CN116399284B - Device and method for measuring perpendicularity error and error direction angle of surface of part with hole - Google Patents

Abstract

The application discloses a device and a method for measuring the perpendicularity error and the error direction angle of the surface of a part with a hole, which belong to the technical field of measurement and comprise a standard flat plate, wherein the standard flat plate is horizontally fixed on a first supporting table; a round through hole is arranged on the standard flat plate; a turntable is in running fit on a second supporting table below the standard flat plate; a rigid rod is vertically and fixedly arranged at the top end of the turntable and upwards penetrates through a round through hole of the standard flat plate; the rigid rod is provided with a first displacement sensor and a second displacement sensor from top to bottom in sequence. The device is simple, is easy and convenient to operate, and has low requirements on the working environment; when the device is used, the first displacement sensor and the second displacement sensor rotate along with the turntable, and the part with the hole is kept still, so that the perpendicularity errors and error direction angles of the upper surface and the lower surface of the part with the hole on the central line of the larger part with the hole can be measured in real time.

Description

Device and method for measuring verticality error and error direction angle of surface of part with hole

technical field

The invention belongs to the technical field of measurement, and in particular relates to a device and method for measuring the verticality error and the error direction angle of the surface of a part with a hole.

Background technique

The upper and lower surfaces of the parts with holes will have a slight tilt error during the machining process, so that the centerline of the middle hole of the parts with holes and the upper and lower surfaces deviate from the vertical relationship, that is, the verticality error between the upper and lower surfaces of the parts with holes to the center line of the hole will occur. In precision and ultra-precision measurement, the existence of the perpendicularity error between the upper and lower surfaces of a part with a hole to the centerline of the hole will affect the movement accuracy of the part, and the improvement of the performance of the part by measuring the perpendicularity error between the upper and lower surfaces of the part with holes to the centerline of the hole has important meaning.

At present, most of the measurements of the verticality error and error direction angle of the upper and lower surfaces of the parts with holes to the center line of the hole need to rely on high-precision measurement benchmarks and instruments, such as three-coordinate measuring instruments. The requirements are also relatively high. In addition, when measuring the verticality error and error direction angle of the upper and lower surfaces of larger parts with holes to the center line of the hole, because the parts are heavier and the rotation of the parts is more difficult, these instruments and equipment are not convenient for these larger parts with holes. Real-time on-site measurement of the verticality error and error direction angle of the surface to the center line of the hole.

Based on the above problems, this application proposes a device and method for measuring the verticality error and the error direction angle of the surface of a part with a hole. The device is simple, easy to operate, and has low requirements for the working environment; Rotation is carried out while the part with the hole remains still, which can realize real-time on-site measurement of the verticality error and the error direction angle of the upper and lower surfaces of the larger part with the hole to the center line of the hole.

Contents of the invention

The object of the present invention is to overcome the deficiencies of the above-mentioned prior art and provide a device for measuring the verticality error and the error direction angle of the surface of a part with a hole.

To achieve the above object, the present invention adopts the following technical solutions:

The device for measuring the verticality error and the error direction angle of the surface of the part with holes includes a standard plate for placing the part with holes, and the standard plate is horizontally fixed on the first support platform;

A circular through hole is set on the standard plate;

A turntable is rotated on the second support platform below the standard plate;

A drive assembly for controlling the rotation of the turntable is provided on the second support table;

The top of the turntable is vertically fixed with a rigid rod, and the rigid rod passes upward through the circular through hole of the standard flat plate;

A first displacement sensor and a second displacement sensor are sequentially arranged on the rigid rod from top to bottom.

Preferably, the drive assembly includes a drive motor, the output shaft of the drive motor is coaxially fixedly connected to the central shaft of the first pulley;

The central axis of the turntable is coaxially fixedly connected with the central axis of the second pulley;

A timing belt is sleeved between the first pulley and the second pulley.

The invention also provides a method for measuring the verticality error and the error direction angle of the surface of the part with holes.

