MATHEMATICAL STUDY OF THE INFLUENCE OF KNIFE GEOMETRY WITH ARC-LIKE CROSS-SECTIONAL SHAPE ON THE PROCESS OF LONGITUDINAL FELT CUTTING

D. А.  Makatora; A. V.  Makatora; M. A. Zenkin

doi:10.32845/msnau.2022.1.4

D. А. Makatora https://orcid.org/0000-0002-1909-900X
A. V. Makatora https://orcid.org/0000-0001-9373-5169
M. A. Zenkin https://orcid.org/0000-0002-8840-0572

DOI: https://doi.org/10.32845/msnau.2022.1.4

Keywords: running force, the total amount of losses, losses due to friction of the material, transporting rollers, knife blade, longitudinal cutting.

Abstract

A promising study is the design and improvement of machines for longitudinal cutting of materials with minimal energy costs to perform the technological process of cutting due to the geometry of the cutting tool. The article considers the issues of reducing energy costs for the process of longitudinal cutting when using a knife blade with an arcuate cross-section. The analysis is carried out, the effective method of the analysis of influence of size of a backlash between generators of transporting rollers and size of distance from a vertical axis of rotation of transporting rollers to an edge of a knife blade with an arc-shaped cross section on the total size to determine the necessary settings in the machine of longitudinal cutting for felt, as well as to verify the reliability of analytical and experimental models of the process of longitudinal cutting with a knife with an arcuate cross-sectional shape. To determine the total amount of losses during longitudinal cutting of the material and the number of losses due to friction of the material on the face of a fixed knife with an arcuate crosssectional shape, as well as linear cutting force, a two-factor experiment was conducted for the study model. The obtained regression equations describe the total amount of losses during longitudinal cutting of the material and the number of losses due to friction of the material on the face of a stationary knife with an arcuate cross-section, suggest the adequacy of analytical and experimental models made earlier. Also make the necessary adjustments, namely, to adjust the degree of compression of the material and set the edge of the knife blade relative to the vertical axis of the transport rollers to reduce friction losses on the edge of the knife, which in turn reduces energy costs for longitudinal cutting. Comparing the total values of losses in the longitudinal cutting of the material of a knife with one-sided sharpening and a knife with an arcuate cross-section, allows you to talk about the feasibility of using a knife with an arcuate cross-section, which will reduce energy costs for the process.

