Universal measuring method for bending and twisting deformation of shaft lever type part with specified section contour

Abstract

The invention discloses a universal measuring method for bending and twisting deformation of shaft lever parts with specified section profiles. The shape of the cross section of a shaft lever type part with a specified cross section outline is not changed in the axis direction in an ideal state, but the part can be inevitably bent and twisted to deform due to external factors in an actual situation. The method is based on continuous rotation measurement, can realize measurement of bending and torsional deformation of a part, and specifically comprises the following steps: establishing a continuous rotation measurement mathematical model, and determining a conversion relation between measurement data and part surface contour data; setting a part original surface contour data expression and a bending-torsion deformation polynomial function; establishing a relational expression of the actual surface profile and the original surface profile of the part, and constructing a total differential gradient successive iteration solving method based on the relational expression; and setting an initial solution of a parameter to be solved, and solving an accurate solution through successive iteration. The invention provides a universal and effective solution for the problem of measuring the bending and twisting deformation of shaft lever parts with specified section contours.

Description

Technical Field

[0001] The invention belongs to the field of precision measurement, and in particular relates to a universal measurement method for bending and torsional deformation of shaft rod parts with specified cross-sectional profiles. Background Art

[0002] Shaft and rod parts are widely used in mechanical systems, especially in transmission systems, support structures and other moving parts. Since the parts themselves have specific functions, their cross-sectional profiles are usually specified. Ideally, the cross-sectional shape of the parts remains unchanged along the axis, such as elliptical shafts, D-shaped shafts, square shafts, polygonal prisms, etc. Shaft and rod parts are subjected to complex external forces in actual work, resulting in bending and torsional deformation after being subjected to force. The bending and torsional deformation of the shaft will directly affect the performance and stability of the mechanical system, so the accurate measurement of this deformation is crucial for the design, manufacturing and quality control of the parts.

[0003] Traditional manual methods for measuring the bending and torsion deformation of shaft parts, such as the micrometer method, the measuring tool method, and the roundness meter, have many limitations. These measurement methods have the disadvantages of insufficient measurement accuracy, high operating technology requirements, and strong dependence of the sensor on the measurement point. In addition, the cross-sectional profile of shaft parts is not only circular or other symmetrical cross-sections. The cross-sectional profile shape characteristics of many shaft parts may show nonlinearity and contain multi-order harmonic components. Traditional measurement methods cannot achieve the bending and torsion deformation measurement of shaft parts with these complex cross-sectional profiles.

[0004] In current technology, although some methods use optical measurement, laser scanning or digital image processing to perform three-dimensional modeling of the deformation of shaft and rod parts, most of these methods rely on high-precision instruments and are complicated to operate. In addition, many methods are usually unable to simultaneously consider the bending and torsional deformation of shaft and rod parts, and often lack effective error compensation and analysis mechanisms.

[0005] In response to these problems, a new measurement method is urgently needed to achieve universal, accurate and efficient measurement of the bending and torsion deformation of shaft parts under various working conditions under conventional measurement conditions and with a specified cross-sectional profile. This method can be applied to shaft parts with different cross-sectional profiles, providing a more accurate and highly adaptable measurement technology to meet the high-precision requirements of modern mechanical engineering for part performance testing. Summary of the invention

[0006] The purpose of the present invention is to provide a universal measurement method for the bending and torsional deformation of shaft-rod parts with specified cross-sectional contours. For shaft-rod parts with specified cross-sectional contours, a measurement method of rotating the part in combination with sensor movement is adopted to realize the measurement of the part's outer surface contour. By processing and analyzing the measurement data, the bending and torsional deformation of the part can be obtained.

