Machining uncertainty calculation method

Abstract

The invention relates to a machining uncertainty calculation method, in particular to a machining uncertainty calculation method of a technological process composed of multiple machining procedures. The method is characterized in that the process processing uncertainty is the synthesis of the regeneration processing uncertainty and the genetic processing uncertainty. The machining uncertainty of each process is a machining uncertainty vector composed of one or more machining uncertainty components. The genetic processing uncertainty is a Hadamard product of the processing uncertainty of the previous process and a genetic coefficient. The regeneration processing uncertainty is the combination of the uncertainty of all error sources and the uncertainty of the Hadamard product of the corresponding sensitivity. The uncertainty of the error source is the uncertainty synthesis of all the uncertainty components of the error source and the Hadamard product of the corresponding sensitivity. The method has the advantages that before the process test is implemented, whether the workpiece precision level which can be achieved by the given process meets the design drawing requirement or not is quantitatively calculated and predicted, the process reasonability and effectiveness are evaluated, the process test risk and cost are reduced, and the first workpiece trial-manufacturing success rate is increased.

Description

Technical Field

[0001] This invention belongs to the field of uncertainty calculation technology, specifically a method for calculating the processing uncertainty of a process flow consisting of multiple processing steps. Background Technology

[0002] Currently, verifying the rationality and effectiveness of workpiece machining process design in engineering mainly relies on process experiments, which are costly and risky. How to quantitatively calculate the effectiveness and rationality of the machining process before implementing high-risk, high-cost process experiments remains an unsolved problem. Current methods for calculating and evaluating uncertainty primarily focus on the measurement field, i.e., calculating and evaluating the uncertainty of measurement results.

[0003] Chengdu Aircraft Industry Group Co., Ltd. (Zhu Xusheng, CN202210865068) proposed a method for calculating the measurement uncertainty of the angle between the axis and the plane of a blind hole, mainly to quantify and evaluate the error level of the measurement results of the angle between the axis and the plane. The Hydrology Bureau of the Yangtze River Water Resources Commission (Xiong Ming, CN202111132322) proposed a method for calculating the full-range measurement uncertainty of river flow with benchmark correction, to evaluate the uncertainty of river flow measurement. Peking University Shenzhen Graduate School (Huang Xiaofeng, CN202211443853) proposed a method for evaluating the uncertainty of PM2.5 sources, used to track and identify possible sources of air pollution. State Grid Henan Electric Power Company (Yang Lei, CN202211541482) proposed a method for calculating the uncertainty of a power cable dielectric loss device, to calculate the uncertainty and correct the error of the measurement deviation of the dielectric loss standard device. Beijing University of Aeronautics and Astronautics (Sun Fuqiang, CN202111552692) proposed...

[0004] A method for evaluating the measurement uncertainty of accelerated degradation experiments is proposed, which quantifies and assesses the measurement uncertainty. Wang Yuhui (TW93136927A) proposed a method for calculating the uncertainty of open test sites, estimating the uncertainty of radiated interference test sites. Chengdu Aircraft Industry Co., Ltd. (Shen Hao, CN202310748310) proposed a method for calculating the uncertainty of vision measurement systems, evaluating the error level of machine vision measurement systems. Beijing University of Aeronautics and Astronautics (Jia Xiaowen, CN201811389601) proposed a method for evaluating the measurement uncertainty of rigid body position and attitude based on point set measurement, evaluating the measurement uncertainty of rigid body position and attitude according to laser measurement results. Tianjin University (He Gaiyun, 201811257063.X) proposed a method for calculating the profile error uncertainty of complex curved surfaces, evaluating the profile of the measured surface based on the measurement results. Mitutoyo Corporation (EP05028743.2) proposed a method for estimating the uncertainty of measuring instruments, evaluating the uncertainty of the measurement results. Shell Oil (Hartmann, US005787997) proposed a deep hole evaluation method, assessing the quality of deep holes based on measurement results. Okuma Corporation (Matsushita, US9002502B2) proposed a method for calculating machine tool corrections, calculating machine tool errors using a reference point and then compensating for these errors using a servo control system to improve machining accuracy. Clarkson University (LaFleur, US10216707B2) proposed a method and system for uncertainty calculation, including a method and mathematical expression for calculating values ​​with accompanying uncertainties. Yoshibiro (US2008 / 0125982A1) proposed a method for evaluating measurement uncertainty, quantifying and calculating measurement uncertainty. MOTT et al. (W002 / 35299A2) proposed a method for evaluating and controlling measurement uncertainty, which calculates measurement uncertainty and provides methods for reducing measurement uncertainty.

[0005] Currently, there is a lack of methods for predicting, calculating, and evaluating the uncertainty of process flow. Summary of the Invention

[0006] The purpose of this invention is to propose a method for calculating the uncertainty of a process flow. Before the implementation of a process experiment, the method quantifies the changes in the uncertainty of each process step, and performs a quantitative pre-evaluation of the rationality and effectiveness of the process design, thereby effectively controlling the risks and costs of the process experiment. At the same time, it provides an effective quantitative basis for process improvement and adjustment.

