# Thermal Model and Thermal Analysis of the Dual Drive Sliding Feed System

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

## 2. Friction Torque Modeling of the Sliding Screw

#### 2.1. Dual Drive Sliding Feed System

#### 2.2. Friction Torque Caused by Differential Sliding

^{2}.

#### 2.3. Frictional Moment Caused by Elastic Hysteresis

#### 2.4. Friction Torque Caused by Lubrication Viscosity

## 3. Thermal Boundary Conditions of the Dual Drive Sliding Feed System

#### 3.1. Analysis of Heat Generation

#### 3.2. Analysis of Heat Transfer

^{2}), $\beta $ is the volume expansion coefficient of air, ${T}_{s}$ is the surface temperature of the part (°C), ${T}_{a}$ is the ambient temperature (°C), and ${v}_{a}$ is the kinematic viscosity of the air (mm

^{2}/s).

#### 3.3. TCRs between Rough Contact Surfaces

## 4. Establishment and Verification of the Thermal Model for Dual Drive Sliding Feed System

#### 4.1. Finite Element Simulation Model of Dual Drive Sliding Feed System

- (1)
- The chamfers and some tiny parts inside the system were ignored;
- (2)
- The screw shaft ignores the grooves on its surface and treats it as a cylinder;
- (3)
- The parameters of heat generation and CHTCs obtained from the previous calculation do not vary with the movement or temperature rise of the components.

#### 4.2. Experimental Verification Device and Scheme

#### 4.3. Comparison of the Simulation and Experimental Results

## 5. Conclusions

- The established thermal simulation model can effectively describe the dynamic thermal characteristics of the dual drive sliding feed system. By comparing the temperature rise and thermal elongation under simulation and experimental conditions, it can be concluded that the temperature rise deviation under five operating conditions is less than 2.1 °C, and the error in the axial thermal deformation of the screw is less than 6.2 µm. The established thermal characteristic simulation model can effectively describe the thermal dynamic response characteristics of the dual drive sliding feed system during operation.
- The thermal field distribution and axial deformation of the dual drive sliding feed system differ from those of conventional feed systems. Due to the difficulty of heat dissipation and the combined effect of the screw and nut bearings, the main heat distribution region of the dual drive feed system is at the nut. Given the numerous heat sources in the system and the significant temperature increase in the sliding screw, the axial deformation of the screw in the dual drive sliding feed system is greater than that in the conventional feed system under the same operating conditions.
- The thermal characteristics of a dual drive sliding system are significantly influenced by both rotational speed and ambient temperature. An increase in rotational speed results in a faster rate of temperature rise and a shorter time to reach thermal equilibrium. Conversely, higher ambient temperatures lead to a quicker temperature rise and a longer time to achieve thermal equilibrium. The ambient temperature also has a significant impact on the axial deformation of the screw. Even when the temperature field is similar, substantial differences in the axial thermal elongation of the screw can occur due to varying ambient temperatures.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 5.**Temperature field and axial deformation under the operating condition I. (

**a**) Temperature field distribution. (

**b**) Axial deformation distribution of the screw shaft.

**Figure 6.**Temperature field and axial deformation under the operating condition II. (

**a**) Temperature field distribution. (

**b**) Axial deformation distribution of the screw shaft.

**Figure 7.**Temperature field and axial deformation under the operating condition III. (

**a**) Temperature field distribution. (

**b**) Axial deformation distribution of the screw shaft.

**Figure 8.**Temperature field and axial deformation under the operating condition IV. (

**a**) Temperature field distribution. (

**b**) Axial deformation distribution of the screw shaft.

**Figure 9.**Temperature field and axial deformation under the operating condition V. (

**a**) Temperature field distribution. (

**b**) Axial deformation distribution of the screw shaft.

**Figure 10.**Comparative analysis results. (

**a**) Temperature field under operating condition I. (

**b**) Temperature field under operating condition II. (

**c**) Temperature field under operating condition III. (

**d**) Temperature field under operating condition IV. (

**e**) Temperature field under operating condition V. (

**f**) Axial thermal elongation under the screw.

Speed of Synthesis (m/Min) | Speed of Screw (Rpm) | Speed of Nut (Rpm) | Heat Production (W) | |||||
---|---|---|---|---|---|---|---|---|

Guideways | Screw Servo Motor | Nut Servo Motor | Front Bearing | Nut Bearing | Rear Bearing | |||

0.18 | 396 | 360 | 0.39 | 1.87 | 1.70 | 4.95 | 5.31 | 4.36 |

Speed of Synthesis (m/Min) | Speed of Screw (Rpm) | Speed of Nut (Rpm) | CHTCS (W/m^{2}·K) | |||||
---|---|---|---|---|---|---|---|---|