[0007] The specific operation steps of the present invention are:

[0008] (1) Establish a continuous rotation measurement mathematical model to determine the measurement data The conversion relationship between the cylindrical coordinate point cloud data set [ρ, θ, x] of the part surface contour;

[0009] (2) Set the original contour cylindrical coordinate point cloud dataset [r, s, x] of the part;

[0010] (3) setting the torsional deformation to a polynomial function γ(x), where the polynomial coefficient vector is b;

[0011] (4) Set the bending deformation to the polynomial function e y (x) and e z (x), the polynomial coefficient vectors are c and d respectively;

[0012] (5) Combined with the bending and torsion deformation polynomial function, the relationship between the original contour point cloud data set [r, s, x] and the actual contour point cloud data set [ρ, θ, x] is established;

[0013] (6) Combined with the relationship in step (5), assuming no torsion, the initial solution is e y (x) and e z (x) polynomial coefficients c0 and d0;

[0014] (7) Combine the relationship in step (5) to construct a total differential gradient iterative solution method, and set the initial estimate of the iterative solution of b to b 0i , and substitute into c0, d0 to accurately solve b, c and d;

[0015] (8) Substitute b, c and d into γ(x), e y (x) and e z (x) Obtain the bending and torsional deformation expression of the part.

[0016] The measurement data w in step (1) is a sensor measurement value vector, is the part rotation angle vector, x is the axial position vector, ρ and θ are the actual cross-section polar radial quantity and polar angle vector of the part respectively.

[0017] In step (2), r and s are the polar coordinates and polar angle vector of the original part section, respectively, which are specified conditions.

[0018] In the step (3), the polar coordinate angle γ(x) is a twisted section (twist angle is 0) based on the initial section (x=0).

[0019] The degree of bending deformation in step (4) is represented by introducing eccentricity, e y (x) and e z(x) is the component of eccentricity in the y and z directions.

[0020] In the step (5), the actual contour data is obtained by geometrically deducing and superimposing the original contour data and the bending and torsion deformation function.

[0021] The number of iterations in step (7) is the same as the length of vector b. The initial estimated solutions of c and d in each iteration are c0 and d0, and the initial estimated solution of b is b 0i , obtained by calculating the previous iteration of each iteration, i is the number of iterations.

[0022] The advantages of the present invention are:

[0023] (1) Traditional manual measurement methods, such as the micrometer method, the measuring tool method, and the roundness meter, are only applicable to the bending or torsional deformation measurement of simple shaft parts such as cylinders and elliptical shafts. This measurement method is not only applicable to simple shaft parts, but also to shaft parts with nonlinear cross-sectional profile features and high-order harmonic components. The proposed method can simultaneously realize the measurement of their bending deformation and torsional deformation.

[0024] (2) Existing methods for measuring shaft and rod parts, such as optical measurement, laser scanning or digital image processing, have the limitation of not being able to simultaneously consider the bending and torsional deformation of shaft and rod parts. This measurement method can also measure the bending deformation and torsional deformation of parts at the same time, solving the problem that existing methods can only measure a single deformation.

[0025] (3) This measurement method is simple to operate and easy to implement. It overcomes the problems of existing measurement methods, such as high technical requirements for operation, reliance on high-precision instruments, and limitations on the measurement environment. It greatly improves the measurement efficiency of bending and torsional deformation of shaft and rod parts.

[0026] (4) The acquisition of part measurement data sets by this method can be achieved through a variety of sensors, both contact and non-contact sensors are applicable, such as lever displacement sensors, point laser displacement sensors, spectral confocal displacement sensors, etc. At the same time, this method can be used to measure parts of different sizes and cross-sectional profiles, and has the advantages of high versatility and wide applicability. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] Figure 1 Technical roadmap of the present invention

[0028] Figure 2 The overall surface profile and single section profile of the part

[0029] Figure 3 Schematic diagram of part measurement principle and measurement section

[0030] Figure 4 is the polar coordinate O′ rsSingle section profile of the lower part

[0031] Figure 5 Schematic diagram of measurement results based on this measurement method DETAILED DESCRIPTION

[0032] The purpose of the present invention is to provide a universal measurement method for bending and torsion deformation of shaft parts with specified cross-sectional profiles. For shaft parts with specified cross-sectional profiles, a measurement method of rotating the parts and combining the movement of the sensor is adopted to measure the outer surface profile of the parts. By processing and analyzing the measurement data, the bending and torsion deformation of the parts can be obtained. The invention is further described below in conjunction with the accompanying drawings.

