Automated Geometric and Computer-aided Non-Circular Gear Formation Modeling

Lyashkov, A. A.; Panchuk, K. L.; Khasanova, I A

doi:10.1088/1742-6596/1050/1/012049

Cited by 11 publications

(8 citation statements)

References 7 publications

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“…The formation of congruent noncircular wheels of two symmetrical arcs of the logarithmic spiral is considered in [9]. Paper [10] proposes a geometric model for solving the problem of profiling an uncircular toothed wheel whose centroid consists of interconnected arcs. The same authors in article [11] proposed a fairly simple and accurate procedure for the automated formation of wheel teeth with an elliptical centroid.…”

Section: Literature Review and Problem Statementmentioning

confidence: 99%

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Designing an outer toothed gear whose wheel teeth are outlined by the logarithmic spiral arcs

Pylypaka

Kresan

Volina

et al. 2021

EEJET

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Toothed gears are the most common mechanical gears in machine building, which are characterized by high reliability and durability, a constant transfer number, and which can transmit high torque. During toothed gear operation, the surfaces of the teeth slide, which gives rise to friction forces and wears their working surfaces. To prevent this, the surfaces of the teeth need constant lubrication. This paper considers the design of a gear tooth engagement, which does not have friction between the surfaces of the teeth since they roll over each other without slipping. The profile of the tooth of such a gear is outlined by congruent arcs, symmetrical relative to the line that connects the center of rotation of the toothed wheel with the top of the tooth. These symmetrical curves at the top of the tooth intersect at the predefined angle. In the depressions of the wheel, adjacent teeth also intersect at the same angle. Such a condition can be ensured by a curve that at all its points crosses the radius-vector emanating from the coordinate origin, also at a stable angle equal to half of the given one. This curve is a logarithmic spiral. If the number of teeth of the drive and driven wheels is the same, then their teeth are congruent. Otherwise, the profiles of the teeth would differ but they could be outlined by congruent arcs of the same logarithmic spiral of the same length taken from different areas of the curve. The minimum possible angle at the top of the teeth is straight. At acute angle, the toothed gear operation is impossible. To build gear wheels with a right angle at the top of the tooth, it would suffice to set the number of teeth of the drive and driven wheels. The center-to-center distance is calculated using the derived formula. The transfer number of such a gear is variable but, with an increase in the number of teeth, the range of its change decreases. The algorithm of wheel construction is given.

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Section: Literature Review and Problem Statementmentioning

confidence: 99%

“…Based on the condition that at α=0, the angle φ=−φ о , the expression of the constant c is defined, considering which renders equality (10) to take the following form:…”

Section: Finding Arc Curves Describing the Profile Of The Teethmentioning

confidence: 99%

Designing an outer toothed gear whose wheel teeth are outlined by the logarithmic spiral arcs

Pylypaka

Kresan

Volina

et al. 2021

EEJET

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“…Xu [16] studied the design method of noncircular gear vice, which can design the noncircular gear pitch curve with its conjugate as well as the tooth profile. Lyashkov [17] established an automated model for the geometric design of noncircular gears, using multisegment arcs instead of complex tooth profile curves to shorten the design cycle of noncircular gears. Many researchers have made substantial contributions to the study of design methods for noncircular gears [18][19][20].…”

Section: Introductionmentioning

confidence: 99%

Design of a Noncircular Planetary Gear Mechanism for Hydraulic Motor

Liu

Gong

et al. 2021

Mathematical Problems in Engineering

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Given the design difficulty and poor accuracy of tooth profile of noncircular gear used in noncircular gear hydraulic motor, it is proposed to reduce the design difficulty and improve the design accuracy by using arc-shaped pitch curve instead of noncircular pitch curve with continuously varying curvature. Based on the geometric relationship and transmission relationship of the noncircular planetary gear mechanism, a nonlinear programming model is constructed for the circular arc-shaped pitch curve. By solving the nonlinear programming model, a noncircular planetary gear mechanism with a modulus of m = 1.5 is designed. The noncircular gear mechanism with the arc-shaped pitch curve was machined and installed in a hydraulic motor, and an efficiency comparison experiment was conducted with a high-order elliptical noncircular gear mechanism with a continuously varying curvature. The experiment shows that the efficiency of the two noncircular gear mechanisms is basically the same, and the best speed range is 100–400 rpm. The noncircular planetary gear mechanism with an arc-shaped pitch curve designed in this paper has reasonable structure, correct transmission relationship, and simple design method, which shows that the design method proposed in this paper has a good engineering application value.

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“…Zhang Jian [12] proposed a simple algorithm for designing pitch curves for non-circular gears based on variable gear ratio functions. A A Lyashkov [13] proposed a geometrical model of solution to the task of profiling a non-circular gear, the centroid of which consists of interconnected arcs. D Mundo [14] presented a concept of epicyclical gear train able to generate a variable gear ratio law.…”

Section: Introductionmentioning

confidence: 99%

Study on Design of Non-Circular Gears for Speed Control of the Squid Belly Opening and Gutting Machine (SBOGM)

Jang¹,

Lee²,

Park³

et al. 2021

Applied Sciences

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Non-circular gears can maintain rotational motions of general gears and implement all varying rotational motions of the cam. They adjust the angular velocity of driven gear according to operating conditions and make precise changes in angular motion. The design of non-circular gears has not been sufficiently studied because of their particularity and complex design methods unlike spur gears. In the gutting section of the Squid Belly Opening and Gutting Machine (SBOGM), spur gears generate rotational impact due to constant angular velocities, causing noise and equipment damage; so, efficiency should be improved by varying sectional angular velocity. Therefore, we derived pitch curves by selecting angular velocity ratio considering operating environments, and the tooth profile was designed by calculating module for each section according to radius through theorical analysis for precise expression of angular velocity ratio. To confirm reliability of design, angular velocity ratio and structural safety of designed non-circular gears were verified using, commercial software, ‘DAFUL 2020 R1′.

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Automated Geometric and Computer-aided Non-Circular Gear Formation Modeling

Cited by 11 publications

References 7 publications

Designing an outer toothed gear whose wheel teeth are outlined by the logarithmic spiral arcs

Designing an outer toothed gear whose wheel teeth are outlined by the logarithmic spiral arcs

Design of a Noncircular Planetary Gear Mechanism for Hydraulic Motor

Study on Design of Non-Circular Gears for Speed Control of the Squid Belly Opening and Gutting Machine (SBOGM)

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