CN108645323B - Involute spur gear wheel total profile deviation assessment method under the influence of installation error - Google Patents
Involute spur gear wheel total profile deviation assessment method under the influence of installation error Download PDFInfo
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- CN108645323B CN108645323B CN201810646085.9A CN201810646085A CN108645323B CN 108645323 B CN108645323 B CN 108645323B CN 201810646085 A CN201810646085 A CN 201810646085A CN 108645323 B CN108645323 B CN 108645323B
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
- G01B5/00—Measuring arrangements characterised by the use of mechanical techniques
- G01B5/20—Measuring arrangements characterised by the use of mechanical techniques for measuring contours or curvatures
- G01B5/202—Measuring arrangements characterised by the use of mechanical techniques for measuring contours or curvatures of gears
Abstract
The invention discloses the involute spur gear wheel total profile deviation assessment methods under the influence of installation error, initially set up coordinate system of machine O0‑X0Y0Z0, tested gear is measured under coordinate system of machine, measurement position includes two Section Points, gear upper end millet cake and the flank profil measurement point up and down of tested gear mandrel, obtains the flank profil measurement point under the influence of installation error；According to two Section Points of mandrel under coordinate system of machine, make Least Square Circle fitting, calculates revolution paraxial equation, establish coordinate system O1‑X1Y1Z1, flank profil measurement point is reverted into initial position, corrects the error of rotary axle of flank profil measurement point；Least square plane fitting is made to tested gear upper surface measurement point, is Z with tested gear upper surface normal vector direction2Axis direction establishes coordinate system O2‑X2Y2Z2, correct the heeling error of flank profil measurement point；Total profile deviation evaluation numerical value is obtained around the rotation angle that the rolling circle center of circle rotates to measurement point by calculating design flank profil, to correct the influence that installation error evaluates total profile deviation.
Description
Technical field
The present invention relates to Precision Inspection and instrument field, the gear-profile under the influence of specifically a kind of installation error is inclined
The assessment method of difference.
Background technique
Gear is most important and most widely used transmission mechanism in machine driving.Gear is widely used in automobile
The fields such as manufacture, aerospace, wind power equipment and equipment manufacturing.The accuracy of gear, quality directly affect the efficiency of equipment, make an uproar
Sound, kinematic accuracy and service life.With the development of science and technology gear is as key components and parts, above-mentioned every profession and trade is to design of gears
The accuracy of manufacture proposes requirements at the higher level.Since gear testing technology complements each other with gear machining technology, the inspection to gear
Survey is just particularly important.
It is known as the measurement of gear individual event deviation by the measurement of measurement item of total profile deviation, spiral deviation and circular pitch deviation.Tooth
Wheel individual event deflection measurements reflect the difference of machine tooling ability and institute's workpieces processing and design size.
Total profile deviation refers to that practical tooth deviates the amount of design flank profil, the telegoniometer in end face and perpendicular to involute profile
Value.Total profile deviation is mainly by the foozle and installation error of cutter during Gear Processing and machine tool drive chain short cycle
Caused by the composite factors such as error.Total profile deviation is defined as tooth profile total deviation, profile geometry by standard ISO1328-1:2013
Deviation and flank profil dip deviation.
The measurement method of total profile deviation generally includes coordinate method and generating, the instrument measured to gear-profile deviation
Have very much, including gear measuring center, three coordinate measuring machine, laser gear measurement machine, gear meshingtester etc., middle gear
Measuring center is most widely used.
When being measured using gear measuring center to gear-profile deviation, due to gear measuring center it is upper and lower it is top not
To just and measurement when the centre of gyration be not overlapped with gear geometric center, to introduce installation error.
The presence of installation error makes the actual measurement location deviation theory measurement position of gear, if not to actual measurement
Data are modified, and will reduce the measurement accuracy of gear measuring center, or even cause gear rating mistake.In order to reduce peace
Influence of the error to gear measurement is filled, the value of installation error should be adjusted to as small as possible, but this requires a great deal of time simultaneously
And installation error cannot completely eliminate.Therefore, quantifier elimination is surveyed with important to the gear-profile deviation under the influence of installation error
Meaning.
