Determination of Forces Acting on a Helical Gear Transmission with an Elastic Element

Anvar Djuraev; Dilshod Abduvakhobov; Davron Khabibullaev

doi:doi:10.11648/j.ajma.20251202.12

Research Article |

| Peer-Reviewed

Determination of Forces Acting on a Helical Gear Transmission with an Elastic Element

Anvar Djuraev

, Dilshod Abduvakhobov

, Davron Khabibullaev^*

Published in American Journal of Mechanics and Applications (Volume 12, Issue 2)

Received: 18 April 2025 Accepted: 27 April 2025 Published: 29 May 2025

Views: Downloads:

Download PDF

Share This Article

Twitter
Linked In
Facebook

Abstract

This paper presents a theoretical analysis of the forces acting on a helical gear transmission with an elastic element. The research investigates the effects of elastic deformation on the load distribution within the gear system, focusing on the influence of the elastic component on axial, radial, and tangential forces. The study employs mathematical models that account for the complex interactions between the helical gears and the elastic element, aiming to optimize the force transmission and enhance the system’s efficiency. Key findings reveal that introducing an elastic element in the helical gear transmission can significantly reduce impact loads, leading to improved durability and operational lifespan of the system. Additionally, the research identifies optimal ranges for the stiffness coefficient of the elastic component, ensuring effective load amortization and minimizing the risk of excessive wear or failure. The proposed model provides a comprehensive understanding of how elastic deformation influences the performance of helical gear systems, particularly under varying loads and operational conditions. The results presented offer valuable insights for the design and optimization of gear mechanisms in engineering applications where durability and efficiency are critical. These findings contribute to the broader field of mechanical transmission systems, particularly in applications where gear longevity and reliability are essential.

Published in	American Journal of Mechanics and Applications (Volume 12, Issue 2)
DOI	10.11648/j.ajma.20251202.12
Page(s)	33-39
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2025. Published by Science Publishing Group

Keywords

Helical Gear Transmission, Elastic Element, Force Analysis, Torque Distribution, Stiffness Coefficient, Deformation, Gear Meshing, Load Reduction, Mechanical Efficiency

1. Introduction

In cylindrical gear transmissions, when a driving gear is subjected to a driving torque M1, the driven gear experiences a resisting torque. In general, the interaction between the gear teeth generates normal and frictional forces. However, in helical cylindrical gear transmissions, the resultant interaction force is inclined and consists of three components: axial force along the shaft, radial force perpendicular to the shaft, and tangential force responsible for rotation

[1]

2. Experimental Procedures

The schematic diagram of the acting forces is shown in Figure 1. In general, when the effect of elastic elements is not considered, the total force Fn acting on the helical tooth is divided into three components.

[2, 3]:

Download: Download full-size image

Figure 1. Schematic representation of the forces acting on the helical tooth in the proposed helical cylindrical gear transmission with an elastic element.

Tangential force,

F_{t} = \frac{2 M_{1}}{d_{1}}

;(1)

Axial force

F_{x} = F_{t} ∙ \tan β

;(2)

Radial force perpendicular to the shaft,

F_{r} = F_{t}^{'} ∙ \tan α_{ω} = F_{t} ∙ \frac{\tan α_{ω}}{\cos β};

(3)

Total force,

F_{n} = \frac{F_{t}^{'}}{\cos α_{ω}} = \frac{F_{t}}{\cos α_{ω} ∙ \cos β}

(4)

Here, M₁ is the driving torque in the helical gear, d₁ is the pitch circle diameter of the driving helical gear, β is the helix angle of the teeth, and αω is the transmission angle.

The proposed composite elastic element gears, when engaged, partially absorb the force due to the deformation of the elastic element. Although the overall deformation occurs, the deformations in the direction of each force component partially dampen these forces. Therefore, we determine the methods for calculating forces considering the deformation and amortization of the elastic element in each force direction. Figure 2 presents the deformation scheme of the elastic element in the composite helical gear under the influence of the torsional moment M₁

[11, 12]

Download: Download full-size image

Figure 2. Deformation scheme of the elastic element in the composite helical gear under the influence of the torsional moment M₁.