[0033] Combination Figure 1 The technical route shown, the specific operation steps of the present invention are:

[0034] (1) Establish a continuous rotation measurement mathematical model to determine the measurement data The conversion relationship between the cylindrical coordinate point cloud data set [ρ, θ, x] of the part surface contour;

[0035] (2) Set the original contour cylindrical coordinate point cloud dataset [r, s, x] of the part;

[0036] (3) setting the torsional deformation to a polynomial function γ(x), where the polynomial coefficient vector is b;

[0037] (4) Set the bending deformation to the polynomial function e y (x) and e z (x), the polynomial coefficient vectors are c and d respectively;

[0038] (5) Combined with the bending and torsion deformation polynomial function, the relationship between the original contour point cloud data set [r, s, x] and the actual contour point cloud data set [ρ, θ, x] is established;

[0039] (6) Combined with the relationship in step (5), assuming no torsion, the initial solution is e y (x) and e z (x) polynomial coefficients c0 and d0;

[0040] (7) Combine the relationship in step (5) to construct a total differential gradient iterative solution method, and set the initial estimate of the iterative solution of b to b 0i , and substitute into c0, d0 to accurately solve b, c and d;

[0041] (8) Substitute b, c and d into γ(x), e y (x) and e z (x) Obtain the bending and torsional deformation expression of the part.

[0042] The detailed operations, formulas and symbols of steps (1) to (8) are explained as follows:

[0043] Assume that the overall surface profile of a part to be tested is as follows: Figure 2 As shown, take any cross section of the part, set the cross section rotation center point O as the coordinate origin, and construct the polar coordinate system O ρθ , place the cross-sectional profile in the polar coordinate system O ρθ The coordinates of any point M on the cross-sectional profile are (ρ(θ),θ).

[0044] Based on displacement sensors (such as single-point laser displacement sensors), the measurement method of parts adopts a measurement method based on the combination of circumferential rotation and axial translation, that is, continuous rotation measurement. Assume that the x-axis coincides with the rotation axis of the part. When the part rotates, the sensor moves linearly along the rotation axis of the part, such as Figure 3 shown.

[0045] Let M be the measuring point. When the rotation angle of the part is When the coordinates of point M become (ρ r (θ r ),θ r ), ρ r and θ r Satisfies formula (1).

[0046]

[0047] The corresponding absolute signal of the distance between the sensor reference and the measuring point M on the part surface is w, the distance between the part rotation axis and the sensor reference line is A, and the angle between the connecting line and the sensor distance measurement direction is α. According to the cosine theorem, the polar diameter ρ at the measuring point M at this time is obtained r for:

[0048]

[0049] The vector angle from the center of rotation of the part section to the measuring point, that is, the polar angle θ at the measuring point M r ,satisfy:

[0050]

[0051] Combining equation (1) and equation (4), we can get:

[0052]

[0053] The cylindrical coordinate system (ρ, θ, x) can describe the contour point cloud dataset [ρ, θ, x] formed by the part surface, which is composed of the measured data It is calculated by the above formula (1), formula (3) and formula (5). Let N p The total number of measurement data points is:

[0054]

[0055] In particular, when the angle α = 0, the conversion relationship becomes a very simple form ρ = Aw,

[0056] Since the part itself has a specific function, the cross-sectional shape of the part does not change along the axis direction. Figure 2 The centroid of the cross section is O′, and the polar coordinates O′ are constructed with it as the origin rs , the coordinates of point M are at O′ rs It can be expressed as (r(s), s), such as Figure 4 shown. Figure 4 Where e is the cross-sectional eccentricity and β is the cross-sectional eccentricity phase angle. Both are functions of the axial position x, satisfying e(x) and β(x). r(s) can be expressed as the original cross-sectional profile of the part without eccentricity and torsion, and is a specified quantity during the calculation process.

