Study on the Anti-Twist Helical Gear Tooth Flank With Longitudinal Tooth Crowning

Tran, Van-The; Hsu, Ruei‐Hung; Tsay, Chung-Biau

doi:10.1115/1.4027166

Cited by 26 publications

(9 citation statements)

References 9 publications

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“…Vectors n g f and n p f are, respectively, the unit normal vector for the unmodified gear and the modified pinion in the fixed coordinate system S f . equation (19) and equation (20) give a system of five independent equations, because jn g f j À jn p f j ¼ 0. Parameter ˘g is given a specific value.…”

Section: Transmission Errormentioning

confidence: 99%

“…Tran 19 used a non-linear function to move the hobbing tool to modify the tooth flank of the gear. Tran et al 20 used a non-linear function and a rotation angle as the variables for the machining of gears for the hobbing process and used these for the longitudinal modification of the flank of helical gears. This produces a significant reduction in the distortion of the tooth flank after longitudinal modification of the gear.…”

Section: Introductionmentioning

confidence: 99%

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Double modification of a rack cutter using a variable pressure angle and modulus

Yang

2022

Proceedings of the Institution of Mechanical Engineers, Part C:

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This study modifies the straight edge of the rack cutter into an arc shape by changing the pressure angle. Using a variable modulus, the tooth surface is longitudinally modified along the axial direction of the rack cutter to create a bulge in the rack teeth in the center of the tooth width. This rack cutter with a double-crowned tooth is used to generate a pinion. An unmodified rack cutter is used to generate a gear. An undercutting analysis of the rack cutter is used to determine the undercutting condition for the double-crowned rack cutter and to determine the limits for the parameter. The transmission error for a gear pair is calculating using a tooth contact analysis. For this study, the assembly error for six cases is used to calculate the transmission error for the gear pair and the contact points for the gear pair are placed on a gear tooth. These contact points used to determine the contact for the gear pair. A transmission error analysis of the gear pair for a double-crowned gear gives a parabolic curve for the transmission error. The distribution of the contact points shows that, regardless of assembly errors, the contact points for the gear teeth are along the center of the tooth surface, starting from the top of the tooth, and gradually moving to the flank and away from the heel. The results show that the values for the transmission error for the modified gear pair for the proposed modification of the variable pressure angle and the variable modulus on a traditional rack cutter are small and the transmission error of the assembly errors are almost similar to those for an ideal assembly.

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Section: Transmission Errormentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Double modification of a rack cutter using a variable pressure angle and modulus

Yang

2022

Proceedings of the Institution of Mechanical Engineers, Part C:

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“…Research on cycloid drives concerning the geometrical design method [20,23], kinematic principle [18,24], and load distribution analysis [4,11,12,14,15,25] have all assumed a two-dimensional planar problem without considering the three-dimensional topological structure of the cycloid gear. However, in practice, like involute cylindrical gears [26][27][28], the cycloid gear is also crowned in the longitudinal direction to avoid edge contact between the teeth and rollers, considerably improving the contact stress distribution. Three types of tooth longitudinal modifications for cycloid gears are proposed in this paper: fully crowned modification (FCM), partially crowned modification (PCM), and logarithmically crowned modification (LCM), as shown in Figure 4a-c, correspondingly.…”

Section: Tooth Longitudinal Modificationmentioning

confidence: 99%

A Semi-Analytical Load Distribution Model for Cycloid Drives with Tooth Profile and Longitudinal Modifications

Zhang

Wang

et al. 2020

Applied Sciences

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The current load distribution model for cycloid drives based on the Hertz contact stiffness typically assumes a two-dimensional planar problem without considering the tooth longitudinal modification effects, which fails to comply with the practical situation. In this paper, this issue is clarified by developing a semi-analytical load distribution model based on a three-dimensional and linear elastic solution. Unloaded tooth contact analysis is introduced to determine the instantaneous mesh information. The tooth compliance model considering tooth contact deformation is established by combining the Boussinesq force–displacement relationships in elastic half-space with an influence coefficient method. With this, the loads, contact patterns, and loaded transmission error are calculated by enforcing the compatibility and equilibrium conditions. Comparisons to predictions made with the assumption of Hertz contact stiffness are presented to demonstrate the effectiveness of the proposed model, which shows good agreement. At the end, the effect of tooth longitudinal modifications on load distributions is investigated along with various loading conditions. This study yields an in-depth understanding of the multi-tooth contact characteristics of cycloid drives and provides an effective tool for extensive parameter sensitivity analysis and design optimization studies.

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“…Lastly, Hsu and Su [16] investigated the gear tooth surface topologies, contact ellipses, and transmission errors of work gear pairs generated by a modified hob with variable tooth thickness. And Tran et al [17][18][19] proposed a novel hobbing method to generate anti-twist tooth flanks of the involute helical gear in longitudinal tooth crowning by supplementing an additional rotation angle of work gear during its hobbing process.…”

Section: Introductionmentioning

confidence: 99%

Generation of a double-crowned involute helical gear with twist-free tooth flanks by a CNC hobbing machine with three synchronous axes

Tran

2017

Vietnam J. Mech.

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In the conventional hobbing process, a double-crowned involute helical gear is generated by the hob cutter with parabolic-curve tooth profiles for the cross-profile crowning and varied the center distance between the hob and work gear for the longitudinal crowning. Therefore, to cut a double-crowned helical gear not only requires at least four synchronous axes and hob cutter regrinding (which increases production costs) but also induces twisted tooth flanks on the generated work gear. In this paper, I propose a hobbing method by applying a modified work gear rotation angle that enables double-crowning of involute helical gear's tooth flanks using a standard hob cutter and a computer numerical control (CNC) hobbing machine with only three synchronous axes. The proposed method has also verified by using two computer simulation examples to compare the meshing-conditions, contact ellipses, and transmission errors of the double-crowned gear pairs with that produced by applying the conventional hobbing method. Computer simulation results reveal the advantages of the proposed novel hobbing method.

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Study on the Anti-Twist Helical Gear Tooth Flank With Longitudinal Tooth Crowning

Cited by 26 publications

References 9 publications

Double modification of a rack cutter using a variable pressure angle and modulus

Double modification of a rack cutter using a variable pressure angle and modulus

A Semi-Analytical Load Distribution Model for Cycloid Drives with Tooth Profile and Longitudinal Modifications

Generation of a double-crowned involute helical gear with twist-free tooth flanks by a CNC hobbing machine with three synchronous axes

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