Using variable modulus to modify a rack cutter and generate a gear pair

In this paper, two normal imaginary helical rack cutters were first established. One of these cutters is a skewed-rack cutter with an asymmetrical straight edge. The other is a rack cutter with an asymmetric parabolic profile. Second, the gear’s tooth surface of the asymmetric parabolic rack cutter is modified to be barrel-shaped based on a variable modulus. The tooth thickness of the gear is gradually reduced along the face width of the tooth from the middle of the tooth surface. Then the coordinate relationship between the gears’ blanks and the imaginary helical rack cutters was established. Through the differential geometry, crowned and uncrowned helical gear pairs were generated. Because of human factors, when the gear pair is installed, it is easy to cause the gear pair edge contact. It is necessary to add artificial assembly error settings through the tooth contact analysis to investigate the kinematic errors and contact conditions of the crowned and uncrowned helical gear pair. The mathematical models and analysis methods proposed for the crowned imaginary rack cutter using variable modulus should be useful for the design and production of double crowned helical gears with asymmetric parabolic teeth.

Influence of Pitch Error on Vibration, Bifurcation, and Chaos Characteristics of the Helical Gear Pair System

Aiming at the problem of pitch error of helical gear pair in engineering practice, the influence of pitch error on vibration, bifurcation, and chaos characteristics of the helical gear pair system is mainly studied. Due to the periodic time-varying nature of pitch error, a method of simulating the pitch error as a sine function is proposed to calculate pitch error. A nonlinear dynamic model of bending-torsion-shaft coupling of the helical gear pair system is established considering the effect of pitch error. The influence of pitch error on the vibration, bifurcation, and chaos characteristics of the system is analyzed by the Runge–Kutta numerical integration method. The research results show that the introduction of pitch error has the most significant impact on the torsional vibration of the system. With the increase in pitch error, the system exhibits rich bifurcation and chaos characteristics in the torsional direction. Moreover, it is also found that the vibration response in the torsional orientation of the system increases or decreases to the same degree when the system is in a periodic motion state, and the pitch error varies by the same extent. Therefore, the impact of pitch error on the dynamic performance of the helical gear pair system should be considered in engineering practice.

Vibration-based fault diagnosis of helical gear pair with tooth surface wear considering time-varying friction coefficient under mixed EHL condition

Based on “slice method”, the improved time-varying mesh stiffness (TVMS) calculation model of helical gear pair with tooth surface wear is proposed, in which the effect of friction force that obtained under mixed elasto-hydrodynamic lubrication (EHL) is considered in the model. Based on the improved TVMS calculation model, the dynamic model of helical gear system is established, then the influence of tooth wear parameters on the dynamic response is studied. The results illustrate that the varying reduction extents of mesh stiffness along tooth profile under tooth surface wear, in addition, the dynamic response in time-domain and frequency-domain present significant decline in amplitude under deteriorating wear condition.

Nonlinear Frequency Response Analysis of Double-helical Gear Pair Based on the Incremental Harmonic Balance Method

The torsional dynamic model of double-helical gear pair considering time-varying meshing stiffness, constant backlash, dynamic backlash, static transmission error, and external dynamic excitation was established. The frequency response characteristics of the system under constant and dynamic backlashes were solved by the incremental harmonic balance method, and the results were further verified by the numerical integration method. At the same time, the influence of time-varying meshing stiffness, damping, static transmission error, and external load excitation on the amplitude frequency characteristics of the system was analyzed. The results show that there is not only main harmonic response but also superharmonic response in the system. The time-varying meshing stiffness and static transmission error can stimulate the amplitude frequency response of the system, while the damping can restrain the amplitude frequency response of the system. Changing the external load excitation has little effect on the amplitude frequency response state change of the system. Compared with the constant backlash, increasing the dynamic backlash amplitude can further control the nonlinear vibration of the gear system.

Lubrication performance of helical gear pair under dynamic load based on local involute profile

The tribological properties of gear interface have been widely concerned in the past decades. In this study, based on the local involute profile and crown modification, a thermal elastohydrodynamic lubrication model is proposed for a helical gear pair. To discuss the influences of dynamic load on the tribological properties of helical gear pair, the dynamic mesh force of tooth surface is obtained by torsional vibration model. The influences of working conditions and surface roughness on the tribological properties of helical gear pair are investigated. The tribological properties are evaluated in terms of the average film thickness, friction coefficient, mechanical power loss etc. Results show that the dynamic effect of gears has a significant effect on the tribological properties, especially at a specific speed, such as resonance speed. In order to simulation gear lubrication accurately, it is recommended to adopt local involute tooth profile and consider tooth profile modification to calculate geometric clearance. The influence of input rotation speed on the dynamic characteristics and tribological properties of gear is more significant than that of input torque. The surface roughness significantly changes the distribution of interface pressure and film thickness. With the increase of roughness amplitude, the local fluctuation amplitude of pressure and film thickness increase and the dry contact occurs at the end of contact line. Meanwhile, the maximum subsurface stress moves toward the tooth surface, especial for the high frequency engineering roughness. This local stress concentration is harmful to the fatigue life of gear meshing process.