According to the analysis of this scheme, under the influence of the torsional moment, the elastic element deforms by a value of ∆φ in the rotational direction of the gear. That is, part of the torsional moment is absorbed by the deformation. Therefore, the generated rotational force in the engagement process of the helical gear with an elastic element can be determined using the following expression

[13]

F_{t 1} = \frac{2}{d_{1}} ∙ (M_{1} - C_{a 1} ∙ ∆ φ_{1})

(5)

here, C_a1 is the rotational stiffness coefficient of the elastic element, and ∆φ₁ is the angular deformation of the elastic element.

Similarly, during the operation of helical gears with elastic elements, the forces acting along the gear shafts cause their elastic elements to deform both axially and radially.

Download: Download full-size image

Figure 3. Deformation schemes of the elastic element under the influence of axial (a) and radial (b) forces in helical gear engagement.

During engagement, the flexible elements partially absorb the overall force due to their deformation, distributing it into axial and radial components. That is, the impact of the forces is partially reduced.

Taking into account the given equations (3), (4), and (5), we can write the following:

Axial force component,

F_{x 1} = (F_{t 1} - C_{a 1} ∙ ∆ φ_{1}) ∙ \tan β - C_{x 1} ∙ ∆ X_{1}

(6)

radial force component perpendicular to the axis,

F_{r 1} = (F_{t 1} - C_{a 1} ∙ ∆ φ_{1}) ∙ \frac{\tan α_{ω}}{\cos β} - C_{r 1} ∙ ∆ r_{1}

(7)

and the total acting force.

F_{n 1} = \frac{2 ∙ (M_{1} - C_{a 1} ∙ ∆ φ_{1})}{d_{1} ∙ \cos α_{ω} ∙ \cos β}

(8)

here, C_x1 and C_r1 are the stiffness coefficients of the elastic element in the axial and radial directions, respectively, while ∆X₁ and ∆r₁ represent the deformation values of the elastic element in the X₁ and r₁ directions

[14, 15]

The given expressions (5), (6), (7), and (8) are derived for the helical gear with a flexible element in the driving transmission. Correspondingly, for the driven gear, the following expressions are applicable:

F_{t 2} = \frac{2}{d_{2}} ∙ (M_{2} - C_{a 2} ∙ ∆ φ_{2})

;

F_{x 2} = (F_{t 2} - C_{a 2} ∙ ∆ φ_{2}) ∙ \tan β - C_{x 2} ∙ ∆ X_{2}

;

F_{r 2} = (F_{t 2} - C_{a 2} ∙ ∆ φ_{2}) ∙ \frac{\tan α_{ω}}{\cos β} - C_{r 2} ∙ ∆ r_{2}

;

F_{n 2} = \frac{2 ∙ (M_{2} - C_{a 2} ∙ ∆ φ_{2})}{d_{2} ∙ \cos α_{ω} ∙ \cos β}

(9)

here, C_a2, C_x2, and C_r2 are the stiffness coefficients of the elastic element in the driven helical gear for different force directions; M₂ and d₂ represent the torsional moment and pitch circle diameter of the driven helical gear, respectively; and ∆φ₂, ∆X₂, and ∆r₂ correspond to the deformation values of the elastic element in the helical gear for torsional, axial, and radial directions

[9, 10].

3. Materials and Methods

It is well known that gear transmissions are widely used in technological machines. One of their main drawbacks is the wear and breakage of the teeth. The primary reason for this is the low number of paired teeth engaged at the same time. This phenomenon is expressed through the contact ratio coefficient.

[7, 8];

ε_{α} = \frac{L_{AB}}{t}

(10)

here, L_AB - line of action, t - pitch.

Typically, the contact ratio coefficient should have a value of ℰα ≥ 1.0. In spur gear transmissions, ℰα can range between (1.0÷1.25). Due to this, the force acting on each tooth during meshing is relatively high. To increase ℰα and reduce the acting force, helical or herringbone gear transmissions are used. According to

[9]

, in a helical gear transmission, the contact ratio coefficient is:

ε_{β} = \frac{b_{ω} ∙ \tan β}{t_{ω}}

(11)

here, bω- represents the gear width, and

t_ω - denotes the line of action or axial pitch.

