CN108036758A - One kind is suitable for the detection of aero-engine casing concentricity and method of adjustment - Google Patents

Abstract

The invention discloses a coaxiality detection and adjustment method suitable for an aero-engine case, belonging to the field of manufacturing quality prediction and control. This method first measures the position coordinates of each point of the casing relative to the rotary center of the turntable, and then obtains the casing pose information through least square fitting and calculation, so as to measure and adjust the coaxiality of the components on the engine casing. Different from the general axis of rotation measurement method, this method allows the offset and inclination of the casing clamping, as long as it does not exceed the detection limit, so as to reduce the manual precise clamping and adjustment links, and reduce the technical requirements for workers. Improve efficiency. Simultaneously, this method simplifies the manual table loading and multiple table loading. In the process of implementation, the method is assisted by computer programming, which reduces manual work such as meter reading, recording, and calculation, reduces the workload of workers, improves the degree of automation, and improves measurement efficiency.

Description

A method suitable for detecting and adjusting the coaxiality of an aero-engine casing

technical field

The invention relates to a method suitable for detecting and adjusting the coaxiality of an aero-engine casing, and belongs to the technical field of manufacturing quality prediction and control.

Background technique

A large number of scientific research and production practices have shown that aero-engines often cause collision and friction between the static and rotor of the engine due to unqualified coaxiality, which causes vibration and affects the operation of the engine. Therefore, coaxiality measurement is of great significance to ensure the normal operation of the engine and improve the reliability of the engine.

Combined with the actual production, in the assembly line of mass-produced aero-engines, it is necessary to detect and adjust the coaxiality of the bearing frame at one end of the engine casing, and now the method of measuring the axis of rotation is used. The method of adjusting the bearing frame is to first measure and adjust so that the center of the bottom end of the case coincides with the center of rotation, then measure and adjust so that the reference axis of the case is perpendicular to the surface of the turntable, and finally measure and adjust so that the bearing frame is coaxial with the case.

However, there are many problems in the current method that need to be solved. The main problem is that manual measurement takes a long time and is inefficient, which affects subsequent assembly and reduces production efficiency. In particular, adjusting the concentric and vertical steps of the parts relative to the measuring turntable requires a high level of worker skill and takes a long time. At the same time, meter installation, meter reading, recording, and calculation are all done manually, with a low degree of automation, laborious work and low efficiency.

Contents of the invention

In view of this, the present invention provides a coaxiality detection and adjustment method suitable for aero-engine casings, which can solve the problem of low detection efficiency in the prior art and improve the automation of casing coaxiality adjustment and measurement and measure efficiency.

A coaxiality detection and adjustment method suitable for an aero-engine casing, the detection and adjustment method comprising the following steps:

Step 1: Measure and collect the position coordinate data of each measured point of the casing relative to the rotary center of the turntable;

Step 2: Fit and calculate the position coordinate data by the least square method to obtain the pose information of each part of the casing;

Step 3: Adjust the coaxiality according to the part pose information in Step 2.

Further, the measurement and acquisition process of the position coordinate data in the step 1 is as follows:

Clamp the casing on the rotary measuring table, install more than three digital dial gauges (according to the actual situation, the number of gauges can be changed, and the type of displacement sensor can be changed) and then turn the turntable at a fixed position. Angle (according to the actual situation, 4 or more angles can be used for circle fitting, 5 or more angles can be used for ellipse fitting) to record the data of the digital dial gauge; in a data collection process, a total of multiple numbers are obtained Data collected by dial gauges in multiple directions.

Further, the pose information of each part of the casing in the step 2 includes: the coordinate information of the center point of each measurement section on the casing and the pose information of the fitting frame reference axis, by determining the relationship between the center point of each measured section and the reference The positional relationship of the axis is used to judge whether the casing and each component meet the coaxiality requirements, and if not, the offset information is given.

