621.992

screw surface, trajectory, whirling process, whirling ring.

The investigation of the parameters in screw surfaces whirling process is presented. The equation of the trajectory of relative movement of the workpiece and the cutter in parametric form taking into account the movement of the whirling ring along the workpiece is obtained. Appropriate graphs are plotted, which allow to make the conclusion that increasing the rotational speed of the whirling ring results the decrease in the thickness of the metal layer, which is cut during one period of contact between the workpiece and the cutter. It is also show on the graphs that the ratio between the rotational speeds of the whirling ring and the workpiece is decisive. The greater this ratio, the smaller the thickness of the cut layer. The obtained equations make it possible, using the appropriate application software, to determine and predict the shape and thickness of the material cut layers in the cylindrical workpiece by each cutter in whirling ring based on plotted graphs, visually observe the change of trajectory movement when changing cutting conditions and machined surface parameters.

1. Liashuk O. L., Diachun A. Ye., Tretiakov O. L. Doslidzhennya deformatsiyi zahotovky v protsesi narizannya zovnishnikh radiusnykh kanavok prystroyem iz dekil'koma riztsyamy. Perspektyvni tekhnolohiyi ta prylady. 2018. Volume. 12. Р. 105–110. [In Ukrainian].
2. Liashuk O. L., Diachun A. Ye., Klendiy V. M., Tretiakov O. L. Doslidzhennya sylovykh parametriv protsesu zmitsnennya hvyntovykh poverkhon' robochykh orhaniv deformuyuchymy puansonamy, Rozvidka ta rozrobka naftovykh i hazovykh rodovyshch. 2018. No. 1 (66). P. 38–43. [In Ukrainian].
3. Stepchyn Y., Otamanskyi V. Decrease of surfaces roughness for parts processed with edge tool by improvement of the lathe working components uniform feed. Scientific Journal of the Ternopil National Technical University. Ternopil. 2017. No. 4 (88). P. 119–128.
4. Kryvyi P., Krupa V., Kobelnyk V., Kosiv Y. Substantiation of parameters for three-cutter boring head with allowance and feed distribution and asymmetric cutter position. Scientific Journal of the Ternopil National Technical University. Ternopil. 2019. No. 4 (96). Р. 57–69.
5. Cheng, E. & Tsai, Tung & Lin, Ming & Wu, Xian & Yeh, Nan & Pan, Bo & Chen, Yi & Kuo, Shien. Study of using internal thread whirling in machining titanium dental implant. Applied Mechanics and Materials. 2012. 268–270: 436–441. DOI: 10.4028/www.scientific.net/AMM.268-270.436.
6. Masakazu Soshi, Franco Rigolone, Jennifer Sheffield, Kazuo Yamazaki. Development of a directly-driven thread whirling unit with advanced tool materials for mass-production of implantable medical parts, CIRP Annals. Volume 67. Issue 1. 2018. Р. 117–120. ISSN 0007-8506, https://doi.org/10.1016/ j.cirp.2018.03.016.
   7.Lexiang Wang, Yan He, Yulin Wang, Yufeng Li, Chao Liu, Shilong Wang, Yan Wang. Analytical modeling of material removal mechanism in dry whirling milling process considering geometry, kinematics and mechanics. International Journal of Mechanical Sciences. Volume 172. 2020. 105419. ISSN 0020-7403, https://doi.org/10.1016/j.ijmecsci.2020.105419.