For the recommended helical gear transmission with an elastic element, a formula has been derived to determine the transmission contact ratio coefficient, considering the deformation of the elastic element:

ε_{α}^{'} = [1.88 - 3.2 ∙ (\frac{1}{z_{1}} + \frac{1}{z_{2}})] ∙ \cos β + ∆ ε_{α}

;(12)

here, Z₁ and Z₂ represent the number of teeth on the gears, while ∆εα is the coefficient accounting for the deformation of the elastic elements in the gears. The values 1.88 and 3.2 are derived from the geometric dimension limits of the gears, as stated in

[4].

Considering the length of the contact line of the meshing teeth (11):

l_{k} = \frac{b_{α}}{\cos β} ∙ ε_{α}

(13)

Therefore, the bending stress calculation for helical gears with elastic elements is determined using the following recommended formula:

Ϭ_{e} = (F_{t 1} ∙ K_{F} ∙ \cos β) ∙ \frac{K_{Fα} ∙ K_{Fβ} ∙ K_{FV}}{K_{C} ∙ ε_{α}^{'} ∙ m ∙ b_{α}} \leq {[Ϭ}_{e}]

;(14)

here: K_Fα - axial contact ratio coefficient; K_F - force variation coefficient; K_Fβ- inclination angle variation coefficient; K_FV - velocity variation coefficient; K_Fα - coefficient representing the accuracy of the transmission; K_c - coefficient considering the elastic element; [Ϭe] - allowable bending stress.

4. Results

The obtained expressions (5), (6), and (7) were used to construct graphs showing the relationship between the variation laws of the forces generated during meshing and the changes in the stiffness coefficients of the elastic element in the corresponding direction, taking into account the numerical values of the parameters.

[5].

Figure 5 presents graphs illustrating the relationship between the torque generated during meshing in a helical gear transmission with an elastic element and the variation of the rotational stiffness of the elastic element.

Based on the analysis of the constructed graphs, it is observed that as the rotational stiffness of the elastic element increases from 2.45 × 10² Nm/rad to 5.0 × 10² Nm/rad, the meshing torque Ft decreases linearly. Specifically, when the gear diameter is d = 125 × 10⁻³ m, Ft decreases from 2.32 × 10 N to 1.53 × 10 N.

[6].

1- d=100 mm; 2- d=125 mm; 3- d=150 mm

Download: Download full-size image

Figure 4. Graphs of the relationship between the torque generated during meshing in a helical gear transmission with an elastic element and the variation of the rotational stiffness of the elastic element.

If the pitch circle diameters are d₁ = 150 × 10⁻³ m, the meshing torque values decrease linearly from 1.74 × 10 N to 1.25 × 10 N (Figure 5).

Thus, to maintain a higher torque, it is advisable to select the rotational stiffness coefficient of the composite gear in the range of (300–350) Nm/rad. In this case, the resistance moments on the gear shafts and their rotational frequencies should be matched with appropriate Ca values. Specifically, for Mq = 100 Nm and na = 1500 rpm, it is recommended that

Ca = (600–700) Nm/rad

[7].

Figure 6 presents graphs illustrating the relationship between the variation of the axial force in the meshing of a helical gear with an elastic element and the linear stiffness coefficient of the elastic element in the radial direction.

According to the analysis, as the axial stiffness coefficient of the elastic element increases from 1.25 × 10⁴ N/m to 2.5 × 10⁴ N/m, the axial force Fx decreases linearly from 5.91 × 10 N to 3.05 × 10 N when β = 10°. This occurs because an increase in stiffness reduces deformation.

Similarly, when the helix angle decreases to 9.0°, the axial force further decreases to 3.82 × 10 N.

1-β=10˚; 2-β=7,0˚; 3-β=4,0˚

Download: Download full-size image

Figure 5. Graphs showing the dependence of the axial force variation in the meshing of a helical gear with an elastic element on the linear stiffness coefficient of the elastic element in the radial direction.

