INVESTIGATION OF THE CONDITIONS FOR GRINDING INVOLUTE PROFILES OF CYLINDRICAL GEAR TEETH BY THE COPYING METHOD

Abstract

References

1. Kane M.M., Suslov A.G. et. al.; under the general editorship of Dr. Sci. (Eng.) M.M. Kane. Quality Management in Mechanical Engineering: Textbook. – Moscow: Mashinostroenie, 2010. – 416 p.
2. Rasulov N. M., Nadirov U. M., Guseinov G.R. (2013) On the quality of manufacturing products and their durability. Modern Methods and Technologies for Creating and Processing Materials, vol. 2, pp. 434–443.
3. Rasulov N.M., Nadirov U.M., Guseynov, G.R. (2014). Relations between production and operating indicators of products quality. Vestnik Mashinostroyeniya, (11), 85–88.
4. Starzhinsky V.E., Kane M.M., eds. Production technology and methods for ensuring the quality of gears and gears. St. Petersburg, Profession, 2007. 832 p.
5. Stephen P. Radzevich. Handbook of Practical GearDesign and Manufacture. Taylor & Francis Group, LLC.2012, - 846 p.
6. Abdullaev, A.I. (2022). Switch Electromechanical Drive for Railways, Eurasian Patent No.040109. Eurasian Patent Office. Edited by A.A. Alifov, B.B. Ahmadov, I.G. Chalabi, G.N. Rasulov, and A.B. Hadjiev, 21 Apr. 2022. https://www.researchgate.net/publication/386135915.
7. Abdullayev A.H., Khalilov İ.A., Rasulov G.N. (2025) Design and Production Technology of Special Friction Clutch Inside Innovative Reducers of Railroad Switches // Electronic Journal Reliability: Theory & Applications. – V ol. 20, Special Issue No. 7 (83). – p. 420–427.
8. Nariman Rasulov, Ugurlu Nadirov, Irada Abbasova, (2024) Improving of Machining Efficiency of Threads and Conical Surfaces of Diverse Directions by Managing Static Technological Relationships. Advances in Science and Technology, ISSN: 1662-0356, V ol. 148, pp 97-102.
9. Rikard Hjelm, et. al. (2023) A multi -perspective method for gear efficiency and contact analysis. Results in Engineering V ol. 20, 101582.
10. Isag Khankishiyev, Elkhan D. Mamedov, Y usif Huseynov. Analysis of literary sources on the reliability and durability of ship machines and mechanisms operating under extreme conditions. XI International Scientific and Theoretical Conference «Scientific foru m: theory and practice of research». San Francisco, USA. March 13, 2026, pp. 156-164.
11. Aziz S. Sh., Jafarli G., Sivanesan S. (2025) Increasing processing efficiency in finefinishing technology of internal cylindrical surfaces by technological methods. Reliability: Theory & Applications, V ol. 20 Iss. SI 10 (88), pp. 307–314.
12. Frumusanu, G.R.; Bordeanu, M.; Susac, F. (2024) Method for Increasing the Energy Efficiency of the Gear Teeth Cutting Process by Smoothing the Cutting Force Variation. Appl. Sci. 14(21), 9751.
13. Rasulov N. M., Nadirov U. M., Amiraslanov P. A. (1995) O tochnosti po diametru narezannykh spetsial'nym dolbyakom zubchatykh poverkhnostei [About the accuracy of the diameter of the cut special shaping cutter jagged surfaces]. Uchenye Zapiski (Azerbaijan State Oil Academy, Baku), no. 1, pp. 60–64.
14. Rasulov, N.M., Alakbarov, M.Z. Mathematical model of actual cuttıng depth ın of a tooth rinding wıth copy method and research of surface quality // Machine -building and Energy: New Concepts and Technologies” International Scientific-practical Conference, – Baku, AzTU, – 2021, – pp. 27-29.