8. Hlembotska L., Balytska N., Melnychuk P., Melnyk O. Computer modelling of power load of face mill cutters with cylindrical rake face of during difficult-to-cut materials machining. Scientific Journal of the Ternopil National Technical University. Ternopil. 2019. № 1 (93). Р. 70–80.
9. Yan He, Chao Liu, Yulin Wang, Yufeng Li, Shilong Wang, Lexiang Wang, Yan Wang. Analytical modeling of temperature distribution in lead-screw whirling milling considering the transient un-deformed chip geometry. International Journal of Mechanical Sciences. Volumes 157–158. 2019. Р. 619–632. ISSN 0020-7403, https://doi.org/10.1016/j.ijmecsci.2019.05.008.
10. Shu-quan Song, Dun-wen Zuo. Modelling and simulation of whirling process based on equivalent cutting volume. Simulation Modelling Practice and Theory. Volume 42. 2014. Р. 98–106. ISSN 1569-190X, https://doi.org/10.1016/j.simpat.2013.12.011.
11. Lexiang Wang, Yan He, Yufeng Li, Yulin Wang, Chao Liu, Xuehui Liu, Yan Wang. Modeling and analysis of specific cutting energy of whirling milling process based on cutting parameters, Procedia CIRP. Volume 80. 2019. Р. 56–61. ISSN 2212-8271, https://doi.org/10.1016/j.procir.2019.01.028.
12. Yan He, Lexiang Wang, Yulin Wang, Yufeng Li, Shilong Wang, Yan Wang, Chao Liu, Chuanpeng Hao. An analytical model for predicting specific cutting energy in whirling milling process, Journal of Cleaner Production. Volume 240. 2019. 118181. ISSN 0959-6526, https://doi.org/10.1016/ j.jclepro.2019.118181.
13. Rop"yak L. Ya., M. V. Makoviychuk, O. V. Rohal'. Teoretychne doslidzhennya zminy kuta pidyomu hvyntovoyi liniyi konichnykh riz'b. Rezaniye i instrumyenty v tekhnolohichyeskikh sistyemakh. Volume 8. 2015. Р. 252–262. [In Ukrainian].
14. Pryhorovska T., Ropyak L. Machining error influnce on stress state of conical thread joint details, 2019 IEEE 8th International Conference on Advanced Optoelectronics and Lasers (CAOL). 2019. Р. 493–497. doi: 10.1109/CAOL46282.2019.9019544.
15. Ropyak L. Ya., Vytvytskyi V. S., Velychkovych A. S., Pryhorovska T. O., Shovkoplias M. V. Study on grinding mode effect on external conical thread quality, 11th Int. Conf. on Advanced Manufacturing Technologies (ICAMaT 2020). Oct 29th, 2020, Bucharest, Romania. IOP Conf. Series: Materials Science and Engineering, 2021, 1018, 012014. doi:10.1088/1757-899X/1018/1/012014.

1. Liashuk O. L., Diachun A. Ye., Tretiakov O. L. Doslidzhennya deformatsiyi zahotovky v protsesi narizannya zovnishnikh radiusnykh kanavok prystroyem iz dekil'koma riztsyamy. Perspektyvni tekhnolohiyi ta prylady. 2018. Volume. 12. Р. 105–110. [In Ukrainian].
2. Liashuk O. L., Diachun A. Ye., Klendiy V. M., Tretiakov O. L. Doslidzhennya sylovykh parametriv protsesu zmitsnennya hvyntovykh poverkhon' robochykh orhaniv deformuyuchymy puansonamy, Rozvidka ta rozrobka naftovykh i hazovykh rodovyshch. 2018. No. 1 (66). P. 38–43. [In Ukrainian].
3. Stepchyn Y., Otamanskyi V. Decrease of surfaces roughness for parts processed with edge tool by improvement of the lathe working components uniform feed. Scientific Journal of the Ternopil National Technical University. Ternopil. 2017. No. 4 (88). P. 119–128.
4. Kryvyi P., Krupa V., Kobelnyk V., Kosiv Y. Substantiation of parameters for three-cutter boring head with allowance and feed distribution and asymmetric cutter position. Scientific Journal of the Ternopil National Technical University. Ternopil. 2019. No. 4 (96). Р. 57–69.
5. Cheng, E. & Tsai, Tung & Lin, Ming & Wu, Xian & Yeh, Nan & Pan, Bo & Chen, Yi & Kuo, Shien. Study of using internal thread whirling in machining titanium dental implant. Applied Mechanics and Materials. 2012. 268–270: 436–441. DOI: 10.4028/www.scientific.net/AMM.268-270.436.
6. Masakazu Soshi, Franco Rigolone, Jennifer Sheffield, Kazuo Yamazaki. Development of a directly-driven thread whirling unit with advanced tool materials for mass-production of implantable medical parts, CIRP Annals. Volume 67. Issue 1. 2018. Р. 117–120. ISSN 0007-8506, https://doi.org/10.1016/ j.cirp.2018.03.016.
   7.Lexiang Wang, Yan He, Yulin Wang, Yufeng Li, Chao Liu, Shilong Wang, Yan Wang. Analytical modeling of material removal mechanism in dry whirling milling process considering geometry, kinematics and mechanics. International Journal of Mechanical Sciences. Volume 172. 2020. 105419. ISSN 0020-7403, https://doi.org/10.1016/j.ijmecsci.2020.105419.

