# A New Optimized Solution for a Flexible Coupling with Bolts Used in the Mechanical Transmissions

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## Abstract

**:**

## 1. Introduction

## 2. Description of the Proposed Flexible Coupling with Milled Bolts and Non-Metallic Elements

_{s}, of four equidistant holes, three of them being threaded, for fixing by means of screws 8 the intermediate disk 7 of the driven semi-coupling 2, and of the fourth orifice for centering by means of the cylindrical pin 9 of the intermediate disc on the driven semi-coupling. The subassembly consists of the half-coupling (2), the milled bolts 12 fixed by the semi-coupling by means of the Grower washers 5 and the M8 nuts 6, the metal plates 10 fixed to the intermediate disc 7 by means of the screws 11 in the space between the plates and the non-metallic elements 3, which come into contact with the milled bolts that are fitted. The intermediate disk 7 is fixed to the semi-coupling driven 2 by means of the screws 8, the centering of the disk in relation to the intermediate disk being achieved by means of the cylindrical pin 9. In the coupling component, in the milled locations on the intermediate disc 7 are mounted four subassemblies plates 10, a non-metallic element 3, and screws 11, one in each milled location of the type shown in Figure 1.

- Driver machine (electric motor): characterized by engine power P(kW) and speed n (rot/min);
- Maximum diameter of d (mm) shafts on which the semi-couplings are mounted;
- Coupling gauge: L (mm)—length of coupling, De (mm)—exterior diameter of semi coupling;
- Limits (minimum, maximum) of the torsion moment transmitted by coupling: M
_{tmin}, M_{tmax}(Nmm); - Performing the functions characteristic of flexible couplings with non-metallic elements: transmission of rotational motion and torsion moment; taking over the position albeit deviations of the shafts; shock and vibration damping;
- Safety in operation: superior mechanical strength of the fastening screws of the two semi-couples of the cylindrical centering stud;
- Economic requirements: execution processes and means of economic processing;
- Establishment of technology for semi-manufactured: non-metallic elements made by vulcanization; semi-couplings are obtained by free forging or molding; the intermediate disc is obtained by free forging; bolts are made of round laminated steel; metal plates are made of square laminated steel;
- Maintenance conditions: simple maintenance; visual control at each use;
- Ergonomic costs and requirements: simple constructive form; minimum material consumption, cost per minimum product.

^{3}, Young’s modulus = 200 GPa, Poisson’s ratio = 0.287.

## 3. Calculus Element, Execution and Testing of Flexible Coupling with Milled Bolts and Non-Metallic Elements

- the bolts are considered uniformly loaded;
- the pressures are considered uniformly distributed along the bolt.

_{tc}. Taking into account the additional loads that may occur at installation or during operation, the so-called torsion moment of calculation M

_{tc}, is calculated with the formula:

_{S}is a safety factor experimentally obtained and offered by literature [1], M

_{tn}is nominal torque calculated using the power of the electric motor P and its corresponding rotation speed n, with the relation ${M}_{tn}=9.55\cdot {10}^{6}\cdot \frac{P\text{}[\mathrm{kW}]}{n\text{}[\mathrm{rot}/\mathrm{min}]}[\mathrm{Nmm}]$ [9].

_{t}is the section area (A

_{t}= (h

_{2}− d

_{b})b—for the shape of Figure 2), σ

_{at}= 1.5 MPa from [9].

_{ti}represents the input torque and M

_{to}the output torque.

_{e}(the area under the load characteristic). Part of this energy (the area between the charging and the discharging characteristics) is transformed into heat, representing the mechanical friction work L

_{f}in the coupling. In non-metallic intermediate elements, friction takes place inside the elastic element (internal friction). From calculus results, mechanical deformation work ${L}_{e}$ = 211.94 J. The high values of the shock absorption capacity lead to the quiet operation of the transmission equipped with such a coupling, even to oscillating loads. The flexible coupling with damping also improves the behavior in vibrational mode.

