Calculation of the Heat Flux from a Ball Screw Nut to the Nut Raceway
In the field of precision machining, temperature fluctuation tends to cause the most significant machining errors. In particular, heat, which is generated in the nut of the ball screw feed system during movement, can deform the screw shaft significantly. In order to calculate and evaluate the therma...
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2023-03-01
|
| Series: | Machines |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2075-1702/11/3/408 |
| _version_ | 1827748996223860736 |
|---|---|
| author | Tzu-Chien Kuo An-Shik Yang Yih-Chyun Hwang Wen-Hsin Hsieh |
| author_facet | Tzu-Chien Kuo An-Shik Yang Yih-Chyun Hwang Wen-Hsin Hsieh |
| author_sort | Tzu-Chien Kuo |
| collection | DOAJ |
| description | In the field of precision machining, temperature fluctuation tends to cause the most significant machining errors. In particular, heat, which is generated in the nut of the ball screw feed system during movement, can deform the screw shaft significantly. In order to calculate and evaluate the thermal deformation of the ball screw shaft, the rate of the heat transfer from the nut to the screw shaft must be known. This rate can be calculated by subtracting the heat transfer rate to the nut raceway from the heat generation rate of the nut. Hence, it is necessary to calculate the heat flux from the nut to the nut raceway. This paper introduces a novel method to calculate the heat flux from the nut to the nut raceway. The new approach also enables calculations for different operating conditions. Furthermore, an experimental setup is established to measure the temperature increase, from 0 to 180 s after the nut starts moving, for various operating conditions. It is then theoretically shown that the 0–180 s temperature increase/heat flux curves for the nut are “universal”, i.e., the curve remains unchanged for the different operating conditions. Subsequently, a thermal model using the finite element method (FEM) is developed to simulate the nut temperature increase over time, which is then compared with the experimental data. As a result, it becomes possible to determine the heat flux from the nut to the nut raceway and calculate the 0–180 s temperature increase/heat flux curve (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mover accent="true"><mrow><mo>Δ</mo><mi mathvariant="normal">T</mi></mrow><mo stretchy="true">˜</mo></mover></mrow><mrow><mrow><mn>0</mn><mo>~</mo><mn>180</mn><mi mathvariant="normal">s</mi><mo>,</mo><mi>Training</mi><mtext> </mtext><mi>Data</mi></mrow></mrow></msub></mrow></semantics></math></inline-formula>) for the training group. Finally, the heat flux from the nut to the nut raceway is calculated for ten different operating conditions in the test group using the 0–180 s temperature increase/heat flux curve of the training group (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mover accent="true"><mrow><mo>Δ</mo><mi mathvariant="normal">T</mi></mrow><mo stretchy="true">˜</mo></mover></mrow><mrow><mrow><mn>0</mn><mo>~</mo><mn>180</mn><mi mathvariant="normal">s</mi><mo>,</mo><mi>Training</mi><mtext> </mtext><mi>Data</mi></mrow></mrow></msub></mrow></semantics></math></inline-formula>). The corresponding temperature curves are then calculated by inputting the values of the heat fluxes into the FEM model. The highest root mean square error (RMSE) between the calculated and experimentally measured temperature increase was 0.16 °C for Test 7 (the error was 10.7%). This result indicates that the new method is valid and feasible for calculating the heat flux from a ball screw nut to the nut raceway. |
| first_indexed | 2024-03-11T06:16:42Z |
| format | Article |
| id | doaj.art-d8e6a4dad1894302bd4deb0e892032ab |
| institution | Directory Open Access Journal |
| issn | 2075-1702 |
| language | English |
| last_indexed | 2024-03-11T06:16:42Z |
| publishDate | 2023-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Machines |
