Large crankshaft machining deformation measuring method based on multi-sensor fusion

Abstract

The invention discloses a large crankshaft machining deformation measurement method based on multi-sensor fusion. The method comprises the steps of S1, sensor deployment and calibration; s2, collecting multi-source data; s3, deflection corresponding to the strain is calculated; s4, deflection corresponding to the coaxiality is calculated; s5, determining a weight coefficient; s6, fusion deflection calculation and verification; a multi-source data acquisition system is constructed by deploying an FBG strain sensor and a line laser sensor array, a double-physical-quantity accurate mapping model is established, and the measurement precision of large crankshaft machining deformation deflection parameters is remarkably improved by combining an error reverse distribution principle and a dynamic weight fusion algorithm of multi-round iterative optimization. The relative error of fusion measurement is controlled within 5%, the technical defects that a single strain sensing model is large in error and single laser sensing is poor in interference resistance are overcome, and the stability and reliability of measured data under the complex machining working condition are enhanced.

Description

Technical Field

[0001] This invention relates to a method for measuring the machining deformation of large crankshafts based on multi-sensor fusion, belonging to the field of crankshaft measurement technology. Background Technology

[0002] As a core component of marine diesel engines, the machining accuracy of large crankshafts directly determines the engine's final performance and reliability. During machining, crankshafts are prone to bending deformation under multiple complex loads. Accurate and real-time measurement of deflection parameters, which characterize this deformation, is crucial for precise control of the machining process. Currently, deflection measurement mainly relies on single sensing technologies, each with its inherent limitations. Strain-sensing methods indirectly calculate deflection by measuring surface strain, reflecting the stress state, but their calculation process heavily relies on simplified assumptions in material mechanics models. This makes them sensitive to non-ideal stress conditions and boundary constraints in actual machining, resulting in significant model errors and difficulty in intuitively reflecting the overall changes in macroscopic geometry. Direct geometric measurement methods based on technologies such as lasers, while capable of obtaining radial displacement or coaxiality deviations of the axis, are highly susceptible to environmental interference from machining site vibrations, oil contamination, and cutting fluid, resulting in insufficient measurement stability and an inability to understand the internal mechanical mechanisms of deformation.

[0003] Therefore, no single measurement method can simultaneously meet the requirements of high precision, strong anti-interference, and high reliability under complex working conditions. Existing research lacks a systematic fusion measurement scheme, the core problems of which are: first, the failure to establish an effective multi-parameter physical mapping model for "strain-deflection" and "coaxiality-deflection" to achieve accurate conversion of different physical quantities to a unified evaluation index (deflection); and second, the lack of an adaptive data fusion and error compensation mechanism, which cannot dynamically optimize the contribution weights of multi-source data based on real-time measurement errors, resulting in compromised accuracy and reliability of the fusion results. These shortcomings make it difficult for existing technologies to support the stringent requirements of deformation measurement for high-quality machining of large crankshafts. Summary of the Invention

[0004] Objective of the Invention: To address the shortcomings of existing technologies, this invention provides a method for measuring the deformation of large crankshafts during machining based on multi-sensor fusion. This invention constructs a dual-physical quantity mapping model by deploying FBG strain sensors and line laser sensor arrays, dynamically determines the weight coefficients of multi-source data by combining the error reverse allocation principle, and uses a weighted fusion algorithm to achieve accurate fusion of strain-derived deflection and coaxiality-derived deflection. At the same time, a real-time error verification mechanism is introduced to optimize the weight allocation, ultimately achieving high-precision real-time measurement of deflection parameters of large crankshafts under complex machining conditions.

[0005] Technical solution: A method for measuring deformation during machining of large crankshafts based on multi-sensor fusion, comprising the following steps:

[0006] S1. Sensor Deployment and Calibration: FBG strain sensors are attached to the non-machined areas of the crankshaft. The distance z from the attachment position of the FBG strain sensor to the neutral axis of the crankshaft section is z=r, where r is the radius of the crankshaft main journal. Linear laser sensor arrays are deployed at equal intervals along the crankshaft axis.

