CN109341632B - Measuring head for measuring blade profile of turbine blade and three-coordinate measuring instrument - Google Patents
Measuring head for measuring blade profile of turbine blade and three-coordinate measuring instrument Download PDFInfo
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- CN109341632B CN109341632B CN201811442463.8A CN201811442463A CN109341632B CN 109341632 B CN109341632 B CN 109341632B CN 201811442463 A CN201811442463 A CN 201811442463A CN 109341632 B CN109341632 B CN 109341632B
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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
- G01B21/00—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant
- G01B21/20—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant for measuring contours or curvatures, e.g. determining profile
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Abstract
The invention discloses a measuring head for measuring the blade profile of a turbine blade and a three-coordinate measuring instrument. A measuring head for turbine blade profile measurement, including measuring stick and measurement bulb, the measurement bulb is in the tip of measuring stick, and the centre of sphere of measurement bulb is on the axis of measuring stick, the appearance of measurement bulb is spherical, the contact point of measurement bulb spherical surface of measuring stick axis and measuring head front end is the spherical summit of measurement bulb, spherical measurement bulb surface is offered and is used for dodging peripheral structure in the measurement process so as to ensure that the spherical summit of measurement bulb contacts with the contact position point of the target of awaiting measuring and the local sunken structure of coincidence. The whole measuring structure is simple to operate, high in working efficiency and high in measuring precision, and is suitable for measuring the sizes of the profiles of the turbine blades with various profiles.
Description
Technical Field
The invention relates to the technical field of turbine blade profile measurement, in particular to a measuring head for turbine blade profile measurement. The invention further relates to a three-coordinate measuring instrument comprising the measuring head for measuring the blade profile of the turbine blade.
Background
The turbine blade is a key part of an aeroengine, and the requirements on the section contour dimension and the center position precision of the blade are high. In order to meet the design requirements of the turbine blades, the section profile of each turbine blade needs to be detected, and the measurement precision directly influences the performance of the aircraft engine. Blade cross-sectional profile measurements are shown in FIG. 1.
The schematic diagram of the leaf profile analysis measurement is shown in fig. 2. The profile detection measuring ball head is generally spherical, the diameter phi is 2 mm-phi 3mm, and the profile is measured along the designated height during detection, as shown in figure 2. However, for a blade root section with a large twist angle relative to the blade tip section, the longitudinal section of the blade has a certain inclination angle α with respect to the horizontal plane. When the measuring ball head is used for measurement, large compensation errors exist when radius compensation is carried out due to the influence of the radius of the measuring ball head. The error diagram is shown in fig. 3.
The three-coordinate measurement error is caused by: when the blade profile of the blade section height Z is measured in a three-coordinate mode, the spherical center of a measuring ball measures the blade profile along the section with constant height, the actual contact point A of the measuring ball (radius R) and the longitudinal section line of the blade is far deviated from the theoretical point B of the blade profile of the section, and the actual value C obtained by measurement after radius compensation is still different from the theoretical point B of the blade profile of the section. The distance delta between the point B and the point C is the measurement error value. The larger the torsional angle of the blade root section relative to the blade tip section of the turbine blade is, the larger the linear inclination angle theta of the longitudinal section of the blade profile is, and the measurement error value delta is increased.
Disclosure of Invention
The invention provides a measuring head for measuring a blade profile of a turbine blade and a three-coordinate measuring instrument, and aims to solve the technical problems that when the blade profile of the turbine blade is measured by using the conventional constant-height section, due to the influence of the radius of a measuring ball head, a compensation error is generated when radius compensation is carried out after measurement, and the measurement precision of the turbine blade is seriously influenced when the measuring ball head is larger and the compensation error is larger.
According to one aspect of the invention, the measuring head for measuring the blade profile of the turbine blade comprises a measuring rod and a measuring ball head, wherein the measuring ball head is arranged at the end part of the measuring rod, the sphere center of the measuring ball head is arranged on the central axis of the measuring rod, the measuring ball head is spherical in shape, the contact point of the central axis of the measuring rod and the spherical surface of the measuring ball head at the front end of the measuring head is the spherical top point of the measuring ball head, and the surface of the spherical measuring ball head is provided with a local concave structure for avoiding a peripheral structure in the measuring process so as to ensure that the spherical top point of the measuring ball head is in point contact with and coincident with the.