| spelling | doaj.art-d8e6a4dad1894302bd4deb0e892032ab2023-11-17T12:16:06ZengMDPI AGMachines2075-17022023-03-0111340810.3390/machines11030408Calculation of the Heat Flux from a Ball Screw Nut to the Nut RacewayTzu-Chien Kuo0An-Shik Yang1Yih-Chyun Hwang2Wen-Hsin Hsieh3Department of Mechanical Engineering, National Chung Cheng University, Chiayi 621, TaiwanDepartment of Energy and Refrigerating Air-Conditioning Engineering, National Taipei University of Technology, Taipei 106, TaiwanHIWIN Technologies Corp., Taichung 408, TaiwanDepartment of Mechanical Engineering and Advanced Institute of Manufacturing with High-Tech Innovations, National Chung Cheng University, Chiayi 621, TaiwanIn the field of precision machining, temperature fluctuation tends to cause the most significant machining errors. In particular, heat, which is generated in the nut of the ball screw feed system during movement, can deform the screw shaft significantly. In order to calculate and evaluate the thermal deformation of the ball screw shaft, the rate of the heat transfer from the nut to the screw shaft must be known. This rate can be calculated by subtracting the heat transfer rate to the nut raceway from the heat generation rate of the nut. Hence, it is necessary to calculate the heat flux from the nut to the nut raceway. This paper introduces a novel method to calculate the heat flux from the nut to the nut raceway. The new approach also enables calculations for different operating conditions. Furthermore, an experimental setup is established to measure the temperature increase, from 0 to 180 s after the nut starts moving, for various operating conditions. It is then theoretically shown that the 0–180 s temperature increase/heat flux curves for the nut are “universal”, i.e., the curve remains unchanged for the different operating conditions. Subsequently, a thermal model using the finite element method (FEM) is developed to simulate the nut temperature increase over time, which is then compared with the experimental data. As a result, it becomes possible to determine the heat flux from the nut to the nut raceway and calculate the 0–180 s temperature increase/heat flux curve (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mover accent="true"><mrow><mo>Δ</mo><mi mathvariant="normal">T</mi></mrow><mo stretchy="true">˜</mo></mover></mrow><mrow><mrow><mn>0</mn><mo>~</mo><mn>180</mn><mi mathvariant="normal">s</mi><mo>,</mo><mi>Training</mi><mtext> </mtext><mi>Data</mi></mrow></mrow></msub></mrow></semantics></math></inline-formula>) for the training group. Finally, the heat flux from the nut to the nut raceway is calculated for ten different operating conditions in the test group using the 0–180 s temperature increase/heat flux curve of the training group (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mover accent="true"><mrow><mo>Δ</mo><mi mathvariant="normal">T</mi></mrow><mo stretchy="true">˜</mo></mover></mrow><mrow><mrow><mn>0</mn><mo>~</mo><mn>180</mn><mi mathvariant="normal">s</mi><mo>,</mo><mi>Training</mi><mtext> </mtext><mi>Data</mi></mrow></mrow></msub></mrow></semantics></math></inline-formula>). The corresponding temperature curves are then calculated by inputting the values of the heat fluxes into the FEM model. The highest root mean square error (RMSE) between the calculated and experimentally measured temperature increase was 0.16 °C for Test 7 (the error was 10.7%). This result indicates that the new method is valid and feasible for calculating the heat flux from a ball screw nut to the nut raceway.https://www.mdpi.com/2075-1702/11/3/408ball screwheat flux between nut and nut–racewayheat transfer calculationthermal deformation of screw shaft |
| spellingShingle | Tzu-Chien Kuo An-Shik Yang Yih-Chyun Hwang Wen-Hsin Hsieh Calculation of the Heat Flux from a Ball Screw Nut to the Nut Raceway Machines ball screw heat flux between nut and nut–raceway heat transfer calculation thermal deformation of screw shaft |
| title | Calculation of the Heat Flux from a Ball Screw Nut to the Nut Raceway |
| title_full | Calculation of the Heat Flux from a Ball Screw Nut to the Nut Raceway |
| title_fullStr | Calculation of the Heat Flux from a Ball Screw Nut to the Nut Raceway |
| title_full_unstemmed | Calculation of the Heat Flux from a Ball Screw Nut to the Nut Raceway |
| title_short | Calculation of the Heat Flux from a Ball Screw Nut to the Nut Raceway |
| title_sort | calculation of the heat flux from a ball screw nut to the nut raceway |
| topic | ball screw heat flux between nut and nut–raceway heat transfer calculation thermal deformation of screw shaft |
| url | https://www.mdpi.com/2075-1702/11/3/408 |
| work_keys_str_mv | AT tzuchienkuo calculationoftheheatfluxfromaballscrewnuttothenutraceway AT anshikyang calculationoftheheatfluxfromaballscrewnuttothenutraceway AT yihchyunhwang calculationoftheheatfluxfromaballscrewnuttothenutraceway AT wenhsinhsieh calculationoftheheatfluxfromaballscrewnuttothenutraceway |