To minimize the values of the axial forces between the gears as much as possible, it is recommended to select the axial stiffness coefficient of the rubber bushing in the range of (2.2–2.8) × 10⁴ N/m.

1-β=10˚; 2-β=7,0˚; 3-β=4,0˚

Download: Download full-size image

Figure 6. Graphs of the variation of the radial force generated during the meshing of teeth in a helical gear transmission depending on the stiffness coefficient of the compliant element in the same direction.

Figure 6 Graphs showing the dependence of the variation of the radial force generated in the meshing of a helical gear with an elastic element on the stiffness coefficient of the elastic element in the same direction.

Analysis of the constructed graphs shows that when the stiffness coefficient of the elastic element in the direction perpendicular to the gear axis increases from 1.24 × 10⁴ N/m to 2.5 × 10⁴ N/m, and the helix angle is β = 10°, the radial force decreases linearly from 6.48 × 10 N to 4.18 × 10 N. However, when β = 4.0°, the Fa values decrease from 3.34 × 10 N to 1.32 × 10 N.

Thus, to reduce the reaction forces in the bearings of the gear shafts, it is advisable to select the stiffness coefficient of the damping rubber bushing in this direction within the range of (2.5–3.0) × 10⁴ N/m.

5. Conclusions

It should be noted that in helical gears, when truncated conical rubber bushings are used as compliant elements, the forces are sufficiently damped due to their deformation in the corresponding directions. This increases the contact ratio. Additionally, considering the damping of forces, it becomes possible to reduce the permissible stress in bending and compression calculations during meshing by (7.0–9.0)%. As a result, the service life of the gear mechanism is extended.

Abbreviations

F_t	Tangential Force
F_x	Axial Force
F_r	Radial Force
F_n	Total Force
d₁	Pitch Circle Diameter of the Driving Helical Gear
β	Helix Angle of the Teeth
α_ω	Transmission Angle
C_a1	Rotational Stiffness Coefficient of the Elastic Element (for the Driving Gear)
∆φ₁	Angular Deformation of the Elastic Element (for the Driving Gear)
C_x1	Stiffness Coefficient of the Elastic Element in the Axial Direction (for the Driving Gear)
∆X₁	Deformation Value of the Elastic Element in the X₁ Direction (for the Driving Gear)
C_r1	Stiffness Coefficient of the Elastic Element in the Radial Direction (for the Driving Gear)
∆r₁	Deformation Value of the Elastic Element in the r₁ Direction (for the Driving Gear)
F_t1	Tangential Force with Elastic Element (for the Driving Gear)
F_x1	Axial Force with Elastic Element (for the Driving Gear)
F_r1	Radial Force with Elastic Element (for the Driving Gear)
F_n1	Total Force with Elastic Element (for the Driving Gear)
M₂	Torsional Moment for the Driven Gear
d₂	Pitch Circle Diameter of the Driven Helical Gear
C_a2	Rotational Stiffness Coefficient of the Elastic Element (for the Driven Gear)
∆φ₂	Angular Deformation of the Elastic Element (for the Driven Gear)
C_x2	Stiffness Coefficient of the Elastic Element in the Axial Direction (for the Driven Gear)
∆X₂	Deformation Value of the Elastic Element in the X₂ Direction (for the Driven Gear)
Cr₂	Stiffness Coefficient of the Elastic Element in the Radial Direction (for the Driven Gear)
∆r₂	Deformation Value of the Elastic Element in the r₂ Direction (for the Driven Gear)
F_t2	Tangential Force with Elastic Element (for the Driven Gear)
F_x2	Axial Force with Elastic Element (for the Driven Gear)
F_r2	Radial Force with Elastic Element (for the Driven Gear)
F_n2	Total Force With Elastic Element (for the Driven Gear)
ℰ_α	Contact Ratio Coefficient (for Spur Gears)
ℰ_β	Contact Ratio Coefficient (for Helical Gears)
b_ω	Gear Width
t_ω	Line of Action or Axial Pitch
ℰα'	Transmission Contact Ratio Coefficient with Elastic Element
Z₁	Number of Teeth on the Driving Gear
Z₂	Number of Teeth on the Driven Gear
∆ε_α	Coefficient Accounting for the Deformation of the Elastic Elements
l_k	Length of the Contact Line of Meshing Teeth
Ϭe	Bending Stress
K_F	Force Variation Coefficient
K_Fα	Axial Contact Ratio Coefficient
K_Fβ	Inclination Angle Variation Coefficient
K_FV	Velocity Variation Coefficient
K_C	Coefficient Considering the Elastic Element

