Modeling the accuracy in the process of mechanical treatment of worm-wheels of worm gears with a concave profile of the worm turn

Abstract

Вперше теоретично доведено й експериментально підтверджено необхідність та доцільність підвищення точності механічної обробки черв’ячних коліс шляхом застосування нових черв’ячних фрез із поділеним на три частини по висоті профілем інструментальної рейки. Встановлено, що для підвищення точності механічної обробки черв’ячного колеса профіль інструментальної рейки черв’ячної фрези необхідно поділити на три частини по висоті, а кількість зубців фрези повинна дорівнювати 12. Отримано математичні моделі процесу механічної обробки черв’ячних коліс циліндричних черв’ячних передач з угнутим профілем витка черв’яка.For the first time it was theoretically proved and experimentally confirmed the necessity and expediency in increase of accuracy in mechanical treatment of worm-wheels using new worm hobs with a divided in three parts according to the height profile of a tool rack. It was stated that in order to increase the accuracy of mechanical treatment of a worm-wheel, the profile of a tool rack of a worm hob should be divided in three parts according to the height and the quantity of teeth of the hob should equal 12. We received mathematical models of the process of treatment of worm-wheels of cylindrical worm gears with concave profile of a worm turn. The object of the research included geometrical characteristics of a worm-wheel such as deviation of output circuit (left and right sides) of teeth of the worm-wheel Fα, μm; deviation of pitch (left and right sides) of teeth of the worm-wheel from nominal fPt, μm; accumulated error of a pitch (left and right sides) FP, μm; radial runout Fn, μm; deviation in tooth profile of a worm-wheel (left and right sides) ff , μm; diameter of a wheel cave Df, mm. We disclosed positive dependence in the process of mechanical treatment of a worm-wheel on the quantity of parts of profile division according to the height of tool rack of a worm hob N, which under other equal conditions with the increase of N there is a redistribution of allowance between passes and a change in the scheme of metal removal out of the caves between teeth of a wheel which is being cut. As a result the quantity of passes of the hob nпр decreases which leads to a decrease in a wheel’s tooth cut and in deviation of output circuit of the right and left sides of a tooth of a worm-wheel which increases the accuracy of treatment. Also we disclosed a considerable influence of the quantity of teeth of the worm hob on the deviation of the output circuit of a worm-wheel under mechanical treatment using tangential infeed. The increase of the number of racks increases the quantity of cuts which allows improving the accuracy of treatment. Moreover, the increase in number of racks leads to the increase of the coefficient of front overlap in machine engagement of a worm hob- blank. This allows decreasing irregularity in cutting, dynamic loading and increasing the accuracy of treatment. Due to the fact that the worm hob with a divided in three parts profile according to the height of a tool rack has located on the same helix teeth for the first, second and third passes with equal diameter of caves and different outer diameters, the treatment of a worm-wheel is carried out with one installation which improves the accuracy in treatment