Installation error is divided into three parts by the present invention: 1) gear error of rotary axle is since gear measuring center pushes up up and down
Point is not to the location error between just caused practical rotating shaft and theoretical rotating shaft；2) Gear tipping error is in gear geometry
Error of tilt between mandrel and practical rotating shaft；3) gear geometric eccentricity error is the geometric center of gear measured section and returns
Turn the location error between center.Traditional installation error treating method often only considers one of installation error, processing
Process is usually the influence for analyzing installation error to total profile deviation evaluation result, and the compensation of installation error is carried out at result.
The present invention is directed to measure to the gear with installation error, the gear measurement number under the influence of installation error is obtained
According to by the assessment method of invention by gear measurement data correction to ideal mounting position and according to standard ISO1328-1:2013
Gear-profile deviation is evaluated, the gear-profile amount of deflection and rating under ideal position are obtained.
Summary of the invention
To solve the problems, such as to propose in background technique, the invention proposes the gear teeth under the influence of a kind of new installation error
The assessment method of wide deviation.It is inclined that installation error is divided into gear error of rotary axle, Gear tipping error and gear geometry by this method
Heart error is established machine by determination, the determination of gear upper surface law vector and the reverse in the basic circle center of circle to rotating shaft and is sat
Transformation relation between mark system and workpiece coordinate system, so that the flank profil measurement point under the influence of installation error is adapted to ideal installation
Total profile deviation is evaluated according to standard ISO1328-1:2013 in position, and the total profile deviation obtained under ideal mounting position is commented
Determine result and rating.
The technical solution adopted by the present invention is the involute spur gear wheel total profile deviation evaluation side under the influence of installation error
The realization process of method, this method is as follows:
1) coordinate system of machine O is established0-X0Y0Z0, tested gear is measured under coordinate system of machine, measurement position packet
Include two Section Points, gear upper end millet cake and the flank profil measurement point up and down of tested gear mandrel；
2) according to two Section Points for being tested gear mandrel under coordinate system of machine, make Least Square Circle fitting, obtain two
The central coordinate of circle in section is Z with two sections circle center line connecting direction1Axis direction is positive direction in orientation, by coordinate system O0-X0Y0Z0
Successively around X0Axis and Y0Axis rotation makes Z0Axis and Z1Axis is parallel, in plane X0O0Y0It is interior that Z is made by the translation of coordinate system0Axis and Z1Axis
It is overlapped, obtains coordinate system O1-X1Y1Z1.Establish coordinate system O0-X0Y0Z0With coordinate system O1-X1Y1Z1Between transformation relation, obtain
Coordinate system O1-X1Y1Z1Under gear upper end millet cake and flank profil measurement point, and flank profil measurement point is reverted into initial position；
3) according to O1-X1Y1Z1Coordinate system lower gear upper surface measurement point makees plane fitting, obtains gear upper end facial plane side
Journey and its normal vector are Z with the normal vector direction2Axis direction is positive in orientation, with Z1The intersection point O of axis and measured section2For original
Point.By coordinate system O1-X1Y1Z1Successively around X1Axis and Y1Axis rotation makes Z1Axis and Z2Axis is parallel, makes O by the translation of coordinate system1Point
With O2Point is overlapped, and obtains coordinate system O2-X2Y2Z2；
4) coordinate system O is established1-X1Y1Z1With coordinate system O2-X2Y2Z2Between transformation relation.Obtain coordinate system O2-X2Y2Z2
Under flank profil measurement point, due to the presence of installation error, so that flank profil actual measurement location deviates measured section, therefore in coordinate
It is O2-X2Y2Z2Under flank profil measurement point position is modified；
5) according to coordinate system O2-X2Y2Z2Under revised flank profil measurement point establish least square target equation, pass through newton
Solution by iterative method is tested the basic circle center of circle of gear, in X2O2Y2Translational coordination system O in plane2-X2Y2Z2, make Z2Axis is cut by tested
The face basic circle center of circle, establishes workpiece coordinate system Ow-XwYwZw, obtain coordinate system O2-X2Y2Z2With coordinate system Ow-XwYwZwBetween transformation
Relationship obtains the flank profil measurement point under workpiece coordinate system；
6) in workpiece coordinate system Ow-XwYwZwIt is lower to be commented according to total profile deviation of the standard ISO1328-1:2013 to gear
It is fixed, total profile deviation numerical value is obtained around the rotation angle that the rolling circle center of circle rotates to measurement point by calculating design flank profil, thus
The influence that amendment installation error evaluates total profile deviation.
