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Κατεργασία Οδοντώσεων

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3D Προσομοίωση φραιζαρίσματος με κύλιση οδοντώσεων - HOB3D


In most of demanding torque transmission systems, the key components are premium well designed and properly fabricated gears. The gear hobbing process is widely applied for the construction of any external tooth form developed uniformly about a rotation center. As presented at the Figures above, the kinematics principle of the process is based on three relative motions between the workpiece and the hob tool. To produce spur or helical gears, the workpiece rotates about its symmetry axis with certain constant angular velocity, synchronized with the relative gear hob rotation. Depending on the hobbing machine used, the worktable or the hob may travels along the work axis with the selected feed rate.

Despite the fact that a big variety of simulating methods have been proposed, their main characteristic is the reduction of the actual 3-Dimensional process to planar models, primarily for simplification reasons. The application of these former approximations is leading to planar results, without to represent the exact solid geometry of a real chip, with accuracy straightly dependent from various input parameters such as the number of the calculation planes. Furthermore, any post processing of the extracted chip and gear planar geometries requires additional data processing which leads to supplementary interpolations of the 2-Dimensional results. Targeting to the realistic and accurate simulation of the gear hobbing process, without inevitable modeling insufficiencies, a new research modeling approach, based on 3-Dimensional Computer Aided Design, is proposed. This effective and factual simulation, in contrast to former modeling efforts, is primitively realistic, since the produced gear and chips geometry are normal results of successive penetrations and material removal of cutting teeth into a solid cutting piece. A software program called HOB3D is developed for the guidance of an existent commercial CAD system, exploiting its powerful modeling and graphic capabilities. HOB3D is built in terms of a computer program in Visual Basic, providing the extend ability to other cutting processes based on the same cutting principle. The resulting solid models output formats offer realistic parts, chips and work gears, easily managed for further individual research or as an input to any other CAD, CAM or FEA commercial software packages.

The essential input data of HOB3D concern the determination of the hob and work gear geometries and the cutting parameters that take place for the completion of the simulation process. When the values of the input parameters are set, the work gear solid geometry is created in the CAD environment and one hob tooth rake face profile is mathematically and visually formed. At the same moment the assembly of the effective cutting hob teeth (N) is determined. The kinematics of gear hobbing process is directly applied in one three dimensional tooth gap of the gear, considering the axisymetric configuration. Moreover, a 3D surface is formed for every generating position, combining the allocation of the two involved parts, following a calculated spatial spline as a track.



These surface paths are used to identify the undeformed chip solid geometry, to split the subjected volume and to create finally the chip and the remaining work gear continuous solid geometries.



After the completion of one work cycle, i.e. the termination of every spatial surface paths and the subtraction of the chip solid geometries, the produced gear gap is finally generated. The following Figure illustrates a cross section (Detail A) of the generated gear gap, formed by the collective work of every generating position. As it is shown, the remaining gear solid geometry holds complete geometrical information, both for the removed and the remaining material.


The flowchart of the simulation process is presented at the figure below.



The output chip solid geometries at fifteen characteristic generating positions of two different test cases for the production of a spur gear, UC and CL, produced by the activation of the HOB3D code, are presented in the left and right parts of the next Figure. Except of the direction of the axial feed, every other input data are identical, for both examined cases. Examining each of the resulting chips, is obvious that so much as the extreme geometrical changes of the chip shapes are sufficiently determined, even if the generated chip solid is parted from more than one domains.



The 3D solid geometrical development of the UC case is presented at the animated figure below:

while the 3D geometrical characteristics of the generating position G.P.: -4 are presented below:



The output chip solid geometries for the production of a helical gear are presented in the following Figure. Examining each of the resulting chips, is obvious that so much as the extreme geometrical changes of the chip shapes are sufficiently determined, even if the generated chip solid is parted from more than one domains.






Για περισσότερες πληροφορίες επικοινωνήστε με:  Δρ. Μηχ. Δημητρίου Βασίλειος - Πτυχ. Μαθηματικός
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