CN103745098A - Numerical control machine tool single-shaft geometrical angle motion error separation method - Google Patents

Numerical control machine tool single-shaft geometrical angle motion error separation method Download PDF

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Publication number
CN103745098A
CN103745098A CN201310732821.XA CN201310732821A CN103745098A CN 103745098 A CN103745098 A CN 103745098A CN 201310732821 A CN201310732821 A CN 201310732821A CN 103745098 A CN103745098 A CN 103745098A
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China
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normal vector
vector
shaft
angular motion
error
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CN201310732821.XA
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Chinese (zh)
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郭俊杰
李海涛
王金栋
王兴
邱娟
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Xian Jiaotong University
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Xian Jiaotong University
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Priority to CN201310732821.XA priority Critical patent/CN103745098A/en
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Abstract

A numerical control machine tool single-shaft geometrical angle motion error separation method comprises the steps of measuring three fixed coordinates of the motion axis to obtain a uniaxial normal vector, and comparing the uniaxial normal vector with an initial standard normal vector to solve a uniaxial geometrical angle motion error. The whole solving process can be finished only by utilizing analytical geometry knowledge, and an algorithm is simple and reliable. Compared with a single geometrical error measurement method, the efficiency is greatly improved. Compared with a comprehensive geometrical error measurement method, the separation method is very simple.

Description

How much angular motion error separation methods of a kind of numerically-controlled machine single shaft
Technical field
The present invention relates to the Errors Measurement for CNC Machine Tools field, particularly how much angular motion error separation methods of a kind of numerically-controlled machine single shaft.
Background technology
Space object has six-freedom degree, is respectively the rectilinear motion degree of freedom of X, Y, Z direction and the rotary freedom around X, Y, Z tri-axles.So, numerically-controlled machine single shaft geometric error also just comprises six, is respectively three straightness errors and the angle of pitch, deflection angle and three angular motion errors of the angle of pitch of X, Y, Z direction.For geometric error, conventionally there are two kinds of individual event geometric error mensuration and composition error mensurations.Individual event geometric error mensuration is measured for a certain error in six errors, this method is simple, with strong points, but often adopts different measuring equipments for each error, six geometric errors detections that complete single shaft are often consuming time very long, inefficiency.Composition error mensuration detects single shaft global error, then adopts error separation algorithm to isolate six errors.The advantage of this method is simple to operate, but often more complicated of error separation algorithm.
Summary of the invention
In order to overcome the shortcoming of above-mentioned prior art, the object of the present invention is to provide how much angular motion error separation methods of a kind of numerically-controlled machine single shaft, can isolate effectively fast any two in three angular motion errors.
For achieving the above object, the present invention has adopted following technical scheme:
How much angular motion error separation methods of a kind of numerically-controlled machine single shaft, comprise the following steps:
1) before measuring, on numerically-controlled machine single shaft, look for any three point of fixity A, B, C, determine its volume coordinate, and ask for the space law vector by these 3 the definite planes of institute, be defined as the vectorial N of basic taper method;
2) while measuring, lathe single shaft moves and starts sampling for the first time after a segment distance, and three point of fixity move to A 1, B 1, C 1position, determines its volume coordinate, and ask for by these 3 the space law vector of definite plane, be defined as follow-up normal vector N 1;
3) solve wherein two angular motion errors, comprise following two substeps:
The first step: by follow-up normal vector N 1place tapered plane is rotated counterclockwise around Z axis, until tapered plane overlaps with basic taper method vector N, rotation angle α is first angular motion error;
Second step: follow-up normal vector N 1after over-rotation, become normal vector N 1', by normal vector N 1the tapered plane at ' place turns clockwise around X-axis until overlap with basic taper method vector N, and rotation angle β is second angular motion error;
4) to all subsequent sampling position repeating step 2) to step 3), obtain the distribution of two angular motion errors in all positions of whole single shaft.
Beneficial effect of the present invention is embodied in:
The present invention, by measuring kinematic axis three fixing coordinates, asks for the normal vector of single shaft, then by and initial baseline normal vector between contrast solve three angular motion errors of single shaft.In whole solution procedure, only need cartesian geometry knowledge just can complete, algorithm is simple and reliable.Greatly improve with individual event geometric error mensuration phase specific efficiency, compared with synthetic geometry error measure method, separation algorithm is very simple.
Accompanying drawing explanation
Fig. 1 is how much angular motion error separation principle figure of single shaft.
Fig. 2 is that normal vector is at each three-dimensional surface perspective view.
Embodiment
Below in conjunction with drawings and Examples, the invention will be further described.
How much angular motion error separation methods of a kind of numerically-controlled machine single shaft, comprise the following steps:
1) before measuring, on numerically-controlled machine single shaft, look for any three point of fixity A, B, C, determine its volume coordinate, and ask for by these 3 the space law vector of definite plane, be defined as basic taper method vector N=(a, b, c), wherein a, b, c is respectively the X of normal vector N, Y, Z coordinate figure;
2) while measuring, machine tool motion axle moves and starts sampling for the first time after a segment distance, and three point of fixity move to A 1, B 1, C 1, determine its volume coordinate, and ask for by these 3 the space law vector of definite plane, be defined as follow-up normal vector N 1=(a 1, b 1, c 1), wherein a 1, b 1, c 1be respectively normal vector N 1x, Y, Z coordinate figure,
3) solve wherein two angular motion errors, comprise following two substeps:
The first step: as shown in Figure 1, by follow-up normal vector N 1place tapered plane A 1b 1g 1h 1around Z axis, be rotated counterclockwise, until tapered plane A 1b 1g 1h 1overlap with basic taper method vector N place tapered plane ABGH, tapered plane A 1b 1g 1h 1and the angle α between tapered plane ABGH is first angular motion error;
To be rotated counterclockwise as just, can obtain following formula:
α = ∠ E 1 A 1 H 1 - ∠ EAH = arcsin a 1 a 1 2 + b 1 2 - arcsin a a 2 + b 2
After over-rotation, tapered plane A 1b 1g 1h 1rotate to A 1b 1g 1' H 1' position, tapered plane A 1b 1g 1' H 1' overlap completely with tapered plane ABGH, follow-up normal vector N 1rotate to N 1' position, N 1' be in same plane with N;
Second step: by normal vector N 1the tapered plane A at ' place 1d 1' G 1' F 1' around X-axis, turn clockwise until overlap with basic taper method vector N place tapered plane ADGF, tapered plane A 1d 1' G 1' F 1' and tapered plane ADGF between angle β be second angular motion error;
β = ∠ EAF - ∠ E 1 ′ A 1 F 1 ′ = arcsin c b 2 + c 2 - arcsin c 1 ′ b 1 ′ 2 + c 1 ′ 2
In formula b 1 ′ = a 1 2 + b 1 2 , c 1 ′ = c 1 ,
So β = arcsin c b 2 + c 2 - arcsin c 1 a 1 2 + b 1 2 + c 1 2
Wherein two of three angular motion error demand solutions, for the proof of conclusions:
As shown in Figure 2, space law vector with it at XOY, YOZ, the sine value of the projection angle of ZOX plane is respectively sin δ = c ′ a ′ 2 + b ′ 2 + c ′ 2 , sin θ = b ′ a ′ 2 + b ′ 2 + c ′ 2 , so there is following relational expression:
Above four equatioies can be regarded as with δ, θ, equation, and separate, therefore, known wherein three equatioies just can be obtained whole unknown numbers.That is to say, known process vector sum plane X OY, YOZ, in ZOX angle any two, just can calculate the 3rd angle, and normal vector is also unique to be determined.
For the discussion of angular motion error separation order and separation value:
In step 3), normal vector first rotates around Z axis, then around X-axis, rotates, and the anglec of rotation is respectively:
α = arcsin a 1 a 1 2 + b 1 2 - arcsin a a 2 + b 2
β = arcsin c b 2 + c 2 - arcsin c 1 a 1 2 + b 1 2 + c 1 2
If first rotate around X-axis, then around rotating around Z axis, the anglec of rotation is respectively:
α = arcsin c 1 b 1 2 + c 1 2 - arcsin c b 2 + c 2
β = arcsin a b 2 + c 2 - arcsin a 1 a 1 2 + b 1 2 + c 1 2
This shows, rotation order difference, the anglec of rotation is also just different.
Select different turning axles, the angle of rotation is also just different.Error compensation global matrix is that the form that six error matrixes multiply each other obtains.This just requires the calculating of error global matrix to carry out according to error separation order.
4) to all subsequent sampling position repeating step 2) to step 3), can obtain the distribution of all position angle kinematic errors of whole kinematic axis.