Ideal mounting position is the workpiece coordinate system position corrected after installation error.Two sections up and down of tested gear mandrel
Millet cake or two Section Points for top circle.
Present invention has an advantage that
Gear with installation error is measured, the flank profil measurement data under the influence of installation error is obtained, passes through hair
Bright assessment method by measurement data be adapted to ideal mounting position and according to standard ISO1328-1:2013 it is inclined to gear-profile
Difference is evaluated, and the gear-profile amount of deflection and rating under ideal position is obtained, to have modified installation error to tooth
The influence of wide deviation evaluation.
Detailed description of the invention
Fig. 1 coordinate system of machine establishes schematic diagram.
Fig. 2 number of gear teeth number schematic diagram.
The amendment schematic diagram of Fig. 3 flank profil measurement point.
Fig. 4 non-linear least square target equation establishes schematic diagram.
Fig. 5 workpiece coordinate system establishes schematic diagram.
Fig. 6 involute cylindrical gear total profile deviation Evaluation model schematic diagram.
Fig. 7 is the implementation flow chart of this method.
Specific embodiment
To be more clear derivation process of the invention, the present invention is done furtherly below in conjunction with attached drawing and derivation formula
It is bright.
Establish coordinate system of machine O as shown in Figure 10-X0Y0Z0, with the rotating shaft of gear measuring center and rotating platform
Intersection point is origin, and X, Y, the tri- axis rail direction Z is change in coordinate axis direction.In coordinate system of machine O0-X0Y0Z0Under gear is surveyed
Amount, measurement position include two Section Points, gear upper end millet cake and the flank profil measurement point up and down of tested gear mandrel.
Mandrel section and gear upper surface are measured when gear measuring center rotating shaft registration is zero, by this position
Initial position when as gear measurement guarantees that gear measuring center rotating shaft is motionless, only operates X at this time0、Y0And Z0Axis variation.
Mandrel Section Point is denoted as { P0 Aj_k(X0 Aj_k, Y0 Aj_k, Z0 Aj_k)}；Gear upper end millet cake is denoted as { P0 Uj(X0 Uj, Y0 Uj, Z0 Uj)}；
Flank profil point measurement needs rotating shaft and X0、Y0And Z0Axis is four-axle linked to be measured, and flank profil point is denoted asWith
Wherein, L and R respectively indicates the left and right flank of tooth, and i indicates that i-th of tooth, j indicate at j-th point, and k represents k-th of section, U
Gear upper surface is represented, A represents mandrel surface.
Number of teeth sequence is as shown in Fig. 2, in the case where measuring initial position, with X0The right flank of tooth in lower section first (including with X0Axis phase
Hand over) where tooth be the 1st tooth, be incremented by a clockwise direction.
To two groups of mandrel surface point { P0 Aj_k(X0 Aj_k, Y0 Aj_k, Z0 Aj_k) Least Square Circle fitting, fitting circle are carried out respectively
Heart coordinate is denoted as (A respectively1 0,B1 0,Z1 0) and (A2 0,B2 0,Z2 0).Obtain revolution paraxial equation are as follows:
Obtain revolution paraxial equation and plane X0O0Y0The coordinate of intersection point be
As shown in Figure 1, being Z with rotating shaft direction1Axis direction, with Z1Axis and plane X0O0Y0Intersection point O1For origin,
By by coordinate system O0-X0Y0Z0Translation makes O0Point and O1Point is overlapped, by successively around X0Axis and Y0Axis rotates so that Z0Axis and Z1Axis
It is overlapped, to obtain coordinate system O1-X1Y1Z1。
The direction vector of rotating shaft isIt takes and is positive counterclockwise, obtain successively
Around X0Axis and Y0The angle of axis rotation is respectively γ0 xAnd γ0 y。
Obtain coordinate system O0-X0Y0Z0And O1-X1Y1Z1Between transformational relation are as follows:
