Michèle Guingand

A wear model for worm gear

This paper presents a numerical model to predict the wear of worm gear. This last is based on well-known Archard’s wear formulation. The influence of lubrication is taken into account with a local wear coefficient, depending on the ratio between the minimum lubricant film thickness and the amplitude of the surface roughness. When material on a wheel flank is worn, it is then necessary to update the surface profile, consequently the contact pressure calculations. To compute the quasi-static load sharing and thus the contact pressures required for the wear model, the equation of displacement compatibility is solved, using the influence coefficient method, which allows a fast and accurate computing. The bending deflections of the worm and wheel, and the local contact deformations of mating surfaces are included. The Boussinesq theory is applied for calculating the local contact deformations. The bending is determined by the combination of only one standard finite element method computation and interpolation functions. This method allows taking into account the environment of the gear meshing, such as the actual shafts, rim, web, bearing locations, which affect the quasi-static results and thus the wear. In addition, the model allows to obtain numerous results, such as load sharing, contact pressures distribution, transmission error, stiffness, wear distribution, etc. A comparison between theoretical wear predictions and experimental results, issued from the literature, are also presented.

Loaded behaviour of steel/bronze worm gear

Worm gears are widely used in power transmission applications, in which a compact high reduction and a relatively low speed drive is required. This paper presents a numerical model developed to compute the quasi-static load sharing. This method uses the equation of displacement compatibility and the influence coefficient method, which allows a fast and accurate computing. The bending deflections of the gear teeth and worm threads, and the local contact deformations of mating surfaces are included. The bending deflections of the gears are determined with the combination of: only one standard FEM computation and interpolation functions. To calculate the local contact deformations, the Boussinesq theory is used. The model allows to obtain numerous results, such as the load sharing, the contact pressure distribution or the loaded transmission error. The method allows taking into account the environment of the gear meshing, such as the actual shafts, rim, web, bearing locations…

Design and analysis of a spiral bevel gear

Spiral Bevel gears are used in power transmission systems with two crossed shafts. The topic of the paper is a model for helping the spiral bevel gear design, depending on meshing parameters. The global parameters of the gear are calculated with the standard ISO 23509 equations. A prediction of the profile modifications has also been performed to center the load pattern on the flank and to minimize the maximum contact pressure. A numerical simulation is achieved with the ASLAN software, developed by LaMCoS laboratory for calculating the quasi-static load sharing of spiral bevel gears.

Comparison of Simulations and Experiments of Loaded Spiral Bevel Gears Behavior

The design of spiral bevel gears is still very complex because tooth geometry and thus kinematics performance depend on the manufacturing process of this type of gear. The cutting process is dominated by two major manufacturers: Gleason and Klingelnberg. The shape of the teeth surfaces are governed by a large number of programmed machine settings, so they cannot be optimized intuitively. Due to the progress made during the last decade by CNC machines and CAM (Computer Aided Manufacturing) softwares, it is now possible to manufacture spiral bevel gears with quite good quality on a 5-axis milling machine.In a previous study, the authors presented a numerical model for calculating the quasi-static load sharing of spiral bevel gears. Two kinds of geometries were developed: a simplified Gleason type, and a geometry based on classical spherical involutes combined with a logarithmic spiral. After being generated using a CAD (Computer-Aided Design) software, these two geometries were manufactured with a 5-axis milling machine controlled by CAM software. A metrological study showed that manufacturing by a 5-axis milling machine can be an alternative to conventional cutting methods.The aim of the present paper is to validate the numerical model. To reach this goal, a test bench was designed to measure the loaded transmission error and visualize the contact patterns. The test bench is integrated inside a numerical 3-axis milling machine: the pinion is mounted on the spindle, while the base of the bench is clamped on its plate. Thus assembly errors can be imposed easily and accurately. Measured and simulated transmission errors are then compared for different axis misalignments cases.Copyright

Quasi-static Load Sharing Model in the Case of Moulded Glass Fibre Reinforced Polyamide 6 Gears

This paper presents a fast and efficient computational method to predict the mechanical behaviour of plastic cylindrical gears made of fibre reinforced polyamide 6. Based on this method, an investigation on the relation between the fibre orientation and the gear behaviour is done. The numerical method uses a viscoelastic model accounting for the temperature, humidity and rotational speed dependence of the gear. This model is developed under the assumption that the material is stressed in its linear domain. The method is performed in three steps: the first one consists of defining the fibre orientation from simulation and experimental results. The second step characterises the viscoelastic behaviour of the material. The third step consists in calculating the load sharing with local meshing, which integrates the viscoelastic model over the entire surface of the tooth. This model permits computation of the load sharing between instantaneously engaged teeth and provides results such as contact pressure, tooth root stress and transmission error. Three fibre orientation models with an increasing complexity are compared. Simulation results show a limited influence of the fibre orientation on the contact pressure and tooth root stress, nevertheless difference up to 10xa0% are observed on the transmission error amplitude.

Experimental and numerical study of a loaded cylindrical glass fibre reinforced PA6 gear

Polymer gears replace metal ones in many motion and light power transmission applications. In order to improve the gears’ performance, glass fibre is added, where their lower cost and higher strength, offers a potential increase in the gears’ performance. This paper presents a numerical method to predict the mechanical and thermal behaviour of fibre reinforced plastic cylindrical gears and its experimental validation. The numerical method uses a viscoelastic model in its linear domain depending on temperature, humidity, rotational speed and fibre orientation. This numerical simulation computes the load sharing between instantaneously engaged gears and provides results such as contact pressure, tooth root stress or transmission error. The numerical results are then compared to experimental measures on a test bench developed at the LaMCoS laboratory. This comparison allows the validation of the load sharing model.

A Static and Dynamic Model of Spiral Bevel Gears

Two three-dimensional lumped parameter dynamic models of spiral bevel gears are presented and compared. The first approach is classic and relies on a single averaged mesh stiffness element connecting the gears whereas a time-varying non-linear distribution of discrete stiffness elements over the potential contact area is used in the second model.