Vilmos Simon

Load distribution in hypoid gears

A new approach for the computerized simulation of load distribution in mismatched hypoid gears with point contact is presented. The load distribution calculation is based on the bending and shearing deflections of gear teeth, on the local contact deformations of the mating surfaces, on gear body bending and torsion, on the deflections of the supporting shafts, and on the manufacturing and alignment errors of the mating members. The tooth deflections of the pinion and gear teeth are calculated by FEM, and the tooth contact is treated in a special way: it is assumed that the point contact under load spreads over a surface along the potential contact line, which line is made up of the points of the mating tooth surfaces in which the separations of these surfaces are minimal, instead of assuming an elliptical contact pattern. The system of governing equations is solved by approximations and by using the successive-over-relaxation method. The corresponding computer program is developed. The calculations, performed by this program, show that in the case of hypoid gears, the new approach gives a more realistic contact pattern and contact pressure than the usually assumed and applied elliptical contact approach, especially for the tooth pairs contacting on the toe and on the heel of teeth, and in the case of load distribution calculations made in misaligned gear pairs. By using this program the influence of design data on load distribution parameters is investigated and discussed.

Design and Manufacture of Spiral Bevel Gears With Reduced Transmission Errors

A method for the determination of the optimal polynomial functions for the conduction of machine-tool setting variations in pinion teeth finishing in order to reduce the transmission errors in spiral bevel gears is presented. Polynomial functions of order up to five are applied to conduct the variation of the cradle radial setting and of the cutting ratio in the process for pinion teeth generation. Two cases were investigated: in the first case the coefficients of the polynomial functions are constant throughout the whole generation process of one pinion tooth-surface, in the second case the coefficients are different for the generation of the pinion tooth-surface on the two sides of the initial contact point. The obtained results have shown that by the use of two different fifth-order polynomial functions for the variation of the cradle radial setting for the generation of the pinion tooth-surface on the two sides of the initial contact point, the maximum transmission error can be reduced by 81%. By the use of the optimal modified roll, this reduction is 61%. The obtained results have also shown that by the optimal variation of the cradle radial setting, the influence of misalignments inherent in the spiral bevel gear pair and of the transmitted torque on the increase of transmission errors can be considerably reduced.

Optimal Tooth Modifications in Hypoid Gears

A method for the determination of optimal tooth modifications in hypoid gears based on improved load distribution and reduced transmission errors is presented. The modifications are introduced into the pinion tooth surface by using a cutter with bicircular profile and optimal diameter. In the optimization of tool parameters the influence of shaft misalignments of the mating members is included. As the result of these modifications a point contact of the meshed teeth surfaces appears instead of line contact; the hypoid gear pair becomes mismatched. By using the method presented in (Simon, V., 2000, “Load Distribution in Hypoid Gears ,” ASME J. Mech. Des., 122, pp. 529–535) the influence of tooth modifications introduced on tooth contact and transmission errors is investigated. Based on the results that was obtained the radii and position of circular tool profile arcs and the diameter of the cutter for pinion teeth generation were optimized. By applying the optimal tool parameters, the maximum tooth contact pressure is reduced by 16.22% and the angular position error of the driven gear by 178.72%, in regard to the hypoid gear pair with a pinion manufactured by a cutter of straight-sided profile and of diameter determined by the commonly used methods.

A survey of message diffusion protocols in mobile ad hoc networks

For the last twenty years, mobile communications have experienced an explosive growth. In particular, one area of mobile communication, the Mobile Ad hoc Networks (MANETs), has attracted significant attention due to its multiple applications and its challenging research problems. On the other hand, the nodes mobility in these networks has introduced new challenges for the routing protocols, especially when the mobility induces multiple disconnections in the network. In this survey, we present an overview of this issue and a detailed discussion of the major factors involved. In particular, we show how messages can be efficiently disseminated in different types of MANETs.

Load Distribution in Cylindrical Worm Gears

A method for the determination of load sharing between the instantaneously engaged worm threads and gear teeth, for the calculation of load distribution along the teeth and transmission errors in different types of cylindrical worm gears is presented. The method covers both cases-that of the theoretical line and point contact. The bending and shearing deflections of worm thread and gear tooth, the local contact deformations of the mating surfaces, the axial deformations of worm body, gear body bending and torsion, deflections of the supporting shafts, and the manufacturing and alignment errors of worm and gear are included. Based on the real load distribution the tooth contact pressure is calculated, in the case of point contact in two different ways, and the obtained results are compared. Also, the total transmission error, consisting of the kinematical transmission error due to the mismatch of the worm gear drive and of the transmission error caused by the deflections of worm thread and gear teeth, is calculated. The method is implemented by a computer program. By using this program the influence of the type of worm gear drive and of design and manufacturing parameters on load distribution and transmission errors is investigated and discussed.

