A novel approach to calculating the dynamic error reflected on an S-shaped test piece

This paper proposes a novel approach to calculating the dynamic error distribution reflected on an S-shaped test piece. First, a numerical model of an S-shaped test piece is established, and the distribution characteristics for the twist angle and curvature are analysed. Second, a delay continuous method (DCM), which can transform the discrete input into a delayed step input, is presented to express the single-axis dynamic error affected by the input quantitatively in the form of a mathematical expression. Based on the sinusoidal input, the feasibility of the DCM is verified by comparing the experimental results of a Simulink simulation model and a mathematical expression derived by the DCM. Third, according to a new three-point tangential (NTPT) positioning algorithm and the DCM, this article makes the first attempt to investigate the quantitative calculation method of the influence of the dynamic performance of a servo feed system for five-axis numerical control (NC) machine tools on the dynamic error distribution for S-shaped test pieces after processing. Parameter p, representing the dynamic characteristic of the servo feed system, is varied to compare the difference of the dynamic error distribution law on S-shaped test pieces. The calculation results show that the parameter p can be adjusted to reduce the dynamic error of the final machined test pieces. It is important to improve the dynamic performance of servo feed systems for five-axis NC machine tools and enhance the machining quality of test pieces. In addition, compared with the calculation results of the dynamic error distribution for an NAS979 test piece, the S-shaped test piece can reflect the dynamic performance of the servo feed system for five-axis NC machine tools more accurately and effectively. Finally, the effectiveness of the proposed calculation method is verified through processing experiments on a five-axis NC machine tool.

Evaluation of Contacting Effect Between Tool and Workpiece on Vibration Characteristics of NC Machine Tools

It is expected that the vibration characteristics of NC machine tools are affected by the contact between the tool and the workpiece during the cutting operations. However, the influences of the contact have not been clarified up to now. In this study, a method to evaluate the contacting effect and evaluated results are described. Frequency response of a vertical type milling machine during cutting operation is evaluated in this study. The evaluation tests of the contacting effect are carried out with and without cutting operations. In order to clearly evaluate the influence of the contact between a tool edge and a workpiece, boring operations of 50 mm diameter are carried out. The frequency responses are measured by using feed motor torque. Impulse signal is applied to the motor torque command during the cutting operations to oscillate the machine tool, and the axial acceleration of the table is measured to obtain the frequency responses. The impulse signal can be applied by refereeing the spindle rotational angle to control the relationships between the cutting edge and workpiece surface. As the results of the evaluations, it is clarified that the proposed method can evaluate the influence of the contact adequately. The natural frequency slightly increases and the vibration amplitude decreases when the tool contacts with the workpiece, regardless of whether non-cutting or cutting. It has also been confirmed that the vibration amplitude of the frequency characteristics is changed due to the contact length and the relative direction of the cutting edge.

Development of Scanning Line Tool Path Generation Algorithm Using Boundary Position Information of Approximate Polyhedron of Complex Molds

In the manufacturing industry, molds are required for mass production operations, and the industry’s recent small lot, multi-product production systems call for such molds to be made by NC machine tools in short periods of time. The tool path point coordinates of NC machine tools are derived by geometric computations, which are used in turn to derive the polyhedron-approximated mold surface and the contact positions of the tool. In the conventional method, however, placing surplus tool path points on the planar section makes it difficult to acquire the boundary position coordinate values in the vicinity of the boundaries of the polyhedrons that constitute the curved surface, resulting in errors in the path point coordinates for the polyhedron-approximated shape of the mold surface. In this study, therefore, we have developed CAM algorithms that can reduce the tool path errors and suppress the number of tool path points by not deriving the path point coordinates in the linearly approximated section. This is done by using the boundary information of the approximate polyhedrons that constitute the concave section of the mold model.