CN104634294A  Method for detecting and evaluating geometric error of grooved pulley of curved groove  Google Patents
Method for detecting and evaluating geometric error of grooved pulley of curved groove Download PDFInfo
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 CN104634294A CN104634294A CN201510059141.5A CN201510059141A CN104634294A CN 104634294 A CN104634294 A CN 104634294A CN 201510059141 A CN201510059141 A CN 201510059141A CN 104634294 A CN104634294 A CN 104634294A
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Classifications

 G—PHYSICS
 G01—MEASURING; TESTING
 G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
 G01B21/00—Measuring arrangements or details thereof in so far as they are not adapted to particular types of measuring means of the preceding groups
Abstract
Description
Technical field
The present invention relates to the geometric error detection and assessment field of complex profile, particularly relate to a kind of detection and assessment method of curved groove sheave geometric error.
Background technology
Sheave is that a kind of structure is simple, and transmission efficiency is high, and can in order to a kind of intermittent motion mechanism of accurate calibration.Usual sheave is all made up of straightline groove, and low cost of manufacture is widely used; But straightline groove is due to defects such as existence impacts, and the relevant design of curved groove sheave is more and more with application, and the manufacture of curved groove also becomes with detection the necessary links ensureing sheave serviceability.Because Geneva mechanism is normally realized by the relative motion of straight pin and groove.In order to ensure that straight pin accurately enters groove, there is higher requirement to groove relative to relative position between the position of benchmark and groove.
Summary of the invention
The invention provides a kind of detection and assessment method of curved groove sheave geometric error, the present invention is basic detecting instrument with three coordinate measuring machine, proposing by rotating the method overlapped, achieving easy measurement and the evaluation of curved groove sheave complex position degree, described below:
A detection and assessment method for curved groove sheave geometric error, described detection and assessment method comprises the following steps:
Three coordinate measuring machine is used to obtain measurement data, the i.e. coordinate of some points of two sides of each groove;
Measurement data is processed: by the coordinate of two sides by calculating the coordinate of measuring point on Central Symmetry face; Then by rotating the theoretical position place measurement point actual coordinate of different curved groove and theoretical coordinate being rotated to same groove;
Calculate the distance of all measurement point actual coordinates to theoretical coordinate successively, find maximum distance, be multiplied by after 2 as the Section 1 error result in complex position degree error;
Calculate the distance of all measurement point actual coordinates to theoretical curved surface successively, the position of a theoretical curved surface is found by optimized algorithm, make the distance of Distance Theory curved surface measurement point Distance surface farthest reach minimum, be multiplied by the Section 2 error result as recombination site error after 2;
Measurement and the evaluation of complex position degree error complete.
The beneficial effect of technical scheme provided by the invention is: this method uses multimeter, data processing method is simple, be applicable to the complex position degree error of all kinds of curved groove of Exact Solution and straightline groove sheave, thus improve detection efficiency and measuring accuracy, reduce testing cost.
Accompanying drawing explanation
The schematic three dimensional views of Fig. 1 a sheave;
The XY scheme of Fig. 1 b sheave;
The method for arranging (two dimension) of Fig. 2 a measuring point;
The method for arranging (threedimensional) of Fig. 2 b measuring point;
The position view of Fig. 3 surving coordinate system;
Fig. 4 measurement point carries out the method schematic diagram rotated;
Fig. 5 tolerance range (dash area) schematic diagram.
Embodiment
For making the object, technical solutions and advantages of the present invention clearly, below embodiment of the present invention is described further in detail.
Detection and assessment error term of the present invention is the race group complex position degree error of sheave, belongs to into the complex position degree error category of stack features.
In ASME14.5 2009, for become the complex position degree of stack features just like giving a definition: complex position degree provides a kind of application process of position degree for the relative position become between the position of each feature in stack features and each feature.Usually, for becoming each feature in stack features all to have a looser position degree requirement, between each feature, relative position has stricter position degree requirement simultaneously.Position due to curved groove sheave is determined by the central plane of its groove face, so should using the complex position degree error of central plane as detection and evaluation project.
101: use three coordinate measuring machine to obtain measurement data, the i.e. coordinate of some points of two sides of each groove;
The present invention is directed have the sheave of curved groove, because plane is special curved surface, be equally also applicable to the sheave of straightline groove.As Fig. 1 a, 1b are respectively a kind of schematic three dimensional views and the XY scheme with the sheave of four curved grooves.Curved groove is generally be made up of two symmetroids, has two kinds of situations during measurement: sheave is regarded as 2D part by one, or measuring accuracy thinner at sheave requires comparatively under low condition usually; Two regard as 3 d part, under sheave thickness is comparatively large or measuring accuracy requires high condition.
