Device and method for measuring return difference of swing arm type fatigue life test bed of precision speed reducer

By designing a precision reducer swing arm fatigue life test bench back measurement device using indirect back measurement method of light reflection triangle block and laser displacement sensor, the problems of complex structure, large error and large space in the existing measurement methods are solved, and the rapid and efficient measurement and evaluation of the back difference of the reducer is achieved.

CN119714876APending Publication Date: 2025-03-28CRRC QISHUYAN INSTITUTE CO LTD
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Patent Information

Application Number
CN202411823253.9
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2024-12-12
Publication Date
2025-03-28

AI Technical Summary

Technical Problem

The existing encoder measurement and dial gauge measurement methods have problems such as complex structure, large errors and large space in the reduction gearbox back-difference measurement, making it difficult to quickly and efficiently evaluate the fatigue life status of the reducer.

Method used

A precision reducer swing arm fatigue life test bench back-difference measurement device is designed, and the indirect back-difference measurement method is used to achieve online measurement of the reducer back-difference by combining the light reflective triangle block and the laser displacement sensor. The device adopts a portable structure, an electronically controlled telescopic swing rod and a quick-removing loading block, which improves the accuracy and adaptability of measurement.

Benefits of technology

It realizes fast and efficient measurement of the reducer back error, reduces structural complexity and error, reduces space occupation, improves anti-interference performance and adaptability, and facilitates storage and portability.

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Abstract

The invention relates to the technical field of fatigue life tests, in particular to a precision reducer swing arm type fatigue life test bed return difference measuring device and measuring method.The precision reducer swing arm type fatigue life test bed return difference measuring device comprises a mounting base, a servo motor and a precision reducer, and two right-trapezoid lateral supporting plates are fixedly assembled on the upper surface of the mounting base. According to the precision reducer swing arm type fatigue life test bench return difference measuring device and measuring method, an indirect return difference measuring method is adopted to measure the return difference value of a tested reducer on line, and the fatigue life state of the tested reducer is evaluated quickly and efficiently; through the portable structural design, translation adjustment can be conducted in idle time, the occupied space of the outer side can be greatly reduced, and storage and carrying are convenient; through mutual cooperation of the light reflection triangular block and the laser displacement sensor, data collection and calculation are carried out in a light distance measurement mode, so that the return difference is accurately obtained, interference to the electric control telescopic swing rod is avoided, and the anti-interference performance is improved.
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Description

Technical Field

[0001] The invention relates to the technical field of fatigue life test, in particular to a hysteresis measuring device and a measuring method for a precision reducer swing arm fatigue life test bench. Background Art

[0002] The precision reducer swing-arm fatigue life test bench is a typical device that simulates the operating conditions of robots. It conducts life tests on reducers with frequent acceleration, deceleration, and reciprocating swings. The backlash is an important indicator for judging the degree of wear of the reducer. Therefore, measuring the backlash of the test reducer can quickly and efficiently evaluate the fatigue life status of the test reducer.

[0003] The research on the test device for measuring the backlash of the integrated reducer in the swing arm fatigue life test is still in its early stages and has limited reference value. At present, the measurement of the backlash of the reducer mainly includes encoder measurement and micrometer measurement. If the encoder is used for measurement, it is necessary to extend the output shaft of the reducer and install an encoder support seat to install the encoder, which increases the inertia of the test system, complicates the structure, and increases the influence of eccentricity; while the micrometer is used for measurement, this measurement method is contact measurement, although it is convenient to operate and has a simple structure, but contact wear will increase the measurement error, and there will be interference with the running swing arm; at the same time, the equipment structure occupies a large space, and it is very inconvenient to store and transport. Summary of the invention

[0004] The technical problem to be solved by the present invention is that currently both encoder measurement and micrometer measurement have obvious defects.

[0005] The technical solution adopted by the present invention to solve its technical problems is: a backlash measuring device of a precision reducer swing-arm fatigue life test bench, comprising a mounting base, a servo motor and a precision reducer, wherein two right-angled trapezoidal lateral support plates are fixedly mounted on the upper surface of the mounting base, the upper end of the mounting base is located on the inner side of the lateral support plate and is slidably mounted with an electrically-controlled translational support back plate, the upper end of the inner part of the electrically-controlled translational support back plate is laterally mounted with a transverse transmission seat for mounting a servo motor and a precision reducer, an electrically-controlled telescopic rocker arm is axially fixed to the outer output end of the precision reducer, a quick-release loading weight is mounted at the outer end position of the electrically-controlled telescopic rocker arm, a laser displacement sensor is fixedly mounted on the side of the electrically-controlled translational support back plate through an adjustable mounting bracket, and a light reflecting triangle block matching the laser displacement sensor is fixedly mounted on the surface of the electrically-controlled telescopic rocker arm adjacent to the lateral support plate.