Further, it is assumed that there are 4 digital dial gauges, and the dial gauges are aligned with the central axis of the turntable on the horizontal plane, and it is assumed that when the turntable turns to the 6 angles of A, B, C, D, E, and F for one measurement, the dial gauges record the dial gauge. Table data. The heights of the 4 digital dial gauges are Z ₁ , Z ₂ , Z ₃ , Z ₄ respectively, and the distances from the gauge head to the reference axis when the compression amount of the gauge is 0 when the casing is not clamped are respectively R ₁ , R ₂ , R _3. R ₄ . When the casing is clamped on the turntable and the turntable is turned to the E direction, that is, the direction of 240°, the four indicators are the compression values R _1E ′, R _2E ′, R _3E ′, and R _4E ′, and the other directions are the same. A total of 24 compression data were measured from 4 meters in 6 directions.

Take the rotation center point on the turntable as the origin, the A direction, that is, the 0° direction, is the X axis, the 90° direction between the B and C directions is the Y axis, and the rotation center axis, that is, the axis passing through the origin and perpendicular to the turntable surface, is the Z axis. After the XYZ coordinate system is established, according to the known Z ₁ , Z ₂ , Z ₃ , Z ₄ , R ₁ , R ₂ , R ₃ , R ₄ and the measured 24 compressions, it is transformed into 24 measured The coordinate value of the point in the coordinate system, the distance from E ₄ to the Z axis of the coordinate system

R _4E =R ₄ +R' _4E

X coordinate value of E ₄

X _4E = R _4E ×cos 240°

Y coordinate value of E ₄

Y _4E ＝ R _4E × sin 240°

The Z coordinate value of E ₄ is Z ₄ , and E ₄ (X _4E , Y _4E , Z ₄ ) can be obtained, and the coordinates of the other 23 measuring points can be obtained in the same way.

After obtaining the coordinates of 24 points, it is necessary to use the least squares method to respectively fit the contours of the four sections and obtain the center coordinates. Taking the section 4 measured in Table 4 as an example, six measuring points A ₄ (X _4A ,Y _4A ,Z ₄ ), B ₄ (X _4B ,Y _4B ,Z ₄ ), C ₄ (X _4C ,Y _4C ,Z ₄ ), D ₄ (X _4D ,Y _4D ,Z ₄ ), E ₄ (X _4E ,Y _4E ,Z ₄ ), F ₄ (X _4F ,Y _4F ,Z ₄ ). Because the six points are at the same height, the Z coordinate of the center of the measured surface is Z ₄ ; the plane ellipse equation can be set

a ₄ x ² +b ₄ x ^y +c ₄ y ² +d ₄ x+e ₄ y+f ₄ =0

According to the common least square method, the values of a ₄ , b ₄ , c ₄ , d ₄ , e ₄ , and f ₄ in the ellipse equation can be calculated according to the six-point coordinates, and then the center coordinates of the section can be calculated according to the formula

The central coordinate T ₄ (X ₄ ,Y ₄ ,Z ₄ ) can be obtained, and the central coordinates T ₁ (X ₁ ,Y ₁ ,Z ₁ ) and T ₂ (X ₂ ,Y ₂ ,Z ₂ ), T ₃ (X ₃ , Y ₃ , Z ₃ ), T ₄ (X ₄ , Y ₄ , Z ₄ ); then select these four points to fit the reference axis of the casing, and also use the least squares method. According to the design requirements of different engines, 2 or more center points can be selected to fit the reference axis. In particular, if 2 points are selected, the calculated result is the straight line where the line connecting the 2 points is located. Set the spatial linear equation

Assume

partial derivative

ask for

By solving the equation, the parameter equation coefficient of the reference axis of the casing can be obtained, and the distances r ₁ , r ₂ , r ₃ , and r ₄ from the 4 points to the straight line can be obtained according to the distance formula from the space point to the straight line. When r ₁ , r ₂ , r ₃ , r ₄ are less than half of the coaxiality required value d ₁ , d ₂ , d ₃ , _d4 respectively, that is, the 4 points are within the minimum containment area of the coaxiality, the casing and its The coaxiality of parts meets the requirements;

When a certain r _i is greater than half of the required value of coaxiality, that is, the point is outside the minimum containment area of coaxiality. Put Z=Z _i into the straight line equation to solve the point Q _i (X _qi , Y _qi ,Z _i ) on the line, compare Q _i with the center coordinate T _i (X _i ,Y _i ,Z _i ) of the measured surface, according to

It can be seen that on the horizontal plane of Z=Z _i , T _i is at r _0i in the θ direction of Q _i , so far, after data processing according to the 24 table compressions, the center coordinates of each measured section and the equation of the casing reference axis are obtained, thus Judging whether the coaxiality is qualified or not, and calculating the offset and offset direction of the unqualified assembly of the measured part when it is unqualified.

