Iterative computation for measurement over pins of gears

Zhan, Jiaxing; Fard, Mohammad; Jazar, Reza N.

doi:10.1016/j.measurement.2014.12.020

Cited by 5 publications

(9 citation statements)

References 13 publications

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“…Figure 4 illustrates the measurement over pins according to the ISO/TR 10 064-2:1996 standard [17] and the corresponding formulae are elaborated in [4,18].…”

Section: Calculation and Measurement Over Pinsmentioning

confidence: 99%

“…an important tool to monitor and control the quality of gear manufacturing [1][2][3][4][5]. This measurement is closely related to the calculation of the inverse involute function.…”

Section: Introductionmentioning

confidence: 99%

“…the IIF α = inv −1 (θ) is to be found. This problem arises quite often in gear tooth geometry calculations, such as in the determination of non-standard center distances, offsets for cutting unconventional gears with teeth of consistent strength, non-standard pin dimensions, and maximum profile heights of spur gears [4][5][6][7][8].…”

Section: Introductionmentioning

confidence: 99%

“…To improve computational efficiency, it is necessary to minimize the number of evolutions of transcendental functions in the above two steps. Some iteration methods such as Newton method and secant method [4] have been used to solve equation (1). These two kinds of iterations are susceptible to divergence depending on the initial guess of α.…”

Section: Introductionmentioning

confidence: 99%

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Calculation of the inverse involute function and application to measurement over pins

Zhou,

Wu,

Chen

et al. 2024

Meas. Sci. Technol.

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Measurement over pins plays a crucial role in ensuring the quality in gear manufacturing, which requires the evolution of the inverse involute function. In this paper, an efficient algorithm for calculating the inverse involute function is proposed. Firstly, the initial approximate solution of the pressure angle near 0 rad is established by using Padé approximation and one step of Schröder iteration. Then the involute equation is transformed into another form by introducing a variable transformation, and the initial approximate solution of the pressure angle near π/2 rad is constructed by using the same method. The piecewise initial approximate solution over the entire interval of expanded angle is obtained by combining these solutions. The accuracy of the initial approximate solution can be significantly improved by using one step of Schröder iteration again. A numerical example of two-pin measurement is presented to show the superiority of our method over traditional iterative approach. The algorithm has high efficiency and accuracy, and is a useful tool for designers to accurately calculate the gear system.

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“…Figure 4 illustrates the measurement over pins according to the ISO/TR 10 064-2:1996 standard [17] and the corresponding formulae are elaborated in [4,18].…”

Section: Calculation and Measurement Over Pinsmentioning

confidence: 99%

“…an important tool to monitor and control the quality of gear manufacturing [1][2][3][4][5]. This measurement is closely related to the calculation of the inverse involute function.…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Calculation of the inverse involute function and application to measurement over pins

Zhou,

Wu,

Chen

et al. 2024

Meas. Sci. Technol.

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show abstract

“…However, the conventional calculation process for the over pins distance is not convenient. This is mainly due to the computation complexity of involute function included within the calculation [28]. The tooth number of CS and FS is usually even, as shown in Fig.…”

Section: Calculation Model Of Thickness Error Of Cs and Fsmentioning

confidence: 99%

Calculation of tooth thickness errors and its influence on meshing backlash of harmonic drive

Yang

Zhang

et al. 2022

Preprint

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Meshing backlash mainly determines the transmission accuracy of harmonic drive, which is an important index in design. In this paper, a design method of short tooth involute profile is proposed, which relies on positive modification to enhance the strength of dedendum. By intercepting part of tooth profile, the meshing interference of addendum can be effectively avoided. Based on the dimensions of over pins of circular spline and flexspline, a calculation method of tooth thickness deviation is proposed, and the positive and negative of tooth thickness deviation are defined. Involute functions need not be calculated by this method, which simplifies the solution process. By discretizing the teeth profile points of circular spline and flexspline, a calculation method of time-varying backlash is proposed, the variation of backlash in the process of meshing in and out is analyzed, and the influence law of tooth thickness deviation on backlash is studied. On this basis, an algorithm of adjusting the radial deformation to compensate the backlash is proposed. The results show that the excessive backlash in the meshing area can be reduced by increasing the radial deformation. when meshing interference occurs, the interference free meshing can be realized by decreasing the radial deformation.

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Calculation of Tooth Thickness Errors and Its Adjustment on Meshing Backlash of Harmonic Drive

Yang

Zhang

et al. 2022

Int. J. Precis. Eng. Manuf.

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Iterative computation for measurement over pins of gears

Cited by 5 publications

References 13 publications

Calculation of the inverse involute function and application to measurement over pins

Calculation of the inverse involute function and application to measurement over pins

Calculation of tooth thickness errors and its influence on meshing backlash of harmonic drive

Calculation of Tooth Thickness Errors and Its Adjustment on Meshing Backlash of Harmonic Drive

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