The method for measuring the verticality error and the error direction angle of the surface of the part with holes is implemented by using the device for measuring the verticality error and the error direction angle of the surface of the part with holes, including the following steps:

Step 1: Establish a Cartesian coordinate system with the center O of the upper surface of the circular through-hole of the standard plate as the origin;

Step 2: Place the part with holes on the standard plate so that the upper surface of the part with holes is attached to the upper surface of the standard plate. The first displacement sensor and the second displacement sensor are located in the holes of the part with holes and correspond to the first First hole section, second hole section;

Step 3: Determine the inclination angle of the upper surface of the part with holes to the hole centerline ;

The distance between the outer end of the upper surface of the part with a hole and the horizontal plane M perpendicular to the centerline of the hole passing through the center of the upper surface of the part with a hole Defined as the perpendicularity error of the upper surface of the part with a hole to the center line of the hole; according to the inclination angle Calculate the verticality error of the upper surface of the part with holes to the center line of the hole ;

Step 4: Place the part with holes on the standard plate so that the lower surface of the part with holes is attached to the upper surface of the standard plate. The first displacement sensor and the second displacement sensor are located in the holes of the part with holes and correspond to the first Three-hole cross-section, fourth-hole cross-section;

Step 5: Determine the inclination angle of the lower surface of the holed part to the centerline of the hole ;

The distance between the outer end of the lower surface of the part with a hole and the horizontal plane N perpendicular to the centerline of the hole passing through the center of the upper surface of the part with a hole Defined as the perpendicularity error of the lower surface of the part with a hole to the center line of the hole; according to the inclination angle Calculate the perpendicularity error of the lower surface of the part with a hole to the center line of the hole ;

Step 6: According to the angle of inclination and tilt angle Make the perpendicularity error direction angle of the upper and lower surfaces of the part with holes to the center line of the hole .

Preferably, in said step 3, determine the inclination angle , Perpendicularity error of the upper surface of the part with a hole to the center line of the hole The method includes the following steps:

Step 31: Turn the turntable so that the initial coordinates of the rigid rod are (x0, 0);

Step 32: Control the turntable to rotate once;

The first displacement sensor measures the distance from the inner wall of the hole at several first hole sections;

The second displacement sensor measures the distance between several second hole sections and the inner wall of the hole;

Step 33: Fitting the coordinates of the first hole section center O1 according to the distance data measured by the first displacement sensor in step 32;

According to the distance data measured by the second displacement sensor in step 32, the coordinates of the center of circle O2 at the second hole section are fitted;

Step 34: Pass the center O1 of the section of the first hole to make a vertical line of the section of the second hole, and the vertical foot is A;

Draw a straight line between points O1 and O2, and draw a straight line between points A and O2;

Then ∠AO2O1 is the inclination angle of the upper surface of the part with a hole to the center line of the hole ;

Perpendicularity error of the upper surface of the part with a hole to the center line of the hole Calculated by formula (1),

(1)

In formula (1), R is the radius of the part with holes.

Preferably, in said step 5, determine the inclination angle , Perpendicularity error of the lower surface of the part with a hole to the center line of the hole The method includes the following steps:

Step 51: Turn the turntable so that the initial coordinates of the rigid rod are (x0, 0);

Step 52: Control the turntable to rotate once;

The first displacement sensor measures the distance between several third hole sections and the inner wall of the hole;

The second displacement sensor measures the distance between several fourth hole sections and the inner wall of the hole;

Step 53: Fitting the coordinates of the circle center O3 at the section of the third hole according to the distance data measured by the first displacement sensor in step 52;

According to the distance data measured by the second displacement sensor in step 52, the coordinates of the center of circle O4 at the hole cross section are fitted;

Step 54: Pass the center O3 of the section of the third hole to make a vertical line of the section of the fourth hole, and the vertical foot is B;

Make a straight line between points O3 and O4, and a straight line between points B and O4;

Then ∠BO4O3 is the inclination angle of the lower surface of the part with a hole to the center line of the hole ;

Perpendicularity error of the lower surface of the part with a hole to the center line of the hole Calculated by formula (2),

(2)

In formula (2), R is the radius of the part with holes.

Preferably, in step 33, the coordinates of the circle center O1 at the first hole section and the coordinates of the circle center O2 at the second hole section are obtained by Matlab software using least squares circle fitting.

Preferably, in step 53, the coordinates of the circle center O3 at the third hole cross section and the circle center O4 coordinates at the fourth hole cross section are obtained by Matlab software using least squares circle fitting.