[0007] The true deflection value of the crankshaft standard part was obtained by using a coordinate measuring machine. The FBG strain sensor and the laser sensor were calibrated respectively. After the calibration was completed, the crankshaft was machined.

[0008] S2. Multi-source data acquisition: During crankshaft machining, the strain value of the journal surface and the coaxiality deviation data of the journal are acquired in real time through FBG strain sensor and laser sensor.

[0009] S3. Calculation of deflection corresponding to strain: Based on the strain value of the journal surface obtained in S2, the relationship between the curvature of the neutral layer of the bending section and the surface strain, and the relationship between the curvature and the second derivative of the deflection curve are established to obtain the mapping relationship between strain and deflection, and then the deflection value corresponding to strain is obtained.

[0010] S4. Deflection calculation corresponding to coaxiality: Based on the journal coaxiality deviation obtained in S2, according to the geometric relationship between the reference axis, the axis of the measured element and the actual axis, minor error terms are ignored, the relationship between coaxiality and deflection is established, and then the deflection value corresponding to coaxiality is obtained.

[0011] S5. Determination of weighting coefficients: Using the coordinate measuring machine measurement results in S1 as the true deflection values, calculate the relative error between the deflection value corresponding to the strain obtained in S3 and the true deflection value, and the relative error between the deflection value corresponding to the coaxiality obtained in S4 and the true deflection value; determine the strain weighting coefficient and the coaxiality weighting coefficient according to the error reverse allocation principle to ensure the reliability of the fusion results.

[0012] S6. Fusion Deflection Calculation and Verification: Using a weighted fusion algorithm, the final fusion deflection value is calculated by combining the weight coefficients in S5, the deflection corresponding to the strain in S3, and the deflection corresponding to the coaxiality in S4.

[0013] Calculate the relative error of the fusion result. If the relative error meets the preset threshold, output the result. If it exceeds the preset threshold, re-optimize the weight coefficients and return to S5 to recalculate the relative error of the weighted fusion result until the preset threshold is met, thus ensuring measurement reliability.

[0014] Preferably, S1 specifically includes:

[0015] FBG strain sensors are attached to the non-machined area of ​​the crankshaft. The distance z from the attachment position of the FBG strain sensor to the neutral axis of the crankshaft section is z=r, where r is the radius of the crankshaft main journal. Linear laser sensor arrays are deployed at equal intervals along the crankshaft axis.

[0016] The true deflection value of the crankshaft standard part is obtained by using a coordinate measuring machine. A known strain load is applied to the FBG strain sensor to establish a strain-wavelength offset calibration curve. A coaxiality-distance measurement calibration curve is established for the standard part with a known coaxiality deviation measured by a laser sensor. After calibration, the crankshaft is machined.

[0017] In a preferred embodiment, S3 specifically includes:

[0018] Establish the relationship between the curvature of the neutral layer and the surface strain in a bending section:

[0019]

[0020] in For surface strain, The curvature of the neutral layer when bent. Let z be the distance from the FBG attachment location to the neutral layer, and since the FBG is attached to the outer surface of the crankshaft journal, z = r;

[0021] Secondly, establish the curvature. Relationship with the second derivative of the deflection curve y(x):

[0022]

[0023] Because the deflection of the crankshaft due to machining is much smaller than the journal radius, that is ;

[0024] Therefore curvature The relationship between the second derivative of the deflection curve y(x) and the second derivative is simplified to:

[0025]

[0026] Combining the two formulas, we obtain the second derivative of the journal section deflection curve:

[0027]

[0028] In the formula, x represents the coordinate along the crankshaft axis with the left end of the crankshaft as the origin; the sign is determined by the direction of bending: if the crankshaft bends downwards, y(x) is positive. If it bends upwards, take the negative sign; if it bends upwards, take the positive sign, and Let be the strain distribution function;

