# Model Based on an Effective Material-Removal Rate to Evaluate Specific Energy Consumption in Grinding

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## Abstract

**:**

## 1. Introduction

## 2. Model of Specific Energy Consumption

#### Model of Effective Material-Removal Rate in Grinding

## 3. Experiment Setup

#### 3.1. Estimation of Grain Number Per Unit Area in Grinding Wheel

#### 3.2. Power-Consumption Measurement

## 4. Results and Discussion

## 5. Conclusions

- A model was successfully developed to evaluate the dissipated energy by the sliding, ploughing, and chip-formation mechanisms in an industrial-scale grinding process. In general, sliding energy governs the process of energy dissipation in grinding.
- The dissipated energy by the sliding mechanism decreases when the depth of cut and workpiece speed increase, allowing to reduce energy consumption and manufacturing cost during grinding. The sliding mechanism represents, on average, 90% of the total energy consumed for the following materials: C45K, C45K quenching, and AISI 304.
- The model also allows to find the specific energy consumed by chip formation, which is the limit value defined by the asymptotic behavior experienced by $SEC$. This validates the hypothesis that, during down-grinding, the energy calculated by the analyzer corresponds to the energy dissipated by sliding.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Nomenclature

$\theta $ | Angular position (°) |

${\theta}^{*}$ | Dimensionless angular position |

a | Depth of cut (mm) |

${A}_{cg}$ | Section cut by a grain (mm${}^{2}$) |

${b}_{g}$ | Width of grain during cutting (mm) |

${C}_{g}$ | Grain number per unit area (mm${}^{-2}$) |

${d}_{g}$ | Grain diameter (mm) |

${D}_{M}$ | Diameter of the grinding wheel (mm) |

f | Feed per grain (mm) |

h | Undeformed chip thickness (mm) |

k | Constant of proportionality |

${l}_{c}$ | Contact length between wheel and workpiece (mm) |

${l}_{g}$ | Distance between grains (mm) |

${N}_{g}$ | Number of grains |

P | Total power consumption (W) |

${P}_{ch}$ | Power consumption by chip formation (W) |

${P}_{pl}$ | Power consumption by ploughing (W) |

${P}_{sl}$ | Power consumption by sliding (W) |

${P}_{v}$ | Idle power consumption (W) |

${Q}_{w}$ | Material removal rate (mm${}^{3}$/s) |

${R}_{g}$ | Grain radius (mm) |

${R}_{M}$ | Radius of the grinding wheel (mm) |

$SCE$ | Specific cutting energy (J/mm${}^{3}$) |

$SEC$ | Specific energy consumption (J/mm${}^{3}$) |

$SE{C}_{ch}$ | Specific energy consumed by chip formation (J/mm${}^{3}$) |

$SE{C}_{pl}$ | Specific energy consumed by ploughing (J/mm${}^{3}$) |

$SE{C}_{sl}$ | Specific energy consumed by sliding (J/mm${}^{3}$) |

${v}_{c}$ | Peripheral cutting speed (m/s) |

${v}_{w}$ | Speed of workpiece (m/s) |

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**Figure 2.**Characteristics of grinding wheel A36H5V: (

**a**) surface-roughness profile and (

**b**) size of detached grains.

**Figure 5.**Relationship between specific energy consumption and (

**a**) depth of cut, and (

**b**) workpiece speed.

Cutting Parameter | Magnitude of Values | ||
---|---|---|---|

Depth of cut (mm) | 0.010 | 0.015 | 0.020 |

Peripheral cutting speed (m/s) | 22.9 | 22.9 | 22.9 |

Speed of workpiece (mm/s) | 57 | 101 | 150 |

Hardness Material | C45K | C45K Quenching | C45K Tempering | AISI 304 |
---|---|---|---|---|

(HRC) | 17.35 ± 1.38 | 56.16 ± 0.52 | 25.72 ± 0.72 | 19.85 ± 0.68 |

Metallic Alloy | $\mathit{SEC}$ (J/mm${}^{3})$ | ${\mathit{SEC}}_{\mathit{sl}}$ (J/mm${}^{3})$ | ${\mathit{SEC}}_{\mathit{pl}}$ (J/mm${}^{3})$ | ${\mathit{SEC}}_{\mathit{ch}}$ (J/mm${}^{3})$ |
---|---|---|---|---|

C45K | 655 | 602 | 30 | 8 |

C45K quenching | 1805 | 1541 | 132 | 36 |

C45K tempering | 351 | 201 | 113 | 11 |

AISI 304 | 958 | 901 | 36 | 13 |

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**MDPI and ACS Style**

Nápoles Alberro, A.; González Rojas, H.A.; Sánchez Egea, A.J.; Hameed, S.; Peña Aguilar, R.M. Model Based on an Effective Material-Removal Rate to Evaluate Specific Energy Consumption in Grinding. *Materials* **2019**, *12*, 939.
https://doi.org/10.3390/ma12060939

**AMA Style**

Nápoles Alberro A, González Rojas HA, Sánchez Egea AJ, Hameed S, Peña Aguilar RM. Model Based on an Effective Material-Removal Rate to Evaluate Specific Energy Consumption in Grinding. *Materials*. 2019; 12(6):939.
https://doi.org/10.3390/ma12060939

**Chicago/Turabian Style**

Nápoles Alberro, Amelia, Hernán A. González Rojas, Antonio J. Sánchez Egea, Saqib Hameed, and Reyna M. Peña Aguilar. 2019. "Model Based on an Effective Material-Removal Rate to Evaluate Specific Energy Consumption in Grinding" *Materials* 12, no. 6: 939.
https://doi.org/10.3390/ma12060939