Preferably, in the step 6, the verticality error direction angle is made The method includes the following steps:

Step 61: mark four points C, D, E, F respectively according to the coordinates of points O1, O2, O3, O4 in the same rectangular coordinate system;

Step 62: Make a straight line l1 through points C and D, and make a straight line l2 through points E and F;

Step 63: The angle between the straight line l1 and the straight line l2 is the perpendicularity error direction angle .

The beneficial effects of the present invention are:

The device of the invention is simple, easy to operate, and has low requirements on the working environment; when in use, the first displacement sensor and the second displacement sensor rotate with the turntable while the parts with holes remain stationary, which can realize the alignment of the upper and lower surfaces of larger parts with holes to the center of the hole The verticality error and error direction angle of the line are measured in real time on site.

Description of drawings

The accompanying drawings constituting a part of the present application are used to provide further understanding of the present application, and the schematic embodiments and descriptions of the present application are used to explain the present application, and do not constitute an improper limitation of the present application.

Fig. 1 is the structural schematic perspective view of the surface verticality error and the error direction angle measuring device of the part with holes of the present invention;

Fig. 2 is the change graph of the distance data collected by the first displacement sensor and the second displacement sensor with the rotation angle of the turntable among the present invention;

Fig. 3 is the inclination angle of the hole center line of the hole center line when the upper surface of the hole part and the upper surface of the standard flat plate are attached together in the present invention schematic diagram;

Fig. 4 is the perpendicularity error of the upper surface of the part with holes to the center line of the hole in the present invention schematic diagram;

Fig. 5 is the angle of inclination of the hole center line of the hole centerline when the lower surface of the hole part is attached to the upper surface of the standard flat plate in the present invention schematic diagram;

Fig. 6 is the perpendicularity error of the upper surface of the part with holes to the center line of the hole in the present invention schematic diagram;

Fig. 7 is the direction angle of the verticality error of two pieces with holes in the present invention schematic diagram;

in:

0-Part with hole, 1-Standard plate, 2-First support platform, 3-Second support platform, 4-Turntable, 5-Rigid rod, 6-First displacement sensor, 7-Second displacement sensor, 8- Drive motor, 9-first pulley, 10-second pulley, 11-synchronous belt.

Detailed ways

It should be pointed out that the following detailed description is exemplary and intended to provide further explanation to the present application. Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs.

It should be noted that the terminology used here is only for describing specific implementations, and is not intended to limit the exemplary implementations according to the present application. As used herein, unless the context clearly dictates otherwise, the singular is intended to include the plural, and it should also be understood that when the terms "comprising" and/or "comprising" are used in this specification, they mean There are features, steps, operations, means, components and/or combinations thereof.

In the present invention, the orientation or positional relationship indicated by terms such as "upper", "lower", "bottom" and "top" are based on the orientation or positional relationship shown in the drawings, and are only for the convenience of describing the various parts or positional relationships of the present invention. The relational words determined by the structural relationship of components do not specifically refer to any component or component in the present invention, and should not be construed as limiting the present invention.

In the present invention, terms such as "connected" and "connected" should be understood in a broad sense, indicating that they can be fixedly connected, integrally connected or detachably connected; they can be directly connected or indirectly connected through an intermediary. For relevant researchers or technical personnel in the field, the specific meanings of the above terms in the present invention can be determined according to specific situations, and should not be construed as limitations on the present invention.

The present invention will be further described below in conjunction with the accompanying drawings and embodiments.

Example 1:

As shown in Figure 1, the device for measuring the verticality error and the error direction angle of the surface of the holed part includes a standard flat plate 1 for placing the holed part O, and the standard flat plate 1 is horizontally fixed on the first support platform 2;

A circular through hole is set on the standard plate 1;

A turntable 4 is rotated on the second support platform 3 below the standard plate 1;

The second support table 3 is provided with a driving assembly for controlling the rotation of the turntable 4;

The top of the turntable 4 is vertically fixed with a rigid rod 5, and the rigid rod 5 passes upward through the circular through hole of the standard flat plate 1;

A first displacement sensor 6 and a second displacement sensor 7 are sequentially arranged on the rigid rod 5 from top to bottom.

Preferably, the drive assembly includes a drive motor 8, the output shaft of the drive motor 8 is coaxially fixedly connected to the central axis of the first pulley 9;

The central axis of the turntable 4 is coaxially fixedly connected with the central axis of the second pulley 10;

A timing belt 11 is sleeved between the first pulley 9 and the second pulley 10 .