[0029] Integrating this formula twice yields the deflection equation for the section containing the journal:

[0030] Given:

[0031]

[0032] Using gradient integration, we obtain:

[0033]

[0034] Substituting the values, we obtain the relationship between strain and deflection:

[0035]

[0036] In a preferred embodiment, S4 specifically comprises:

[0037] Deflection calculation based on laser coaxiality data:

[0038] Given the reference axis The axis of the measured element Actual axis The geometric relationship, let Up to point P The distance is the deflection. , arrive The distance from point P to point D is given by the distance D, where D represents half of the coaxiality. The distance is ;

[0039] have to:

[0040]

[0041] Depend on ;

[0042] have to:

[0043]

[0044] make ,have to ;

[0045] Will The maximum deflection value is obtained as follows:

[0046]

[0047] because:

[0048]

[0049] and ,neglect ;

[0050] have to:

[0051]

[0052] The relationship between coaxiality and deflection is as follows:

[0053]

[0054] Preferably, in step S5, the relative error between the deflection value corresponding to the strain obtained in step S3 and the true deflection value is calculated. Specifically:

[0055]

[0056] in, This represents the deflection derived from the strain measured by the FBG strain sensor. This represents the true value of deflection measured by a coordinate measuring machine.

[0057] Preferably, in step S5, the relative error between the deflection value corresponding to the coaxiality obtained in step S4 and the actual deflection value is calculated. Specifically:

[0058]

[0059] in, This represents the deflection derived from the coaxiality measured by the laser sensor. This represents the true value of deflection measured by a coordinate measuring machine.

[0060] In the preferred embodiment, determining the strain weighting coefficient according to the error reverse allocation principle in S5 specifically involves:

[0061]

[0062] Preferably, the determination of the coaxiality weighting coefficient according to the error reverse allocation principle in S5 is specifically as follows:

[0063]

[0064] in, The smaller the error, the greater the weight of the parameter, to ensure the reliability of the fusion result.

[0065] In a preferred embodiment, S6 specifically includes:

[0066] The final deflection value is calculated using a weighted fusion algorithm:

[0067]

[0068] Calculate the relative error of the fusion result:

[0069]

[0070] like Then the output result, if Then the weighting coefficients are re-optimized until the accuracy requirements are met, ensuring measurement reliability.

[0071] The preferred option is that the re-optimization of the weighting coefficients specifically involves:

[0072] Weight adjustment value calculation:

[0073]

[0074]

[0075] in, , These are the corrected strain and coaxiality weight values; Let be the error correction factor, and take . .

[0076] Weight normalization calculation:

[0077]

[0078]

[0079] in, The corrected strain weighting coefficients. This is the corrected coaxiality weighting coefficient.

[0080] Beneficial effects: This invention constructs a multi-source data acquisition system by deploying FBG strain sensors and line laser sensor arrays, establishes a precise mapping model of dual physical quantities, and combines the error reverse allocation principle with a dynamic weight fusion algorithm optimized through multiple rounds of iteration. This significantly improves the measurement accuracy of the deflection parameters of large crankshafts, keeping the relative error of the fusion measurement within 5%. It overcomes the technical shortcomings of large errors in single strain sensing models and poor anti-interference capabilities of single laser sensing, and enhances the stability and reliability of measurement data under complex processing conditions. Attached Figure Description

[0081] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0082] Figure 1 This is a schematic diagram of the method principle of the present invention;

[0083] Figure 2 This is a schematic diagram of the geometric position of the axis of the present invention, wherein, L 实 L0 represents the actual axis, L0 represents the reference axis, and L... b P represents the axis of the measured element and P represents the point with the greatest deflection.