[0006] The inner walls on both sides of the lateral support plate are symmetrically provided with transverse guide sliding grooves, and the upper surface of the mounting base is provided with a bottom transmission sliding groove.

[0007] The electrically controlled translation support back plate comprises a longitudinal back plate, sliding guide blocks fixed on both sides of the longitudinal back plate, an internal threaded translation block fixed on the bottom of the longitudinal back plate and an electrically controlled translation lead screw installed inside a bottom transmission slide groove.

[0008] The transverse transmission seat comprises a transverse fixing seat fixed on the longitudinal back plate and a sliding installation cover slidably plugged on the outer side of the transverse fixing seat.

[0009] The output end side wall of the servo motor is fixedly assembled with the inner side of the sliding mounting cover, and the precision reducer is fixedly mounted on one side inside the transverse fixing seat.

[0010] The transverse fixing seat and the sliding installation cover are fixedly assembled by elastic lock buckles.

[0011] The electrically controlled telescopic rocker arm comprises a lateral mounting plate axially fixed to the output end of the precision reducer, an outer swing arm fixed to the outer arc surface of the lateral mounting plate, and a telescopic extension arm slidably inserted into the inner part of the outer swing arm, and the telescopic extension arm is fixed to the outer swing arm by bolts.

[0012] The outer side surface of the telescopic extension arm is located at the back of the telescopic section and is provided with a front installation through hole with a sinking groove, and the inner wall of the front installation through hole is provided with an installation notch connected with the sinking groove.

[0013] The quick-release loading weight block is connected to the telescopic extension arm by inserting an assembly shaft with installation limit blocks on both sides of the assembly surface into the installation notch.

[0014] A method for measuring the hysteresis of a precision reducer swing arm fatigue life test bench, the test steps are as follows:

[0015] (1) The output shaft center of the precision reducer is the rotation center O of the electrically controlled telescopic swing arm;

[0016] Set the rotation center O of the electrically controlled telescopic swing arm to point vertically to the horizontal ground direction as the 0° reference line, and the counterclockwise rotation direction as the positive direction;

[0017] (2) The light reflection triangle block is perpendicular to the electric telescopic swing arm, and the triangular surface pointing to the side of the rotation point of the electric telescopic swing arm is △BCD;

[0018] (3) The electrically controlled telescopic swing arm is rotated so that its center line is parallel to the 0° reference line. The laser displacement sensor emits a laser beam perpendicular to the electrically controlled telescopic swing arm, and the direction of the extended line of the beam intersects with the center line of the electrically controlled telescopic swing arm. At this time, the effective measurement point on the reflecting slope S2 is recorded as the starting point A1, and the point projected on the inner plane S1 of the electrically controlled telescopic swing arm is E1;

[0019] (4) Then the straight line OE1 is perpendicular to the side BC, and the intersection point is G;

[0020] (5) The distance from the record point A1 to the reference point is h1;

[0021] (6) Control the electrically controlled telescopic swing arm to rotate counterclockwise by a certain angle φ, and then rotate clockwise by the same angle. At this time, the effective measurement point on the reflection slope is recorded as the starting point A2, and the point projected on the inner plane S1 of the electrically controlled telescopic swing arm is E2;

[0022] (7) The equivalent rotation radius of the arc E1E2 is L;

[0023] (8) Then the straight line OE2 forms a certain angle ∠E2OE1 with the set 0° reference line direction, which is the hysteresis angle;

[0024] (9) The distance from the record point A2 to the reference point is h2;

[0025] (10) Then the projection length of the straight lines A1 and A2 on the DC side is △h = |h1-h2|, and the projection length on the BC side is |h1-h2| / tanɑ. At the same time, the projection length of the arc E1E2 on the BC side is also |h1-h2| / tanɑ.