References

1. Cherno-Ivanov, V. S. (1998). Razrabotka mekhanizma prokol’nogo rezaniya detaley niza obuvi : dis. … kand. tekhn. nauk: 05.05.10 [Development of a mechanism for piercing the details of the bottom of shoes: dissertations of a candidate of technical sciences: specialty 05.05.10]. Kyiv. 165 p. (in Russian).
2. Makatora, D. A. (2013). Vyznachennia pohonnoho zusyllia rizannia mikroporystoi humy nozhem z dvostoronnoiu zatochkoiu [Determination of running force of cutting microporous rubber with a double-edged knife]. Visnyk ChDTU = Bulletin of ChSTU, 2 (65), 92–97 (in Ukrainian).
3. Makatora, D. A. (2014). Eksperymentalne doslidzhennia z vyznachennia pohonnoho zusyllia rizannia povsti, nozhem z odnostoronnoiu zatochkoiu [Experimental study to determine the linear effort of cutting felt, a knife with one-sided sharpening]. Visnyk Kyivskoho natsionalnoho universytetu tekhnolohii ta dyzainu = Bulletin of Kyiv National University of Technologies and Design, 2 (76), 113–123 (in Ukrainian).
4. Makatora, D. A. (2020a). Eksperymentalne doslidzhennia zusyllia rizannia nozhem z duhopodibnoiu formoiu poperechnoho pererizu [Experimental study of the cutting force with a knife with an arcuate cross-section]. Visnyk Khmelnytskoho natsionalnoho universytetu = Bulletin of Khmelnytsky National University, 2(283), 229–234 (in Ukrainian).
5. Makatora, D. A. (2020b). Matematychne modeliuvannia vtrat pry pozdovzhnomu rizanni materialu ryflenym nozhem z odnostoronnoiu formoiu poperechnoho pererizu [Mathematical modeling of losses during longitudinal cutting of the material with a corrugated knife with a one-sided cross-sectional shape]. Visnyk Khmelnytskoho natsionalnoho universytetu = Bulletin of Khmelnytsky National University, 4 (287), 100–106 (in Ukrainian).
6. Makatora, D. A., Kniaziev, V. I. (2004a). Matematychna model protsesu povzdovzhnoho rizannia duhopodibnym nozhem [Mathematical model of the process of longitudinal cutting with an arcuate knife]. Visnyk TUP, Seriia tekhnichni nauky = Bulletin of TUP, Technical Sciences Series, 1, 48–53 (in Ukrainian).
7. Makatora, D. A., Kniaziev, V. I. (2004b). Analiz ratsionalnoho polozhennia nozha ta formy yoho poperechnoho pererizu v mashynakh typu “DN” [Analysis of the rational position of the knife and the shape of its cross section in machines such as "DN"]. Visnyk Kyivskoho natsionalnoho universytetu tekhnolohii ta dyzainu = Bulletin of Kyiv National University of Technologies and Design, 1, 159–163 (in Ukrainian).
8. Makatora, D. A., Panasiuk, I. V. (2014a). Vyznachennia pohonnoho zusyllia rizannia monolitnoi humy nozhem z dvostoronnoiu zatochkoiu [Determination of running force of cutting monolithic rubber with a knife with double-sided sharpening]. Visnyk Khmelnytskoho natsionalnoho universytetu = Bulletin of Khmelnytsky National University, 1(209), 31–35 (in Ukrainian).
9. Makatora, D. A., Panasiuk, I. V. (2014b). Vyznachennia pohonnoho zusyllia rizannia mikroporystoi humy nozhem z odnostoronnoiu zatochkoiu [Determination of running force of cutting microporous rubber with a knife with one-sided sharpening]. Visnyk Khmelnytskoho natsionalnoho universytetu = Bulletin of Khmelnytsky National University, 2 (211), 19–25 (in Ukrainian).
10. Makatora, D. A., Panasiuk, I. V. (2014c). Vyznachennia pohonnoho zusyllia rizannia monolitnoi humy nozhem z odnostoronnoiu zatochkoiu [Determination of running force of cutting monolithic rubber with a knife with one-sided sharpening]. Visnyk ChDTU = Bulletin of ChSTU, 1 (71), 36–42 (in Ukrainian).
11. Makatora, D. A., Panasiuk, I. V. (2014d). Vyznachennia pohonnoho zusyllia rizannia povsti nozhem z dvostoronnoiu zatochkoiu [Determination of running force of felt cutting with a knife with double-sided sharpening]. Visnyk Kyivskoho natsionalnoho universytetu tekhnolohii ta dyzainu = Bulletin of Kyiv National University of Technologies and Design, 1 (75), 41–48 (in Ukrainian).
12. Mykoliuk, O., Bobrovnyk, V. (2019). Peredumovy formuvannia polityky enerhozberezhennia u rozvytku pidpryiemstv mashynobudivnoho kompleksu [Prerequisites for the formation of energy saving policy in the development of machinebuilding enterprises]. Ekonomichnyi analiz = Economic analysis, Ternopil, 29(2), 62–72 (in Ukrainian).
13. Patent № 70012 Ukraina, MPK B 23 B 1/00, G 01 L 3/00. Sposib vyznachennia potuzhnosti, shcho vytrachaietsia na povzdovzhnie rizannia materialu [Method of determining power consumed for longitudinal cutting of material]. D. A. Makatora, V. I. Kniaziev; applicant and patent owner Kyiv State University of Technologies and Design. № u20031212100; stated 23.12.2003; published 15.09.2004, Bulletin № 9 (in Ukrainian).
14. Polishchuk, O. S. (2019). Eksperymentalne doslidzhennia protsesu rizannia vzuttievykh materialiv [Experimental study of the process of cutting shoe materials]. Visnyk Khmelnytskoho natsionalnoho universytetu = Bulletin of Khmelnytsky National University, 1(269), 17–26 (in Ukrainian).
15. Sevastianov, R. V. (2016). Enerhoefektyvnist promyslovykh pidpryiemstv Ukrainy ta bariery z yii vprovadzhennia [Energy efficiency of industrial enterprises of Ukraine and barriers to its implementation]. Ekonomichnyi visnyk Zaporizkoi derzhavnoi inzhenernoi akademii = Economic Bulletin of the Zaporozhye State Engineering Academy, 1(01), 28–35 (in Ukrainian).
16. Tikhomirov, V. B. (1974). Planirovaniye i analíz eksperimenta [Planning and analysis of the experiment]. Moscow: Legkaya industriya. 262 p. (in Russian).