Further, the process of adjusting the coaxiality of the parts in the third step is as follows:

When the coaxiality of the casing does not meet the requirements, rotate the turntable so that the meter is printed in the offset direction displayed by the data processing results, and use the tool to adjust the measured part in this direction while observing the data change of the meter; when the compression amount changes When it is approximately equal to the offset direction, the adjustment is completed; in order to ensure the accuracy of the adjustment result, it should be measured again after adjustment; according to the actual situation, sometimes when the coaxiality is unqualified and the measured part cannot be adjusted, the casing should be reassembled.

Beneficial effect:

1) The method disclosed in the present invention is applicable to the detection and adjustment of the coaxiality of the aero-engine casing. The position of the meter is fixed, which simplifies manual meter installation and multiple meter installation. If a digital dial gauge is used and connected to a computer, manual meter reading, recording, and calculation are eliminated, worker operations are reduced, and the degree of automation is improved.

2) The measurement method of the present invention can obtain the pose information of each part of the assembly, greatly reducing the influence of clamping errors on the detection of the coaxiality of the assembly. The clamping error here refers to the error caused by the misalignment of the reference axis and the rotation axis when the casing is clamped on the turntable. Different from the general rotary axis measurement method, this method allows the center of the bottom surface to be offset during clamping, and does not need to precisely adjust the concentricity of the bottom surface of the casing and the rotation axis of the turntable. This method allows the reference axis of the casing to have a large inclination during clamping, and does not need to accurately adjust the reference axis of the casing to be perpendicular to the bottom surface of the turntable. This method only needs to make the casing offset and tilt not exceed the detection limit through tooling and clamping (that is, the measuring gauge will not exceed the range during the measurement process), which can simplify or even skip the reference axis of each clamping casing The adjustment link reduces the technical requirements for workers, saves time and improves efficiency.

3) The table position of this method is fixed, and the data collection is accurate. This method uses mathematical calculation and least squares fitting to ensure the accuracy of each measurement section contour fitting, the accuracy of the datum axis fitting and the accuracy of the spatial position relationship between the center point of the section and the fitting straight line, and can accurately provide Coaxiality judgment and component adjustment reference to ensure measurement accuracy and achieve measurement purposes.

Description of drawings

FIG. 1 is a schematic diagram of the composition of a detection device according to an embodiment of the present invention.

Fig. 2 is the front view of measurement principle of the present invention;

Fig. 3 is a top view of the measurement principle of the present invention;

Fig. 4 is a schematic diagram showing that the spatial relationship between the center point of the measured casing section and the fitting reference axis meets the requirements;

Fig. 5 is a schematic diagram showing that the spatial relationship between the center point of the measured casing section and the fitting reference axis does not meet the requirements.

Among them, 1-turntable, 2-fixture, 3-tested casing, 4-horizontal table frame, 5-reinforced meter head, 6-digital dial indicator, 7-slider, 8-slide rail, 9-adjustable Horizontal table frame, 10-positioning plate, 11-upper sleeve, 12-vertical table frame, 13-lower sleeve, 14-column, 15-revolving measuring platform.

Detailed ways

The present invention will be described in detail below with reference to the accompanying drawings and examples.

The invention provides a method suitable for detecting and adjusting the coaxiality of the aero-engine casing, which is different from the general rotation axis measurement method. The general rotation measurement first ensures that the reference axis of the casing coincides with the rotation center axis of the turntable through measurement and adjustment, and then By measuring the runout of the parts and performing data processing, it is judged whether the coaxiality of each part of the engine casing is qualified. However, this method is to first establish a coordinate system on the turntable, measure and obtain the coordinates of each measured point of the casing in this coordinate system, and then obtain the casing profile and pose information through the least squares fitting calculation, so as to achieve measurement and adjustment. The purpose of concentricity. To obtain the coordinates of each point, the gauge must be in a fixed position every time it is measured, so that the coordinates of the dial indicator and the compression amount of the gauge can be directly brought into the fitting and calculation. In order to realize the detection, a set of mechanical devices can be used to ensure the positioning accuracy of the watch. For purposes of describing specific embodiments, the present invention provides a possible, but not exclusive, model of the mechanism. At the same time, in order to reflect the degree of automation of the method, a method of connecting a digital dial gauge and a photoelectric switch to a computer is used to collect data, process data, and display results. This computer programming is based on MATLAB's DAQ data acquisition workbox, GUI interface and other related modules.