Screw Pair | Screw Shaft | Nut Servo Motor | Nut Housing | Slider | Worktable | |||

0.18 | 396 | 360 | 9.17 | 56.3 | 15.52 | 31.26 | 14.53 | 16.23 |

Joint Component | TCR (m^{2}·K/W) |
---|---|

Bearing outer ring-bearing housing | 1.25 × 10^{−3} |

Bearing inner ring-screw shaft | 1.48 × 10^{−4} |

Nut-screw | 1.65 × 10^{−4} |

Guideway-slider | 6.89 × 10^{−4} |

Nut servo motor-nut | 3.68 × 10^{−3} |

Application Components | Material | Density (kg/m^{3}) | Modulus of Elasticity (GPa) | Poisson’s Ratio | Linear Expansion Coefficient (10^{−5}/K) | Thermal Conductivity (W/m·K) | Specific Heat Capacity (J/kg·K) |
---|---|---|---|---|---|---|---|

Nut | Copper alloy | 8400 | 110 | 0.34 | 1.7 | 115 | 387 |

Screw/bearing | GCr15 | 7800 | 200 | 0.28 | 1.2 | 48 | 729 |

Base/bearing housing | Q345B | 7850 | 206 | 0.3 | 1.2 | 46 | 460 |

Guideways/slider | 40Cr | 7850 | 200 | 0.3 | 1.13 | 51 | 477 |

Operating Condition | Speed of Synthesis (m/Min) | Speed of Screw (Rpm) | Speed of Nut (Rpm) | Ambient Temperature (°C) |
---|---|---|---|---|

I | 0.18 | 396 | 360 | 20 |

II | 0.36 | 1116 | 1080 | 20 |

III | 0.54 | 2214 | 2160 | 20 |

IV | 0.36 | 1116 | 1080 | 15 |

V | 0.36 | 1116 | 1080 | 25 |

Operation Condition | Measured Position | Simulated Value (°C) | Measured Value (°C) | Deviation (°C) |
---|---|---|---|---|

I | T1 | 28.1 | 27.1 | 1.0 |

T2 | 25.7 | 24.5 | 1.2 | |

T3 | 35.9 | 34.5 | 1.4 | |

T4 | 33.9 | 33.2 | 0.7 | |

T5 | 33.7 | 31.9 | 1.8 | |

II | T1 | 30.8 | 29.6 | 1.2 |

T2 | 27.4 | 26.2 | 1.2 | |

T3 | 38.5 | 37.1 | 1.4 | |

T4 | 36.4 | 35.8 | 0.6 | |

T5 | 36.2 | 34.2 | 2.0 | |

III | T1 | 31.1 | 30.1 | 1.0 |

T2 | 28.3 | 27.3 | 1.0 | |

T3 | 42.1 | 40.1 | 2.0 | |

T4 | 39.2 | 38.2 | 1.0 | |

T5 | 38.7 | 36.6 | 2.1 | |

IV | T1 | 24.7 | 23.6 | 1.1 |

T2 | 21.9 | 20.9 | 1.0 | |

T3 | 33.4 | 31.8 | 1.6 | |

T4 | 30.2 | 29.5 | 0.7 | |

T5 | 30.0 | 28.5 | 1.5 | |

V | T1 | 34.5 | 33.2 | 1.3 |

T2 | 31.7 | 30.5 | 1.2 | |

T3 | 42.4 | 40.8 | 1.6 | |

T4 | 39.9 | 38.8 | 1.1 | |

T5 | 40.0 | 37.9 | 2.1 |

Operation Condition | Simulated Value (µm) | Measured Value (µm) | Deviation (µm) |
---|---|---|---|

I | 32.8 | 29.9 | 2.9 |

II | 38.9 | 35.5 | 3.4 |

III | 46.3 | 42.5 | 3.8 |

IV | 22.1 | 20.3 | 1.8 |

V | 77.7 | 71.5 | 6.2 |

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**MDPI and ACS Style**

Li, H.; Liu, H.; Feng, X.; Liu, Y.; Yao, M.; Wang, A.
Thermal Model and Thermal Analysis of the Dual Drive Sliding Feed System. *Machines* **2023**, *11*, 1084.
https://doi.org/10.3390/machines11121084

**AMA Style**

Li H, Liu H, Feng X, Liu Y, Yao M, Wang A.
Thermal Model and Thermal Analysis of the Dual Drive Sliding Feed System. *Machines*. 2023; 11(12):1084.
https://doi.org/10.3390/machines11121084

**Chicago/Turabian Style**

Li, Hui, Haiyang Liu, Xianying Feng, Yandong Liu, Ming Yao, and Anning Wang.
2023. "Thermal Model and Thermal Analysis of the Dual Drive Sliding Feed System" *Machines* 11, no. 12: 1084.
https://doi.org/10.3390/machines11121084