Abstract: A new approach has been developed to estimate the
load share and distribution of worm gear drives, and to calculate the
instantaneous tooth meshing stiffness. In the approach, the worm gear
drive was modelled as a series of spur gear slices, and each slice was
analyzed separately using the well-established formulae of spur gear
loading and stresses. By combining the results obtained for all slices,
the entire envolute worm gear set loading and stressing was obtained. The geometric modelling method presented allows tooth elastic
deformation and tooth root stresses of worm gear drives under
different load conditions to be investigated. Based on the slicing
method introduced in this study, the instantaneous meshing stiffness
and load share are obtained. In comparison with existing methods,
this approach has both good analysis accuracy and less computing
time.
Abstract: Large rotating systems, especially gear drives and gearboxes, occur as parts of many mechanical devices transmitting the torque with relatively small loss of power. With the increased demand for high speed machinery, mathematical modeling and
dynamic analysis of gear drives gained importance. Mathematical description of such mechanical systems is a complex task evolving for several decades. In gear drive dynamic models, which include flexible shafts, bearings and gearing and use the finite elements, nonlinear effects due to gear mesh and bearings are usually ignored, for such models have large number of degrees of freedom (DOF) and it is computationally expensive to analyze nonlinear systems with large number of DOF. Therefore, these models are not suitable for simulation of nonlinear behavior with amplitude jumps in frequency response. The contribution uses a methodology of nonlinear large rotating system modeling which is based on degrees of freedom (DOF) number reduction using modal synthesis method (MSM).
The MSM enables significant DOF number reduction while keeping
the nonlinear behavior of the system in a specific frequency range.
Further, the MSM with DOF number reduction is suitable for
including detail models of nonlinear couplings (mainly gear and
bearing couplings) into the complete gear drive models. Since each
subsystem is modeled separately using different FEM systems, it
is advantageous to parameterize models of subsystems and to use
the parameterization for optimization of chosen design parameters.
Final complex model of gear drive is assembled in MATLAB and
MATLAB tools are used for dynamical analysis of the nonlinear
system. The contribution is further focused on developing of a
methodology for investigation of behavior of the system by Nonlinear
Normal Modes with combination of the MSM using numerical
continuation method. The proposed methodology will be tested using
a two-stage gearbox including its housing.