Differential Tooth Surface Modification Method for Reducing Vibration in Spiral Bevel and Hypoid Gears

High-performance tooth flank collaborative optimization model for spiral bevel and hypoid gears

Gears with a complex curve tooth, such as spiral bevel and hypoid gears, lack an ideal technique for the final finishing process. Pulse electrochemical finishing (PECF) is considered a promising method for surface finishing due to its micro-removal characteristics. A PECF system for spiral bevel gear (SBG) is established according to the generation of SBG tooth surfaces. An SBG (module, 12 mm; number of teeth, 38) is selected as the processing test piece, and mathematical models are developed for analyzing the characteristics of PECF. The influence of the experimental variables, including applied voltage, interelectrode gap, and finishing time, on the total removal thickness and surface roughness is discussed. The calculated values are found to be approximately consistent with the experimental values. The other parameters, including the concentration of electrolyte, tool rotational speed, flow rate of electrolyte, and pulse period, are also studied. Results show that the roughness of the SBG tooth surface is reduced from Rz 7.13 to 4.32 μm. The precision of the SBG is also improved.

A general mathematical model for the generated gear tooth surfaces of spiral bevel and hypoid gears is established based on the three-axis CNC bevel gear machine. According to the principle and the method for the function-oriented design of point-contact tooth surfaces, the locus of spatial tooth contact points on the tooth surface is described on the axial plane of the gear, and then the detailed formulae for the design with the generated gear are derived from the mathematical model. The mathematical model and the formulae can be used in the function-oriented design of point-contact tooth surfaces of spiral bevel and hypoid gears with the gear generated in different types on both the three-axis CNC bevel gear machine and the conventional cradle one.

The Gleason face hobbing process has been widely applied by the gear industry. But so far, few papers have been found regarding exact modeling and simulation of the tooth surface generations and tooth contact analysis (TCA) of face hobbed spiral bevel and hypoid gear sets. This paper presents the generalized theory of the face hobbing generation method, mathematic models of tooth surface generations, and the simulation of meshing of face hobbed spiral bevel and hypoid gears. The face hobbing indexing motion is described and visualized. A generalized description of the cutting blades is introduced by considering four sections of the blade edge geometry. A kinematical model is developed and analyzed by breaking down the machine tool settings and the relative motions of the machine elemental units and applying coordinate transformations of the elemental motions. The developed face hobbing generation model is directly related to a physical bevel gear generator. A generalized and enhanced TCA algorithm is proposed. The face hobbing process has two categories, non-generated (Formate®) and generated methods, applied to the tooth surface generation of the gear. In both categories, the pinion is always finished with the generated method. The developed tooth surface generation model covers both categories with left-hand and right-hand members. Based upon the developed theory, an advanced tooth surface generation and TCA program is developed and integrated into Gleason CAGE™for Windows Software. Two numerical examples are provided to illustrate the implementation of the developed mathematic models.

In this paper, we present a method for the global optimization of the tooth contact pattern and transmission error of spiral bevel and hypoid gears, which includes three optimization objectives, three control parameters, and a complex-constrain genetic algorithm solving method. A new set of fundamental equations for pitch cone parameters of hypoid gear drives are established, as well as the relationships between pitch cone and curvature parameters. Based on this theory, three control parameters are selected to determine the pinion tooth surface. A hypoid gear drive is chosen for case studies. The results verify that the optimization methodology can achieve the expected optimization objectives and has good convergence. Correlations between optimization objectives and control parameters are discussed. Furthermore, a finite element model of a simplified hypoid gear drive system is established and its quasi-static meshing characteristics analyzed. The results again confirm the correctness of the optimization method. The effects of torque load on the contact pattern and transmission error are discussed. The results provide a theoretical reference for geometric calculations, quasi-static analysis, and optimal design of spiral bevel and hypoid gears.

Because the contact patterns of spiral bevel and hypoid gears are highly sensitive to tooth flank geometry, it is desirable to reduce the flank deviations caused by machine errors and heat treatment deformation. Several methods already proposed for flank correction are based on the cutter parameters, machine settings, and kinematical flank motion parameters of a cradle-type universal generator, which are modulated according to the measured flank topographic deviations. However, because of the recently developed six-axis Cartesian-type computer numerical control (CNC) hypoid generator, both face-milling and face-hobbing cutting methods can be implemented on the same machine using a corresponding cutter head and NC code. Nevertheless, the machine settings and flank corrections of most commercial Cartesian-type machines are still translated from the virtual cradle-type universal hypoid generator. In contrast, this paper proposes a flank-correction methodology derived directly from the six-axis Cartesian-type CNC hypoid generator in which high-order correction is easily achieved through direct control of the CNC axis motion. The validity of this flank-correction method is demonstrated using a numerical example of Oerlikon Spirac face-hobbing hypoid gears made by the proposed Cartesian-type CNC machine.