Author Contributions

Anvar Djuraev: Conceptualization, Data curation, Formal Analysis, Funding acquisition, Methodology, Resources, Software, Validation, Writing – original draft, Writing – review & editing

Dilshod Abduvakhobov: Conceptualization, Supervision, Visualization, Writing – review & editing

Davron Khabibullaev: Conceptualization, Data curation, Formal Analysis, Funding acquisition, Investigation, Methodology, Resources, Software, Validation, Writing – original draft, Writing – review & editing

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	I I Artobolevsky Theory of mechanisms and machines. Ed. Science, M.: 1988, 639 p.
[2]	Djuraev A Dj, and others. Theory of machines and mechanisms. Publishing house named after Gafur Gulam, Toshken-2004.
[3]	Rivin E I, Dynamics of machine tool drives, Mechanical Engineering, 1966., 204 p.
[4]	J Kh Beknazarov, Sh Sh Kenjabayev, Development of an Effective Resourceving-Saving Desing and Methods for Calculating the Parameters of Gears with Compound Wheels 2019.
[5]	Sh Kenzhabaev, Development of structural schemes and scientific basis for analysis of lever mechanisms with elastic elements and flexible links. Drive links of technological machines Namangan 2019, 268.
[6]	Abduvakhobov, D. A., Khabibullaev, D. K., Makhsudov, A. P., Mukhammajonov, K. O., & Mirzaabdullayev, M. M. (2022). A New Method for Determining the Stability Indicators of the Depth of Soil Tillage. Scientific and Technical Progress as a Mechanism for the Development of Modern Society, 81-84.
[7]	Dj, D. A., Abduvakhobov, D. A., Khabibullaev, D. H., & Gofurjanov, I. I. (2023). Helical Cylindrical Gear with Elastic Elements. Doctrines, Schools, and Concepts of Sustainable Development of Science in Modern Conditions, 163.
[8]	Djuraev, A. D., Abduvakhobov, D. A., & Khabibullaev, D. H. (2023). Gear Transmission with Elastic Elements. Mechanics and Technology, 2(11), 32-35.
[9]	Djuraev, A. D., Abduvakhobov, D. A., Khabibullaev, D. H., & Ulmasov, S. A. (2023, December). Calculation of the Deformation Values of the Ammortizer in the Compound Angle Gear Transmission. IOP Conference Series: Earth and Environmental Science (Vol. 1284, No. 1, p. 012033). IOP Publishing. https://doi.org/10.1088/1755-1315/1284/1/012033
[10]	Helical Cylindrical Gear Transmission. Utility Model Patent of the Republic of Uzbekistan, Ministry of Justice. Patent No. FAP 2420.
[11]	Djuraev A., Yuuldoshev K., Teshaboyev O. Analysis of the Dynamics of a Single-Mass Machine Unit of a Screw Conveyor. Machine Engineering Scientific Journal, Andijan. 2022, pp. 277-282.
[12]	Mamasoliyeva, S. X., & Abduvahobov, D. A. (2021, March). Analysis Of Reduced Vibration In Geared Mechanisms. In Science in modern society: regularities and development trends: Collection of articles following the results of the International Scientific and Practical Conference (p. 49).
[13]	Abdurakhmonov, S., Abdurahmanov, I., Murodova, D., Pardaboyev, A., Mirjalolov, N., & Djurayev, A. (2020). Development of demographic mapping method based on GIS technologies. ИнтерКарто. ИнтерГИС, 26(1), 319-328. https://doi.org/10.35595/2414-9179-2020-1-26-319-328
[14]	Bolat, B., & Bogoclu, M. E. (2012). Increasing of screw conveyor capacity. Journal of Trends in The Development of Machinery and Associated Technology, 16(1), 207-210.
[15]	Djurayev, A., Davidbayev, B. N., & Jurayev, N. N. (2022). Scientific basis of the design and parameter calculation of the construction and parameters of a double-inlet and wavy surface resource controller screw conveyor for spillable materials. Global Book Publishing Services, 1-113.