## 4. Discussion

## 5. Conclusions

- the coupling has the possibility to transmit the torque in any direction;
- the proposed solution of coupling ensures compensation of radial and angular deviations;
- in the case of small deformations, E $\approx $ constant, and taking into account the other constants in the expression of rigidity, it appears that the characteristic of the coupling is linear;
- the calculation algorithm of the flexible coupling with milled bolts and non-metallic elements presented is original and based on the hypothesis made in the paper;
- the maximum moment that can be transmitted by the coupling is 188.232 N∙m for the third form of the non-metallic element;
- when exceeding the torsion moment determined from the tensile strength condition of the non-metallic element, the elastic element will break, thus the coupling can also perform the safety function (load limitation);
- from the calculations performed, it results that the rigidity of the coupling is small when the non-metallic elements are made of natural rubber (NR);
- the rigidity of the coupling is high when the non-metallic elements are made of ethylene propylene diene rubber (EPDM);
- this type of coupling can be used in mechanical engineering, lifting installations, or in electromechanical systems;
- the coupling designed and executed has a simple construction, small size, and a low cost compared to the classic ones with non-metallic elements and bolts.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**The flexible coupling with milled bolts and non-metallic elements. 1—driver semi-coupling; 2—driven semi-coupling; 3—non-metallic elements; 4—milled bolts; 5—Grower washers; 6—M8 nuts 6; 7—intermediary disk; 8—screws; 9—cylindrical pin; 10—metal plates; 11—screws; 12—milled bolts.

**Figure 8.**The measurement stand (

**a**) experimental stand for static and dynamic testing; (

**b**) non-metallic elements from natural rubbers.

**Figure 10.**Variation of moments to the input and the output shaft in dynamic approach; input and output shafts are collinear.

**Table 1.**Results of verification calculations at the solicitation of traction and crushing for non-metallic element (theoretical values).

Form Shape | Obtain Results |
---|---|

Shape 1 | ${\sigma}_{tF1}=0.43\mathrm{MPa}\text{}\langle \text{}{\sigma}_{at}=1.5\mathrm{MPa}$; ${\sigma}_{sF1}=0.24\mathrm{MPa}\text{}\langle \text{}{\sigma}_{as}=7\mathrm{MPa}$. |

Shape 2 | ${\sigma}_{tF2}=0.55\mathrm{MPa}\text{}\langle \text{}{\sigma}_{at}=1.5\mathrm{MPa}$;${\sigma}_{sF1}=0.24\mathrm{MPa}\text{}\langle \text{}{\sigma}_{as}=7\mathrm{MPa}$. |

Shape 3 | ${\sigma}_{tF2}=0.35\mathrm{MPa}\text{}\langle \text{}{\sigma}_{at}=1.5\mathrm{MPa}$; ${\sigma}_{sF1}=0.24\mathrm{MPa}\text{}\langle \text{}{\sigma}_{as}=7\mathrm{MPa}$. |

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**MDPI and ACS Style**

Ghiţescu, M.; Ghiţescu, I.-M.; Borza, P.N.; Vlase, S.
A New Optimized Solution for a Flexible Coupling with Bolts Used in the Mechanical Transmissions. *Symmetry* **2021**, *13*, 171.
https://doi.org/10.3390/sym13020171

**AMA Style**

Ghiţescu M, Ghiţescu I-M, Borza PN, Vlase S.
A New Optimized Solution for a Flexible Coupling with Bolts Used in the Mechanical Transmissions. *Symmetry*. 2021; 13(2):171.
https://doi.org/10.3390/sym13020171

**Chicago/Turabian Style**

Ghiţescu, Marilena, Ion-Marius Ghiţescu, Paul Nicolae Borza, and Sorin Vlase.
2021. "A New Optimized Solution for a Flexible Coupling with Bolts Used in the Mechanical Transmissions" *Symmetry* 13, no. 2: 171.
https://doi.org/10.3390/sym13020171