Example 2:

The method for measuring the verticality error and the error direction angle of the surface of the part with holes is implemented by using the surface verticality error and the error direction angle measurement device of the part with holes in Embodiment 1, including the following steps:

Step 1: Establish a Cartesian coordinate system with the center O on the upper surface of the circular through hole of the standard plate 1 as the origin; as shown in Figure 1, the direction of the x-axis is to the right, and the direction of the y-axis is vertical to the inside;

Step 2: Place part 0 with holes on standard plate 1, make the upper surface of part 0 with holes stick to the upper surface of standard plate 1, the first displacement sensor 6 and the second displacement sensor 7 are located on the part 0 with holes inside the hole and respectively corresponding to the first hole section and the second hole section;

Step 3: Determine the inclination angle of the upper surface of the part with holes 0 to the hole centerline ;

The distance between the outer end of the upper surface of the part with a hole and the horizontal plane M perpendicular to the centerline of the hole passing through the center of the upper surface of the part with a hole Defined as the perpendicularity error of the upper surface of the part with a hole to the center line of the hole; according to the inclination angle Calculate the verticality error of the upper surface of the part with holes to the center line of the hole ;

Specifically, in the step 3, determine the inclination angle , Perpendicularity error of the upper surface of the part with a hole to the center line of the hole The method includes the following steps:

Step 31: Turn the turntable 4 so that the initial coordinates of the rigid rod 5 are (x0, 0);

Step 32: Control the turntable 4 to rotate once;

The first displacement sensor 6 measures the distance from the inner wall of the hole at some first hole sections;

The second displacement sensor 7 measures the distance from the hole inner wall at some second hole cross-sections;

Wherein, the change curves of the distance data collected by the first displacement sensor 6 and the distance data collected by the second displacement sensor 7 with the rotation angle of the turntable 4 are shown in Figure 2;

Step 33: Fitting the coordinates of the first hole section center O1 according to the distance data measured by the first displacement sensor 6 in step 32;

According to the distance data that the second displacement sensor 7 measures in step 32, the coordinates of the center of circle O2 at the second hole section are fitted;

Specifically, in the step 33, the coordinates of the center of circle O1 at the first hole section and the coordinates of the center of circle O2 at the second hole section are obtained by Matlab software using least squares circle fitting;

Step 34: Pass the center O1 of the section of the first hole to make a vertical line of the section of the second hole, and the vertical foot is A;

Draw a straight line between points O1 and O2, and draw a straight line between points A and O2;

Then ∠AO2O1 is the inclination angle of the upper surface of the part with hole 0 to the center line of the hole , as shown in Figure 3; in this application, the inclination angle is the angle between the centerline of the hole of the part with a hole and the upper surface of the part with a hole;

Perpendicularity error of the upper surface of the part with a hole to the center line of the hole Calculated by formula (1),

(1)

In the formula (1), R is the radius of the part with holes 0.

As shown in Figure 4, the formula (1) can be obtained by the trigonometric function relationship.

Step 4: Place part 0 with holes on the standard plate 1, make the lower surface of part 0 with holes stick to the upper surface of standard plate 1, and the first displacement sensor 6 and the second displacement sensor 7 are located on the opposite side of the part with holes. inside the hole and correspond to the third pair of hole cross-sections and the fourth pair of hole cross-sections respectively;

Step 5: Determine the inclination angle of the lower surface of the part with holes 0 to the hole centerline ;

The distance between the outer end of the lower surface of the part with a hole and the horizontal plane N perpendicular to the centerline of the hole passing through the center of the upper surface of the part with a hole Defined as the perpendicularity error of the lower surface of the part with a hole to the center line of the hole; according to the inclination angle Calculate the perpendicularity error of the lower surface of the part with a hole to the center line of the hole ;

Specifically, in the step 5, determine the inclination angle , Perpendicularity error of the lower surface of the part with a hole to the center line of the hole The method includes the following steps:

Step 51: Turn the turntable 4 so that the initial coordinates of the rigid rod 5 are (x0, 0);

Step 52: Control the turntable 4 to rotate once;

The first displacement sensor 6 measures the distance from the inner wall of the hole at some third hole cross-sections;

The second displacement sensor 7 measures the distance from the hole inner wall at some fourth hole cross-sections;

Step 53: Fitting the coordinates of the circle center O3 at the section of the third hole according to the distance data measured by the first displacement sensor 6 in step 52;