Cite This Article

Plain Text BibTeX RIS

APA Style

Djuraev, A., Abduvakhobov, D., Khabibullaev, D. (2025). Determination of Forces Acting on a Helical Gear Transmission with an Elastic Element. American Journal of Mechanics and Applications, 12(2), 33-39. https://doi.org/10.11648/j.ajma.20251202.12

Copy | Download

ACS Style

Djuraev, A.; Abduvakhobov, D.; Khabibullaev, D. Determination of Forces Acting on a Helical Gear Transmission with an Elastic Element. Am. J. Mech. Appl. 2025, 12(2), 33-39. doi: 10.11648/j.ajma.20251202.12

Copy | Download

AMA Style

Djuraev A, Abduvakhobov D, Khabibullaev D. Determination of Forces Acting on a Helical Gear Transmission with an Elastic Element. Am J Mech Appl. 2025;12(2):33-39. doi: 10.11648/j.ajma.20251202.12

Copy | Download

@article{10.11648/j.ajma.20251202.12,
  author = {Anvar Djuraev and Dilshod Abduvakhobov and Davron Khabibullaev},
  title = {Determination of Forces Acting on a Helical Gear Transmission with an Elastic Element
},
  journal = {American Journal of Mechanics and Applications},
  volume = {12},
  number = {2},
  pages = {33-39},
  doi = {10.11648/j.ajma.20251202.12},
  url = {https://doi.org/10.11648/j.ajma.20251202.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajma.20251202.12},
  abstract = {This paper presents a theoretical analysis of the forces acting on a helical gear transmission with an elastic element. The research investigates the effects of elastic deformation on the load distribution within the gear system, focusing on the influence of the elastic component on axial, radial, and tangential forces. The study employs mathematical models that account for the complex interactions between the helical gears and the elastic element, aiming to optimize the force transmission and enhance the system’s efficiency. Key findings reveal that introducing an elastic element in the helical gear transmission can significantly reduce impact loads, leading to improved durability and operational lifespan of the system. Additionally, the research identifies optimal ranges for the stiffness coefficient of the elastic component, ensuring effective load amortization and minimizing the risk of excessive wear or failure. The proposed model provides a comprehensive understanding of how elastic deformation influences the performance of helical gear systems, particularly under varying loads and operational conditions. The results presented offer valuable insights for the design and optimization of gear mechanisms in engineering applications where durability and efficiency are critical. These findings contribute to the broader field of mechanical transmission systems, particularly in applications where gear longevity and reliability are essential.
},
 year = {2025}
}

Copy | Download

TY  - JOUR
T1  - Determination of Forces Acting on a Helical Gear Transmission with an Elastic Element

AU  - Anvar Djuraev
AU  - Dilshod Abduvakhobov
AU  - Davron Khabibullaev
Y1  - 2025/05/29
PY  - 2025
N1  - https://doi.org/10.11648/j.ajma.20251202.12
DO  - 10.11648/j.ajma.20251202.12
T2  - American Journal of Mechanics and Applications
JF  - American Journal of Mechanics and Applications
JO  - American Journal of Mechanics and Applications
SP  - 33
EP  - 39
PB  - Science Publishing Group
SN  - 2376-6131
UR  - https://doi.org/10.11648/j.ajma.20251202.12
AB  - This paper presents a theoretical analysis of the forces acting on a helical gear transmission with an elastic element. The research investigates the effects of elastic deformation on the load distribution within the gear system, focusing on the influence of the elastic component on axial, radial, and tangential forces. The study employs mathematical models that account for the complex interactions between the helical gears and the elastic element, aiming to optimize the force transmission and enhance the system’s efficiency. Key findings reveal that introducing an elastic element in the helical gear transmission can significantly reduce impact loads, leading to improved durability and operational lifespan of the system. Additionally, the research identifies optimal ranges for the stiffness coefficient of the elastic component, ensuring effective load amortization and minimizing the risk of excessive wear or failure. The proposed model provides a comprehensive understanding of how elastic deformation influences the performance of helical gear systems, particularly under varying loads and operational conditions. The results presented offer valuable insights for the design and optimization of gear mechanisms in engineering applications where durability and efficiency are critical. These findings contribute to the broader field of mechanical transmission systems, particularly in applications where gear longevity and reliability are essential.