The mechanical device provided by this method is as shown in Figure 1. The column 14 is installed on the rotary measuring table 15, and the digital dial indicator 6 is installed on the meter frame. The vertical meter frame 12 and the column 14 pass through the bearing and the upper sleeve 11 and the lower sleeve. Tube 13 is connected, and vertical table frame 12 rotates around column 14 by upper sleeve 11 and lower sleeve 13, and column top is fixedly connected a positioning plate 10 that is clothed with a circle of positioning holes with straight pin and screw. When measuring, the self-locking spring indexing pin can be used to make it positionally locked with the upper sleeve 11. When clamping and removing the casing 3, the pin can be pulled out to remove the meter frame to prevent damage to the meter head. And the horizontal meter frame 4 and the vertical meter frame 12 of the meter frame are fastened with glands and screws, the two holes in the middle are the compression screw holes for adjustment, and the position of the meter is fine-tuned with gaskets inside the connection to ensure the reinforced meter head 5 Align the center of rotation of the turntable; the uppermost end of the vertical table frame is installed with an adjustable horizontal table frame 9, and the front end of the adjustable horizontal table frame 9 is equipped with a slide rail 8, and the slide block 7 cooperates with the slide rail 8 and is fixed. Before the measuring equipment is put into use, standard parts can be used for strict installation to adjust the position of the meter. In addition, a U-groove photoelectric switch is installed near the turntable, and six baffles are fixed on the edge of the rotary measuring table 15 and the angles are marked, which are used to trigger the photoelectric switch at a specific angle to make the computer record the compression of each digital dial indicator at this position. quantity.

At the same time, for the least squares fitting process in the simulated measurement process, a set of simulated measurement data is given, including the coordinate array converted from 24 table compressions into three coordinates. The way to obtain this group of data is to first set up a space straight line

And take four points as the center of the measured section, draw four ellipses or circles with different shapes and poses with four points respectively, and then take four points in six directions of 0°, 60°, 120°, 180°, 240°, and 300° The coordinates of 24 points of the 4 sections are shown in Table 1.

Table 1 Coordinates of measured points

This method is specifically:

Step 1, receiver clamping and preparation:

Loosen the positioning pin, turn the meter stand to remove the digital dial indicator, then clamp the casing on the tooling fixture on the turntable, turn the meter stand again to move the meter to a fixed position, so that the gauge head hits the measured surface of the casing There is a certain amount of compression on the table, and the positioning pin is locked to make the table frame and the column firmly connected, and finally the computer program is operated to prepare for measurement.

Step 2, data acquisition and data storage:

The 6 baffles marked with angles on the edge of the turntable protrude a certain distance to ensure that the baffles can cover the U-groove photoelectric switch against the light rays during the rotation of the turntable. The data collection starts, turn the turntable, and the 6 shutters pass through the U-shaped slot to trigger the photoelectric switch in turn during the rotation process. The photoelectric switch sends out a total of 6 switching signals, which are converted into digital quantities by the data acquisition card and received by the computer. The MATLAB program receives the signal. Immediately afterwards, read and record the compression data of the gauge heads transmitted by the 4 digital dial gauges to the computer at this time. 4 digital dial indicators, 6 trigger photoelectric switches, a total of 24 beatings are obtained, and stored in the form of an Excel table.