Claims (1)

1. how much angular motion error separation methods of numerically-controlled machine single shaft, is characterized in that, comprise the following steps:
1) before measuring, on numerically-controlled machine single shaft, look for any three point of fixity A, B, C, determine its volume coordinate, and ask for the space law vector by these 3 the definite planes of institute, be defined as the vectorial N of basic taper method;
2) while measuring, lathe single shaft moves and starts sampling for the first time after a segment distance, and three point of fixity move to A 1, B 1, C 1position, determines its volume coordinate, and ask for by these 3 the space law vector of definite plane, be defined as follow-up normal vector N 1;
3) solve wherein two angular motion errors, comprise following two substeps:
The first step: by follow-up normal vector N 1place tapered plane is rotated counterclockwise around Z axis, until tapered plane overlaps with basic taper method vector N, rotation angle α is first angular motion error;
Second step: follow-up normal vector N 1after over-rotation, become normal vector N 1', by normal vector N 1the tapered plane at ' place turns clockwise around X-axis until overlap with basic taper method vector N, and rotation angle β is second angular motion error;
4) to all subsequent sampling position repeating step 2) to step 3), obtain the distribution of two angular motion errors in all positions of whole single shaft.
CN201310732821.XA 2013-12-24 2013-12-24 Numerical control machine tool single-shaft geometrical angle motion error separation method Pending CN103745098A (en)

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CN107806825A (en) * 2017-09-29 2018-03-16 西安交通大学 The line lathe space geometry error measure discrimination method of three face five based on plane grating

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Publication number Priority date Publication date Assignee Title
CN107806825A (en) * 2017-09-29 2018-03-16 西安交通大学 The line lathe space geometry error measure discrimination method of three face five based on plane grating

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