Above-mentioned transformation is to correct error of rotary axle.At this point, in coordinate system O1-X1Y1Z1It is lower by flank profil measurement point around Z1Axis is inverse
Hour hands revolutionAngle obtains the initial position co-ordinates of measurement point, is denoted as { P at this time1 Lij(X1 Lij, Y1 Lij, Z1 Lij) and { P1 Rij
(X1 Rij, Y1 Rij, Z1 Rij)}.Spin matrix are as follows:
To gear upper end millet cake { P1 Uj(X1 Uj, Y1 Uj, Z1 Uj) least square plane fitting is carried out, obtain gear upper surface method
Vector is denoted as
Assuming that in coordinate system O1-X1Y1Z1The height value in tested gear section is downThe then friendship of rotating shaft and measured section
It puts and is
By gear upper surface law vector andPoint determines linear equation are as follows:
As shown in Figure 1, withPoint is origin, and above-mentioned rectilinear direction is Z2Axis direction, by by coordinate system O1-X1Y1Z1It is flat
Shifting makes O1Point and O2Point is overlapped, by successively around X1Axis and Y1Axis rotates so that Z1Axis and Z2Overlapping of axles, to obtain coordinate system O2-
X2Y2Z2。
It is obtained according to fit Plane law vector around X1Axis and Y1The angle of axis rotation is respectively γ1 xAnd γ1 y。
Obtain coordinate system O1-X1Y1Z1And O2-X2Y2Z2Between transformational relation are as follows:
Above-mentioned transformation is corrected gear heeling error.At this point, in coordinate system O2-X2Y2Z2Under to flank profil measurement carry out such as
Flank profil measurement point is adapted to measured section X by amendment shown in Fig. 32O2Y2On, guarantee tested flank profil point in the same plane, repairs
Point after just is denoted as { P2 Lij(X2 Lij, Y2 Lij, 0) } and { P2 Rij(X2 Rij, Y2 Rij, 0) }.
In view of the basic circle center of circle of gear measured section and O2The gear geometric eccentricity error that point does not introduce again, it is therefore desirable to
Determine rolling circle central coordinate of circle.According to involute basic circle center of circle reverse schematic diagram as shown in Figure 4, exist on involute profile
Multiple measurement points, for any one measurement point PK(x2 K,y2 K), according to principle of forming involute:
θK=ξK-αK
Wherein:
Ideally, all measurement points are on same involute, therefore, the involute starting point of excessively each measurement point
It is identical, i.e., excessively each measurement point PK(XK,YK) involute starting point and circle center line connecting and X2Axle clamp angle δKIt is identical.
Wherein:
δK=arctan ((y2 K-b)/(x2 K-a))-θK(right flank profil)
δK=arctan ((x2 K-a)/(y2 K-b))-θK(left flank profil)
Under actual conditions, due to the presence of measurement error and flank profil itself error, flank profil measurement point is not opened gradually in same
On line, therefore least square target equation is established according to residual sum of squares (RSS) minimum principle:
Wherein:
N is the number of measurement point.
Flank profil measurement point data is substituted into above-mentioned target equation and is solved according to Newton iteration method, the basic circle center of circle is obtained
Coordinate is denoted as Ow 0(aw 0,bw 0)
Translational coordination system O2-X2Y2Z2, makeWith the obtained center of circleIt is overlapped, obtains work as shown in Figure 5
Part coordinate system Ow-XwYwZw.Establish coordinate system O2-X2Y2Z2With workpiece coordinate system Ow-XwYwZwBetween transformation relation are as follows:
Above-mentioned transformation is corrected gear geometric eccentricity error.At this point, obtaining flank profil measurement point under workpiece coordinate system and being
{Pw Lij(Xw Lij, Yw Lij, 0) } and { Pw Rij(Xw Rij, Yw Rij, 0) }.
Gear-profile deviation is evaluated under workpiece coordinate system, establishes design involute equation as shown in FIG. 6:
ξ is the exhibition angle of involute.α is pressure angle.θ is the angle of spread.