Fitting the coordinates of the center of circle O4 at the fourth hole section according to the distance data measured by the second displacement sensor 7 in step 52;

Specifically, in step 53, the coordinates of the center of circle O3 at the third hole section and the coordinates of the circle center O4 at the fourth hole section are obtained by Matlab software using least squares circle fitting;

Step 54: Pass the center O3 of the section of the third hole to make a vertical line of the section of the fourth hole, and the vertical foot is B;

Make a straight line between points O3 and O4, and a straight line between points B and O4;

Then ∠BO4O3 is the inclination angle of the lower surface of the part with hole 0 to the center line of the hole , as shown in Figure 5; in this application, the inclination angle is the angle between the centerline of the hole of the part with a hole and the lower surface of the part with a hole;

Perpendicularity error of the lower surface of the part with a hole to the center line of the hole Calculated by formula (2),

(2)

In formula (2), R is the radius of the part with holes 0.

As shown in Figure 6, formula (2) can be obtained from the relationship of trigonometric functions.

Step 6: According to the angle of inclination and tilt angle Make the perpendicularity error direction angle of the upper and lower surfaces of the part with holes to the center line of the hole .

Specifically, in the step 6, the verticality error direction angle is made The method includes the following steps:

Step 61: Mark four points C, D, E, and F according to the coordinates of points O1, O2, O3, and O4 in the same rectangular coordinate system; the coordinates of point C are consistent with the coordinates of O1, and the coordinates of point D are It is consistent with the coordinates of O2, the coordinates of point E are consistent with the coordinates of O3, and the coordinates of point F are consistent with the coordinates of O4;

Step 62: Make a straight line l1 through points C and D, and make a straight line l2 through points E and F;

Step 63: The angle between the straight line l1 and the straight line l2 is the perpendicularity error direction angle , as shown in Figure 7.

The device of the present invention is simple, easy to operate, and has low requirements on the working environment; when in use, the first displacement sensor 6 and the second displacement sensor 7 rotate with the turntable 4 while the parts with holes 0 remain stationary, which can realize the up and down movement of larger parts with holes Real-time on-site measurement of the verticality error and error direction angle of the surface to the center line of the hole.

Although the specific implementation of the present invention has been described above in conjunction with the accompanying drawings, it is not a limitation of the present invention. Those skilled in the art should understand that on the basis of the technical solution of the present invention, those skilled in the art do not need to pay creative work. Various modifications or variations made are still within the protection scope of the present invention.

Claims (4)

1. The method for measuring the surface verticality error and the error direction angle of the part with holes is characterized by being implemented by adopting a device for measuring the surface verticality error and the error direction angle of the part with holes, wherein the device for measuring the surface verticality error and the error direction angle of the part with holes comprises a standard flat plate for placing the part with holes, and the standard flat plate is horizontally fixed on a first supporting table;

a round through hole is formed in the standard flat plate;

a turntable is in running fit on a second supporting table below the standard flat plate;

the second supporting table is provided with a driving component for controlling the rotation of the turntable;

the top end of the turntable is vertically and fixedly provided with a rigid rod, and the rigid rod upwards penetrates through a round through hole of the standard flat plate;

the rigid rod is sequentially provided with a first displacement sensor and a second displacement sensor from top to bottom;

the measuring method comprises the following steps:

step 1: establishing a rectangular coordinate system by taking the circle center O of the upper surface of the standard flat plate circular through hole as an origin;

step 2: placing the part with the hole on a standard flat plate, enabling the upper surface of the part with the hole to be attached to the upper surface of the standard flat plate, and enabling the first displacement sensor and the second displacement sensor to be located in the hole of the part with the hole and correspond to the first hole section and the second hole section respectively;

step 3: determining the inclination angle of the upper surface of a perforated part to the centre line of the hole；

Distance between outer end of upper surface of the part with hole and horizontal plane M perpendicular to center line of hole at center of upper surface of part with holeThe perpendicularity error of the upper surface of the part with the hole to the center line of the hole is defined; according to the inclination angle->Calculating perpendicularity error of upper surface of part with hole to center line of hole>；

Step 4: placing the part with the hole on a standard flat plate, enabling the lower surface of the part with the hole to be attached to the upper surface of the standard flat plate, and enabling the first displacement sensor and the second displacement sensor to be located in the hole of the part with the hole and correspond to the third hole section and the fourth hole section respectively;

step 5: determining the inclination angle of the lower surface of a perforated part to the center line of the hole；

