Cam

#### 2.3. Stage III: Topology Optimization

#### 2.4. Stage IV: Analysis and Smoothing of the Calculated Discrete Shape

#### 2.5. Stage V: Modeling Load-Bearing Capacity

## 3. Results

#### 3.1. Topology Optimization

#### 3.2. Analyzing and Smoothing of the Calculated Discrete Shape

#### 3.3. Modeling of Load-Bearing Capacity

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

AWB | Ansys Workbench |

SLCD | Spring-Loaded Camming Device |

FE | Finite Element |

FEM | Finite Element Method |

NURBS | Non-Uniform Rational Basis Splines |

PRG | Protection Gears |

LTMS | Lever-Type Mechanical Stopper |

TOP | Topology Optimization |

SCDM | SpaceClaim Direct Modeler |

2D | Two-dimensional |

3D | Three-dimensional |

SIMP | Solid Isotropic Material with Penalty |

DOF | Degrees of Freedom |

CAD | Computed Aided Design |

STL | Standart Triangle Language |

CNC | Computer Numerical Control |

MPC | Multiple Point constraints |

PB6 | Permon Biaxial 6 |

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**Figure 1.**The passive PRG (from left): Nut, Hexentric, Tricam, and the active PRG (from right): LTMS and single-axle SLCD.

**Figure 3.**The PB6 SLCD produced by Petr Kouba [7], its cam and a simplified cam model for determination of its contact shape (points on curve: 1—starting point, 2—end point).

**Figure 6.**The finite element mesh used for description of the cam (

**left**) and boundary conditions of linear computational model (

**right**).

**Figure 7.**Boundary conditions for the nonlinear computational model (1—scheme of the cam, 2—jaw) and detail of mesh.

**Figure 8.**The first optimization run–density distribution field in grey-scale: black color—keep element, white color—remove element (

**left**) and pseudo-density distribution field using the density limit value ${x}_{lim}=$ 0.1 (

**right**).

**Figure 9.**The second optimization run–density distribution field in grey-scale: black color—keep element, white color—remove element (

**left**) and pseudo-density distribution field using the density limit value ${x}_{lim}=$ 0.1 (

**right**).

**Figure 10.**Four steps of the smoothing process (from the left): (i) importing the calculated shape, (ii) analyzing the external shape, (iii) approximation of external nodes, and (iv) generation of the smoothed geometric model.

**Figure 11.**Cam shape after smoothing achieved by calculations using various values of polynomial degrees of k = 5, 10, and 100 (from the left), and the optimal cam design with k = 250 (right).

**Figure 12.**Von Mises stress fields corresponding to the force ${F}_{min}$ = 5.00 kN (F = 1.25 kN) for different widths of the rock crack w = 75, 86, 97, 108 mm (from left).

**Figure 13.**Maximum principal stress fields corresponding to the force ${F}_{min}$ = 5.00 kN (F = 1.25 kN) for different widths of the rock crack w = 75, 86, 97, 108 mm (from left).

Active PRG | Ratio of the Working Range | Passive PRG | Ratio of the Working Range |
---|---|---|---|

Dual-Axle SLCD | R = 41% | Tricam | R = 37% |

Single-Axle SLCD | R = 35% | Hexentrics | R = 26% |

LTMS | R = 22% | Nuts | R = 10% |

Property | Symbol | Value | Unit |
---|---|---|---|

Poisson ratio | $\mu $ | 0.33 | - |

Young’s modulus | E | 72.5 | GPa |

Yield stress | ${\sigma}_{y}$ | 260 | MPa |

Ultimate stress | ${\sigma}_{u}$ | 370 | MPa |

Elongation | A | 0.06 | - |

Tangent modulus | ${E}_{T}$ | 2 343 | MPa |

Limit plastic strain | ${\epsilon}_{pl}$ | 0.055 | - |

Density | $\rho $ | 2 820 | kg·m ${}^{-3}$ |

Property | Symbol | Value | Unit |
---|---|---|---|

Poisson ratio | $\mu $ | 0.30 | - |

Young’s modulus | E | 206 | GPa |

Material | Material | Coefficient of Static Friction | Limit Angle of the Beam |
---|---|---|---|

AW2011 | S235 | ${f}_{T}$ = 0.27 | $\alpha $ = 15.1${}^{\circ}$ |

Parameter | Symbol | Value | Unit |
---|---|---|---|

Initial radius of the cam | ${r}_{0}$ | 35.7 | mm |

Coefficient of static friction | ${f}_{T}$ | 0.27 | - |

Maximal radius of the cam | ${r}_{max}$ | 65.0 | mm |

Maximal rotation of the cam | ${\phi}_{max}$ | 127 | ${}^{\circ}$ |

Diameter of the hole for pin | $\varphi d$ | 6.00 | mm |

Distance between pins | e | 16.0 | mm |

Thickness of the cam | t | 6.00 | mm |

Nodes | Elements | DOF |
---|---|---|

17,800 | 17,500 | 35,600 |

Nodes | Elements | DOF |
---|---|---|

121,000 | 39,000 | 242,000 |

Width of the Rock Crack w [mm] | Plastic Strain ${\mathit{\epsilon}}_{\mathit{pl}}$ [%] for Force ${\mathit{F}}_{\mathit{min}}$ = 5.00 kN | Load-Bearing Capacity ${\mathit{F}}_{\mathit{max}}$ [kN] for Limit Plastic Strain ${\mathit{\epsilon}}_{\mathit{pl}}$ = 5.50% |
---|---|---|

64.0 | 2.74 | 7.33 |

69.5 | 2.75 | 7.34 |

75.0 | 2.49 | 7.83 |

80.5 | 2.21 | 8.26 |

86.0 | 1.97 | 8.98 |

91.5 | 1.87 | 8.13 |

97.0 | 1.76 | 9.88 |

102.5 | 3.02 | 10.21 |

108.0 | 0.90 | 7.09 |

Type | Weight of the Cam | Load-Bearing Capacity |
---|---|---|

PB6’s cam | ${m}_{c}$ = 33.8 g | ${F}_{max}$ = 14.0 kN |

Optimal cam design | ${m}_{c}$ = 28.9 g (14.5%) | ${F}_{max}$ = 7.09 kN (49.3%) |

EN 12276 limit | - | ${F}_{max}$ = 5.00 kN |

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**MDPI and ACS Style**

Rybansky, D.; Sotola, M.; Marsalek, P.; Poruba, Z.; Fusek, M.
Study of Optimal Cam Design of Dual-Axle Spring-Loaded Camming Device. *Materials* **2021**, *14*, 1940.
https://doi.org/10.3390/ma14081940

**AMA Style**

Rybansky D, Sotola M, Marsalek P, Poruba Z, Fusek M.
Study of Optimal Cam Design of Dual-Axle Spring-Loaded Camming Device. *Materials*. 2021; 14(8):1940.
https://doi.org/10.3390/ma14081940

**Chicago/Turabian Style**

Rybansky, David, Martin Sotola, Pavel Marsalek, Zdenek Poruba, and Martin Fusek.
2021. "Study of Optimal Cam Design of Dual-Axle Spring-Loaded Camming Device" *Materials* 14, no. 8: 1940.
https://doi.org/10.3390/ma14081940