15. T.N. Ivanova, et al. (2018) Research of grinding process of gears with involute profile to increase its efficiency. IOP Conf. Series: Materials Science and Engineering 327, 042046.
16. Abdullaev, A.I., Rasulov, G.N., Huseynov, I.D., and Ismayilov, O.F. (2022). Innovative Reducer for Railroad Switch Drives and Evaluation of Friction Work on Double Sliding Bearings. SOCAR Proceedings, Special Issue 1, 1–6. https://doi.org/10.5510/OGP2022SI100700
17. Fuad Alakbarov. Effects and characteristics of settlements on operation. VII International Scientific and Theoretical Conference « Modern Tools and Methods of Scientific Investigations» Antwerp; Kingdom of Belgium. April 3, –2026. – pp. 106-115.
18. Fuad Alakbarov. Fundamentals of Planning Operations at the Strategic, Operational and Tactical Levels in the Military Decision -Making Process. Military Knowledge, No. 1, 2025, pp. 17 –25. DOI: 10.30546/mk.2024.4.0130.
19. Fuad Alakbarov. Characteristics of the Employment of Tactical Airborne Forces in Armed Conflicts. Military Knowledge, No. 4, 2022, pp. 15–20.
20. Fuad Alakbarov. Factors Influencing the Military Decision-Making Process. Military Knowledge, No. 2, 2023, pp. 46–53.
21. Abdullayev A.I., Rasulov G.N., Ismayilov O.F. (2020) Mathematical modeling of angular difference between teeth direction in zone of engagement and completeness of contact in gears. Scientific and Technical Journal of Information Technologies, Mechanics and Optics, vol. 20, no. 1, pp. 110–117 (in Russian). doi: 10.17586/2226- 1494-2020-20-1-110-117
22. Abdullayev A.H., Rasulov G.N. (2020) Design optimization of multi -stage cylindrical reducers in accordance with the gear ratios // The 7th International Conference on Control and Optimization with Industrial Applications (COIA). – Baku, Azerbaijan, – V ol. II. – p. 20–23.
23. Abbasov V. et. al. (2024) Formation of Shaft Accuracy during Mechanical Processing on CNC Machines. Advances in Science and Technology, 148, pp.81-86.
24. Aziz S.Sh. (2020) Kinematic features of the lapping process and determination of its basic parameters. Computational Nanotechnology, №3 (V ol.7), pp. 11–16.
25. Aziz S.Sh. (2025) The general regularity of surface layer work hardening in the honing operation of medium carbon steels. Reliability: Theory & Applications, 20 (SI 7 (83)), pp.372–378.
26. Douglas C. Montgomery. Introduction to statistical quality control 7th edition. 2013 by John Wiley & Sons, Inc. ISBN: 978-1-118-14681-1.
27. Yusubov N., Abbasova H. (2021) Full -factor matrix model of accuracy of dimensions performed on multi - purpose CNC machines. Obrabotka Metallov, 23(4), pp. 6–20. DOI: 10.17212/1994-6309-2021-23.4-6-20
28. Yusubov N., Abbasova H., Khankishiyev İ. (2021) Entwicklung einer Projektierungstheorie für die Mehrwerkzeugbearbeitung mit den Möglichkeiten der modernen CNC -Werkzeugmaschinen. Forschung im Ingenieurwesen, 85, pp. 661-678.
29. Aziz S. Sh. (2024) Improving surface quality in flat grinding operations using modern technological methods. Machine science, V ol. 13, Iss. 2, pp. 59–64.