As shown in Figures 2 and 3, OO' is the rotation centerline of the turntable, and O ₂ O ₂ ' is the reference axis of the casing. The black dot on the left side of the figure is the position of the meter head when the compression amount is 0, and the black point on the right side is the position of the meter head when there is a certain amount of compression after the casing is clamped, that is, the measured point on the casing. The gauge heights are Z ₁ , Z ₂ , Z ₃ , and Z ₄ , and the distances from the gauge head to OO′ when the compression of the gauge is 0 when the casing is not clamped are R ₁ , R ₂ , R ₃ , and R ₄ respectively. E direction, that is, 240°direction, represents compression amounts R _1E ′, R _2E ′, R _3E ′, R _4E ′. Turn the turntable, when the turntable turns to 0°, 60°, 120°, 180°, 240°, 300° (depending on the actual situation, 4 or more measurement angles can be used for circle fitting, and 5 or more measurement angles can be used for ellipse fitting Measure the angle) to record the compression amounts of the four gauges at this time. Since the rotation center line of the turntable is fixed and the table position is fixed, Z ₁ , Z ₂ , Z ₃ , Z ₄ and R ₁ , R ₂ , R ₃ , R ₄ are all fixed and known. In one data acquisition process, a total of 24 table compression data of four tables in six directions are obtained (compression data quantity=table number×measurement angle number).

Step 3, data processing and result display:

The purpose of data processing is to calculate the coordinates of the center point of the measurement section of each component in the casing and fit the pose of the casing reference axis O ₂ O ₂ ′, and determine the relationship between each center point and the casing reference axis O ₂ O ₂ ′ The positional relationship is used to judge whether the casing and each component meet the coaxiality requirements, and if not, the offset information is given.

Before data processing, an XYZ coordinate system needs to be established. The coordinate system takes the rotation center on the turntable as the origin, the Z axis goes upward along the OO′ direction of the turntable rotation center, and the X axis goes along the A direction, that is, the 0° direction. According to the characteristics of the right-handed coordinate system, Y can be obtained axis direction.

After the coordinate system is established, according to the known Z ₁ , Z ₂ , Z ₃ , Z ₄ , R ₁₁ , R ₁₂ , R ₁₃ , R ₁₄ and the measured 24 compressions are transformed into 24 measured points respectively. In this coordinate system, the coordinate values of 24 points are shown in Table 1.

After obtaining the coordinates of 24 points, the next step is to use the least square method to fit the contours of the four sections to obtain the center coordinates T ₁ (0.24000,0.620,40), T ₂ (0.280,0.740,80), T ₃ ( 0.600,1.700400), _T4 (0.800,2.300,600).

After calculating the center coordinates of the four sections, the least squares method is used to fit the casing reference axis O ₂ O ₂ ′. Find the equation of a straight line in space

By solving the equations, the parametric equations of the casing datum axis can be obtained. According to the distance formula from a point to a straight line in space, the distances from four points to a straight line can be calculated as r ₁ =0.0000107, r ₂ =0.0000063, r ₃ =0.0000258, r ₄ =0.0000166. r ₁ , r ₂ , r ₃ , r ₄ are all less than half of the coaxiality requirements of the measured surfaces d ₁ =0.02, d ₂ =0.15, d ₃ =0.03, d ₄ =0.02 (in order to reflect the flexibility of measurement , Different measured surfaces set different coaxiality requirements.), the coaxiality of the casing and its parts meets the requirements, and the results are shown in Figure 4.

When the coaxiality of the casing and its components meets the requirements, the measurement ends. When not satisfied, such as shown in Figure 5, then enter the next step for adjustment. Among them, the coordinate data in Figure 5 is based on the coordinate data used in Figure 4, using the computer software MATLAB to add a random number from -0.05 to 0.05 to the X and Y values of each coordinate of the 24 coordinates. Simulate casing assembly or machining errors in actual production.

Step 4, display and adjust parts in real time:

If the coaxiality requirements are not met, as shown in Figure 5, the computer will display the distance and deflection angle of the unqualified point relative to the straight line based on the spatial relationship between the center points of each section calculated in the previous step and the fitting datum axis, so as to This is used as a reference for adjusting the casing and its internal bearing frame, bearing and other parts. According to the offset direction displayed by the computer, rotate the turntable so that the measuring table is placed in the offset direction of the part to be adjusted, such as 304° of section 3 in this example, and observe the digital micrometer while fine-tuning along the offset direction with tools The amount of compression changes on the display screen of the meter, when the amount of compression changes to the offset given by the computer:

Δr=0.0121-0.010=0.0021mm

This adjustment is complete. In order to ensure that the adjusted casing and its internal parts are coaxial, the measurement should start from step 2 again, and so on, until the computer displays "pass" in step 3, and the measurement ends at this time.