[0084] Figure 3This is the strain-wavelength offset calibration curve of the present invention;

[0085] Figure 4 This is the coaxiality-distance measurement calibration curve of the present invention. Detailed Implementation

[0086] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0087] In the description of this invention, it should be understood that the terms "upper", "lower", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on this invention.

[0088] In this invention, unless otherwise explicitly specified and limited, "above" or "below" the second feature can include direct contact between the first and second features, or contact between the first and second features through another feature between them. Furthermore, "above," "over," and "on top" of the second feature includes the first feature directly above or diagonally above the second feature, or simply indicates that the first feature is at a higher horizontal level than the second feature. "Below," "below," and "under" the second feature includes the first feature directly below or diagonally below the second feature, or simply indicates that the first feature is at a lower horizontal level than the second feature.

[0089] In this embodiment, the FBG strain sensor has a range of -20000με to 20000με and a wavelength accuracy of ±1pm; the laser sensor is a line laser sensor with a measurement accuracy of ±2μm and a sampling frequency of 2kHz; the calibration equipment is a high-precision coordinate measuring machine with a measurement accuracy of ±1μm.

[0090] like Figure 1 As shown, S1, sensor deployment and calibration: FBG strain sensors are attached to the non-machined area of ​​the crankshaft. The distance z from the attachment position of the FBG strain sensor to the neutral axis of the crankshaft section is z=r, where r is the radius of the crankshaft main journal; a linear laser sensor array is deployed at equal intervals along the crankshaft axis.

[0091] like Figure 3 and Figure 4As shown, a coordinate measuring machine is used to obtain the true deflection value of a crankshaft standard component. A known strain load is applied to the FBG strain sensor to establish a strain-wavelength offset calibration curve. ,in Wavelength offset, in units of , This is the strain value, in units of Fitted strain-wavelength shift calibration coefficient K= For standard parts with known coaxiality deviations measured by laser sensors, establish a coaxiality-distance measurement calibration curve. Where D is the measured distance value of the laser sensor, in units of f represents the known coaxiality of the standard part, in units of... The calibration coefficient C for the proposed coaxiality-distance measurement is... After calibration, crankshaft machining is performed.

[0092] S2. Multi-source data acquisition: During crankshaft machining, the strain value of the journal surface and the coaxiality deviation data of the journal are acquired in real time through FBG strain sensor and laser sensor.

[0093] In this embodiment, the FBG strain sensor is connected to a fiber Bragg grating demodulator. The FBG strain sensor acquires real-time strain changes on the journal surface, and the fiber Bragg grating demodulator converts the wavelength shift signal into strain values. The fiber Bragg grating demodulator then uploads the strain data to the data processing unit via the Zigbee wireless transmission protocol. The laser sensor is connected to the data processing unit via a serial bus interface and acquires journal coaxiality deviation data in real-time at a preset sampling frequency during processing intervals. The data processing unit uses an industrial control computer configured with LabVIEW data acquisition software. The preset sampling frequency matches the inherent sampling frequency of the laser sensor to ensure the real-time performance and completeness of the data acquisition.

[0094] S3. Calculation of deflection corresponding to strain: Based on the strain value of the journal surface obtained in S2, the relationship between the curvature of the neutral layer of the bending section and the surface strain, and the relationship between the curvature and the second derivative of the deflection curve are established to obtain the mapping relationship between strain and deflection, and then the deflection value corresponding to strain is obtained.

[0095] Establish the relationship between the curvature of the neutral layer and the surface strain in a bending section:

[0096]

[0097] in For surface strain, The curvature of the neutral layer when bent. Let z be the distance from the FBG attachment location to the neutral layer, and since the FBG is attached to the outer surface of the crankshaft journal, z = r;

[0098] Secondly, establish the curvature. Relationship with the second derivative of the deflection curve y(x):

[0099]

[0100] Because the deflection of the crankshaft due to machining is much smaller than the journal radius, that is ;

[0101] Therefore curvature The relationship between the second derivative of the deflection curve y(x) and the second derivative is simplified to:

[0102]

[0103] Combining the two formulas, we obtain the second derivative of the journal section deflection curve:

[0104]

[0105] In the formula, x represents the coordinate along the crankshaft axis with the left end of the crankshaft as the origin; the sign is determined by the direction of bending: if the crankshaft bends downwards, y(x) is positive. If it bends upwards, take the negative sign; if it bends upwards, take the positive sign, and Let be the strain distribution function;

[0106] Integrating this formula twice yields the deflection equation for the section containing the journal:

[0107] Given:

[0108]

[0109] Using gradient integration, we obtain:

[0110]

[0111] Substituting the values, we obtain the relationship between strain and deflection:

[0112]

[0113] S4. Deflection calculation corresponding to coaxiality: Based on the laser coaxiality deviation data obtained in S2, according to the geometric relationship between the reference axis, the axis of the measured element and the actual axis, minor error terms are ignored, the relationship between coaxiality and deflection is established, and then the deflection value corresponding to coaxiality is obtained.

[0114] Deflection calculation based on laser coaxiality data:

[0115] Given the reference axis The axis of the measured element Actual axis geometric relationships such as Figure 2 As shown, let Up to point P The distance is the deflection. , arrive The distance from point P to point D is given by the distance D, where D represents half of the coaxiality. The distance is ;

[0116] have to:

[0117]

[0118] Depend on ;

[0119] have to:

[0120]

[0121] make ,have to ;

[0122] Will The maximum deflection value is obtained as follows:

[0123]

[0124] because:

[0125]

[0126] and ,neglect ;

[0127] have to:

[0128]

[0129] The relationship between coaxiality and deflection is as follows:

[0130]

[0131] S5. Determination of weighting coefficients: Using the coordinate measuring machine measurement results in S1 as the true deflection values, calculate the relative error between the deflection value corresponding to the strain obtained in S3 and the true deflection value, and the relative error between the deflection value corresponding to the coaxiality obtained in S4 and the true deflection value; determine the strain weighting coefficient and the coaxiality weighting coefficient according to the error reverse allocation principle to ensure the reliability of the fusion results.

[0132] Calculate the relative error between the deflection value corresponding to the strain obtained by S3 and the actual deflection value. Specifically:

[0133]

[0134] in, This represents the deflection derived from the strain measured by the FBG strain sensor. This represents the true value of deflection measured by a coordinate measuring machine.

[0135] Calculate the relative error between the deflection value corresponding to the coaxiality obtained by S4 and the actual deflection value. Specifically:

[0136]

[0137] in, This represents the deflection derived from the coaxiality measured by the laser sensor. This represents the true value of deflection measured by a coordinate measuring machine.

[0138] The strain weighting coefficient is determined based on the error reverse allocation principle as follows:

[0139]

[0140] The coaxiality weighting coefficient is determined based on the error reverse allocation principle as follows:

[0141]

[0142] in, The smaller the error, the greater the weight of the parameter, to ensure the reliability of the fusion result;

[0143] S6. Fusion Deflection Calculation and Verification: Using a weighted fusion algorithm, the final fusion deflection value is calculated by combining the weight coefficients in S5, the deflection corresponding to the strain in S3, and the deflection corresponding to the coaxiality in S4.

[0144] Calculate the relative error of the fusion result. If the relative error meets the preset threshold, the result is output. If it exceeds the preset threshold, the weight coefficients are re-optimized, and the process returns to S5 to recalculate the relative error of the weighted fusion result until the preset threshold is met, thus ensuring measurement reliability.

[0145] The final deflection value is calculated using a weighted fusion algorithm:

[0146]

[0147] Calculate the relative error of the fusion result:

[0148]

[0149] like Then the output result, if Then the weighting coefficients are re-optimized until the accuracy requirements are met, ensuring measurement reliability;

[0150] The re-optimization of the weight coefficients specifically refers to:

[0151] Weight adjustment value calculation:

[0152]

[0153]

[0154] in, , These are the corrected strain and coaxiality weight values; Let be the error correction factor, and take . .