[0026] (11) Draw a perpendicular line through point E2 to OE1, intersecting OE1 at point F. Since OE1 is perpendicular to side BC, E2F∥BC, so E2F=|h1-h2| / tanɑ;

[0027] (12) For the right triangle △E2OE1 formed by the hysteresis, it is known that the right-angled side E2F = |h1-h2| / tanɑ and the hypotenuse E2O = L, then the hysteresis ∠E2OE1 = arcsin(E2F / E2O) = arcsin(|h1-h2| / (Ltanɑ)).

[0028] The beneficial effects of the present invention are:

[0029] (1) The precision reducer swing arm fatigue life test bench hysteresis measurement device and measurement method of the present invention adopts an indirect hysteresis measurement method to measure the hysteresis value of the reducer under test online, and quickly and efficiently evaluates its fatigue life status;

[0030] (2) The portable structure design allows for translational adjustment when not in use, which can greatly reduce the space occupied by the outside, making it easier to store and carry;

[0031] (3) By cooperating with the light reflection triangle block and the laser displacement sensor, the optical ranging method is used to collect and calculate data, so as to accurately obtain the hysteresis, which will not interfere with the electronically controlled telescopic swing arm and improve the anti-interference performance;

[0032] (4) By adopting a quick-release structure design, the quick-release loading weight can be quickly replaced as needed, which greatly improves the adaptability;

[0033] (5) The length of the electrically controlled telescopic swing arm can be adjusted according to different reducer requirements, which greatly improves operability and adaptability, and is also convenient for storage;

[0034] (6) The servo motor can be quickly separated from the reducer, which is convenient for storage and later maintenance;

[0035] (7) The laser displacement sensor and light reflection triangle block are installed externally, which is convenient for loading and unloading and adjustment, and reduces the cost of later use. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] The present invention is further described below in conjunction with the accompanying drawings and embodiments.

[0037] Figure 1 It is a structural schematic diagram of the present invention.

[0038] Figure 2 It is an internal schematic diagram of the present invention in the unfolded state.

[0039] Figure 3 It is an internal schematic diagram of the present invention in the storage state.

[0040] Figure 4 It is a schematic diagram of the rotation of the electrically controlled telescopic swing arm in the present invention.

[0041] Figure 5 It is a schematic diagram of light reflection measurement in the present invention.

[0042] In the figure, 1. mounting base, 2. servo motor, 3. precision reducer, 4. lateral support plate, 5. electrically controlled translation support back plate, 6. horizontal transmission seat, 20. electrically controlled telescopic swing arm, 7. quick-release loading weight, 8. adjustable mounting bracket, 9. laser displacement sensor, 10. light reflection triangle block, 41. horizontal guide slide, 42. bottom transmission slide, 51. longitudinal back plate, 52. sliding guide block, 53. internal thread translation block, 54. electrically controlled translation screw, 61. horizontal fixing seat, 62. sliding mounting cover, 63. elastic lock buckle, 201. lateral assembly plate, 202. outer swing arm, 203. telescopic extension arm, 204. front mounting through hole, 205. mounting notch, 71. mounting limit block, 72. assembly shaft. DETAILED DESCRIPTION

[0043] The present invention will now be described in further detail with reference to the accompanying drawings. These drawings are simplified schematic diagrams, which only illustrate the basic structure of the present invention in a schematic manner, and therefore only show the components related to the present invention.

[0044] In the description of the present invention, it should be noted that, unless otherwise clearly specified and limited, the terms "connected" and "connection" should be understood in a broad sense, for example, it can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be a direct connection or an indirect connection through an intermediate medium. For ordinary technicians in this field, the specific meanings of the above terms in the present invention can be understood according to specific circumstances.

[0045] Figure 1 , Figure 2 and Figure 3 The precision reducer swing-arm fatigue life test bench backlash measuring device shown comprises a mounting base 1, a servo motor 2 and a precision reducer 3. Two right-angled trapezoidal lateral support plates 4 are fixedly mounted on the upper surface of the mounting base 1. The upper end of the mounting base 1 is located on the inner side of the lateral support plate 4 and is slidably mounted with an electrically-controlled translational support back plate 5. The upper end of the inner part of the electrically-controlled translational support back plate 5 is laterally mounted with a transverse transmission seat 6 for mounting the servo motor 2 and the precision reducer 3. An electrically-controlled telescopic rocker arm 20 is axially fixed at the outer output end of the precision reducer 3. A quick-release loading weight block 7 is mounted at the outer end position of the electrically-controlled telescopic rocker arm 20. A laser displacement sensor 9 is fixedly mounted on the side of the electrically-controlled translational support back plate 5 through an adjustable mounting bracket 8. A light reflecting triangle block 10 matching the laser displacement sensor 9 is fixedly mounted on the surface of the electrically-controlled telescopic rocker arm 20 adjacent to the lateral support plate 4.

