with the merits of the easy manufacture and the long service life and the processing the inside or outside form surface, round body form tool is extensive use in large scales production. Its main demerit is the big hy...with the merits of the easy manufacture and the long service life and the processing the inside or outside form surface, round body form tool is extensive use in large scales production. Its main demerit is the big hyperbolic error which is caused in the process of processing cone, but about the discussion of hyperbolic error, there are two drawbacks in the current books and documents: (1) The error measuring plane is established on the rake face of tool, which doesn’t coincide with the actual measuring plane (axial plane) of work piece; (2) When the influential elements of error are analyzed, single parameter is only discussed. In order to overcome these demerits, the mathematical model of hyperbolic error on the axial plane of work piece is built in this paper when round body form tool processes cone. The fundamental reason which causes hyperbolic error when round body form tool processes cone is that the line profile replaces the curve profile of theory in the radial cut plane of tool in the design and manufacture of tool. In order to evaluate the mathematical formula of its error, firstly, the equation of cone of work piece must be established, secondly, the equation of cutting lip in the rake face is established, then, the profile equation of the radial plane of tool is evaluated on the condition that coordinate is changed, at last, the hyperbolic error is derived according to the equation and the substitutional line equation, and the error is converted to the axial plane of work piece which is coincided with the measuring plane. The actual calculation and the theory analysis indicated that if the cone length and the coning of the cone of work piece are fixed, the main elements which affect the hyperbolic error in the axial plane of work piece are the outside diameter R of round body form tool, the rake angle and the rear angle in "base point". If these three parameters are combined rationally, the hyperbolic error is minimum when round body form tool process cone, and the machining precision of work piece can be improved, on the condition that neither the work capacity of the tool design nor the manufacture cost of tool increases.展开更多
文摘with the merits of the easy manufacture and the long service life and the processing the inside or outside form surface, round body form tool is extensive use in large scales production. Its main demerit is the big hyperbolic error which is caused in the process of processing cone, but about the discussion of hyperbolic error, there are two drawbacks in the current books and documents: (1) The error measuring plane is established on the rake face of tool, which doesn’t coincide with the actual measuring plane (axial plane) of work piece; (2) When the influential elements of error are analyzed, single parameter is only discussed. In order to overcome these demerits, the mathematical model of hyperbolic error on the axial plane of work piece is built in this paper when round body form tool processes cone. The fundamental reason which causes hyperbolic error when round body form tool processes cone is that the line profile replaces the curve profile of theory in the radial cut plane of tool in the design and manufacture of tool. In order to evaluate the mathematical formula of its error, firstly, the equation of cone of work piece must be established, secondly, the equation of cutting lip in the rake face is established, then, the profile equation of the radial plane of tool is evaluated on the condition that coordinate is changed, at last, the hyperbolic error is derived according to the equation and the substitutional line equation, and the error is converted to the axial plane of work piece which is coincided with the measuring plane. The actual calculation and the theory analysis indicated that if the cone length and the coning of the cone of work piece are fixed, the main elements which affect the hyperbolic error in the axial plane of work piece are the outside diameter R of round body form tool, the rake angle and the rear angle in "base point". If these three parameters are combined rationally, the hyperbolic error is minimum when round body form tool process cone, and the machining precision of work piece can be improved, on the condition that neither the work capacity of the tool design nor the manufacture cost of tool increases.
