Spherical Involute Research Articles

Study on Transmission Error of Straight Bevel Gear (Influence of Tooth Profiles)

Bevel gears are greatly influenced by the deflection of gear shafts and bearings. The reason is that both gear shafts cross and one of them is at least cantilever. Those have great influence on the transmission error which is related to the vibration and noise. In the previous report, the transmission errors were calculated, when gear shafts were supported by two bearings. However, these transmission error were greatly influenced by tooth profiles. Therefore, in this report, transmission error was calculated, when tooth profiles were spherical involute tooth type and Gleason tooth type. It were clarified how transmission error on tooth profiles were influenced by assembly errors, torque and crowning.

Algorithms for Involute and Octoidal Bevel-Gear Generation

A suitable formulation and the implementing algorithms for involute and octoidal bevel-gear generation are proposed in this paper. In particular, the exact spherical involute tooth profile of bevel gears and their crown rack is obtained through the pure-rolling motion of a great circle of the fundamental sphere on the base cone. Moreover, the tooth flank surface of octoidal bevel gears is obtained as the envelope of the tooth flat flank of the octoidal crown rack during the pure-rolling motion of its flat pitch (surface) on the pitch cone. The proposed algorithms have been implemented in MATLAB; several examples are included to illustrate their applicability.

2526 すぐばかさ歯車の回転伝達特性に関する研究 (歯形の違いによる影響)

Bevel gears are easily influenced by the deflection of gear shafts and bearings. The reason is that both gears shafts cross and one of them is largely cantilever. Those have great influence on the transmission error which is related to the vibration and noise. In the previous report, the transmission error were calculated, when gear shafts were supported by two bearings. However, those transmission error is greatly influenced by tooth profiles. Therefore, in this report, transmission error was calculated, when tooth profiles were spherical Involute tooth type and Gleason tooth type. Effects of tooth profiles on transmission error were clarified with effects of assembly error, torque and crowning.

Establishing gear tooth surface geometry and normal deviationPart II—bevel gears

In this part, the concept of enveloping tangent planes dealing with gear geometry and normal deviations is applied to bevel gears. Exact spherical involute is established by the procedure outlined in this paper. Straight tooth and spiral tooth bevel gears are considered in this paper. The method of determining the normal deviation from the idealized surface and the validation of the method are reported here. Effectiveness of the proposed method for obtaining normal deviation is established by considering spiral bevel gear geometry based on circular arc.

The Modeling of Bevel Gears Using the Exact Spherical Involute

The solid modeling of bevel gears has been recognized as a major design challenge. Various approaches have been proposed to approximate the theoretical involute-generated contact surface of bevel gears. As a means to accurately represent contact surfaces of these gears, the exact spherical involute is introduced here. The solid models of straight and spiral bevel gears are obtained by applying simple sweeping techniques to their tooth profiles, which are described by the exact spherical involute. Futhermore, the volumetric properties of the modeled bevel gears are readily computed from their piecewise-linear approximation.

Effects of Bearing Offset and Flexibility on the Mesh Force Distribution of Spiral Bevel Gears

For straight or spiral bevel gears of nominal spherical involute design, the resultant total force vector transmitted by the gear mesh, in the absence of friction, lies in the plane of tooth contact. This force vector can be characterized by three scalar components, two orthogonal force components lying in the plane of contact and the resultant moment taken about the nominal center of the zone of contact. Equations for these three generalized force components are derived. The equations are expressed in terms of tooth pair/gear body stiffnesses, bearing/bearing support flexibility influence coefficients, the shaft input torque, deviations of the tooth running surfaces from perfect spherical involute surfaces, and bearing centerline offsets from the positions occupied by the base cone axes of the perfect involute bevel gear counterparts to the actual gears under consideration. Inertial forces arising from transverse and axial vibrations of the gear bodies are assumed to be negligible in comparison with the bearing support reaction forces.

Surface Geometry of Straight and Spiral Bevel Gears

The fundamental geometrical characteristics of bevel gears have been discussed in this study. The mathematical modeling of the tooth surface geometry of bevel gears can be developed based on the basic gearing kinematics and involute geometry along with the tangent planes geometry. The parametric representations of the spherical involute and the involute spiraloid, which are the tooth surface geometry of straight bevels and spiral bevels, respectively, have been derived in this paper. This study may provide some fundamentals for computer numerical controlled manufacturing of bevel gears.

The Generalized Transmission Error of Spiral Bevel Gears

The traditional definition of the transmission error of parallel-axis gear pairs is reviewed and shown to be unsuitable for characterizing the deviation from conjugate action of bevel gear pairs for vibration excitation characterization purposes. This situation is rectified by generalizing the concept of the transmission error of parallel-axis gears to a three-component transmission error for spiral bevel gears of nominal spherical involute design. A general relationship is derived which expresses the contributions to the three-component transmission error from each gear of a meshing spiral bevel pair as a linear transformation of the six coordinates that describe the deviation of the shaft centerline position of each gear of the pair from the position of its rigid perfect involute counterpart.

Study on Bending Fatigue Strength of Bevel Gears : 1st Report, Tooth Profile and Root Stresses of Straight Bevel Gears of Gleason Type

The characteristics of tooth profile of straight bevel gears of Gleason type were examined and the root stresses were investigated experimentally by making use of a static loading apparatus, which was developed by the authors. It was found that the tooth profile of straight bevel gears of Gleason type deviates from spherical involute curve in both the tip and the root of the tooth and that the root stresses at the middle of tooth trace are larger than those at the toe and the heel. Furthermore various calculating methods for contact ratio of straight bevel gears were compared on the basis of the measured contact ratio.

On the Generating Methods of the Spherical Involute Teeth

On the Generating Methods of the Spherical Involute Teeth