Tooth surface geometry optimization of spiral bevel and hypoid gears generated by duplex helical method with circular profile blade

In order to effectively improve meshing performance of spiral bevel and hypoid gears generated by the duplex helical method, the effects of straight lined and circular cutting edges profile on meshing and contact of spiral bevel and hypoid gears were investigated analytically. Firstly, a mathematical model of spiral bevel and hypoid gears with circular blade profile was established according to the cutting characteristics of the duplex helical method. Based on a hypoid gear drive, the tooth bearings and the functions of transmission errors of four design cases were analyzed respectively by the use of the tooth contact analysis(TCA), and the contact stresses of the four design cases were analyzed and compared using simulation software. Finally, the curvature radius of the circular profile blade was optimized. The results show that the contact stresses are availably reduced, and the areas of edge contact and severe contact stresses can be avoided by selecting appropriate circular blade profile. In addition, the convex and concave sides are separately modified by the use of different curvature radii of inside and outside blades, which can increase the flexibility of the duplex helical method.

Tooth surface error correction of hypoid gears machined by duplex helical method

In this work,synchronous cutting of concave and convex surfaces was achieved using the duplex helical method for the hypoid gear,and the problem of tooth surface error correction was studied.First,the mathematical model of the hypoid gears machined by the duplex helical method was established.Second,the coordinates of discrete points on the tooth surface were obtained by measurement center,and the normal errors of the discrete points were calculated.Third,a tooth surface error correction model is established,and the tooth surface error was corrected using the Levenberg-Marquard algorithm with trust region strategy and least square method.Finally,grinding experiments were carried out on the machining parameters obtained by Levenberg-Marquard algorithm with trust region strategy,which had a better effect on tooth surface error correction than the least square method.After the tooth surface error is corrected,the maximum absolute error is reduced from 30.9μm before correction to 6.8μm,the root mean square of the concave error is reduced from 15.1 to 2.1μm,the root mean square of the convex error is reduced from 10.8 to 1.8μm,and the sum of squared errors of the concave and convex surfaces was reduced from 15471 to 358μm^(2).It is verified that the Levenberg-Marquard algorithm with trust region strategy has a good accuracy for the tooth surface error correction of hypoid gear machined by duplex helical method.

Virtual System Solution of CNC Machine for Spiral Bevel and Hypoid Gears

A virtual computerized numerical control C CNC） processing system is built for spiral bevel and hypoid gears. The pre-designed process of the solution to locate the way of realization is investigated. A kind of combined programming method and principle of solid modeling are chosen. Multienvironmental programming thought and the inter-connected mechanisms between different environments are applied in the proposed system. The problems of data exchange and compatibility of modules are settled. Environment of the system is founded with object oriented programming thought. AutoCAD is located as the graphic environment. Matlab is used for editing the computation module. Virtual C ＋＋6.0 is the realization environment of the main module. Windows is the platform for realizing the multi-environmental method. Through establishing the virtual system based windows message handling mechanism and the component object model, the application of multienvironmental programming is realized in the manufacture system simulation. The virtual gear product can be achieved in the accomplished software.

NC METHOD FOR GENERATION OF CONJUGATING HYPOID GEARS BASED ON NC’S FLEXIBILITY

It is known that manufacture of hypoid gears is difficult and complicated,the reason lies on the limitation of traditional mechanical machine tools. With the development ofNC machine tools, there should be new ways of cutting this kind of gear. Therefore, an idea togenerate gears with conjugating tooth surfaces is proposed, based on the 'flexibility'characteristic of NC that means various motions, in a sense, can be performed, arbitrarily on NCmachine tools. Using this method, the direction of the contact path on tooth surfaces can becontrolled, and also, theoretically, the generated tooth surfaces can transmit motion at specifictransmission ratio curve.

NEW DESIGN METHOD FOR HYPOID GEARS

A digital model is presented for the purpose of design, manufacture and measurement of hypoid gear, based on the non-uniform rational B-spline surface （NURBS） method. The digital model and the function-oriented active design technique are combined to form a new design method for hypoid gears. The method is well adaptable to CNC bevel gear cutting machines and CNC-controlled gear inspection machines, and can be used to create the initial machine tool cutting location data or program measurement path. The presented example verifies the method is correct.

TOOTH CONTACT FINITE ELEMENT ANALYSIS OF SPIRAL BEVEL AND HYPOID GEARS

A very useful new method of tooth contact finite element analysis(TCFEA) for spiralbevel and hypoid gears is presented, combines 3-d finite element contact stress analysis withLTCA (Loaded Tooth Contact Analysis). The TCFEA uses mixed finite element method to ana-lyze the 3-d contact stress. The related formulas are derived and an efficient analyzing method asseveral pairs of teeth in contact occurs is presented, which greatly reduce the computationalamount. It is of great significance that the tooth stress. geometry. contact condition and load areall considered in the same model. Finally the related experimental results are used to verify thesolution of TCFEA .

Application and dynamical performance simulation of tooth surface measured data of hypoid gear

The tooth surface shape of hypoid gear is very complicated, and tooth surface accuracy of hypoid gear can be measured by using the latticed measurement and scanning measurement. Advantages and disadvantages of the two measurement patterns are compared and application of their measurement data on hypoid gear＇s quality management is analyzed. How to use these measurement data to simulate the dynamical performance of hypoid gear is researched, and the intelligent predicton of the dynamical performance indexes of contact spot, root stress, vibration exciting forces and load distribution and hertz contact stress on the tooth surface are carried out. This research work has an important guiding sense to design and ma- chine hypoid gear with low vibration and noise.

Accurate Modeling of the Spiral Bevel and Hypoid Gear with a New Tooth Profile

Distinguishing with traditional tooth profile of spiral bevel and hypoid gear, it proposed a new tooth profile namely the spherical involute. Firstly, a new theory of forming the spherical involute tooth profile was proposed. Then, this theory was applied to complete parametric derivation of each part of its tooth profile. For enhancing the precision, the SWEEP method used for formation of each part of tooth surface and G1 stitching schema for obtaining a unified tooth surface are put forward and made the application in the accurate modeling. Lastly, owing to the higher accuracy of tooth surface of outputted model, it gave some optimization approaches. Given numerical example about the model can show that this designed gear with spherical involute tooth profile can achieve fast and accurate parametric modeling and provide a foundation for tooth contact analysis （TCA） in digitized design and manufacture.

Parametric relationship between hypoid gear teeth and accurate face-milling cutter

The cutter systems of hypoid gear cutting machines contain groups of inside and outside blades.In these cutter systems,the side cutting edges of the blades machine the convex and concave gear teeth while rotating about the cutter rotation axis.The side cutting edges lay on the rake face formed through the blade,rake,and relief angles;hence,the normal cross-section of the cutter swept surface forms hyperboloid gear teeth.Using the accurate geometry of the cutter system,a relationship between the pressure and spiral angles of the gear tooth and the parameters of the cutter system is developed for the FORMAT machining of a hypoid gear.A new parameterization of the gear tooth surfaces is introduced to determine these angles for the accurate gear tooth by the accurate cutter system.A numerical example with different cutter systems and blade parameters is presented,demonstrating the effects of rake and relief angles over the pressure and spiral angles on mea n point projections and gear tooth surface.Finally,the change in pressure and spiral angles with respect to the rake and relief angles are plotted,and the results are analyzed.Finally,it is concluded that the pressure and spiral angles are changed up to a few seconds of a degree in the operating area of the tooth with the change in the back and side rake angles.The side relief angle exhibited little or no effect over the geometry of the gear tooth.