For the first situation, two groove faces of sheave can think plane curve, a plane parallel with sheave reference field A should be chosen in a rational position of NSide surf and a certain side of sheave crossing, obtain an intersection curve, and on this curve reasonable Arrangement measuring point.
For the second situation, two groove faces of sheave are all space curved surfaces, now, should use some parallel with sheave benchmark A planes and a certain side of sheave crossing after, obtain the curve of respective numbers, and reasonably arrange measuring point on these curves.
The point layout mode of two kinds of situations is as shown in Fig. 2 a, 2b.
Three coordinate measuring machine (CMM) is used to measure
1. surving coordinate system sets up: surving coordinate system is determined (as Fig. 3) by the measurement basal plane of CMM and the axis of sheave endoporus.
2. measure: according to the measuring point arranged, touch a NSide surf and after obtaining the actual coordinate of measuring point, along the direction touching opposite side curved surface of curved surface normal vector, and the actual coordinate obtained the measuring point of NSide surf, at this, two sides on groove are designated as U face and V face, as Fig. 2 a, shown in 2b.
Be defined as follows several symbol:
On a kth groove, the theoretical coordinate of ith measuring point in U face is designated as be respectively X, Y, Z coordinate figure; Actual coordinate is designated as be respectively X, Y, Z coordinate figure.
On a kth groove, the theoretical coordinate of ith measuring point in V face is designated as be respectively X, Y, Z coordinate figure; Actual coordinate is designated as be respectively X, Y, Z coordinate figure.
The threedimensional of the point in sheave U, V face measured by CMM asks for the threedimensional deriving key element (central plane), assuming that each of each groove upper measurement n point.The theoretical coordinate of ith point on the central plane of a kth groove is designated as
By the coordinate of the point on U, V face point on computing center face with the computing method of coordinate as shown in the formula:
Overlapping inclusion principle: suppose that the theoretical equation of each groove center face under respective local coordinate system is S
^{k}(x, y, z), by CMM obtain and on the kth calculated a groove center face actual coordinate of ith point be
theoretical coordinate is
Each groove of sheave has symmetrical feature, if by each groove by rotational transform to same position, the theoretical center face of each groove just can overlap, simultaneously, the measurement point belonging to each groove center face is rotated in the same way, the relative position in measuring point and theoretical center face can't be changed, as shown in Figure 4.Therefore, will utilize this principle that measurement point is overlapped to same position, then carry out error evaluation.
The actual coordinate of the point after rotation is designated as
theoretical coordinate is designated as
For four groove sheaves shown in Fig. 2, it is as follows that actual coordinate rotates the method overlapped:
It is as follows that theoretical coordinate rotates the method overlapped:
Wherein the correct angle of theory of the physical location of each groove measurement point and the position after rotating, the actual coordinate of the point after rotation, it is the theoretical coordinate of the point after rotation.
The process that such as the 2nd slotted eye rotates to the position at groove 1 place is
I.e. postrotational theoretical coordinate actual coordinate
102: measurement data is processed: by the coordinate of two sides by calculating the coordinate of measuring point on Central Symmetry face; Then by rotating the theoretical position place measurement point actual coordinate of different curved groove and theoretical coordinate being rotated to same groove;
103: calculate the distance of all measurement point actual coordinates to theoretical coordinate successively, find maximum distance, be multiplied by after 2 as the Section 1 error result in complex position degree error;
104: calculate the distance of all measurement point actual coordinates to theoretical curved surface successively, the position of a theoretical curved surface is found by optimized algorithm, make the distance of Distance Theory curved surface measurement point Distance surface farthest reach minimum, be multiplied by the Section 2 error result as recombination site error after 2;
105: measurement and the evaluation of complex position degree error complete.
The Tolerance of Degree of position of curve sheave central plane (line) should be: derive key element (for face centered by 3D by theory, line centered by 2D) centered by face (line), width is the region of the formation of two symmetroids (line) of t.For qualified sheave, the upper any point of its actual central plane (line) must be positioned within this region.