Optimal Machine Tool Setting for Hypoid Gears Improving Load Distribution

A method for the determination of optimal machine tool setting for manufacturing modified (mismatched) hypoid gears based on improved load distribution and reduced transmission errors is presented. The applied load distribution calculation is based on the conditions that the total angular position errors of the gear teeth being instantaneously in contact under load must be the same, and along the contact line of every tooth pair instantaneously in contact, the composite displacements of tooth surface points-as the sums of tooth deformations, geometrical surface separations, gear body bending and torsion, deflections of the supporting shafts, misalignments, and composite tooth errors-should correspond to the angular position of the gear. The tooth deformations consists of the bending and shearing deflections of gear teeth and of the local contact deformations of the mating surfaces. The tooth deflections are calculated by the finite element method. As the equations governing the load sharing and load distribution are nonlinear, an approximate and iterative technique is used to solve this system of equations. The method is implemented by a computer program. Using the program that was developed the influence of machine tool setting parameters for pinion manufacture on maximum tooth contact pressure, load distribution factor, and transmission errors is investigated. By successively choosing the optimal value for every machine tool setting parameter, and by applying the optimal set of these parameters, the maximum tooth contact pressure is reduced by 5.8%, the load distribution factor by 5.9%, and the angular position error of the driven gear by 65.4%, in regard to the hypoid gear pair manufactured by the machine tool setting determined by the commonly used method.

FEM stress analysis in hypoid gears

Abstract Stress analysis in hypoid gears by using finite element method is performed in order to develop simple equations for the calculation of tooth deflections and stresses. A displacement type finite element method is applied with curved, twenty-node isoparametric elements. A method is developed for the automatic finite element discretization of the pinion and the gear. The full theory of mismatched hypoid gears is applied for the determination of the nodal point coordinates on the teeth surfaces. The corresponding computer program is developed. By using this program the influence of design parameters and load position on tooth deflections and fillet stresses is investigated. On the basis of the results, obtained by performing a big number of computer runs, by using regression analysis and interpolation functions, equations for the calculation of tooth deflections and fillet stresses are derived. The advantages of the use of these equations in load distribution calculation in hypoid gears are shown.

Machine-Tool Settings to Reduce the Sensitivity of Spiral Bevel Gears to Tooth Errors and Misalignments

The method for loaded tooth contact analysis is applied for the investigation of the combined influence of machine-tool settings for pinion teeth finishing and misalignments of the mating members on load distribution and transmission errors in mismatched spiral bevel gears. By using the corresponding computer program, the influence of pinions offset and axial adjustment error, angular position error of the pinion axis, tooth spacing error, and machine-tool setting correction for pinion teeth finishing, on tooth contact pressure, tooth root stresses, and angular displacement of the driven gear member from the theoretically exact position based on the ratio of the numbers of teeth is investigated. On the basis of the obtained results, the optimal combination of machine-tool settings is determined. By the use of this set of machine-tool settings, the maximum tooth contact pressure and transmission errors can be significantly reduced. However, in some cases, by the use of appropriate machine-tool settings for the reduction of tooth contact pressure, the angular displacement of the driven gear increases. Therefore, different optimized combinations of machine-tool settings for pinion tooth finishing for the reduction of the sensitivity of gears to misalignments in regard to maximum tooth contact pressure and transmission errors should be applied. By the use of the combination of machine-tool settings to reduce the sensitivity of gears to misalignments in regard to transmission errors, a slight reduction of maximal tooth contact pressure is achieved, too.

Computer Aided Loaded Tooth Contact Analysis in Cylindrical Worm Gears

A method for computer aided loaded tooth contact analysis in different types of cylindrical worm gears is proposed. The method covers both cases-that of the theoretical line and point contact. The geometry and kinematics of a worm gear pair based on the generation of worm gear teeth by a hob is presented. The full loaded tooth contact analysis of such a gear pair is performed. A computer program based on the theoretical background presented has been developed. By using this program the path of contact, the potential contact lines, the separations of mating surfaces along these contact lines, the load distribution and transmission errors for different types of modified and nonmodified worm gear pairs are calculated and graphically presented. The influence of gear tooth modifications on tooth contact is investigated and discussed.

Load distribution in double enveloping worm gears

A method for the determination of load sharing among the instantaneously engaged worm threads and gear teeth of double enveloping worm gears and for the calculation of load distribution along their instantaneous contact lines is presented. The bending and shearing deflection of worm thread and gear tooth, the contact deformation, the axial deformation of worm body, and the manufacturing and alignment errors of worm and gear are included. The obtained system of integral equations is solved by using approximations and an iterative technique. The corresponding computer program is developed. By using this program, the load distribution in the classical and in a new type of double enveloping worm gear drives is calculated. The influence of design parameters on load distribution factor and on maximum tooth pressure is investigated and discussed.