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.

A revised method to calculate time-varying mesh stiffness of helical gear

Time-varying mesh stiffness (TVMS) of gear plays vital role in analysing dynamic characteristic of gear transmission. So accurately evaluating the TVMS is important and essential. In this paper, a revised method to calculate the TVMS of helical gear is proposed. Based on slice method, the helical gear is sliced into pieces along the tooth width direction. The proposed method corrects the fillet foundation stiffness within multi-tooth in contact and considers the non-linearity and load-dependence of the Hertzian contact stiffness. The effect of the axial mesh force is considered. Finally, an equivalent helical gear model is established in ANSYS to study the mesh stiffness. The results show the proposed method has high effectiveness compared with FEM (finite element method).

Application of computer technologies for calculation of gears at studying of a course " Details of machines"

The computer program GearKURT has been created to calculate mechanical gears. The program allows you to calculate gears: - closed cylindrical spur gear - closed cylindrical helical gear - open cylindrical spur gear - Novikov's gear - closed bevel spur gear - closed bevel gear with indirect teeth - open bevel gear - worm-gear. The computer program has a dialog interface written in the object-oriented programming language Delphi and compiled into an exe-file. The program allows you to choose the necessary material and method of heat treatment for the manufacture of gears, to calculate the optimal geometric dimensions and transmission parameters, to determine the design of gears. The program provides all the necessary reference materials in the form of tables and graphs, which must be used to select the coefficients and other values necessary for calculations. The program provides access to the theoretical material of the course "Machine Parts" and the ability to save the results of calculations in a separate file. Recommendations for using this program are given.

Bending-torsional-axial-pendular nonlinear dynamic modeling and frequency response analysis of a marine double-helical gear drive system considering backlash

The double-helical gear system was widely used in ship transmission. In order to study the influence of backlash on the nonlinear frequency response characteristics of marine double-helical gear system, according to the structural characteristics of double-helical gear transmission, considering the time-varying meshing stiffness, backlash, damping, comprehensive transmission error, external load excitation, and other factors, a three-dimensional bending-torsional-axial-pendular coupling nonlinear dynamic modeling and dynamic differential equation of 24-DOF double-helical gear transmission system were established. The Runge–Kutta numerical method was used to analyze the influence of backlash, time-varying meshing stiffness, damping, error and external load excitation on the amplitude frequency characteristics. The results show that the backlash can cause the runout of the double-helical gear system, and the system has first harmonic and second harmonic response. With the increase of backlash, the amplitude of the system increases and the jumping phenomenon remains unchanged. The amplitude frequency response of the system is stimulated by time-varying meshing stiffness and comprehensive transmission error, and restrained by damping and external load excitation. The vibration displacement amplitude of the system increases with the increase of vibration displacement and has little effect on the state change of the system. The vibration test of double-helical gear is carried out. The frequency response components obtained by numerical simulation are basically consistent with the experimental results, which proves the correctness of the theoretical calculation. It provides a technical basis for the study of vibration and noise reduction performance of double-helical gear.

Effect of Tooth Surface Modification on Dynamic Transmission Efficiency of Double Helical Gear Trains

To analyse the influence mechanism of vibration loads on dynamic transmission efficiency (DTEF) of double helical gear trains (DHGT), a calculation method of DTEF which takes into consideration the real-time dynamic loads is proposed from the perspective of improving both efficiency and precision. The average DTEF is taken as the dynamic objective function of optimization for three-dimensional modification technology of tooth surface. An engineering example is given in form of numerical simulation, which proves that the average DTEF with the consideration of dynamic loads is obviously lower than the static transmission efficiency (STEF), especially for the resonance speed region. The results also show that the DTEF after 3-D modification is significantly improved, owing to the improvement of meshing state of tooth surface. The comparison of DTEF with different loads and speeds via simulation and experiment furtherly demonstrates the credibility of this theoretical perspectives. This study gives the explanation on the importance of DTEF in determination of driveline parameters and estimation of transmission quality of DHGT. The developed method for DTEF analysis is practical in engineering, and establishes a reliable foundation for further research on design of high-quality double helical gear trains.

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.