Spherical Surface Machining Method of CNC Machine Tool Based on Quaternion Helical Spherical Interpolation Method
A technology for CNC machine tools and spherical surface processing, which is applied in the direction of program control, computer control, and general control systems, etc., and can solve problems such as unfavorable interpolation calculations of Euler angles and universal joint locking.
Active Publication Date: 2020-09-22
KEDE NUMERICAL CONTROL CO LTD
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Problems solved by technology
For the calculation of space arc and helix, it is necessary to use Euler angles for rotational motion calculations, but Euler angles are not conducive to interpolation operations, and there are problems such as universal joint locking
Method used
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Embodiment 1
[0071] Embodiment 1: Spherical helix quaternion interpolation method
[0072] Utilize the foregoing formula to carry out the technical description in this paper in conjunction with examples, specifically as Figure 7 process shown.
[0073] Functional requirements: Given a space sphere, the center of the sphere Ball radius r, for spherical interpolation.
[0074] First, the spherical helix is generated using formula 2.3. To take the value of the program control variable, the helix rotates 100 times. When t=0, it is the starting point of the helix; when t=1, it is the end point of the helix.
[0075]
[0076] Then, use the formula 3.2 to convert to the quaternion q(t) representation.
[0077]
[0078] Finally, perform interpolation according to formula 3.3, and the quaternion value after interpolation is represented by V(u). u∈[0,1] is a variable controlled by the program. and The quaternion representation of two adjacent points generated for the helix, the ...
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The invention discloses a numerical control machine tool spherical surface processing method based on a quaternion helical line spherical surface interpolation method. The processing method comprisesthe following steps of S1, obtaining numerical control machine tool given parameter information: processing sphere center coordinates, processing sphere radius r, taking sphere processing range t andthreaded generated turn number n; S2, performing generated spherical surface helical line quaternion; S3, on the basis of a principle of performing space circular arc interpolation by a quaternion method, performing interpolation between every two points of the helical line from the starting point until the operation is performed to the finished point; completing the whole spherical surface helical line interpolation calculation; S4, moving a numerical control machine tool to a processing starting point; realizing spherical surface processing of the numerical control machine tool on the basisof the interpolation result of the S3. The method is applied to spherical surface interpolation occasions; the problem of gimbal lock of Euler angle and the problem of overgreat rotation matrix calculation quantity can be effectively solved, so that the processing efficiency and the processing quality of a five-axis numerical control machine tool are improved.
Description
technical field [0001] The invention relates to a spherical surface processing of a five-axis numerical control machine tool, and more specifically relates to the acquisition and processing of a spherical surface. Background technique [0002] At present, in the numerical control system, for the processing of the space spherical surface, the method of approximating the space curve with a small line segment is generally used, but this method has poor accuracy, large amount of calculation and low efficiency. In this paper, the interpolation method of space arc is adopted, and the curve to be processed is approached by space arc. For the calculation of space arcs and helical lines, Euler angles need to be used for rotational motion calculations, but Euler angles are not conducive to interpolation operations, and there are problems such as universal joint locking. [0003] In addition, in order to illustrate the technical content of the present invention, the following backgrou...
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IPC IPC(8): G05B19/41
CPCG05B19/41
Inventor 王磊刘沛董大鹏林猛程浩李荣东黄玉彤李欣泽李耀东
Owner KEDE NUMERICAL CONTROL CO LTD