[0046] The light reflecting triangle block 10 is fixed to the inner side of the loading end of the electrically controlled telescopic swing arm 20 by bolting. The slope of the inclined edge of the light reflecting triangle block 10 is used as a reflecting surface to point to the side of the test bench support seat. At the same time, the slope ɑ is set to be smaller than the maximum angle without interference when the swing arm swings.

[0047] The laser displacement sensor 9 is fixed on the electrically controlled translation support back plate 5 at a vertical distance L from the rotation axis through an adjustable tooling bolt. The front and rear positions of the laser displacement sensor 9 are adjusted so that the emitted laser beam forms an effective measuring point A on the reflecting slope. At this time, the equivalent rotation radius of the measuring point is L, and the distance h from the measuring point to the reference point is output at the same time.

[0048] The input end of the laser displacement sensor 9 is connected to the data acquisition processor through a conveyor line, and the single-cycle reciprocating motion position of the telescopic rocker 20 is electrically controlled to obtain the distance h from the two measuring points to the reference point. According to the slope ɑ of the reflecting surface and the equivalent rotation radius L of the measuring point, the hysteresis value of the tested precision reducer 3 is determined through the data acquisition processor.

[0049] The inner walls on both sides of the lateral support plate 4 are symmetrically provided with transverse guide slots 41 , and the upper surface of the mounting base 1 is provided with a bottom transmission slot 42 .

[0050] The electrically controlled translation support back plate 5 includes a longitudinal back plate 51 , sliding guide blocks 52 fixed on both sides of the longitudinal back plate 51 , an internal threaded translation block 53 fixed on the bottom of the longitudinal back plate 51 , and an electrically controlled translation screw 54 installed inside the bottom transmission slot 42 .

[0051] The transverse transmission seat 6 includes a transverse fixing seat 61 fixed on the longitudinal back plate 51 and a sliding mounting cover 62 slidably inserted on the outer side of the transverse fixing seat 61 .

[0052] The output end side wall of the servo motor 2 is fixedly assembled with the inner side of the sliding mounting cover 62 , and the precision reducer 3 is fixedly mounted on one side inside the transverse fixing seat 61 .

[0053] The transverse fixing seat 61 and the sliding mounting cover 62 are fixedly assembled by an elastic lock buckle 63 .

[0054] The electrically controlled telescopic rocker arm 20 comprises a lateral mounting disk 201 axially fixed to the output end of the precision reducer 3, an outer swing arm 202 fixed to the outer arc surface of the lateral mounting disk 201, and a telescopic extension arm 203 slidably inserted into the inner part of the outer swing arm 202. The telescopic extension arm 203 is fixed to the outer swing arm 202 by bolts.

[0055] The outer side surface of the telescopic extension arm 203 is provided with a front mounting through hole 204 with a sinking groove at the back of the telescopic section, and the inner wall of the front mounting through hole 204 is provided with a mounting notch 205 connected with the sinking groove.

[0056] The quick-release loading weight 7 is connected to the telescopic extension arm 203 by inserting the assembly shaft 72 with the installation limit blocks 71 on both sides of the assembly surface into the installation notch 205 .

[0057] like Figure 4 and Figure 5 The following is a method for measuring the hysteresis of a precision reducer swing arm fatigue life test bench. The test steps are as follows:

[0058] (1) The output shaft center of the precision reducer 3 is the rotation center O of the electrically controlled telescopic swing arm 20;

[0059] The rotation center O of the electrically controlled telescopic swing arm 20 is set to point vertically to the horizontal ground direction as the 0° reference line. Any direction can be set as the 0° reference line, and the counterclockwise rotation direction is the positive direction;

[0060] (2) The light reflection triangle block is perpendicular to the swing rod, and the triangular surface pointing to the side of the rotation point of the electrically controlled telescopic swing rod 20 is △BCD;

