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 PDF

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Publication number
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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CN
China
Prior art keywords
theoretical
coordinate
curved
error
groove
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CN201510059141.5A
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Chinese (zh)
Inventor
何改云
郭龙真
丁伯慧
桑一村
郎爱蕾
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天津大学
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Priority to CN201510059141.5A priority Critical patent/CN104634294A/en
Publication of CN104634294A publication Critical patent/CN104634294A/en

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    • GPHYSICS
    • G01MEASURING; TESTING
    • G01BMEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
    • G01B21/00Measuring arrangements or details thereof in so far as they are not adapted to particular types of measuring means of the preceding groups

Abstract

The invention discloses a method for detecting and evaluating the geometric error of a grooved pulley of a curved groove. The detection and evaluation method comprises the following steps: processing measurement data: calculating coordinates on two side faces to obtain the coordinate of a measuring point on a center symmetrical plane; rotating the practical coordinates and theoretical coordinates of the measuring points of different curved grooves to the theoretical position of an identical groove; calculating the distances between the practical coordinates to the theoretical coordinates of all the measuring points in sequence, finding a maximum distance, and multiplying the maximum distance by 2 to obtain a first error result in a composite position error; calculating the distances between the practical coordinates of all the measuring points and a theoretical curved surface in sequence, finding the position of a theoretical curved surface through an optimization algorithm in order that the distance between a farthest measuring point of the theoretical curved surface and the curved surface is minimized, and multiplying the minimized distance by 2 to obtain a second error result of the composite position error; finishing the measurement and evaluation of the composition position error. By adopting the method, simple measurement and evaluation of the composite position degree of the grooved pulley of the curved groove are realized.

Description

A kind of detection and assessment method of curved groove sheave geometric error

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 straight-line groove, and low cost of manufacture is widely used; But straight-line 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 straight-line 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 X-Y scheme of Fig. 1 b sheave;

The method for arranging (two dimension) of Fig. 2 a measuring point;

The method for arranging (three-dimensional) 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 ASME-14.5 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 straight-line groove.As Fig. 1 a, 1b are respectively a kind of schematic three dimensional views and the X-Y 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 N-Side 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 N-Side 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 N-Side 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 i-th 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 i-th 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 three-dimensional of the point in sheave U, V face measured by CMM asks for the three-dimensional deriving key element (central plane), assuming that each of each groove upper measurement n point.The theoretical coordinate of i-th point on the central plane of a kth groove is designated as Q i C k = ( q xi C k , q yi C k , q zi C k ) , Actual coordinate is designated as P i C k = ( p xi C k , p yi C k , p zi C k ) .

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:

( q xi C k , q yi C k , q zi C k ) = 1 2 [ ( q xi u k , q yi u k , q zi u k ) + ( q xi v k , q yi v k , q zi v k ) ]

( p xi C k , p yi C k , p zi C k ) = 1 2 [ ( p xi u k , p yi u k , p zi u k ) + ( p xi v k , p yi v k , p zi v k ) ]

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 i-th point be theoretical coordinate is Q i C k = ( q xi C k , q yi C k , q zi C k ) .

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 Q i C k ~ = ( q xi C k ~ q yi C k ~ , q zi C k ~ ) .

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 above-mentioned 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)=||p-q|| 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:

f 1 = max { max { | d 1 k ( P i C k ~ , S 1 ) | , i = 1,2 , . . . , n } , k = 1,2,3,4 } = max { max { | P i C k ~ - Q i C k ~ | , i = 1,2 , . . . , n } , k = 1,2,3,4 }

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,

f 2 = min { max { | d 2 k ( P i C k ~ , S 2 ) | , i = 1,2 , . . . , n , k = 1,2,3,4 } } = min { max { | P i C k ~ - ( R Q i C k + T ~ ) | , i = 1,2 , . . . , n , k = 1,2,3,4 } }

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 above-mentioned formula,

represent that the measurement point belonging to a kth race central plane is to the distance of mathematical point;

S 1representation theory curved surface (line), i.e. race theoretical center face (line);

S 2represent the theoretical curved surface (line) moved through over-rotation peace, namely rotate and translation trailing wheel groove theoretical center face (line);

F 1represent that in each groove, face is relative to the distance of the point farthest of self theoretical position;

F 2represent the distance of all grooves relative to the point farthest of position, common center face;

R represents a rotation matrix R = 1 γ - β - γ 1 α β - α 1 , α, beta, gamma represents the angle rotated around X, Y, Z axis respectively, and T represents a translation vector T = δ x δ y δ z , δ x, δ y, δ zrepresent the distance along X, Y, Z axis translation respectively;

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:

f 1 = max { max { | d 1 k ( P i C k ~ , S 1 ) | , i = 1,2 , . . . , n } , k = 1,2,3,4 } = max { max { | P i C k ~ - Q i C k ~ | , i = 1,2 , . . . , n } , k = 1,2,3,4 }

f 2 = min { max { | d 2 k ( P i C k ~ , S 2 ) | , i = 1,2 , . . . , n , k = 1,2,3,4 } } = min { max { | P i C k ~ - ( R Q i C k + T ~ ) | , i = 1,2 , . . . , n , k = 1,2,3,4 } }

Design variable: R = 1 γ - β - γ 1 α β - α 1 , T = δ x δ y δ z

Adopt the above-mentioned 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.

Claims (1)

1. a detection and assessment method for curved groove sheave geometric error, is characterized in that, 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.
CN201510059141.5A 2015-02-04 2015-02-04 Method for detecting and evaluating geometric error of grooved pulley of curved groove CN104634294A (en)

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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN109341634A (en) * 2018-11-29 2019-02-15 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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JP2005127825A (en) * 2003-10-23 2005-05-19 Asanuma Giken:Kk Simple accuracy evaluation program for coordinate measuring machine
CN1773213A (en) * 2004-11-13 2006-05-17 鸿富锦精密工业(深圳)有限公司 Complex position degree computing system and method
CN101413793A (en) * 2008-11-27 2009-04-22 天津大学 Method for assessing composite space type face geometric error
US20110044513A1 (en) * 2009-08-19 2011-02-24 Harris Corporation Method for n-wise registration and mosaicing of partial prints
CN102809364A (en) * 2012-07-09 2012-12-05 天津大学 Method for determining complex curved surface profile error

Patent Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JP2005127825A (en) * 2003-10-23 2005-05-19 Asanuma Giken:Kk Simple accuracy evaluation program for coordinate measuring machine
CN1773213A (en) * 2004-11-13 2006-05-17 鸿富锦精密工业(深圳)有限公司 Complex position degree computing system and method
CN101413793A (en) * 2008-11-27 2009-04-22 天津大学 Method for assessing composite space type face geometric error
US20110044513A1 (en) * 2009-08-19 2011-02-24 Harris Corporation Method for n-wise registration and mosaicing of partial prints
CN102809364A (en) * 2012-07-09 2012-12-05 天津大学 Method for determining complex curved surface profile error

Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN109341634A (en) * 2018-11-29 2019-02-15 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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