In this chapter, a general survey is first done on the tooth bending strength of bevel gears in the broadest meaning, including straight, helical (or skew), Zerol, spiral bevel and hypoid gears and the main factors affecting the tooth root stress state are defined. Attention is paid to the fatigue breakage at the tooth root of these gears and safety factor to be used for their design. The theoretical bases of calculation of tooth bending strength, already discussed in previous chapters, are then recalled, particular those concerning the Lewis constant strength parabola, 30° tangent and cantilever rectangular plate with constant thickness subject to bending load, with which the gear tooth is simulated. The methods of adaption of these theoretical bases to bevel gears are then described. A large part of the chapter is reserved for the procedures to calculate the tooth bending strength of these types of gears in accordance with the ISO standards, highlighting when deemed necessary as the relationships used by the same ISO are founded on the theoretical bases previously recalled.

<div class="htmlview paragraph">Current and future motor vehicle development demands improvement in the areas of economy, environmental acceptability and noise reduction. The performance and manufacture of bevel and hypoid gear sets will also be subject to the same improvement requirements.</div> <div class="htmlview paragraph">The above issues will be discussed from a viewpoint of an industrial mass production environment and highlight new developments in gear manufacturing with special emphasis on finish grinding of bevel gear sets. Additionally, new procedures and methods, permitting objective gear quality measurement and noise performance, as well as direct correlation to vehicle performance will be taken under consideration.</div> <div class="htmlview paragraph">The integration of manufacturing and test procedures in a closed loop production process will show the best approach to fulfill future OEM demands.</div>

Deproximating Tredgold's Approximation

It is quite difficult to design, manufacture and measure hypoid gears, because it has a complex tooth flank form. Noise and vibration caused by inaccurate tooth flank form of hypoid gears is a big problem in automotive industry, and it becomes clear that a small deviation in tooth flank form can change gear noise considerably. High precision measurement of geometrical accuracy of tooth flank form of hypoid gears becomes recently possible not only by point-to-point measuring method but also by scanning tooth flanks. The measurement of hypoid gear tooth flank form and its data treatment are very difficult jobs because the gear tooth flank form is quite complex. The scanning measurement method which is first developed in the world to measure tooth flank form by using the virtual conjugate reference tooth surface, and the method of usage and treatment of its measured data for hypoid gears are introduced in detail. The scanning measurement has great information and enables quick, fully automated measurement of tooth profile and lead, therefore it is to suit controlling and management of tooth flank form quality for mass production of spiral bevel and hypoid gears. Some experiences and the effectiveness of the measurement of tooth flank form accuracy of hypoid gears are discussed.

The special computer system KONTEPS for calculation of spiral and hypoid bevel gears generally supports technology for the conventional and CNC machines (milling machines). In this system environment, the special computer application generates solid or surface models of gears by cutting simulation. Other computer application, based on Matlab functions and methods of artificial intelligence, supports the tooth contact development. The special classifiers which allow to recognize the tooth contact, select the first, second and third order of changes and support the technologist in manufacturing process. This paper describes computerized integration of design and manufacturing of the spiral and hypoid bevel gear supported by the artificial intelligence.

<div class="htmlview paragraph">There has always been a great deal of misconception about the development of hypoid and spiral bevel contact patterns. Certain design criteria, no load and loaded contact pattern checks, test machine comparisons, and simple deflection tests can be performed quickly to give an idea if the initial contact pattern development is correct. Development time can be shortened and the correct contact pattern can be determined before the long term field and dynamometer testing starts.</div>

<div class="htmlview paragraph">This paper describes and discusses the result of a comprehensive simulation analysis we have carried out to clarify the effects of gear dimensions, tooth surface modification, and manufacturing error on the static transmission error of automotive hypoid gears. Three representative factors have been analyzed contact ratio, crowning and pitch error because these characteristics play the most important role in tooth dimensions, tooth surface modification and manufacturing error. The analysis has clarified the effect of each factor on gear noise, making it possible to prepare a guideline for optimal design of gear dimensions and tooth surface modification under various conditions.</div>

This paper presents a new method to design a seventh-order transmission error for high contact ratio spiral bevel gears by the modified curvature motion method to reach the purpose of reducing or eliminating gear vibration and noise. In this paper, firstly, based on the predesigned seventh-order transmission error, the polynomial coefficients of transmission error curve can be obtained. Secondly, a method named modified curvature motion method is used to generate the spiral bevel gear with the predesigned transmission error. Lastly, based on TCA and LTCA, we verify the feasibility of the modified curvature motion method to generate spiral bevel gear with seventh-order transmission error, and the meshing impact of gear set with the seventh-order and second-order function of transmission error is analyzed and compared. The results of a numerical example show that the seventh-order transmission error acquired by the modified curvature motion method can effectively reduce the meshing impact of spiral bevel gears. The tooth modification method and meshing impact analysis method can serve as a basis for developing a general technique of flank modification for spiral bevel gears.

Dudley's Handbook of Practical Gear Design and Manufacture