Further, the local depressions are configured as segments.
Furthermore, the segment is arranged on one side of the measuring head, and the section formed by the segment is arranged in parallel with the central axis of the measuring rod.
Furthermore, a space for ensuring the size precision when a contact position point which cannot directly measure the target to be measured is reserved between the section formed by the segment and the sphere center of the measuring ball head to measure the interference surface.
Furthermore, the segment is arranged at the front end of the measuring head, and the section formed by the segment is vertical to the central axis of the measuring rod.
Further, the local recess is configured as an annular groove arranged along the circumferential direction of the measuring head.
Further, the ring channel encloses to close and forms the rod-shaped structure of laying along the measuring stick axial, and the tip of rod-shaped structure is the sphere surface, and the sphere surface of rod-shaped structure tip and the sphere surface of measuring the bulb belong to concentric sphere.
Further, the connecting part of the bottom of the rod-shaped structure adopts arc transition.
According to another aspect of the invention, a three-coordinate measuring machine is also provided, which comprises the measuring head for measuring the blade profile of the turbine blade.
Furthermore, a holographic automatic focusing device used for enabling the spherical vertex to be in point contact with and overlapped with the contact position of the target to be measured is arranged on the measuring head and/or the three-coordinate measuring instrument; the holographic automatic focusing device adopts a laser generator to send laser beams to the coincident position between the spherical top point and the contact position point of the target to be measured, and realizes the automatic alignment of the spherical top point and the contact position point of the target to be measured through the movement control of the intersection point of the laser beams.
The invention has the following beneficial effects:
the measuring head for measuring the blade profile of the turbine blade is based on the problem that the spherical vertex of the measuring ball head is in point contact with the contact position of the target to be measured due to the obstruction of the structure of the spherical vertex of the measuring ball head in the measuring process, and the structure of the measuring ball head is improved to eliminate the obstruction brought by the structure of the measuring ball head body. The blocking part on the measuring ball head is designed into a local concave structure to form structure avoidance during measurement, so that the spherical top point of the measuring ball head and the contact position point of the target to be measured can be superposed, and the measuring precision is improved. The whole measuring structure is simple to operate, high in working efficiency and high in measuring precision, and is suitable for measuring the sizes of the profiles of the turbine blades with various profiles.
In addition to the objects, features and advantages described above, other objects, features and advantages of the present invention are also provided. The present invention will be described in further detail below with reference to the drawings.
Drawings
The accompanying drawings, which are incorporated in and constitute a part of this application, illustrate embodiments of the invention and, together with the description, serve to explain the invention and not to limit the invention. In the drawings:
FIG. 1 is a schematic view of a profile to be inspected for a blade of a precision cast turbine blade;
FIG. 2 is a schematic view of a measuring turbine blade;
FIG. 3 is a schematic diagram of a three-coordinate measurement error analysis;
FIG. 4 is a schematic illustration of a probe measurement for turbine blade profile measurement in accordance with a preferred embodiment of the present invention;
FIG. 5 is a schematic structural diagram of a lateral hemispherical probe for turbine blade profile measurement according to a preferred embodiment of the present invention;
FIG. 6 is a schematic structural diagram of a front-end hemispherical probe for turbine blade profile measurement according to a preferred embodiment of the invention;
FIG. 7 is a schematic structural view of a rod-type probe for turbine blade profile measurement in accordance with a preferred embodiment of the present invention;
fig. 8 is a schematic view of the measurement by the measuring head shown in fig. 7.
Illustration of the drawings:
1. a measuring rod; 2. measuring a ball head; 201. a spherical apex; 3. a partially recessed configuration; 301. a segment; 302. cutting the surface; 303. an annular groove; 4. a rod-shaped structure; 401. and (4) arc transition.
Detailed Description
The embodiments of the invention will be described in detail below with reference to the accompanying drawings, but the invention can be embodied in many different forms, which are defined and covered by the following description.