VL  - 12
IS  - 2
ER  -

Copy | Download

Author Information

Anvar Djuraev

The Department of "Labor Protection and Ecology, Tashkent Institute of Textile and Light Industry, Tashkent, Uzbekistan

Biography: Anvar Djuraev is a highly respected Doctor of Technical Sciences and a professor, renowned for his extensive contributions to the field of machine details. He has authored numerous articles and books, which are considered fundamental references in the industry. His expertise and profound knowledge have earned him recognition both locally and internationally. Currently, he serves as a department professor at the prestigious Tashkent Institute of Textile and Light Industry, where he imparts his valuable knowledge to the next generation of engineers. Throughout his distinguished career, Professor Djuraev has mentored numerous students, many of whom have gone on to achieve great success in their professional fields. His dedication to research, education, and the advancement of machine design has made him a key figure in his field, with a lasting impact on both academia and industry.

Research Fields: heory of Machines and Mechanisms, Mechanical Engineering, Elastic Elements in Gear Transmissions, Dynamics and Kinematics of Technological Machines, Vibration Analysis in Gear Systems, Reliability and Efficiency of Machine Components.

Contact Email

http://orcid.org/0009-0005-0231-1966
Dilshod Abduvakhobov

The Department of Mechanics, Namangan Engineering and Construction Institute, Namangan, Uzbekistan

Biography: Dilshod Abduvakhidovich is a Doctor of Philosophy (PhD) in Technical Sciences and an Associate Professor at the Department of Mechanics of Namangan Engineering-Construction Institute. His scientific activity is focused on the fields of agricultural machinery and mechanics, and he is the author of numerous research papers and publications in these areas. Abduvakhobov's research primarily covers the vibration analysis of agricultural machinery and the enhancement of their operational efficiency. His work has gained international recognition and has been published in reputable databases such as Scopus and Google Scholar. He is the author of 3 Scopus-indexed articles and has received 175 citations on Google Scholar. His h-index is 7, and his i10-index is 4. His significant contributions to science and his dedication to educating and mentoring the younger generation have established him as a leading expert in his field.

Research Fields: Agricultural Machinery, Mechanical Vibrations and Oscillations, Optimization of Soil Tillage Equipment, Vibro-dynamics of Agricultural Machines, Analysis and Improvement of Operational Stability, Application of Elastic Elements in Mechanical Systems.

Contact Email

http://orcid.org/0000-0002-6551-1931
Davron Khabibullaev

The Department of Mechanics, Namangan Engineering and Construction Institute, Namangan, Uzbekistan

Biography: Davron Khabibullaev is a PhD candidate and a junior lecturer at the Department of Mechanics. He is currently working on his doctoral research and contributing to the field through teaching and academic involvement. He graduated Namangan Engi-neering-Construction Institute in 2020, and his Master of Ground vehicles and systems (by mode of transport) from the same institu-tion in 2022. He has participated in multiple international research collaboration projects in recent years.

Research Fields: Helical Gear Transmission with Elastic Elements, Applied Mechanics, Machine Design and Analysis, Dynamic Behavior of Mechanical Systems, Torsional and Axial Vibration Analysis, Structural Optimization in Mechanical Drives.