Left tooth Profile Design involute is with YwThe intersection point of axis and basic circle is starting point, equation are as follows:
Flank profil, which is calculated, according to standard ISO1328-1:2013 controls diameter dcfAnd its length Lcf, tooth top shape diameter dFaAnd
Its length LFa, tooth tip diameter daAnd its length La, evaluation range Lα。
Flank profil measurement point is screened, arbitrary profile point P is calculatedw Rij(Xw Rij, Yw Rij, Zw C) corresponding involute angle of spread ξRij。
According to angle of spread ξRij, the coordinate value for calculating design involute is (xw D_Rij,yw D_Rij)。
Design involute is rotated around workpiece coordinate system origin, makes to design each survey that involute passes through practical involute
Point is measured, rotation angle γ is calculatedRij。
According to the definition of total profile deviation it is found that tooth profile total deviation are as follows:
Fα=rb·(max(γRij)-min(γRij))
Calculate deviation discrete data:
Least squares line fitting is carried out to discrete discrepancy data, obtains being fitted average flank profil line equation are as follows:
yEi=kEi·xEi+bEi
kEiFor the slope of most average flank profil line.
Calculate flank profil dip deviation are as follows:
fHα=kEi·(La-Lcf)
Evaluation range LαInterior calculating profile geometry deviation are as follows:
ffα=| max (γRij·rb-yEi)-min(γRij·rb-yEi)|
Algorithm is evaluated to the total profile deviation under the influence of above-mentioned installation error by Matlab to emulate.It is 5mm with modulus,
The number of teeth 18, for the involute spur gear wheel of reference diameter angle 90mm, according to international standards for gears ISO1328-1:2013
2 class precisions of middle regulation choose emulation data-oriented are as follows:
The given every error value of the installation error studied according to the present invention is respectively as follows:
The measurement point under the coordinate system of machine with installation error is generated by MATLAB are as follows:
Algorithm according to the present invention carries out total profile deviation evaluation to the above-mentioned flank profil measurement data with installation error, obtains
Simulation figure and total profile deviation numerical value.
If directly carrying out total profile deviation evaluation without the amendment of installation error to above-mentioned flank profil measurement data, being imitated
True figure and total profile deviation numerical value.
Obtain given total profile deviation numerical value and the simulation result table of comparisons.
It can be seen that for modulus be 5mm by the above-mentioned table of comparisons, the number of teeth 18, reference diameter is 2 grades of involutes of 90mm
Spur gear wheel, the total profile deviation assessment method under the influence of installation error measures the flank profil with installation error through the invention
Data are evaluated, and obtained evaluation result and given value are almost the same, and gear rating is identical；Without installation error
The evaluation result that amendment directly evaluates the flank profil measurement data with installation error differs larger with given value, tooth
Taking turns rating is 5 grades, is far longer than given grade.Prove that the total profile deviation assessment method under the influence of installation error of the present invention is repaired
The just influence of installation error, algorithm is correctly feasible.
Claims (6)
1. the involute spur gear wheel total profile deviation assessment method under the influence of installation error, it is characterised in that: the reality of this method
Existing process is as follows:
1) coordinate system of machine O is established0-X0Y0Z0, tested gear is measured under coordinate system of machine, measurement position includes tested
Two Section Points, gear upper end millet cake and the flank profil measurement point up and down of gear mandrel；Two Section Points are referred to two groups of mandrels
Surface point { P0 Aj_k(X0 Aj_k, Y0 Aj_k, Z0 Aj_k) Least Square Circle fitting is carried out respectively, fitting central coordinate of circle is denoted as (A respectively1 0,
B1 0,Z1 0) and (A2 0,B2 0,Z2 0)；Flank profil measurement point needs rotating shaft and X0、Y0And Z0Axis is four-axle linked to be measured, flank profil
Measurement point is denoted asWith
2) according to two Section Points for being tested gear mandrel under coordinate system of machine, make Least Square Circle fitting, obtain two sections
Central coordinate of circle, be Z with the circle center line connecting direction of two sections1Axis direction is positive direction in orientation, by coordinate system O0-X0Y0Z0According to
It is secondary around X0Axis and Y0Axis rotation makes Z0Axis and Z1Axis is parallel, in plane X0O0Y0It is interior that Z is made by the translation of coordinate system0Axis and Z1Axis weight
It closes, obtains coordinate system O1-X1Y1Z1；Establish coordinate system O0-X0Y0Z0With coordinate system O1-X1Y1Z1Between transformation relation, sat