FIG. 4 is a schematic illustration of a probe measurement for turbine blade profile measurement in accordance with a preferred embodiment of the present invention; FIG. 5 is a schematic structural diagram of a lateral hemispherical probe for turbine blade profile measurement according to a preferred embodiment of the present invention; FIG. 6 is a schematic structural diagram of a front-end hemispherical probe for turbine blade profile measurement according to a preferred embodiment of the invention; FIG. 7 is a schematic structural view of a rod-type probe for turbine blade profile measurement in accordance with a preferred embodiment of the present invention; fig. 8 is a schematic view of the measurement by the measuring head shown in fig. 7.
As shown in fig. 4 and 5, the measuring head for measuring the blade profile of the turbine blade of this embodiment includes a measuring rod 1 and a measuring ball 2, the measuring ball 2 is located at an end of the measuring rod 1, a center of sphere of the measuring ball 2 is located on a central axis of the measuring rod 1, the measuring ball 2 is spherical, a contact point between the central axis of the measuring rod 1 and a spherical surface of the measuring ball 2 at a front end of the measuring head is a spherical vertex 201 of the measuring ball 2, and a local concave structure 3 for avoiding a peripheral structure in a measuring process to ensure that the spherical vertex 201 of the measuring ball 2 is in point contact with and coincident with a contact position of a target to be measured is formed on the surface of the spherical measuring ball 2. The measuring head for measuring the blade profile of the turbine blade is based on the problem that the spherical vertex 201 of the measuring ball head 2 is in point contact with the contact position of an object to be measured due to the obstruction of the structure of the spherical vertex 201 of the measuring ball head 2 in the measuring process of the measuring ball head 2, and the obstruction caused by the structure of the body of the measuring ball head 2 is eliminated by improving the structure of the measuring ball head 2. The blocking part on the measuring ball head 2 is designed into a local concave structure 3 to form structure avoidance during measurement, so that the contact position point of the spherical top point 201 of the measuring ball head 2 and the target to be measured can be superposed, and the measuring precision is improved. The whole measuring structure is simple to operate, high in working efficiency and high in measuring precision, and is suitable for measuring the sizes of the profiles of the turbine blades with various profiles. Optionally, the measuring rod 1 and the measuring ball 2 are welded together by a full penetration weld. Back chipping is adopted between the measuring rod 1 and the measuring ball head 2. Optionally, the measuring rod 1 includes an assembling portion for assembling connection, a limiting portion for assembling limitation, and a connecting portion for connecting with the measuring ball 2. Optionally, the connecting portion has a marking area thereon. Alternatively, the connecting end of the connecting portion is provided as a tapered end with a radial dimension that tapers towards the measuring bulb 2. Alternatively, the measuring rod 1 is a symmetrical structure symmetrical along the central axis. Optionally, the measuring rod 1 is provided with an eccentric structure matched with the measuring ball 2 with the local concave structure 3, so that a corresponding structure is formed, and obstruction of the measuring rod 1 to the measuring process in the measuring process is reduced. Optionally, the measuring ball head 2 adopts a silicon nitride measuring ball, a zirconium oxide measuring ball or a ruby measuring ball. When scanning aluminum materials or cast iron materials, if a ruby ball is adopted, the two materials interact with each other in the contact process to generate adhesive abrasion on the surface of the ruby ball, so that a silicon nitride ball is required to be adopted. The measuring rod is a stainless steel rod, a tungsten carbide rod or a ceramic rod. Alternatively, the measuring ball 2 may be made of tool steel, such as T8A, or hardened by HRC 55-60. Alternatively, the measuring rod 1 is a stainless steel rod, a tungsten carbide rod, or a ceramic rod.
As shown in fig. 4, 5 and 6, in the present embodiment, the local recessed structure 3 is a segment 301. The structure of the measuring ball head 2 is convenient to manufacture, and meanwhile, the contact coincidence condition of the spherical top point 201 of the measuring ball head 2 and the contact position of the object to be measured is convenient to determine. The measuring ball head 2 with the corresponding part forming the ball segment 301 can be selected according to the profile surface condition of the target to be measured, so that the contact position point of the spherical top point 201 of the measuring ball head 2 and the target to be measured can be in contact in place.
