Novel mathematical modelling methods of comprehensive mesh stiffness for spur and helical gears

One important source of noise in drive trains are transmissions. In numerous applications, it is necessary to use helical instead of spur gear stages due to increased noise requirements. Besides a superior excitation behaviour, helical gears also show additional disadvantageous effects (e.g. axial forces and tilting moments), which have to be taken into account in the design process. Thus, a low noise spur gear stage could simplify design and meet the requirements of modern mechanical drive trains. The authors explore the possibility of combining the low noise properties of helical gears with the advantageous mechanical properties of spur gears by using spur gears with variable tip diameter along the tooth width. This allows the adjustment of the total length of active lines of action at the beginning and end of contact and acts as a mesh stiffness modification. For this reason, several spur gear designs are experimentally investigated and compared with regard to their excitation behaviour. The experiments are performed on a back-to-back test rig and include quasi-static transmission error measurements under load as well as dynamic torsional vibration measurements. The results show a significant improvement of the excitation behaviour for spur gears with variable tip diameter.

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Assessment of emergency consequences and hazardous factors impact from the process of explosive conversion products and materials disposal

MATEC Web of Conferences ◽

10.1051/matecconf/202030500012 ◽

2020 ◽

Vol 305 ◽

pp. 00012

Author(s):

Vasyl Holinko ◽

Yevhen Ustymenko ◽

Volodymyr Bondarenko ◽

Iryna Kovalevska

Keyword(s):

Probability Theory ◽

Mathematical Modelling ◽

Probabilistic Model ◽

Economic Assessment ◽

Main Task ◽

Material Resources ◽

Disposal Facility ◽

Integral Measure ◽

Is Development ◽

Modelling Methods

Purpose is development of tools for assessing the emergency hazard of facility for disposal of explosive conversion products and materials. Results have been obtained by means of the economic and mathematical modelling methods, with use of the fundamental provisions of probability theory. The main task of conversion products and materials disposal is the creation and organization of safe technological processes aimed at returning the material resources contained in the conversion products to the state’s economy after the appropriate processing, rather than at destroying these resources. As a methodological basis for assessing the emergency hazard of a facility, a provision has been accepted that an integral measure of the disposal process hazard is the economic assessment of accidents. A scheme has been constructed of successiveness of the disposal facility events and states that can lead to an accident, on the basis of which a probabilistic model of its occurrence is developed. Proposed probabilistic model of an accident initiation at the facility for disposal of explosive conversion products and materials makes it possible to predict the behaviour of facility, based on results of the equipment and service personnel state survey, as well as on the analysis of the environmental conditions.

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Coupled Dynamic and Vibration Analysis of Beveloid Geared System

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.215-216.917 ◽

2012 ◽

Vol 215-216 ◽

pp. 917-920

Author(s):

Rong Fan ◽

Chao Sheng Song ◽

Zhen Liu ◽

Wen Ji Liu

Keyword(s):

Transmission Error ◽

Time Varying ◽

Spur Gears ◽

Dynamic Coupling ◽

Nonlinear Dynamic Model ◽

Mesh Stiffness ◽

Hypoid Gears ◽

Helical Gears ◽

Beveloid Gears ◽

Vibration Model

Dynamic modeling of beveloid gears is less developed than that of spur gears, helical gears and hypoid gears because of their complicated meshing mechanism and 3-dimsional dynamic coupling. In this study, a nonlinear systematic coupled vibration model is created considering the time-varying mesh stiffness, time-varying transmission error, time-varying rotational radius and time-varying friction coefficient. Numerical integration applying the explicite Runge-Kutta formula and the implicit direct integration is used to solve the nonlinear dynamic model. Also, the dynamic characteristics of the marine gear system are investigated.

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