To sum up, the above are only preferred embodiments of the present invention, and are not intended to limit the protection scope of the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present invention shall be included within the protection scope of the present invention.

Claims (5)

1. It is 1. a kind of suitable for the concentricity detection of aero-engine casing and method of adjustment, it is characterised in that the detection and adjustment Method comprises the following steps：

   Step 1：Measure and gather position coordinate data of each measured point of casing relative to rotation of rotary table center；

   Step 2：Position coordinate data is fitted by least square method and each part posture information of casing is calculated；

   Step 3：Concentricity adjustment is carried out according to the part posture information of step 2.
2. 2. as claimed in claim 1 suitable for the concentricity detection of aero-engine casing and method of adjustment, it is characterised in that The measurement of position coordinate data and gatherer process are as follows in the step 1：

   By casing clamping on revolution test desk, by the digital dial gauge of more than three behind the fixed position rotating table, The data of digital dial gauge are recorded when rotating to fixed angle；In a data acquisition, multiple digital thousand are obtained The data for dividing table to gather in a plurality of directions.
3. 3. as claimed in claim 1 suitable for the concentricity detection of aero-engine casing and method of adjustment, it is characterised in that Each part posture information of casing includes in the step 2：The coordinate information and fitting casing of kernel of section point are respectively measured on casing The posture information of datum axis, by judging the position relationship of each measured section central point and datum axis, judge casing and Whether each parts meet concentricity requirement, if conditions are not met, providing offset information.
4. 4. as claimed in claim 2 suitable for the concentricity detection of aero-engine casing and method of adjustment, it is characterised in that It is assumed that digital dial gauge is 4, amesdial is directed at turntable center axis in the horizontal plane, and assumes that one-shot measurement intermediate station turns To record amesdial data during this 6 angles of A, B, C, D, E, F.The height of 4 digital dial gauges is respectively Z₁、Z₂、Z₃、Z₄, no The distance of gauge outfit to datum axis is respectively R when table decrement is 0 during clamping casing₁、R₂、R₃、R₄.By casing clamping in turntable On, and when turntable is turned to E directions i.e. 240 ° direction, 4 table decrements are respectively R_1E′、R_2E′、R_3E′、R_4E', other directions Similarly.4 tables amount in 6 directions and measure 24 decrement data.

   Using rotary middle point on table with revolvable top as origin, A directions i.e. 0 ° direction is X-axis, and 90 ° of directions among B and C directions are Y-axis, Center of rotation axis was that origin perpendicular to the axis of table with revolvable top is Z axis.After establishing XYZ coordinate system, according to known Z₁、Z₂、Z₃、 Z₄、R₁、R₂、R₃、R₄It is converted into 24 decrements measured and obtains the coordinate value of 24 measured points in the coordinate system, E respectively₄ To coordinate system Z axis distance

   R_4E=R₄+R′_4E

   E₄X-coordinate value

   X_4E=R_4E×cos240°

   E₄Y-coordinate value

   Y_4E=R_4E×sin240°

   E₄Z coordinate value be Z₄, E can be obtained₄(X_4E, Y_4E, Z₄), and other 23 measurement point coordinates are obtained in the same way；

   , it is necessary to be fitted the profile in 4 sections respectively with least square method and obtain centre coordinate after 24 point coordinates are obtained, with Exemplified by the section 4 that table 4 is surveyed, six measuring point A on the section are taken₄(X_4A, Y_4A, Z₄)、B₄(X_4B, Y_4B, Z₄)、C₄(X_4C, Y_4C, Z₄)、 D₄(X_4D, Y_4D, Z₄)、E₄(X_4E, Y_4E, Z₄)、F₄(X_4F, Y_4F, Z₄)；Because 6 points on sustained height, so tested surface center Z coordinate It is Z₄；Planar elliptical equation can be set

   a₄x²+b₄xy+c₄y²+d₄x+e₄y+f₄=0

   According to general least square method, α in elliptic equation can be obtained according to six point coordinates₄、b₄、c₄、d₄、e₄、f₄Value, then The kernel of section coordinate is obtained according to formula