[0061] (3) The electrically controlled telescopic swing arm 20 is rotated so that its center line is parallel to the 0° reference line. The laser displacement sensor emits a laser beam perpendicular to the electrically controlled telescopic swing arm 20, and the direction of the extended line of the laser beam intersects with the center line of the electrically controlled telescopic swing arm 20. At this time, the effective measurement point on the reflecting slope S2 is recorded as the starting point A1, and the point projected on the inner plane S1 of the electrically controlled telescopic swing arm 20 is E1;

[0062] (4) Then the straight line OE1 is perpendicular to the side BC, and the intersection point is G;

[0063] (5) The distance from the record point A1 to the reference point is h1;

[0064] (6) Control the electrically controlled telescopic swing arm 20 to rotate counterclockwise by a certain angle φ, and then rotate clockwise by the same angle. At this time, the effective measurement point on the reflection slope is recorded as the starting point A2, and the point projected on the inner side plane S1 of the electrically controlled telescopic swing arm 20 is E2;

[0065] (7) The equivalent rotation radius of the arc E1E2 is L;

[0066] (8) Then the straight line OE2 forms a certain angle ∠E2OE1 with the set 0° reference line direction, which is the hysteresis angle;

[0067] (9) The distance from the record point A2 to the reference point is h2;

[0068] (10) Then the projection length of the straight lines A1 and A2 on the DC side is △h = |h1-h2|, and the projection length on the BC side is |h1-h2| / tanɑ. At the same time, the projection length of the arc E1E2 on the BC side is also |h1-h2| / tanɑ.

[0069] (11) Draw a perpendicular line through point E2 to OE1, intersecting OE1 at point F. Since OE1 is perpendicular to side BC, E2F∥BC, so E2F=|h1-h2| / tanɑ;

[0070] (12) For the right triangle △E2OE1 formed by the hysteresis, it is known that the right-angled side E2F = |h1-h2| / tanɑ and the hypotenuse E2O = L, then the hysteresis ∠E2OE1 = arcsin(E2F / E2O) = arcsin(|h1-h2| / (Ltanɑ)).

[0071] Based on the above ideal embodiments of the present invention, the relevant staff can make various changes and modifications without departing from the technical concept of the present invention through the above description. The technical scope of the present invention is not limited to the contents of the specification, and its technical scope must be determined according to the scope of the claims.

Claims

1. A precision reducer swing arm fatigue life test bench backlash measurement device, comprising a mounting base (1), a servo motor (2) and a precision reducer (3), characterized in that: The upper surface of the mounting base (1) is fixedly equipped with two right-angled trapezoidal lateral support plates (4); the upper end of the mounting base (1) is located inside the lateral support plate (4) and is slidably equipped with an electrically controlled translation support back plate (5); the upper end of the inner part of the electrically controlled translation support back plate (5) is laterally equipped with a transverse transmission seat (6) for installing a servo motor (2) and a precision reducer (3); an electrically controlled telescopic swing arm (20) is axially fixed to the outer output end of the precision reducer (3); a quick-release loading weight (7) is installed at the outer end position of the electrically controlled telescopic swing arm (20); a laser displacement sensor (9) is fixedly equipped on the side of the electrically controlled translation support back plate (5) through an adjustable mounting bracket (8); and a light reflection triangle block (10) matched with the laser displacement sensor (9) is fixedly equipped on the surface of the electrically controlled telescopic swing arm (20) adjacent to the lateral support plate (4).

2. The precision reducer swing arm fatigue life test bench hysteresis measuring device according to claim 1 is characterized by: The inner walls on both sides of the lateral support plate (4) are symmetrically provided with transverse guide sliding grooves (41), and the upper surface of the mounting base (1) is provided with a bottom transmission sliding groove (42).

3. The precision reducer swing arm fatigue life test bench hysteresis measuring device according to claim 1 is characterized by: The electrically controlled translation support back plate (5) comprises a longitudinal back plate (51), sliding guide blocks (52) fixed on both sides of the longitudinal back plate (51), an internal threaded translation block (53) fixed on the bottom of the longitudinal back plate (51), and an electrically controlled translation screw rod (54) installed inside a bottom transmission slide groove (42).

4. The precision reducer swing arm fatigue life test bench hysteresis measuring device according to claim 3 is characterized by: The transverse transmission seat (6) comprises a transverse fixing seat (61) fixed on the longitudinal back plate (51) and a sliding installation cover (62) slidably inserted on the outside of the transverse fixing seat (61).