30. N. M. Rasulov, et. al. (2022) Improving the efficiency of thread rolling with management of technological connections // SOCAR Proceedings. Special Iss. 1 011 -015. DOI: 10.5510/OGP2022SI100694. https://proceedings.socar.az/en/journal/85
31. Simon, S., Y usubov, N. D., Amirli, S. F., & Amirov, F. G. (2025). Hardness of surface layers of blanks made of chromium–nickel alloys at hydroabrasive machining. Vestnik Mashinostroyeniya, 104(10), 873 –877. https://doi.org/10.36652/0042-4633-2025-104-10-873-877
32. Hasanov Y.N., Aziz S., Agayev A. (2026) analysis of the technological characteristics of the honing operation of 32CRMOV12-10 steels used under severe friction conditions. Scientia: Collection of Scientific Papers with the Proceedings of the X Internationa l Scientific and Theoretical Conference “Current Issues of Science, Prospects and Challenges”, Sydney, Australia, pp. 88–97.
33. Yusubov N., Abbasova H., Dadashov R. (2025) Matrix Model of Accuracy in Machining Conical Surfaces on CNC Lathes. Reliability Theory and Applications, V ol. 20, Iss. 7, pp. 393-400.
34. Yusubov N.D., Abbasova H.M. (2020) Models for Machining Accuracy in Multi-Tool Adjustment. International Journal of Automotive and Mechanical Engineering, V ol. 17, No. 3, pp. 8067–8085.
35. Yusubov N.D. (2013) Matrix Models of Processing Accuracy in Multitool Turning. Mechanical Engineering Technology, no.1, pp. 57-63.
36. Yusubov N.D. et. al. (2023) Matrix models of machining errors in multi -tool multi carriage adjustments. International Journal on Technical and Physical Problems of Engineering (IJTPE), 15(3), pp. 309–315.
37. Yusubov N.D., Abbasova H.M. (2017) The fundamental principles of the mechanism for forming the scatter field of dimensions in dual -support setups. Proceedings of the 2nd International Scientific and Technical Conference "Problems of Metallurgy and Materials Science", pp. 375-380.
38. Yusubov N.D., Abbasova H.M. (2018) Generalized Segmented -Matrix Model of Multi -Tool Machining Accuracy. Scientific works, No 4, pp. 16-22.
39. Yusubov N., Abbasova H., Dadashov R. (2026) Full factorial model of dimensional distortion in multi -tool dualcarriage setups. Scientia: Collection of Scientific Papers with the Proceedings of the X International Scientific and Theoretical Conference “Current Issues of Science, Prospects and Challenges”, Sydney, Australia, pp. 127–136.
40. Yusubov N.D. (2013) Fundamentals of matrix theory of accuracy of multi-tool turning. (Principles and structure of the theory, design and management of multi -tool machining processes). A V Akademikerverlag Gmbh & Co. KG / LAP LAMBERT Academic Publishing, Saarbrücken.
41. Yusubov N.D. (2008) Matrix full -factor model of dimensional distortions in multi -tool setups. Mechanical Engineering Technology, No 1, pp. 36-39.
42. Yusubov N.D., Abbasova H.M. (2019) Full Factorial Models of Dimensional Accuracy of Multi Tool Machining on Automatic Turning Machines. Bulletin of the South Ural State University. Ser. Mechanical Engineering Industry, vol. 19, no. 1, pp. 56–67.
43. Yusubov N., Abbasova H., Dadashov R. (2025) Matrix Model of Accuracy in Machining Conical Surfaces on CNC Lathes, Reliability Theory and Applications, V ol. 20, Iss. 7, pp. 393-400.
44. Yusubov N.D. (2008) Algorithmization of analytical model of dimensions stray field, executed in multi -tool multi-carriage adjustments. Bulletin of Mechanical Engineering, No 2, pp. 54-56.
45. Yusubov N.D. (2009) Matrix models of the accuracy in multitool two -support setup. Russian Engineering Research, 29(3), pp. 268–271. DOI: 10.3103/S1068798X09030125
46. Abdullaev, A. I., Najafov, A. M., Ahmedov, B. B., Chelebi, I. G.,Abdullaev, A. A., Hajiyev, A. B. (2022). Eurasian patent for in -vention No. 039650. Mechanical drive of sucker -rod pumping unit.13. Abdullaev, A. I., Najafov, A. M., Ahmedov, B. B., Chelebi, I. G.,Abdullaev, A. A., Hajiyev, A. B. (2021). Azerbaijan Intellec-tual Property Agency patent for invention No. a2019 0162.Mechanical drive of sucker-rod pumping unit.
