• Journal of the Korean Society of Manufacturing Process Engineers
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• v.21 no.2
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• pp.64-72
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• 2022

Gear designers need to select the proper tolerances for deviations in both the center distance and parallelism of axes because these deviations cause high stresses and lead to fatigue breakage of the teeth. In this study, a three-dimensional finite element analysis model was developed for a helical gear used in metro vehicles, and a bending stress analysis method for gear pairs was established according to the contact position change. Using this model, the effect of shaft misalignment due to the center distance and shaft parallelism deviations on the bending stress of the gear was analyzed. As a result, the magnitude of the bending stress changed nearly linearly with the change in the center distance deviation. The tooth contact of the helical gear is biased toward the end of the tooth width when the parallelism deviations of the shaft occur, and the tooth root bending stress increases.

• Progress in Superconductivity
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• v.8 no.2
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• pp.152-157
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• 2007

Uniaxial square Helmholtz coils for testing SQUID sensors were designed and their field distributions were calculated. Optimum parameters for maximizing the uniform region in the Helmholtz mode were obtained for different uniformity tolerances. The coil system consists of 2 pairs of identical square loops, a Helmholtz pair for generating uniform fields and the other for the 2nd-order gradient fields in combination with the Helmholtz pair. Full expressions of the axial component of the field were calculated by using Biot-Savart's law. To understand the behavior of the field near the coil center, analytical expressions were obtained up to the 4th-order in the midplane and along the coil axis. The Helmholtz condition for generating uniform fields was calculated to be $d/{\alpha}=0.544505643$, where 2d is the inter-coil distance and $2{\alpha}$ is the side length of the coil square. Maximized uniform range can be obtained for a given nonuniformity tolerance by choosing $d/{\alpha}$ slightly lower than the Helmholtz condition. The pure second-order gradient field can be generated by subtracting the Helmholtz field from the field of the 2nd pair with equal magnitudes of the center fields of the two pairs. The coil system is useful for testing balance and sensitivity of SQUID gradiometers.