As shown in fig. 4 and 5, in the present embodiment, the ball segment 301 is located on one side of the probe. According to the profile characteristics of the position to be measured, the position which possibly forms the obstruction is judged, so that the ball segment 301 is designed at the position which forms the obstruction, the spherical top point 201 of the measuring ball head 2 can directly contact the contact position point of the target to be measured in the actual measuring process, and the measuring precision is ensured. The cross section 302 formed by the segment 301 runs parallel to the central axis of the measuring shaft 1. The processing of the structure is convenient, and the contact between the spherical top point 201 of the measuring ball head 2 and the contact position point of the target to be measured can be conveniently measured; meanwhile, when a special object to be measured is faced, when the spherical vertex 201 of the measuring ball head 2 is in point contact with the contact position of the object to be measured, a measuring error still occurs, namely the contact position of the spherical vertex 201 of the measuring ball head 2 is not the actual object position to be measured, so that the position of the section 302 needs to be controlled, the section 302 is spaced relative to the central axis of the measuring head, the measuring error is eliminated, and the section 302 formed by the segment 301 and the central axis of the measuring rod 1 are arranged in parallel, so that the distance can be conveniently adjusted.
As shown in fig. 5, in this embodiment, a distance for ensuring the dimensional accuracy when a contact position point for directly measuring the target to be measured is not available between the cross section 302 formed by the segment 301 and the spherical center of the measuring ball 2 to measure the interference surface. When a special object to be measured is faced, when the spherical vertex 201 of the measuring ball 2 is in point contact with the contact position of the object to be measured, a measurement error still occurs, that is, the contact position of the spherical vertex 201 of the measuring ball 2 is not the actual object position to be measured, so the position of the cross section 302 needs to be controlled, and the cross section 302 is spaced from the central axis of the measuring head to eliminate the measurement error.
As shown in fig. 6, in the present embodiment, the ball segment 301 is located at the front end of the measuring head, and a cross section 302 formed by the ball segment 301 is perpendicular to the central axis of the measuring rod 1. When a special object to be measured is faced, when the spherical vertex 201 of the measuring ball 2 is in point contact with the contact position of the object to be measured, a measuring error still occurs, namely, the contact position of the spherical vertex 201 of the measuring ball 2 is not the actual object to be measured, the sphere segment 301 is arranged at the front end of the measuring head, and the outer edge of the section 302 formed by the sphere segment 301 is in point contact with the contact position of the object to be measured, namely, the vertical distance between the virtual spherical vertex 201 and the section 302 is adjusted, so that the measuring error is eliminated.
As shown in fig. 7 and 8, in the present embodiment, the local recess structure 3 is an annular groove 303 arranged along the circumferential direction of the gauge head. According to the profile characteristics of the position to be measured, the position which possibly forms the obstruction is judged, so that the annular groove 303 is designed at the position which forms the obstruction, the spherical peak 201 of the measuring ball head 2 can directly contact the contact position point of the target to be measured in the actual measuring process, and the measuring precision is ensured.
As shown in fig. 7 and 8, in this embodiment, the annular groove 303 encloses and forms a rod-shaped structure 4 arranged along the axial direction of the measuring rod 1, the end of the rod-shaped structure 4 is a spherical surface, and the spherical surface at the end of the rod-shaped structure 4 and the spherical surface of the measuring ball 2 are concentric spherical surfaces. The measurement is carried out by the point contact of the end of the rod-shaped structure 4 with the contact position of the object to be measured. Optionally, the spherical apex 201 is on the central axis of the rod-shaped structure 4. Optionally, the spherical apex 201 is located at the edge of the rod-shaped structure 4, i.e. the rod-shaped structure 4 is an eccentric structure, offset from the centre axis of the measuring head. When a special object to be measured is faced, when the spherical vertex 201 of the measuring ball 2 is adopted to be in point contact with the contact position of the object to be measured, the measuring error still can be caused, namely, the contact part of the spherical vertex 201 of the measuring ball 2 is not the actual object position to be measured, the rod-shaped structure 4 is set into an eccentric structure, and the eccentric rod-shaped structure 4 is in point contact with the contact position of the object to be measured, namely, the eccentricity of the rod-shaped structure 4 is adjusted, so that the measuring error is eliminated.