Distance between outer end of lower surface of the part with hole and horizontal plane N perpendicular to center line of hole at center of upper surface of part with holeThe perpendicularity error of the lower surface of the part with the hole to the center line of the hole is defined; according to the inclination angle->Calculating the center of the lower surface of the part with the hole to the holeLine perpendicularity error->；

Step 6: according to the inclination angleAnd tilt angle->Making a perpendicularity error direction angle of the upper surface and the lower surface of the part with the hole to the center line of the hole>；

In the step 3, the inclination angle is determinedPerpendicularity error of upper surface of part with hole to center line of hole>The method of (1) comprises the following steps:

step 31: rotating the turntable so that the initial coordinates of the rigid rods are (x 0, 0);

step 32: controlling the turntable to rotate for one circle;

the first displacement sensors measure distances from the inner wall surfaces of the holes at the sections of the plurality of first holes;

the second displacement sensors measure the distances from the inner wall surfaces of the holes at the sections of the second holes;

step 33: fitting the coordinates of the circle center O1 of the first hole section according to the distance data measured by the first displacement sensor in the step 32;

fitting the coordinates of the circle center O2 at the section of the second hole according to the distance data measured by the second displacement sensor in the step 32;

step 34: making a perpendicular line of the section of the second hole through the circle center O1 of the section of the first hole, wherein the foot drop is A;

a straight line is made between points O1, O2, and a straight line is made between points A, O2;

then AO2O1 is the inclination angle of the upper surface of the part with hole to the center line of the hole；

Perpendicularity error of upper surface of part with hole to center line of holeCalculated from the formula (1) of the present application,

（1）

in the formula (1),Rthe radius of the part with the hole;

in the step 5, the inclination angle is determinedPerpendicularity error of lower surface of part with hole to center line of hole>The method of (1) comprises the following steps:

step 51: rotating the turntable so that the initial coordinates of the rigid rods are (x 0, 0);

step 52: controlling the turntable to rotate for one circle;

the first displacement sensor measures the distance between the sections of the third holes and the inner wall surface of the holes;

the second displacement sensor measures the distance from the inner wall surface of the hole at the sections of the fourth holes;

step 53: fitting the coordinates of the circle center O3 at the section of the third hole according to the distance data measured by the first displacement sensor in the step 52;

fitting the coordinates of the circle center O4 at the cross section of the first pair of holes according to the distance data measured by the second displacement sensor in the step 52;

step 54: making a perpendicular line of the section of the fourth hole through the circle center O3 of the section of the third hole, and taking the foot as B;

a straight line is made between points O3, O4, and a straight line is made between points B, O4;

then BO4O3 is the inclination angle of the lower surface of the perforated part to the center line of the hole；

Perpendicularity error of lower surface of part with hole to center line of holeCalculated from the formula (2) of the present application,

（2）

in the formula (2),Rthe radius of the part with the hole;

in the step 6, a perpendicularity error direction angle is madeThe method of (1) comprises the following steps:

step 61: four points C, D, E, F are marked in the same rectangular coordinate system according to the coordinates of the points O1, O2, O3 and O4;

step 62: passing point C, D as straight linel1, passing point E, F as a straight linel2；

Step 63: straight linel1 and straight linel2 is the error direction angle of verticality。

2. The method for measuring the perpendicularity error and the error direction angle of the surface of the part with the hole according to claim 1, wherein the driving assembly comprises a driving motor, and an output shaft of the driving motor is coaxially and fixedly connected with a central shaft of the first belt wheel;

the central shaft of the turntable is coaxially and fixedly connected with the central shaft of the second belt wheel;

and a synchronous belt is sleeved between the first belt pulley and the second belt pulley.

3. The method for measuring surface verticality error and error direction angle of a part with holes according to claim 1, wherein in the step 33, coordinates of a circle center O1 at a first hole section and coordinates of a circle center O2 at a second hole section are obtained by least square circle fitting through Matlab software.

4. The method for measuring the surface verticality error and the error direction angle of the part with holes according to claim 1, wherein in the step 53, coordinates of a center O3 at a third hole section and coordinates of a center O4 at a fourth hole section are obtained by least square circle fitting through Matlab software.