[0155] Weight normalization calculation:

[0156]

[0157]

[0158] in, The corrected strain weighting coefficients. This is the corrected coaxiality weighting coefficient.

[0159] Then, return to S5 to calculate the relative error after weighted fusion until it meets the preset threshold, ensuring measurement reliability. The preset threshold is set according to the deformation measurement requirements of high-end large crankshaft machining, ensuring that the fusion result meets the actual machining accuracy control requirements.

[0160] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the apparatus disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the description is relatively simple; relevant parts can be referred to the method section.

[0161] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for measuring deformation during machining of large crankshafts based on multi-sensor fusion, characterized in that: Includes the following steps: S1. Sensor Deployment and Calibration: FBG strain sensors are attached to the non-machined area of ​​the crankshaft. The distance z from the attachment position of the FBG strain sensor to the neutral axis of the crankshaft section is z=r, where r is the radius of the crankshaft main journal; a linear laser sensor array is deployed at equal intervals along the crankshaft axis. The true deflection value of the crankshaft standard part was obtained by using a coordinate measuring machine. The FBG strain sensor and the laser sensor were calibrated respectively. After the calibration was completed, the crankshaft was machined. S2. Multi-source data acquisition: During crankshaft machining, the strain value of the journal surface and the coaxiality deviation data of the journal are acquired in real time through FBG strain sensor and laser sensor. S3. Calculation of deflection corresponding to strain: Based on the strain value of the journal surface obtained in S2, the relationship between the curvature of the neutral layer of the bending section and the surface strain, and the relationship between the curvature and the second derivative of the deflection curve are established to obtain the mapping relationship between strain and deflection, and then the deflection value corresponding to strain is obtained. S4. Deflection calculation corresponding to coaxiality: Based on the laser coaxiality deviation data obtained in S2, according to the geometric relationship between the reference axis, the axis of the measured element and the actual axis, minor error terms are ignored, the relationship between coaxiality and deflection is established, and then the deflection value corresponding to coaxiality is obtained. S5. Determination of weighting coefficients: Using the coordinate measuring machine measurement results in S1 as the true deflection values, calculate the relative error between the deflection value corresponding to the strain obtained in S3 and the true deflection value, and the relative error between the deflection value corresponding to the coaxiality obtained in S4 and the true deflection value; determine the strain weighting coefficient and the coaxiality weighting coefficient according to the error reverse allocation principle to ensure the reliability of the fusion results. S6. Fusion Deflection Calculation and Verification: Using a weighted fusion algorithm, the final fusion deflection value is calculated by combining the weight coefficients in S5, the deflection corresponding to the strain in S3, and the deflection corresponding to the coaxiality in S4. Calculate the relative error of the fusion result. If the relative error meets the preset threshold, output the result. If it exceeds the preset threshold, re-optimize the weight coefficients and return to S5 to recalculate the relative error of the weighted fusion result until the preset threshold is met, thus ensuring measurement reliability.

2. The method for measuring deformation during machining of large crankshafts based on multi-sensor fusion according to claim 1, characterized in that: S1 specifically includes: FBG strain sensors are attached to the non-machined area of ​​the crankshaft. The distance z from the attachment position of the FBG strain sensor to the neutral axis of the crankshaft section is z=r, where r is the radius of the crankshaft main journal. Linear laser sensor arrays are deployed at equal intervals along the crankshaft axis. The true deflection value of the crankshaft standard part is obtained by using a coordinate measuring machine. A known strain load is applied to the FBG strain sensor to establish a strain-wavelength offset calibration curve. A coaxiality-distance measurement calibration curve is established for the standard part with a known coaxiality deviation measured by a laser sensor. After calibration, the crankshaft is machined.

