Design and Application of Non-Circular Gear with Cusp Pitch Curve

Liu, Jiangang; Tong, Zhipeng; Yu, Guo; Zhao, Xiong; Zhou, Haili

doi:10.3390/machines10110985

Cited by 6 publications

(6 citation statements)

References 29 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Such a pair consists of a helical noncircular gear and eccentric helical curved face. In [11], a new composite profile of the tooth was proposed with an analysis of the dependence of design parameters in accordance with various elliptical eccentricities. The practical side of the issue of manufacturing non-circular wheels is revealed in [12], which presents a device for the manufacture of non-circular gears.…”

Section: Literature Review and Problem Statementmentioning

confidence: 99%

“…5, c, one spherical wheel rotates around the OZ axis at an angle of γ = 60°. The magnitude of the angle of rotation of the second wheel around the OX axis is found from formula (11) when substituting into it γ = 60°. From it, we find j = -35.8°.…”

Section: Application Of the Proposed Approach To The Design Of Spheri...mentioning

confidence: 99%

“…On the sphere of a single radius, it is equal to the angular θ, that is, 90°. Based on the condition that the curves roll one by one without sliding, that is, they pass the lengths of their arcs, the relationship between the angles of γ and j in the form (11) has been established. The resulting dependence (11) makes it possible to construct the profile of the second non-circular wheel when substituting it into parametric equations (7).…”

Section: Application Of the Proposed Approach To The Design Of Spheri...mentioning

confidence: 99%

“…Based on the condition that the curves roll one by one without sliding, that is, they pass the lengths of their arcs, the relationship between the angles of γ and j in the form (11) has been established. The resulting dependence (11) makes it possible to construct the profile of the second non-circular wheel when substituting it into parametric equations (7). It was found out during the construction and mathematically proved that the profile curve will be a congruent loxodrome.…”

Section: Application Of the Proposed Approach To The Design Of Spheri...mentioning

confidence: 99%

“…To confirm the reliability of the results obtained, four of their positions are shown when rotating around their axes. In this case, the angle of rotation γ for one wheel was set, and for the second -calculated from formula (11). When turning the wheels at the appropriate angles, the point of contact is always on the arc of the meridian depicted by the dashed line.…”

Section: Application Of the Proposed Approach To The Design Of Spheri...mentioning

confidence: 99%

See 4 more Smart Citations

Construction of spherical non-circular wheels formed by symmetrical arcs of loxodrome

Kresan

Ahmed

Pylypaka

et al. 2023

EEJET

View full text Add to dashboard Cite

Bevel gears are used to transmit torque between intersecting axes. They demonstrate high reliability and durability of work, as well as a constant gear ratio. The disadvantage of such a transmission is the mutual sliding of the surfaces of the teeth of the gears, which leads to the emergence of friction forces and wear of their working surfaces. In this regard, there is a task to design such bevel gears that would have no slip. Non-circular wheels are understood as a pair of closed curves that rotate around fixed centers and at the same time roll over each other without sliding. They can serve as centroids for the design of cylindrical gears between parallel axes. If the axes of rotation of the wheels intersect, then the gears are called conical. An analog of gears between parallel axes, in which centroids are flat closed curves, for gears with intersecting axes are spherical closed curves. For a bevel gear with a constant gear ratio, such spherical curves are circles on the surface of the sphere, and with a variable gear ratio, spatial spherical curves. This paper considers the construction of closed spherical curves that roll around each other without sliding when they rotate around the axes intersecting in the center of the spheres. These curves are formed from symmetrical arcs of the loxodrome, a curve that crosses all the meridians of the ball at a constant angle. This angle should be 45°, which ensures the intersection of the loxodrome at right angles. Analytical dependences have been derived underlying the calculations of profiles of spherical non-circular wheels and their visualization by means of computer graphics. The results could be used to design non-circular wheels for textile machines, hydraulic machine pumps, pump dispensers, etc.

show abstract

Section: Literature Review and Problem Statementmentioning

confidence: 99%

Section: Application Of the Proposed Approach To The Design Of Spheri...mentioning

confidence: 99%

Section: Application Of the Proposed Approach To The Design Of Spheri...mentioning

confidence: 99%

Section: Application Of the Proposed Approach To The Design Of Spheri...mentioning

confidence: 99%

Section: Application Of the Proposed Approach To The Design Of Spheri...mentioning

confidence: 99%

See 3 more Smart Citations

Construction of spherical non-circular wheels formed by symmetrical arcs of loxodrome

Kresan

Ahmed

Pylypaka

et al. 2023

EEJET

View full text Add to dashboard Cite

show abstract

Research on the seedling picking trajectory error of the gear train seedling picking mechanism considering tooth backlash

Du,

Liu,

2024

Engineering Reports

View full text Add to dashboard Cite

The research investigated the tooth backlash influences the error in seedling picking trajectories of the gear train SPM. First, a sine function and the sum of random errors are taken into account is utilized to fit the tooth backlash of the firstly and secondary transmissions. Additionally, the analysis established the relationship between the fitting parameters and the tooth backlash of the firstly and secondary transmissions, in order to determine the appropriate fitting parameters. Next, the relationship between the tooth backlash of the firstly and secondary transmission in the seedling picking mechanism (SPM) and the x, y coordinates, as well as the velocity and acceleration of the seedling needle tip (SNT), is examined. This analysis is based on the error and movement variance of the coordinate and kinematic parameters of SNT. The results indicate that the tooth backlash of the firstly transmission has a more significant influence on the error of the seedling picking trajectory compared to the tooth backlash of the secondary transmission. When the tooth backlash of the noncircular gear in the firstly transmission reaches its maximum value of 0.24 mm, the x and y coordinates of the SNT can reach maximum values of 1 and 3.5 mm. The test of the jumping of the needle tip and idling trajectory description indicated that noncircular gears with larger tooth backlash exhibit higher positional jumping at the tip of the seedling needle.

show abstract

Design of and research on a noncircular gear with a high-contact-ratio composite tooth profile

Liu,

Du,

et al. 2024

J Mech Sci Technol

View full text Add to dashboard Cite

Design and Application of Non-Circular Gear with Cusp Pitch Curve

Cited by 6 publications

References 29 publications

Construction of spherical non-circular wheels formed by symmetrical arcs of loxodrome

Construction of spherical non-circular wheels formed by symmetrical arcs of loxodrome

Research on the seedling picking trajectory error of the gear train seedling picking mechanism considering tooth backlash

Design of and research on a noncircular gear with a high-contact-ratio composite tooth profile

Contact Info

Product

Resources

About