For complex position degree tolerance, except abovementioned tolerance, there is another location degree tolerance for this sheave, in order to guarantee the accuracy of the relative position between race.Contrary in order to avoid there is the central plane bias direction of each groove, cause the relative position error excessive, a tolerance range should be specified, after now requiring that the actual coordinate of any measurement point on the central plane of all grooves rotates to the same coordinate system, the tolerance range of requirement width should be positioned at.
Finally, the measurement point of qualified part should be positioned at the overlapping region of two tolerance ranges.For the tolerance of such as Fig. 5, namely require the point on each groove center face to be positioned at region that width is the formation of two symmetroids of t1, the position in this region should be positioned at the symmetrical both sides in groove theoretical center face; Meanwhile, a little should be positioned at a width be t2 two symmetroids form region, the position in this region is not fixed.
Represented by limited measurement point owing to measuring curved surface, each measurement point has a unique point corresponding with it on theoretical central plane, and be called mathematical point, measurement point and mathematical point form two separately and gather, and measures point set and theoretical point set.Obviously, now to form a point right for measurement point and corresponding mathematical point, the Euclidean distance of 2 between measurement point can be expressed as a little pair to the d distance of tested curved surface:
d(p,S)＝pq _{2}
Wherein p measures any point in point set P, and q is any point in theoretical point set Q, S representation theory curved surface (line).
Because error depends on the distance of that point to curved surface that error is maximum.Therefore target finds Distance surface that point farthest.
The actual coordinate that sheave according to definition is put and theoretical coordinate, Evaluation model should be:
Represent and calculate the distance of each some actual coordinate to theoretical coordinate, and the distance finding that maximum, be designated as f _{1};
And,
Represent the distance of the theoretical coordinate of actual coordinate after rotation and translation calculating each point, and the distance finding that maximum, be designated as f _{2};
In abovementioned formula,
represent that the measurement point belonging to a kth race central plane is to the distance of mathematical point;
S _{1}representation theory curved surface (line), i.e. race theoretical center face (line);
S _{2}represent the theoretical curved surface (line) moved through overrotation peace, namely rotate and translation trailing wheel groove theoretical center face (line);
F _{1}represent that in each groove, face is relative to the distance of the point farthest of self theoretical position;
F _{2}represent the distance of all grooves relative to the point farthest of position, common center face;
R represents a rotation matrix
Then position error value is e _{1}=2f _{1}, e _{2}=2f _{2}.
Evaluation algorithm:
Evaluation process is a kind of optimizing process, and evaluation algorithm is in fact a kind of optimized algorithm.
Design variable is R and T, unconfined condition, and mathematical form is designated as:
Objective function:
Design variable:
Adopt the abovementioned optimization problem of the common optimization algorithm solution such as genetic algorithm or particle cluster algorithm, namely can obtain f _{1}, f _{2}, then position error value is e _{1}=2f _{1}, e _{2}=2f _{2}.
It will be appreciated by those skilled in the art that accompanying drawing is the schematic diagram of a preferred embodiment, the invention described above embodiment sequence number, just to describing, does not represent the quality of embodiment.
The foregoing is only preferred embodiment of the present invention, not in order to limit the present invention, within the spirit and principles in the present invention all, any amendment done, equivalent replacement, improvement etc., all should be included within protection scope of the present invention.
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CN109341634A (en) *  20181129  20190215  株洲中航动力精密铸造有限公司  Precision cast turbine blades molding surface size measurement method 
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CN101413793A (en) *  20081127  20090422  天津大学  Method for assessing composite space type face geometric error 
US20110044513A1 (en) *  20090819  20110224  Harris Corporation  Method for nwise registration and mosaicing of partial prints 
CN102809364A (en) *  20120709  20121205  天津大学  Method for determining complex curved surface profile error 

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Patent Citations (5)
Publication number  Priority date  Publication date  Assignee  Title 

JP2005127825A (en) *  20031023  20050519  Asanuma Giken:Kk  Simple accuracy evaluation program for coordinate measuring machine 
CN1773213A (en) *  20041113  20060517  鸿富锦精密工业（深圳）有限公司  Complex position degree computing system and method 
CN101413793A (en) *  20081127  20090422  天津大学  Method for assessing composite space type face geometric error 
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CN102809364A (en) *  20120709  20121205  天津大学  Method for determining complex curved surface profile error 
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CN109341634A (en) *  20181129  20190215  株洲中航动力精密铸造有限公司  Precision cast turbine blades molding surface size measurement method 
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