8. Hlembotska L., Balytska N., Melnychuk P., Melnyk O. Computer modelling of power load of face mill cutters with cylindrical rake face of during difficult-to-cut materials machining. Scientific Journal of the Ternopil National Technical University. Ternopil. 2019. № 1 (93). Р. 70–80.
9. Yan He, Chao Liu, Yulin Wang, Yufeng Li, Shilong Wang, Lexiang Wang, Yan Wang. Analytical modeling of temperature distribution in lead-screw whirling milling considering the transient un-deformed chip geometry. International Journal of Mechanical Sciences. Volumes 157–158. 2019. Р. 619–632. ISSN 0020-7403, https://doi.org/10.1016/j.ijmecsci.2019.05.008.
10. Shu-quan Song, Dun-wen Zuo. Modelling and simulation of whirling process based on equivalent cutting volume. Simulation Modelling Practice and Theory. Volume 42. 2014. Р. 98–106. ISSN 1569-190X, https://doi.org/10.1016/j.simpat.2013.12.011.
11. Lexiang Wang, Yan He, Yufeng Li, Yulin Wang, Chao Liu, Xuehui Liu, Yan Wang. Modeling and analysis of specific cutting energy of whirling milling process based on cutting parameters, Procedia CIRP. Volume 80. 2019. Р. 56–61. ISSN 2212-8271, https://doi.org/10.1016/j.procir.2019.01.028.
12. Yan He, Lexiang Wang, Yulin Wang, Yufeng Li, Shilong Wang, Yan Wang, Chao Liu, Chuanpeng Hao. An analytical model for predicting specific cutting energy in whirling milling process, Journal of Cleaner Production. Volume 240. 2019. 118181. ISSN 0959-6526, https://doi.org/10.1016/ j.jclepro.2019.118181.
13. Rop"yak L. Ya., M. V. Makoviychuk, O. V. Rohal'. Teoretychne doslidzhennya zminy kuta pidyomu hvyntovoyi liniyi konichnykh riz'b. Rezaniye i instrumyenty v tekhnolohichyeskikh sistyemakh. Volume 8. 2015. Р. 252–262. [In Ukrainian].
14. Pryhorovska T., Ropyak L. Machining error influnce on stress state of conical thread joint details, 2019 IEEE 8th International Conference on Advanced Optoelectronics and Lasers (CAOL). 2019. Р. 493–497. doi: 10.1109/CAOL46282.2019.9019544.
15. Ropyak L. Ya., Vytvytskyi V. S., Velychkovych A. S., Pryhorovska T. O., Shovkoplias M. V. Study on grinding mode effect on external conical thread quality, 11th Int. Conf. on Advanced Manufacturing Technologies (ICAMaT 2020). Oct 29th, 2020, Bucharest, Romania. IOP Conf. Series: Materials Science and Engineering, 2021, 1018, 012014. doi:10.1088/1757-899X/1018/1/012014.