[0057] Assume that the original contour cylindrical coordinate point cloud dataset of the part is [r, s, x], and the actual surface contour of the part [ρ, θ, x] is a composite of the original contour of the part [r, s, x] and the nonlinear deformation of torsion and bending, where r and s satisfy:

[0058]

[0059] The degree of torsional deformation of the part section is expressed by introducing the polar coordinate angle γ(x), taking the initial section (x=0) as the reference torsional section (torsion angle is 0), and expressing it through a polynomial function:

[0060]

[0061] Among them, N y is the order of the twist polynomial, and L is the total length of the part.

[0062] Unlike torsion, eccentricity is the displacement of the centroid of the cross section from the cross section’s center of rotation, so it is not necessarily zero at the initial cross section. The degree of bending deformation is calculated by introducing the eccentricity components e in the y and z directions. y 、e z Expression, can be e y 、e z Expressed as a polynomial function:

[0063]

[0064] Among them, N e is the order of the eccentric polynomial.

[0065] The polar coordinate system O ρθConvert to rectangular coordinate system O yz , combining equation (8) and equation (9) we get Figure 4 The coordinates of any point M on the cross-sectional profile are (y, z), satisfying equation (10):

[0066]

[0067] The point cloud data set of the actual surface contour of the part in the spatial rectangular coordinate system is [x, y, z], where y and z satisfy:

[0068]

[0069] Assuming that the torsion angle of the part is 0, in this case, formula (10) gives:

[0070]

[0071] Combining equation (9) and equation (12) to solve the initial estimated solutions c0 and d0 of c and d:

[0072]

[0073] In order to accurately solve b, c and d, the total differential gradient is used to solve iteratively. Let the initial estimate of b in the iterative solution be b 0i :

[0074]

[0075] It can be seen from formula (14) that to accurately solve b, c and d, N steps need to be performed successively. y Iterative solution.

[0076] Performing trigonometric transformation on formula (10) yields:

[0077]

[0078] To construct the specific steps of a single iteration solution, firstly, the first-order Taylor approximation expansion is performed on equation (15):

[0079]

[0080] Assume the initial value g0 = [b 0i T c0 T d0 T ] T , combined with formula (8) and formula (9), we can get:

[0081]

[0082]

[0083] Expanding ignores higher-order minterms:

[0084]

[0085] Introduce a vector of composite unknowns:

[0086] Δg=[Δb T Δc T Δd T ] T (twenty two)

[0087] Rearranging the above equations yields:

[0088] K(g0)Δg=f(g0) (23)

[0089]

[0090] in,

[0091]

[0092] Using the least squares regression fitting method, we get:

[0093] Δg=K(g0)\f(g0) (27)

[0094] Iterative solution:

[0095]

[0096] Where q is the number of iterations.

[0097] The average of the absolute values ​​of the vector Δg is selected as the iteration termination condition. When the average of the absolute values ​​of Δg approaches 0, the iteration stops.

[0098] Combined with formula (14), it is solved iteratively:

[0099] In the first iteration, let b 01 = 0, then b 01 =b 01 =0, initial value g0 = [b 01 T c0 T d0 T ] T , iteratively calculate through formula (28) to obtain the iterative vector b 01 ;

[0100] In the second iteration, let b 02 = 0, then b 02 =[b 01 T b 02 ] T , where b01 is the result of the first iteration, and the initial value of the second iteration is g0 = [b 02 T c0 T d0 T ] T , iteratively calculate through formula (28) to obtain the iterative vector b 02 ;

[0101] To solve the i-th iteration, let b 0i = 0, then b 0i =[b 0(i-1) T b 0i ] T , where b 0(i-1) The solution is obtained by the i-1th iteration. The initial value of the i-th iteration is g0 = [b 0i T c0 T d0 T ] T , iteratively calculate through formula (28) to obtain the iterative vector b 0i ;

[0102] Repeat the above steps for a total of N y Iterate the solution by Nth y The vector g obtained by iterative solution q+1 , we can get the exact solutions of b, c and d, and we have g q+1 =[b T c T d T ] T .

[0103] Substituting the obtained b, c and d into equations (8) and (9), we can obtain the expressions for the bending and torsion of the part, and the solution is now complete. Figure 5 shown.