Contact Email

http://orcid.org/0000-0002-8952-6580

Download PDF

Submit an Article

Plain Text BibTeX RIS

APA Style

Djuraev, A., Abduvakhobov, D., Khabibullaev, D. (2025). Determination of Forces Acting on a Helical Gear Transmission with an Elastic Element. American Journal of Mechanics and Applications, 12(2), 33-39. https://doi.org/10.11648/j.ajma.20251202.12

Copy | Download

ACS Style

Djuraev, A.; Abduvakhobov, D.; Khabibullaev, D. Determination of Forces Acting on a Helical Gear Transmission with an Elastic Element. Am. J. Mech. Appl. 2025, 12(2), 33-39. doi: 10.11648/j.ajma.20251202.12

Copy | Download

AMA Style

Djuraev A, Abduvakhobov D, Khabibullaev D. Determination of Forces Acting on a Helical Gear Transmission with an Elastic Element. Am J Mech Appl. 2025;12(2):33-39. doi: 10.11648/j.ajma.20251202.12

Copy | Download

@article{10.11648/j.ajma.20251202.12,
  author = {Anvar Djuraev and Dilshod Abduvakhobov and Davron Khabibullaev},
  title = {Determination of Forces Acting on a Helical Gear Transmission with an Elastic Element
},
  journal = {American Journal of Mechanics and Applications},
  volume = {12},
  number = {2},
  pages = {33-39},
  doi = {10.11648/j.ajma.20251202.12},
  url = {https://doi.org/10.11648/j.ajma.20251202.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajma.20251202.12},
  abstract = {This paper presents a theoretical analysis of the forces acting on a helical gear transmission with an elastic element. The research investigates the effects of elastic deformation on the load distribution within the gear system, focusing on the influence of the elastic component on axial, radial, and tangential forces. The study employs mathematical models that account for the complex interactions between the helical gears and the elastic element, aiming to optimize the force transmission and enhance the system’s efficiency. Key findings reveal that introducing an elastic element in the helical gear transmission can significantly reduce impact loads, leading to improved durability and operational lifespan of the system. Additionally, the research identifies optimal ranges for the stiffness coefficient of the elastic component, ensuring effective load amortization and minimizing the risk of excessive wear or failure. The proposed model provides a comprehensive understanding of how elastic deformation influences the performance of helical gear systems, particularly under varying loads and operational conditions. The results presented offer valuable insights for the design and optimization of gear mechanisms in engineering applications where durability and efficiency are critical. These findings contribute to the broader field of mechanical transmission systems, particularly in applications where gear longevity and reliability are essential.
},
 year = {2025}
}

Copy | Download

TY  - JOUR
T1  - Determination of Forces Acting on a Helical Gear Transmission with an Elastic Element

AU  - Anvar Djuraev
AU  - Dilshod Abduvakhobov
AU  - Davron Khabibullaev
Y1  - 2025/05/29
PY  - 2025
N1  - https://doi.org/10.11648/j.ajma.20251202.12
DO  - 10.11648/j.ajma.20251202.12
T2  - American Journal of Mechanics and Applications
JF  - American Journal of Mechanics and Applications
JO  - American Journal of Mechanics and Applications
SP  - 33
EP  - 39
PB  - Science Publishing Group
SN  - 2376-6131
UR  - https://doi.org/10.11648/j.ajma.20251202.12
AB  - This paper presents a theoretical analysis of the forces acting on a helical gear transmission with an elastic element. The research investigates the effects of elastic deformation on the load distribution within the gear system, focusing on the influence of the elastic component on axial, radial, and tangential forces. The study employs mathematical models that account for the complex interactions between the helical gears and the elastic element, aiming to optimize the force transmission and enhance the system’s efficiency. Key findings reveal that introducing an elastic element in the helical gear transmission can significantly reduce impact loads, leading to improved durability and operational lifespan of the system. Additionally, the research identifies optimal ranges for the stiffness coefficient of the elastic component, ensuring effective load amortization and minimizing the risk of excessive wear or failure. The proposed model provides a comprehensive understanding of how elastic deformation influences the performance of helical gear systems, particularly under varying loads and operational conditions. The results presented offer valuable insights for the design and optimization of gear mechanisms in engineering applications where durability and efficiency are critical. These findings contribute to the broader field of mechanical transmission systems, particularly in applications where gear longevity and reliability are essential.

VL  - 12
IS  - 2
ER  -

Copy | Download