47. Tukhtaboev, N. Saidmakhamadov, N. Yusubov, N. Rasulov, O. Toshpulatov. Improvement Of The Technology For Producing High -Quality Castings Through Out -Of-Furnace Treatment Of Molten Metal. American Innovator: Journal of Emerging Technologies and Research, ISSN: 3071-186X, V ol. 01, Issue 02, March, 2026. (in USA).
48. Nadirov, U.M., Rasulov, N. M. (2019) Analysis and mathematical model of the circumferential accuracy of the groove cut on the surface of rotation. Journal of the Brazilian Society of Mechanical Sciences and Engineering, 9(41), pp. 481–492.
49. N.M. Rasulov, E.T. Shabiyev. (2016) "Instability of Cutting Depth when Grinding Gearwheel Teeth by Copying" Proceedings of Higher Educational institutions. Machine Building, no. 12 (681), pp. 79 -86. ISSN 0536 -1044. N.M. Rasulov, E.T. Shabiyev. (2017) Incre asing the Efficiency of Gear Teeth Grinding by Copying Using Management of the Cutting Depth. Proceedings of Higher Educational institutions. Machine Building, no. 2 (683), pp. 90-97. ISSN 0536-1044.
50. Rasulov N.M., Shabiyev E.T. (2014) Depth of Cut in Grinding Teeth by Copying. “Advanced Technologies and Systems of Mechanical Engineering” International Collection of Scientific Papers. Don. GTU, Donetsk, No. 2 (48) pp. 76-81.
51. Rasulov N.M., Mammadov A.S., Shabiyev E.T. (2016) Change in the cutting depth of gear teeth during grinding by the copying method under stable conditions. Eastern European Scientific Journal, 11(2), 61 –66.
52. Yusubov N.D., Movlazade V.Z., Abbasova H.M. (2022) Accuracy Models of Machining in Multi -Tool Adjustments. Proceedings of the 8th International Conference on Control and Optimization with Industrial Applications (COIA 2022), V ol. 2, pp. 477–479.
53. Yusubov N.D., Abbasova H.M. (2018) The basic principles of the mechanism for the formation of scattering areas in the two-carriage adjustments. Machine science, vol. 7, No1, pp. 57-61.
54. Simon, S., Yusubov, N., & Amirli, S. (2024). Formation of geometric parameters of the surfaces of cylindrical parts during waterjet cutting. Advances in Science and Technology, 148, 59–64.
55. Rasulov, N.M., Nadirov, U.M., Alekberov, M.Z. (2020) Generalized Assessment of Machined Surfaces Quality. Russ. Engin. Res. 40, 822-825. https://link.springer.com/article/10.3103/S1068798X20100202
56. N. Rasulov, et. al. (2025) "Issues of Increasing the Efficiency of Cylindrical Gear Grinding Using Copying Methods Through a Systematic Approach" Reliability: Theory & Applications, vol. 20, no. SI 7 (83), pp. https://doi.org/10.24412/1932-2321-2025-783-259-266
57. Nariman Rasulov, Mursal Alakbarov. Systematic Investigation of the Contact Surface Relationships between the Workpiece and Tool in Gear Grinding by the Copying Method // International scientific and scientific-technical conference on "In Digital Machining: Automation, Intellectual Systems, Trends, Problems and Solutions", Tashkent, Uzbekistan, -3 June, -2026, V ol. 1, No 2, – pp. 471-472.