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   <mrow> <msub> <mi>Y</mi> <mn>4</mn> </msub> <mo>=</mo> <mfrac> <mrow> <mn>2</mn> <msub> <mi>a</mi> <mn>4</mn> </msub> <msub> <mi>e</mi> <mn>4</mn> </msub> <mo>-</mo> <msub> <mi>b</mi> <mn>4</mn> </msub> <msub> <mi>d</mi> <mn>4</mn> </msub> </mrow> <mrow> <msup> <msub> <mi>b</mi> <mn>4</mn> </msub> <mn>2</mn> </msup> <mo>-</mo> <mn>4</mn> <msub> <mi>a</mi> <mn>4</mn> </msub> <msub> <mi>c</mi> <mn>4</mn> </msub> </mrow> </mfrac> </mrow>

   Centre coordinate T can be obtained₄(X₄, Y₄, Z₄), it can seek all measured section centre coordinate T with method₁(X₁, Y₁, Z₁)、T₂(X₂, Y₂, Z₂)、T₃(X₃, Y₃, Z₃)、T₄(X₄, Y₄, Z₄)；Then select at this 4 points to when casing datum axis is fitted, same use is most Small square law, according to the design requirement of different engines, may be selected wherein 2 and more than 2 central points to be fitted datum axis, It is straight line where 2 lines to calculate gained, if space line equation

   <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mi>X</mi> <mo>=</mo> <mi>a</mi> <mi>Z</mi> <mo>+</mo> <mi>b</mi> </mtd> </mtr> <mtr> <mtd> <mi>Y</mi> <mo>=</mo> <mi>c</mi> <mi>Z</mi> <mo>+</mo> <mi>d</mi> </mtd> </mtr> <mtr> <mtd> <mi>Z</mi> <mo>=</mo> <mi>Z</mi> </mtd> </mtr> </mtable> </mfenced>

   If

   <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mi>f</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>a</mi> <mo>,</mo> <mi>b</mi> <mo>)</mo> </mrow> <mo>=</mo> <munderover> <mi>&amp;Sigma;</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mn>4</mn> </munderover> <msup> <mrow> <mo>(</mo> <msub> <mi>aZ</mi> <mi>i</mi> </msub> <mo>+</mo> <mi>b</mi> <mo>-</mo> <msub> <mi>X</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>f</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <mi>c</mi> <mo>,</mo> <mi>d</mi> <mo>)</mo> </mrow> <mo>=</mo> <munderover> <mi>&amp;Sigma;</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mn>4</mn> </munderover> <msup> <mrow> <mo>(</mo> <msub> <mi>cZ</mi> <mi>i</mi> </msub> <mo>+</mo> <mi>d</mi> <mo>-</mo> <msub> <mi>Y</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mrow> </mtd> </mtr> </mtable> </mfenced>

   Seek local derviation

   <mrow> <mfrac> <mrow> <mo>&amp;part;</mo> <msub> <mi>f</mi> <mn>1</mn> </msub> </mrow> <mrow> <mo>&amp;part;</mo> <mi>a</mi> </mrow> </mfrac> <mo>=</mo> <mfrac> <mrow> <mo>&amp;part;</mo> <msub> <mi>f</mi> <mn>1</mn> </msub> </mrow> <mrow> <mo>&amp;part;</mo> <mi>b</mi> </mrow> </mfrac> <mo>=</mo> <mfrac> <mrow> <mo>&amp;part;</mo> <msub> <mi>f</mi> <mn>2</mn> </msub> </mrow> <mrow> <mo>&amp;part;</mo> <mi>c</mi> </mrow> </mfrac> <mo>=</mo> <mfrac> <mrow> <mo>&amp;part;</mo> <msub> <mi>f</mi> <mn>2</mn> </msub> </mrow> <mrow> <mo>&amp;part;</mo> <mi>d</mi> </mrow> </mfrac> <mo>=</mo> <mn>0</mn> </mrow>