Mark system O1-X1Y1Z1Under gear upper end millet cake and flank profil measurement point, and flank profil measurement point is reverted into initial position；
3) according to O1-X1Y1Z1Coordinate system lower gear upper surface measurement point makees plane fitting, obtain gear upper surface plane equation and
Its normal vector is Z with the normal vector direction2Axis direction is positive in orientation, with Z1The intersection point O of axis and measured section2For origin；It will
Coordinate system O1-X1Y1Z1Successively around X1Axis and Y1Axis rotation makes Z1Axis and Z2Axis is parallel, makes O by the translation of coordinate system1Point and O2Point
It is overlapped, obtains coordinate system O2-X2Y2Z2；
4) coordinate system O is established1-X1Y1Z1With coordinate system O2-X2Y2Z2Between transformation relation；Obtain coordinate system O2-X2Y2Z2Under
Flank profil measurement point, due to the presence of installation error, so that flank profil actual measurement location deviates measured section, therefore in coordinate system
O2-X2Y2Z2Under flank profil measurement point position is modified；
5) according to coordinate system O2-X2Y2Z2Under revised flank profil measurement point establish least square target equation, pass through Newton iteration
Method solves the basic circle center of circle of tested gear, in X2O2Y2Translational coordination system O in plane2-X2Y2Z2, make Z2Axis is by being tested gear
Workpiece coordinate system O is established in the basic circle center of circlew-XwYwZw, obtain coordinate system O2-X2Y2Z2With coordinate system Ow-XwYwZwBetween transformation close
System, obtains the flank profil measurement point under workpiece coordinate system；
6) in workpiece coordinate system Ow-XwYwZwUnder the total profile deviation of gear is evaluated, by calculate design flank profil around gear base
The rotation angle that the round heart rotates to measurement point obtains total profile deviation numerical value, to correct what installation error evaluated total profile deviation
It influences.
2. the involute spur gear wheel total profile deviation assessment method under the influence of installation error according to claim 1,
Be characterized in that: ideal mounting position is the workpiece coordinate system position corrected after installation error.
3. the involute spur gear wheel total profile deviation assessment method under the influence of installation error according to claim 1,
It is characterized in that: two Section Points up and down or two Section Points for top circle of tested gear mandrel.
4. the involute spur gear wheel total profile deviation assessment method under the influence of installation error according to claim 1,
It is characterized in that: installation error is divided into gear error of rotary axle, Gear tipping error and gear geometric eccentricity error.
5. the involute spur gear wheel total profile deviation assessment method under the influence of installation error according to claim 1,
It is characterized in that: gear-profile deviation being evaluated according to standard ISO 1328-1:2013.
6. the involute spur gear wheel total profile deviation assessment method under the influence of installation error according to claim 1,
Be characterized in that: the eccentricity of tested gear is by solving in coordinate system O2-X2Y2Z2The least square target equation of lower foundation obtains
It arrives.
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| CN112880528B (en) * | 2021-01-15 | 2021-12-03 | 大连理工大学 | Active regulation and control method for tooth profile deviation of involute template of gear |
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| CN102147331B (en) * | 2010-11-25 | 2012-09-05 | 哈尔滨工业大学 | Mounting eccentric error compensating method based on CNC (Computerized Numerical Control) gear measuring center |
| CN103148828B (en) * | 2013-03-08 | 2016-01-20 | 北京工业大学 | A kind of gear wheel measuring method exempting from mounting and adjusting |
| CN103353270B (en) * | 2013-07-24 | 2015-10-28 | 东南大学 | A kind of flank of tooth is from benchmark large-scale straight spur gear circular pitch deviation measurement mechanism |
| CN103615998B (en) * | 2013-12-13 | 2016-08-17 | 西安工业大学 | Gear measuring center clamping workpiece tilts to be measured and compensation method with eccentric error |
| RU2624412C1 (en) * | 2016-02-29 | 2017-07-03 | Федеральное государственное бюджетное образовательное учреждение высшего образования "Владимирский Государственный Университет имени Александра Григорьевича и Николая Григорьевича Столетовых" (ВлГУ) | Stand for testing screw-nut gear rolling |
| CN107167105B (en) * | 2017-06-23 | 2018-03-27 | 湖北工业大学 | A kind of error compensating method of cycloid gear detection |
| CN108645322B (en) * | 2018-06-21 | 2019-06-14 | 北京工业大学 | Involute spur gear wheel circular pitch deviation assessment method under the influence of installation error |
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| CN108645323A (en) | 2018-10-12 |
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