58. Rasulov N.M., Mammadov A.S., Alakbarov M.Z. (2024) Indirect improvement of the efficiency of gear grinding by the copying method based on system analysis. Azerbaijan State Maritime Academy, Scientific Works, No. 2, pp. 70–76.
59. Rasulov N.M., Alakbarov M.Z. (2025) Direct improvement of the efficiency of gear grinding by the copying method based on system analysis. Azerbaijan Technical University, Scientific Works, No. 1, 2025, pp. 67–72.
60. Nariman Rasulov, Mursal Alakbarov, Nosir Saidmakhamadov. Indirect improvement of gear grinding efficiency based on a systematic approach through material quality control. International Scientific and Technical Conference on “Modern Technical Education: Inn ovative Approaches and Training of Intellectual Engineers” NamDTU 29-30 iyun, 2026, pp. 23-28.
61. N. M. Rasulov, et. al. (2022) Improving the efficiency of thread rolling with management of technological connections // SOCAR Proceedings. Special Iss. 1 011 -015. DOI: 10.5510/OGP2022SI100694. https://proceedings.socar.az/en/journal/85
62. N.M. Rasulov, U.M. Nadirov, M. Z. Alakbarov. (2022) Improving the efficiency of grinding teeth by copying with the control of dynamic technological connections. / SOCAR Proceedings. Special Issue 1 029 -035. DOI: 10.5510/OGP2022SI100697. https://proceedings.socar.az/en/journal/85
63. Nariman Rasulov, et. al. (2024) Increasing the Efficiency of Forming Complex Rotating Surfaces with the Controlling of Technological Connections // Key Engineering Materials. – Trans Tech Publications Ltd, Switzerland. – ISSN: 1662 -9795. – V ol. 979. – pp. 55–62. – DOI: 10.4028/p -t6EtmD. – 23574. https://doi:10.4028/p-jc7OVU
64. Rasulov N.M., Alekberov M.Z., Nadirov U.M. (2021) More Efficient Copy Grinding of Complex Surface. Russian Engineering Research, V ol. 41, pp. 829–831. https://link.springer.com/article/10.3103/S1068798X21090227
65. Rasulov N.M., et. al. (2021) Increasing the efficiency of grinding shaped surfaces by the copying method. Azerbaijan National Academy of Sciences, Scientific Proceedings, V ol. 23, No. 3, pp. 22–31.
66. Nariman Rasulov, Mursal Alakbarov, Elgun Shabiyev / Issues of increasing the efficiency of gear grinding by copying method // VI International Scientific and Theoretical Conference «Scientific review of the actual events, achievements and problems» Berlin, Germany. March 27, –2026. – pp. 103-112.
67. Nariman Rasulov, et. al. (2024) The issues of improving surface quality and productivity in the ginding with copy method of shaped and tooth surfaces. IntechOpen - Open Access books “Advances in Materials Processing - Recent Trends and Applications in Weld ing, Grinding, and Surface Treatment Processes”, pp. 103 -122, London, DOI: 10.5772/intechopen.1004849. https://www.intechopen.com/chapters/1180557
68. Rasulov N.M. (2003) Management of technological dimensional relationships and the efficiency of processing machine parts. Engineering, No. 3, pp. 18-22.
69. Rasulov N.M. et. al. (2020) Advanced Technology for Machining Tapered Threads of Pipe Coupling. American Journal of Engineering and Technology Management. V ol. 5, Issue 2, pp. 35-40.
70. Rasulov N.M., Nadirov U.M. (2024) Ensuring the quality of taper pipe threads rolled in pipes with the control of kinematic technological connections. Russian Engineering Research, vol. 44, no. 1, pp. 20 –22.
71. Dadashov R.Y., Y usubov N.D., Abbasova H.M. (2023) Modeli sil rezaniya pri mekhanicheskoy obrabotke na sovremennykh stankakh tokarnoy gruppy (Models of Cutting Forces During Mechanical Machining on Modern Machines of Turning Group). Proceedings of the All-Russian Forum of Y oung Researchers – 2023, pp. 236–246.