Claims

1. A universal measurement method for bending and torsional deformation of shaft parts with a specified cross-sectional profile, characterized in that: The specific steps include: (1) Establish a continuous rotation measurement mathematical model to determine the conversion relationship between the measurement data [w, φ, x] and the part surface contour cylindrical coordinate point cloud data set [ρ, θ, x]; (2) Set the original contour cylindrical coordinate point cloud dataset [r, s, x] of the part; (3) setting the torsional deformation to a polynomial function γ(x), where the polynomial coefficient vector is b; (4) Set the bending deformation to the polynomial function e y (x) and e z (x), the polynomial coefficient vectors are c and d respectively; (5) Combined with the bending and torsion deformation polynomial function, the relationship between the original contour point cloud data set [r, s, x] and the actual contour point cloud data set [ρ, θ, x] is established; (6) Combined with the relationship in step (5), assuming no torsion, the initial solution is e y (x) and e z (x) polynomial coefficients c0 and d0; (7) Combine the relationship in step (5) to construct a total differential gradient iterative solution method, and set the initial estimate of the iterative solution of b to b 0i , and substitute into c0, d0 to accurately solve b, c and d; (8) Substitute b, c and d into γ(x), e y (x) and e z (x) Obtain the bending and torsional deformation expression of the part.

2. A universal measurement method for bending and torsional deformation of shaft parts with a specified cross-sectional profile according to claim 1, characterized in that: The relationship between the original contour point cloud dataset [r, s, x] and the actual contour point cloud dataset [ρ, θ, x] in step (5) is as follows: Assume that the original contour point cloud dataset of the part is [r, s, x], and the actual surface contour of the part [ρ, θ, x] is a composite of the original contour of the part [r, s, x] and the nonlinear deformation of torsion and bending, where r and s satisfy: The degree of torsional deformation of the part section is expressed by introducing the polar coordinate angle γ(x), taking the initial section (x=0) as the reference torsional section (torsion angle is 0), and expressing it through a polynomial function: Among them, N y is the order of the twist polynomial, L is the total length of the part; Unlike torsional deformation, eccentricity is the displacement of the centroid of the cross section compared to the center of rotation of the cross section. Therefore, the eccentricity is not necessarily zero at the initial cross section. The degree of bending deformation is calculated by introducing the eccentricity components e in the y and z directions. y 、e z Expression, can be e y 、e z Expressed as a polynomial function: Among them, N e is the order of the eccentric polynomial; The actual surface profile of the part [ρ, θ, x] is a composite of the original contour of the part and the nonlinear deformation of torsion and bending. ρθ Convert to rectangular coordinate system O yz , combining equations (8) and (9), the coordinates of any point M on the cross-sectional profile of the part are (y, z), satisfying equation (10):

3. A universal measurement method for bending and torsional deformation of shaft parts with a specified cross-sectional profile according to claim 1, characterized in that: In step (7), the total differential gradient successive iteration solution method is constructed to accurately solve b, c and d as follows: In order to accurately solve b, c and d, the total differential gradient is used to solve iteratively. Let the initial estimate of b in the iterative solution be b 0i : It can be seen from formula (14) that to accurately solve b, c and d, N steps need to be performed successively. y Iterative solution; Performing trigonometric transformation on formula (10) yields: To construct the specific steps of a single iteration solution, firstly, the first-order Taylor approximation expansion is performed on equation (15): Assume the initial value g0 = [b 0i T c0 T d0 T ] T , combined with formula (8) and formula (9), we can get: Expanding ignores higher-order minterms: Introduce a vector of composite unknowns: Δg=[Δb T Δc T Δd T ] T (22) Rearranging the above equations yields: K(g0)Δg=f(g0) (23) in, Using the least squares regression fitting method, we get: Δg=K(g0)\f(g0) (27) Iterative solution: Where q is the number of iterations; The average of the absolute values ​​of the vector Δg is selected as the iteration termination condition. When the average of the absolute values ​​of Δg approaches 0, the iteration stops.

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