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Influence of Gear Eccentricity with Non-Parallel Axis on the Dynamic Behaviour of a Gear Unit Using a Gear Slice Model with 26 Degrees of Freedom

Jedliński Łukasz

Advances in Science and Technology. Research Journal

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2024

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Vol. 18, no 2

88--102

EN

This study investigates the problems of eccentricity and backlash using an analytical spur gear model with 26 degrees of freedom (DOF). Previous studies have only investigated the case of eccentricity with a parallel shift of the axis of rotation of the gear relative to its geometric axis of symmetry. This study presents a novel method for determining the radius of eccentricity and its angular position at any distance from the bearing support, in which the axis of rotation and the geometric axis of symmetry of the gear are non-parallel. The effect of gear motion in the line of action (LOA) and off-line of action (OLOA) directions on backlash is precisely determined, despite the fact that most studies usually ignore gear displacement along the OLOA direction. Numerical simulations are performed to determine the effect of eccentricity on backlash, and their results confirm that the proposed method for determining the radius of eccentricity for any eccentricity type is correct. A gear slice model is used for dynamic analysis. Results show that the type of eccentricity has a significant effect on the gear dynamics and that eccentricity analyses have to include other cases than merely eccentricity with parallel axes of gears.

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Influence of the movement of involute profile gears along the off-line of action on the gear tooth position along the line of action direction

Jedliński Łukasz

Eksploatacja i Niezawodność

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2021

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Vol. 23, no. 4

736--744

EN

When gears change their distance along the off-line of action (OLOA) direction, this affects the distance between the working surfaces of the meshing teeth along the line of action (LOA). This effect is usually neglected in studies. To include this effect precise equations are derived for spur gears. The analysis is carried out for the general case of spur gears with shifted profiles frequently used in the industry. The influence of OLOA gear displacement on LOA direction is also a function of gears parameters. An analysis is conducted, and the impact of parameters such as module, pressure angle, gear ratio, and the number of teeth is determined. As an example, a simulation of a 12 DOF analytical model is presented. The movement of gears along OLOA is caused by a frictional force that can be high during tooth degradation e.g. scuffing. Results show that when the movement of gears along the OLOA direction is significant, its influence on the distance between the mating teeth should not be neglected.

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New Analytical Model of Spur Gears with 5 DOF Shafts and its Comparison with Other DOF Models

Jedliński Łukasz

Advances in Science and Technology. Research Journal

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2021

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Vol. 15, no 1

79--91

EN

This study relates to the research on improving analytical models of gears. A new analytical model of gear shaft with 5 DOF was proposed. Equations of vibration were derived without small-angle approximation and were presented in a form that could be implemented in Simulink. In order to determine the effect of the additional DOF, four popular models having 2 DOF, 4 DOF, 6 DOF and 8 DOF were investigated, too. The proposed model has 12 DOF in total. This number of DOF could be increased; this, however, would result in a greater difference between the considered models, thus making it more difficult to evaluate the impact of the additional DOF of shafts. As a benchmark, the dynamic meshing force in the considered analytical models was calculated. Simulations were carried out with and without friction. Additionally, for the 12 DOF model, the effects of the position of the centre of gear and the centre of mass were investigated.