3. The method for measuring deformation during machining of large crankshafts based on multi-sensor fusion according to claim 2, characterized in that: Specifically, S3 is: Establish the relationship between the curvature of the neutral layer and the surface strain in a bending section: ； in For surface strain, The curvature of the neutral layer when bent. Let z be the distance from the FBG attachment location to the neutral layer, and since the FBG is attached to the outer surface of the crankshaft journal, z = r; Secondly, establish the curvature. Relationship with the second derivative of the deflection curve y(x): ； Because the deflection of the crankshaft due to machining is much smaller than the journal radius, that is ; Therefore curvature The relationship between the second derivative of the deflection curve y(x) and the second derivative is simplified to: ； Combining the two formulas, we obtain the second derivative of the journal section deflection curve: ； In the formula, x represents the coordinate along the crankshaft axis with the left end of the crankshaft as the origin; the sign is determined by the direction of bending: if the crankshaft bends downwards, y(x) is positive. If it bends upwards, take the negative sign; if it bends upwards, take the positive sign, and Let be the strain distribution function; Integrating this formula twice yields the deflection equation for the section containing the journal: Given: ； Using gradient integration, we obtain: ； Substituting the values, we obtain the relationship between strain and deflection: 。 4. The method for measuring deformation during machining of large crankshafts based on multi-sensor fusion according to claim 3, characterized in that: Specifically, S4 is: Deflection calculation based on laser coaxiality data: Given the reference axis The axis of the measured element Actual axis The geometric relationship, let Up to point P The distance is the deflection. , arrive The distance from point P to point D is given by the distance D, where D represents half of the coaxiality. The distance is ; have to: ； Depend on ; have to: ； make ,have to ; Will The maximum deflection value is obtained as follows: ； because: ； and ,neglect ; have to: ； The relationship between coaxiality and deflection is as follows: 。 5. The method for measuring deformation during machining of large crankshafts based on multi-sensor fusion according to claim 4, characterized in that: In step S5, the relative error between the deflection value corresponding to the strain and the true deflection value is calculated in step S3. Specifically: ； in, This represents the deflection derived from the strain measured by the FBG strain sensor. This represents the true value of deflection measured by a coordinate measuring machine.

6. The method for measuring deformation during machining of large crankshafts based on multi-sensor fusion according to claim 5, characterized in that: In step S5, the relative error between the deflection value corresponding to the coaxiality and the true deflection value is calculated in step S4. Specifically: ； in, This represents the deflection derived from the coaxiality measured by the laser sensor. This represents the true value of deflection measured by a coordinate measuring machine.

7. The method for measuring deformation during machining of large crankshafts based on multi-sensor fusion according to claim 6, characterized in that: The specific steps for determining the strain weighting coefficient according to the error reverse allocation principle in S5 are as follows: 。 8. The method for measuring deformation during machining of large crankshafts based on multi-sensor fusion according to claim 7, characterized in that: The determination of the coaxiality weighting coefficient in S5 based on the error reverse allocation principle is as follows: ； in, The smaller the error, the greater the weight of the parameter, to ensure the reliability of the fusion result.

9. The method for measuring deformation during machining of large crankshafts based on multi-sensor fusion according to claim 8, characterized in that: Specifically, S6 is: The final deflection value is calculated using a weighted fusion algorithm: ； Calculate the relative error of the fusion result: ； like Then the output result, if Then the weighting coefficients are re-optimized until the accuracy requirements are met, ensuring measurement reliability.

10. The method for measuring deformation during machining of large crankshafts based on multi-sensor fusion according to claim 9, characterized in that: The re-optimization of the weight coefficients specifically refers to: Weight adjustment value calculation: ； ； in, , These are the corrected strain and coaxiality weight values; Let be the error correction factor, and take . ; Weight normalization calculation: ； ； in, The corrected strain weighting coefficients. This is the corrected coaxiality weighting coefficient.

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