   Ask

   <mrow> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mi>a</mi> </mtd> <mtd> <mi>b</mi> </mtd> </mtr> <mtr> <mtd> <mi>c</mi> </mtd> <mtd> <mi>d</mi> </mtd> </mtr> </mtable> </mfenced> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mn>4</mn> </munderover> <msup> <msub> <mi>Z</mi> <mi>i</mi> </msub> <mn>2</mn> </msup> </mrow> </mtd> <mtd> <mrow> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mn>4</mn> </munderover> <msub> <mi>Z</mi> <mi>i</mi> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mn>4</mn> </munderover> <msub> <mi>Z</mi> <mi>i</mi> </msub> </mrow> </mtd> <mtd> <mn>4</mn> </mtd> </mtr> </mtable> </mfenced> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mn>4</mn> </munderover> <msub> <mi>Z</mi> <mi>i</mi> </msub> <msub> <mi>X</mi> <mi>i</mi> </msub> </mrow> </mtd> <mtd> <mrow> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mn>4</mn> </munderover> <msub> <mi>X</mi> <mi>i</mi> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mn>4</mn> </munderover> <msub> <mi>Z</mi> <mi>i</mi> </msub> <msub> <mi>Y</mi> <mi>i</mi> </msub> </mrow> </mtd> <mtd> <mrow> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mn>4</mn> </munderover> <msub> <mi>Y</mi> <mi>i</mi> </msub> </mrow> </mtd> </mtr> </mtable> </mfenced> </mrow>

   Casing datum axis parametric equation coefficient can be obtained by solving equation, and can obtain at 4 points to directly according to space distance between beeline and dot formula Linear distance r₁、r₂、r₃、r₄, work as r₁、r₂、r₃、r₄It is respectively smaller than the half d of concentricity required value₁、d₂、d₃、d₄When, i.e., 4 points same In axis degree minimally surrounded area, casing and its parts concentricity are met the requirements；

   As a certain r_iMore than concentricity required value half when, i.e., the point is overseas in concentricity minimum tolerance area.Make Z=Z_iBring into Linear equation solves Points on Straight Line Q_i(X_qi,Y_qi,Z_i), compare Q_iWith tested surface centre coordinate T_i(X_i,Y_i,Z_i), according to

   <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <mi>&amp;Delta;</mi> <mi>X</mi> <mo>=</mo> <msub> <mi>X</mi> <mi>i</mi> </msub> <mo>-</mo> <msub> <mi>X</mi> <mrow> <mi>q</mi> <mi>i</mi> </mrow> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>&amp;Delta;</mi> <mi>Y</mi> <mo>=</mo> <msub> <mi>Y</mi> <mi>i</mi> </msub> <mo>-</mo> <msub> <mi>Y</mi> <mrow> <mi>q</mi> <mi>i</mi> </mrow> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>r</mi> <mrow> <mn>0</mn> <mi>i</mi> </mrow> </msub> <mo>=</mo> <msqrt> <mrow> <msup> <mi>&amp;Delta;X</mi> <mn>2</mn> </msup> <mo>+</mo> <msup> <mi>&amp;Delta;Y</mi> <mn>2</mn> </msup> </mrow> </msqrt> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>&amp;theta;</mi> <mo>=</mo> <msup> <mi>tan</mi> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <mfrac> <mrow> <mi>&amp;Delta;</mi> <mi>Y</mi> </mrow> <mrow> <mi>&amp;Delta;</mi> <mi>X</mi> </mrow> </mfrac> </mrow> </mtd> </mtr> </mtable> </mfenced>

   Understand in Z=Z_iHorizontal plane on, T_iIn Q_iθ directions on r_OiPlace, so far, according to 24 table decrements through data processing After obtain each measured section centre coordinate, casing datum axis equation, so as to judge whether concentricity qualified, and when unqualified Calculate the offset for assembling underproof tested part and offset direction.
5. 5. as claimed in claim 1 suitable for the concentricity detection of aero-engine casing and method of adjustment, it is characterised in that The process that part concentricity adjustment is carried out in the step 3 is as follows：

   When casing concentricity is unsatisfactory for requiring, revolving-turret, makes table beat on the offset direction that data processed result is shown, on one side Tested part is just adjusted upward herein using instrument, while the data variation of observation table；When decrement change is approximately equal to offset side Xiang Shi, adjustment finish；It is accurate to ensure to adjust result, it should remeasure after the adjustment once；According to actual conditions, sometimes coaxially When adjustment can not be continued by spending unqualified and measured piece, casing should be ressembled.