In the present embodiment, as shown in fig. 7 and 8, the connecting portion of the bottom of the rod-shaped structure 4 is an arc transition 401. The structure is convenient to process and manufacture; so that the connecting part between the rod-shaped structure 4 and the measuring ball 2 forms local reinforcement to avoid the rod-shaped structure 4 from being broken in the measuring process.
The three-coordinate measuring machine of the embodiment comprises the measuring head for measuring the blade profile of the turbine blade.
In this embodiment, the measuring head and/or the three-coordinate measuring machine is provided with a holographic automatic focusing device for enabling the spherical vertex 201 to be in point contact with and coincide with the contact position of the target to be measured; the holographic automatic focusing device adopts a laser generator to send laser beams to the coincident position between the spherical vertex 201 and the contact position point of the target to be measured, and realizes the automatic alignment of the spherical vertex 201 and the contact position point of the target to be measured through the movement control of the intersection point of the laser beams. Optionally, the holographic autofocus device further comprises at least one of a reflective target, a laser pointer, a photosensitive element. Optionally, the holographic autofocus device includes multiple sets of laser generators, and the multiple sets of laser intersections are formed from different wind directions to achieve position deviation and alignment control. Optionally, the measuring head is mounted on a movable support, the movable support comprises a vertical adjusting device, a horizontal transverse moving device and a horizontal longitudinal moving device, and the movable support can control the measuring head to move in all directions. Optionally, a position sensor is further provided on the movable support. Optionally, the three-coordinate measuring machine is further provided with a control system, the control system is respectively connected with the holographic automatic focusing device and the movable support, and the intersection points of the laser beams of the holographic automatic focusing device are used for confirming the position deviation judgment between the spherical vertex 201 and the contact position point of the target to be measured, so that the movable support is controlled to drive the measuring head to move, and finally the spherical vertex 201 is opposite to and in contact with the contact position point of the target to be measured.
In implementation, a design method of a measuring head for a leaf analyzer is provided, which specifically comprises the following steps:
1. a hemispherical probe design scheme. In order to accurately measure profile data and reduce measurement errors caused by interference, the design method of the invention comprises the following steps: the spherical measuring head designed in the prior art is designed into a hemispherical head, and a contact A originally interfered by a profile is overlapped with a theoretical contact B when the hemispherical measurement is adopted, so that the profile measurement interference can be reduced, the radius compensation error is eliminated, and the measurement precision is improved. The measurement schematic is shown in fig. 4 and 5.
2. A probe gauge head design scheme. In order to accurately measure profile data and reduce measurement errors caused by interference, the design method of the invention comprises the following steps: on the basis of hemispherical measuring head design, the contact area between the measuring head and the blade is further reduced, the spherical measuring head designed in the prior art is designed into a probe form, and the contact A interfered by the profile originally during measurement is coincided with the theoretical contact B during hemispherical measurement, so that the profile measurement interference can be reduced, the radius compensation error is eliminated, and the measurement precision is improved. The measurement schematic is shown in fig. 7 and 8.
The invention relates to the measurement of the cross section profile of a turbine blade of an aeroengine, solves the problem of the size measurement of a precisely cast turbine blade, and particularly relates to two design methods of measuring heads for a blade profile analyzer. Simple operation, high working efficiency and remarkable effect. And the scheme is feasible through test and actual production verification.
The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention, and various modifications and changes may be made by those skilled in the art. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (4)
1. A measuring head for measuring the blade profile of a turbine blade comprises a measuring rod (1) and a measuring ball head (2), wherein the measuring ball head (2) is arranged at the end part of the measuring rod (1), the center of the measuring ball head (2) is arranged on the central axis of the measuring rod (1),
it is characterized in that the preparation method is characterized in that,
the measuring ball head (2) is spherical in shape, the contact point of the central axis of the measuring rod (1) and the spherical surface of the measuring ball head (2) at the front end of the measuring head is the spherical top point (201) of the measuring ball head (2),
the surface of the spherical measuring ball head (2) is provided with a local concave structure (3) which is used for avoiding a peripheral structure in the measuring process so as to ensure that the spherical top point (201) of the measuring ball head (2) is in point contact with and coincided with the contact position of the object to be measured,
the measuring rod is characterized in that the local sunken structure (3) is an annular groove (303) distributed along the circumferential direction of the measuring head, the annular groove (303) is enclosed to form an edge, the rod-shaped structure (4) is distributed along the axial direction of the measuring rod (1), the end part of the rod-shaped structure (4) is a spherical surface, and the spherical surface of the end part of the rod-shaped structure (4) and the spherical surface of the measuring ball head (2) belong to a concentric spherical surface.