5. The precision reducer swing arm fatigue life test bench hysteresis measuring device according to claim 4 is characterized by: The output end side wall of the servo motor (2) is fixedly assembled with the inner side of the sliding mounting cover (62), and the precision reducer (3) is fixedly mounted on one side inside the transverse fixing seat (61).

6. The precision reducer swing arm fatigue life test bench hysteresis measuring device according to claim 3 is characterized by: The transverse fixing seat (61) and the sliding mounting cover (62) are fixedly assembled by means of elastic lock buckles.

7. The precision reducer swing arm fatigue life test bench hysteresis measuring device according to claim 1 is characterized by: The electrically controlled telescopic swing arm (20) comprises a lateral mounting plate (201) axially fixed to the output end of the precision reducer (3), an outer swing arm (202) fixed to the outer arc surface of the lateral mounting plate (201), and a telescopic extension arm (203) slidably inserted into the inner part of the outer swing arm (202), wherein the telescopic extension arm (203) and the outer swing arm (202) are locked and fixed by bolts.

8. The precision reducer swing arm fatigue life test bench hysteresis measuring device according to claim 6 is characterized by: The outer side surface of the telescopic extension arm (203) is located at the back of the telescopic section and has a front mounting through hole (204) with a sinking groove, and the inner wall of the front mounting through hole (204) is provided with a mounting notch (205) connected to the sinking groove.

9. The precision reducer swing arm fatigue life test bench hysteresis measuring device according to claim 6 is characterized by: The quick-detachable loading weight (7) is connected to the telescopic extension arm (203) by inserting an assembly shaft (72) having installation limit blocks (71) on both sides of the assembly surface into the installation notch.

10. A method for measuring the hysteresis of a precision reducer swing arm fatigue life test bench, characterized in that: Here are the steps: (1) The center of the output shaft of the precision reducer (3) is taken as the rotation center O of the electrically controlled telescopic swing arm (20); The rotation center O of the electrically controlled telescopic swing arm (20) is set to point vertically to the horizontal ground direction as the 0° reference line, and the counterclockwise rotation direction is the positive direction; (2) The light reflecting triangle block is perpendicular to the electrically controlled telescopic swing rod (20), and the triangular surface pointing to the side of the rotation point of the electrically controlled telescopic swing rod (20) is △BCD; (3) The electrically controlled telescopic swing arm (20) is rotated so that its center line is parallel to the 0° reference line, and the laser displacement sensor emits a laser beam perpendicular to the electrically controlled telescopic swing arm (20), and the direction of the extended line of the laser beam intersects with the center line of the electrically controlled telescopic swing arm (20). At this time, the effective measurement point on the reflection slope surface S2 is recorded as the starting point A1, and the point projected on the inner side plane S1 of the electrically controlled telescopic swing arm (20) is E1; (4) Then the straight line OE1 is perpendicular to the side BC, and the intersection point is G; (5) The distance from the record point A1 to the reference point is h1; (6) Control the electrically controlled telescopic swing arm (20) to rotate counterclockwise by a certain angle φ, and then rotate clockwise by the same angle. At this time, the effective measurement point on the reflection slope is recorded as the starting point A2, and the point projected on the inner side plane S1 of the electrically controlled telescopic swing arm (20) is E2; (7) The equivalent rotation radius of the arc E1E2 is L; (8) Then the straight line OE2 forms a certain angle ∠E2OE1 with the set 0° reference line direction, which is the hysteresis angle; (9) The distance from the record point A2 to the reference point is h2; (10) Then the projection length of the straight lines A1 and A2 on the DC side is △h = |h1-h2|, and the projection length on the BC side is |h1-h2| / tanɑ. At the same time, the projection length of the arc E1E2 on the BC side is also |h1-h2| / tanɑ. (11) Draw a perpendicular line through point E2 to OE1, intersecting OE1 at point F. Since OE1 is perpendicular to side BC, E2F∥BC, so E2F=|h1-h2| / tanɑ; (12) For the right triangle △E2OE1 formed by the hysteresis, it is known that the right-angled side E2F = |h1-h2| / tanɑ and the hypotenuse E2O = L, then the hysteresis ∠E2OE1 = arcsin(E2F / E2O) = arcsin(|h1-h2| / (Ltanɑ)).