72. Yusubov N., Abbasova H. (2023) Model of Machining Process Control on Multi -Tool Single -Carriage Adjustments. Machine Science, V ol. 1, No. 1, pp. 22–27.
73. Yusubov N., Abbasova, H. (2024) Models of Cutting Forces in The Matrix Theory of Multitool Machining Accuracy. Key Engineering Materials, 979, pp. 27–38. DOI: 10.4028/p-bW48Sb
74. Yusubov N., Abbasova H., Dadashov R. (2023). Theoretical basis for the development of an algorithmic unified complex of mathematical models of cutting forces. Machine science, N1, pp. 55 -60.
75. Shipulin, L.V., Y usubov, N.D., Frolov, A.A. (2023). Study of the Microrelief Obtained During Single Abrasive Grain Cutting. In: Radionov, A.A., Gasiyarov, V.R. (eds) Proceedings of the 8th International Conference on Industrial Engineering. ICIE 2022. Lecture Notes in Mechanical Engineering. Springer, Cham.
76. Abbasov, V., Amirov, F., & Karimov, A. (2025). Wear properties of camshaft cams and improvement of their wear resistance. Reliability: Theory & Applications, 20(SI 7 (83)), 297-303.
77. Abbasov V., Amirov, F., Karimov, A. (2024, May). Features of the New Design of the Camshaft of Internal Combustion Engines. In International Symposium on Unmanned Systems and The Defense Industry (pp. 282 288). Cham: Springer Nature Switzerland.
78. Nosir S. et al. Development of technology for obtaining quality castings from steel alloys//Eurasian Journal of Engineering and Technology. – 2022. – Т. 5. – С. 135 – 138.
79. Turakhodjaev, N.D., Saidmakhamadov, N.M., Zokirov, R.S., Odilov, F.U., Tashkhodjaeva, K.U.: Analysis of defects in white cast iron. Theoret. Appl. Sci. 6, 675–682 (2020).
80. Turakhodjaev, N., Saidmakhamadov, N., Turakhujaeva, S., Akramov, M., Turakhujaeva, A., Turakhodjaeva, F.: Effect of metal crystallation period on product quality. Theoret. Appl. Sci. 11, 23–31 (2020).
81. Nariman Rasulov, Mursal Alakbarov. Issues of Ensuring the Efficiency of Gear Grinding by the Copying Method // International scientific and scientific-technical conference on "In Digital Machining: Automation, Intellectual Systems, Trends, Problems and Solutions", Tashkent, Uzbekistan, -3 June, -2026, -V ol. 1, No 2, – pp. 76-77.
82. N.M. Rasulov, M.Z. Alakbarov, E.T. Shabiyev. (2019) Linkages Between Cutting Depth and Prison grinding The Teeth Of Gear Wheels By Method Of Copying// Modern methods and technologies for creating and processing materials: collection of scientific papers. - Minsk: Physical -Technical Institute of the National Academy of Sciences of Belarus. - P. 280-286.
83. Rasulov, N.M., Nadirov, U.M., Alekberov, M.Z. (2020) Generalized Assessment of Machined Surfaces Quality. Russ. Engin. Res. 40, 822-825. https://link.springer.com/article/10.3103/S1068798X20100202
84. Rasulov, N.M. Formation of allowance when the grinding the teeth of gears by copying method / N.M. Rasulov, A.S. Mammadov, M.Z.Alakbarov // International Journal of Engineering Sciences &Research Technologi, – 2018, №7(10), – pp. 1-5.
85. Rasulov N.M., Alakbarov M.Z. (2020) Mathematical models of the components of machining allowance for grinding the teeth of cylindrical gears, Azerbaijan Technical University, Mechanical Engineering, ISSN 2227 - 6912, No. 1, pp. 47–52. https://msj.aztu.edu.az/