2. A probe for turbine blade profile measurement according to claim 1,
the connecting part at the bottom of the rod-shaped structure (4) adopts arc transition (401).
3. A three coordinate measuring machine comprising a probe for turbine blade profile measurement as claimed in any one of claims 1 to 2.
4. Three coordinate measuring machine according to claim 3,
the measuring head and/or the three-coordinate measuring instrument is/are provided with a holographic automatic focusing device which is used for enabling the spherical vertex (201) to be in point contact with the contact position of the target to be measured and to be superposed;
the holographic automatic focusing device adopts a laser generator to send laser beams to the coincident position between the spherical vertex (201) and the contact position point of the target to be measured, and realizes the automatic alignment of the spherical vertex (201) and the contact position point of the target to be measured through the movement control of the intersection point of the laser beams.
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| CN201811442463.8A CN109341632B (en) | 2018-11-29 | 2018-11-29 | Measuring head for measuring blade profile of turbine blade and three-coordinate measuring instrument |
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| CN201811442463.8A CN109341632B (en) | 2018-11-29 | 2018-11-29 | Measuring head for measuring blade profile of turbine blade and three-coordinate measuring instrument |
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| CN110132195B (en) * | 2019-05-30 | 2021-04-20 | 华中科技大学无锡研究院 | Three-dimensional radius compensation method for probe ball measurement of blade section contact type scanning measurement |
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| JP2961065B2 (en) * | 1995-03-17 | 1999-10-12 | 三菱重工業株式会社 | Gas turbine blade |
| US6460261B1 (en) * | 1999-11-18 | 2002-10-08 | Mitutoyo Corporation | V-groove shape measuring method and apparatus by using rotary table |
| EP1460434A4 (en) * | 2001-12-25 | 2008-12-03 | Sumitomo Electric Industries | Contact probe |
| FR2890164A1 (en) * | 2005-08-31 | 2007-03-02 | Saint Louis Inst | Landmine clearance optical probe has rod with mobile tip divided into two or more sectors, one or more optical fibres and radiation emitter |
| US7625178B2 (en) * | 2006-08-30 | 2009-12-01 | Honeywell International Inc. | High effectiveness cooled turbine blade |
| DE102013015237A1 (en) * | 2013-09-13 | 2015-03-19 | Blum-Novotest Gmbh | Roughness measuring instrument for use in a machine tool and method for measuring roughness in a machine tool |
| CN104089599B (en) * | 2014-07-04 | 2017-01-25 | 北京工业大学 | Quasi morphological filtering method for extracting two-dimensional contour in contact measuring head measurement |
| US11159784B2 (en) * | 2014-10-23 | 2021-10-26 | Cognex Corporation | System and method for calibrating a vision system with respect to a touch probe |
| CN205342669U (en) * | 2015-12-21 | 2016-06-29 | 江苏艾思飞精密零部件有限公司 | Probe |
| CN205748188U (en) * | 2016-03-17 | 2016-11-30 | 河南省特种设备安全检测研究院平顶山分院 | Steel wire rope grooving abrasion Special measuring scale |
| CN106225740B (en) * | 2016-08-31 | 2019-05-31 | 洛阳轴承研究所有限公司 | A kind of Pneumatic measuring head measuring high-precision ball-and-socket sphere diameter |
| CN206484365U (en) * | 2017-02-20 | 2017-09-12 | 重庆机床(集团)有限责任公司 | Gear compound graduation circular diameter locating and detecting device |
| CN108286937B (en) * | 2018-01-30 | 2020-03-24 | 京东方科技集团股份有限公司 | Contact type scanning probe, coordinate measuring device, system and method |
| CN108692644B (en) * | 2018-03-26 | 2019-09-27 | 华中科技大学 | A kind of complex-curved Three-coordinate measurer and error compensating method |
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