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.

Melody, not Beat Perception, Predicts Rhythmic Error Detection

The purpose of this study was to examine the relationships among beat perception, error detection, and musical experience. We presented monophonic rhythms using a piano timbre along with two measures of beat perception (Harvard Beat Finding and Interval Test [BFIT] and Goldsmiths Beat Alignment Test) and a measure of melodic error detection. College musicians’ ( N = 43) ability to detect rhythm errors was not significantly correlated to their ability to perceive beat alignment (Goldsmiths test) or tempo change (BFIT). Age was related to performance on only one of the measures, the BFIT test. A regression model yielded pitch error detection as the only significant predictor of rhythmic error detection. We suggest that college musicians already possess a requisite ability for beat processing that allows them to perform error detection. The lack of relationship between beat perception and rhythmic error detection is explained by this requisite ability in the population, and we promote future research for pitch and rhythm processing as it relates to rhythm perception or performance.

Dynamical Modelling and Simulation of Spur Gears with Flank Pitch Error

Gearbox is commonly regarded as the most important power section of wind turbines which has been widely valued for its high malfunction rate. Gear fault researches mainly include wearing, pitting, spalling, breakage, falling off, etc, while little attention was paid to tooth Flank Pitch Error(FPE). Taking a single-stage parallel shaft spur gear as the research object, an 8-DOF gear transmission model and the FPE model were established in this paper and the gear’s time-varying meshing stiffness (TVMS) models with & without tooth FPE were obtained respectively, which the dynamic models with various tooth FPE values under different rotating speeds were simulated after. The simulation results showed that the TVMS mathematical model proposed in the paper under tooth FPE is practical at both low and high rotating speeds. Under the FPE model, side-bands are formed around each multiple of meshing frequency whose peaks are distributed by a fixed fault characteristic frequency ffp interval. The gearbox vibrates severely as the tooth FPE values and rotational speed grow. The peak value of the vibration signal is about 3 times that in case of fault-free state when the FPE value reaches 0.001rad, thus the impact of FPE on gearboxes cannot be neglected.

Effect of Pitch Error on Static and Dynamic Characteristics of Hydrostatic Worm-Rack-Drive

Hydrostatic worm-rack-drive has obvious advantages on large-sized machine tools, and its performance is significantly affected by pitch errors. This paper theoretically researches the axial static and dynamic characteristics of hydrostatic worm-rack-drive, including the effects of the amplitude, period, and phase of pitch errors. Based on the expanded view of the helicoid of threads, a numerical calculation method is implemented where the Reynolds’ equation and flow continuity equation are solved simultaneously. The influence rule of pitch errors on pocket pressure, flow, axial fluid-film force, axial stiffness coefficient, and axial damping coefficient are discussed in detail, for providing beneficial guidance for the design and performance optimization of hydrostatic worm-rack-drive.

DEVELOPMENT OF A METHOD FOR PREDICTING THE ACCURACY OF SPIROID WHEELS

The article considers the possible errors of the spiroid transmission based on mathematical modeling of the process of shaping the teeth of the spiroid wheel. Typical errors such as tooth profile error, tooth pitch error, tooth thickness error, tooth longitudinal line error are applicable to spiroid wheel tooth errors. Currently, the accuracy standards for spiroid transmissions are not standardized. It is shown that the mandrel of a cylindrical spiroid cutter for processing spiroid wheels has an increased length, which contributes to its greater squeezing from the spiroid wheel during the shaping process. Based on the components of the cutting forces, a graph of the vibrations of the milling cutter mandrel is presented. In the study of precision spiroid wheels on the basis of a comprehensive analysis of the formation of the tooth profile of spiroid wheel revealed that the geometric deviations of the lateral surfaces of the teeth of wheels due to the errors of gear cutting tools and technological factors.

Influence of manufacturing error tolerances on contact pressure in gears

Gear manufacturing always results in some degree of manufacturing errors, i.e. deviations from the desired gear geometry. These errors alter how the gears mesh, typically causing increased contact pressure which in turn shortens service life. It is therefore crucial to choose tolerances such that excessive contact pressure, and especially tip contact, is avoided. With increasing demands due to electrification, this becomes even more important. The aim of this paper is to study how pitch error and profile slope error affect the contact pressure in spur gears sets. The meshing is simulated using a novel simulation approach that uses a parametric description of the reference profile and gear geometry, and a hybrid model for the compliance. The method includes tooth modifications such as tip relief, and uses the true geometry to find contacts. Thus, it also handles contact outside the nominal line of action, including tip contact. The study includes cases where a gear is subjected to both pitch error and profile slope error simultaneously. Numerical examples, relevant to the automotive industry, show the outcome of the simulations. It is shown how simulation-based tolerances for relevant industrial applications can be used to improve manufacturing outcome.