Error analysis of worm grinding wheel precise dressing by diamond roller with straight profile

In worm grinding wheel dressing with diamond roller, using straight line instead of theoretical curve of roller will result in dressing error. Method of the precise dressing is studied, while the mathematical model is presented. Theoretical curve of diamond roller is calculated based on the space meshing theory and helicoid equation of worm grinding wheel. The fitting error between the theoretical curve and approximate straight line which is obtained by the theoretical curve is calculated. The dressing error on normal section of worm grinding wheel is analyzed. The case study of a kind of worm grinding wheel with single head shows that the dressing error increases with diameter decreasing of worm grinding wheel and diamond roller, while the variation of diamond roller’s diameter makes little contribution. The validity of worm grinding wheel dressing using straight line diamond roller is proved, and the algorithm can be used as guidance in practice.     

Envelope to a two-parameter family of point vectors method for surface swept by wheel during 5-axis gear form grinding

The wheel generating curve for gear grinding is always a composited curve which is composed of lines and arcs,and the calculation of the envelope surface is more complex than conventional rotary cutter. A method of envelope to a two-parametric family of point vectors is proposed,which defines the point and its normal vector on the wheel generating curve as a point vector. Each point vector corresponds to a virtual ball uniquely. The rotation of point vector forms latitude circle and the valid envelopment movement forms sectional circle. The intersection of latitude circle and sectional circle is grazing point. The analytical calculation model is established,in which the grazing point is determined by the geometry parameters of virtual ball and the velocity of virtual ball center,and the geometry parameters of virtual ball can be directly calculated from point vector. The kinematic geometry of 5-axis form gear grinder is analyzed. The coordinate transformation between fixed frame and moving frame is conducted,and the velocity of virtual ball center based on NC codes is obtained. An example is presented to demonstrate the effectiveness of the method which can be used for 5-axis gear grinding geometry simulation,accuracy evaluation and optimization of the wheel path.     

Meshing performance analysis of planar internal gear enveloping crown worm driving

A new worm driving,i.e. planar internal gear enveloping crown worm driving,is presented. Its mathematical model of meshing functions and teeth surface equations are established basing on the theory of differential geometry and gear mesh. Various types of the driving,the macroscopic meshing performance and the microcosmic meshing performance are analyzed. The results show that the inclination angle of generating plane determines the distribution of contact lines,the planar internal gear primary-enveloping crown worm driving has ideal lubrication property,and the planar internal gear second-enveloping crown worm driving has high loading capacity. The studies are practicably instructive for developing new worm driving with high loading capacity,ideal lubrication and small volume.     

Accurate mathematical models for relief grinding of gear hob cutters

A mathematical model for accurate relief grinding of gear hob cutters along radial directions is presented based on the analysis of grinding geometry. Both the design and manufacturing models of gear hob cutters are carefully derived and presented. By employing the plane envelope theory, the reference contour of the grinding wheel is determined in order to attain the design tool profile precisely. The tooth profile error model after regrinding is also given to confirm the grinding parameters. The model provides accurate solutions for both the tool profile and the sectional contour of the grinding wheel. It is simple and straightforward and can be used to produce high precision hob cutters systematically. Two numerical examples are presented to illustrate the effectiveness of the proposed method. The model computing results indicate that the proposed method is practical, precise and reliable. The method provides valuable reference for the design and machining of hob cutters.     

The machine setting reverse method of spiral bevel gear

The profile error correction of spiral bevel gears is difficult. To solve this problem, the inspected method of spiral bevel gears tooth surface is studied in 3906 gear measuring center. The grids of tooth surface is measured by measurement software. Taking reference tooth surface as the goal, a method of machine setting reverse using approximation algorithms is proposed, and a mathematical model is build. At last, a reverse example based on grinded spiral gear is given. The result shows that the cutting machine setting of bevel gear tooth surface can be exactly calculated.     

The design and application of heavy-duty CNC abrasive belt grinding machine with high precision controllable pitch propeller

Aiming at the backward hand-grinding ways of controllable pitch propeller in China shipbuilding industry, a highly efficient precision grinding method is brought forward, and a four axes simultaneous grinding machine is designed which can machining complex profile with abrasive belt grinding technology by CNC. The key techniques to develop this new grinding machine is presented in detail such as heavy-duty belt grinding head, NC grinding computer aided software, etc. The application experiments of grinding and polishing propeller blade are carried out on the basis of different parameters, and the trial results provide foundation for the confirmation and application of reasonable belt grinding and polishing parameters.