[0007] The objective of this invention is achieved as follows: a method for calculating processing uncertainty, comprising the following steps:

[0008] Determine the number of processes n in the process flow;

[0009] The processing uncertainty U(i) of process i is a combination of the reproduction uncertainty R(i) and the inherited uncertainty, and its calculation formula is as follows:

[0010] U(i)=R(i)<+>G(i)×.U(i-1) (1)

[0011] Where, <+> represents the combination of uncertainties, ×. represents the Hadamard product (commonly known as dot product); i is the process number, U(i) is the processing uncertainty of the i-th process, G(i) is the genetic coefficient, U(i-1) is the processing uncertainty of the previous process, and i≤n.

[0012] In one possible embodiment, the regeneration uncertainty is expressed as:

[0013] R(i)=±ΔR(i) (2)

[0014] Wherein, ΔR(i) is the range estimate of the uncertainty R(i). When using statistical analysis methods, this value is the standard deviation of the evaluated quantity; when using non-statistical methods for evaluation, this value is the estimate of its standard deviation.

[0015] In one possible embodiment, the processing uncertainty of the preceding process is expressed as:

[0016] U(i-1)=±ΔU(i-1) (3)

[0017] Wherein, ΔU(i-1) is the range estimate of the uncertainty U(i-1). When using statistical analysis methods, this value is the standard deviation of the evaluated quantity; when using non-statistical methods for evaluation, this value is the estimate of its standard deviation.

[0018] In one possible embodiment, the genetic uncertainty is the Hadamard product of the genetic coefficient G(i) and the processing uncertainty U(i-1) of the preceding process (i-1), calculated as follows:

[0019]

[0020] Where m is the number of processing uncertainties being evaluated, g(i,k) is the k-th component of the genetic coefficient G(i), and ΔU(i-1,k) is the k-th component of the processing uncertainty U(i-1) of the preceding process.

[0021] In one possible embodiment, the processing uncertainty U(i) of process i is calculated using the following formula:

[0022]

[0023] In one possible embodiment, the number of uncertainties to be evaluated for each process is m, the number of error sources for each process is p, and the number of error components for each error source is q; the j-th regeneration uncertainty R(i,j) of process i is the synthesis of the Hadamard product of the regeneration uncertainty R(i,j,k) of all p error sources and the sensitivity C(i,j,k) of each error source, i.e.

[0024]

[0025] in, Represents the synthesis of regenerated uncertainties from a series of error sources; j≤m; when the angle between the direction of the regenerated processing uncertainty component R(i,j,k) and the direction of the synthesized regenerated processing uncertainty R(i,j) is α. k At that time, C(i,j,k)=cosα k .

[0026] In one possible embodiment, assuming that the error source k of the j-th processing uncertainty component of process i has q error components, then the regenerative processing uncertainty R(i,j,k) generated by this error source is the synthesis of the product of all q error source uncertainty components u(i,j,k,l) ​​and the corresponding sensitivity C(i,j,k,l), i.e.

[0027]

[0028] In the formula, when the angle between the direction of the uncertainty component u(i,j,k,l) ​​of the error source q and the uncertainty R(i,j,k) of the combined error source k is β l At that time, C(i,j,k,l)=cosβ l .

[0029] In one possible embodiment, the j-th processing uncertainty U(i,j) of process i is:

[0030]

[0031] The advantages of this invention are:

[0032] (1) Quantitatively calculate and predict the processing uncertainty and the change process of each processing step in the process flow, and evaluate the contribution of each step to the processing accuracy;

[0033] (2) Compare the accuracy levels achievable by different process designs and select the optimal process route;

[0034] (3) Before the implementation of the process test, quantitatively calculate and predict whether the workpiece accuracy level that the given process can achieve can meet the requirements of the design drawings, and evaluate the rationality and effectiveness of the process.

[0035] (4) Effectively assess process risks and key processes to improve the success rate of first-piece trial production and process testing. Attached Figure Description

[0036] Figure 1 It is a process flow diagram consisting of n processes;

[0037] Figure 2 It is the process of generating processing uncertainty in a technological flow consisting of n steps;

[0038] Figure 3 It is the composition of the uncertainty j of the reprocessing of process i;

[0039] Figure 4 It is the composition of the error source component k of the regeneration uncertainty j of process i;

[0040] Figure 5 This is a schematic diagram of the structure of a certain toothed ring;

[0041] Figure 6 This is a schematic diagram of the error source components of each process;

[0042] Figure 7 This is a schematic diagram comparing the sensitivity of error sources;

[0043] Figure 8 This is a diagram showing the comparison of heritability coefficients;

[0044] Figure 9 This is a diagram showing the comparison of the combined uncertainty of each process. Detailed Implementation

[0045] The process flow consists of multiple steps, and the processing uncertainty of each step is composed of the regeneration processing uncertainty of the current step and the inherited uncertainty of the previous step. In other words, the processing uncertainty of a step is a combination of the regeneration processing uncertainty and the inherited processing uncertainty.

[0046] The processing uncertainty can be dimensional uncertainty, geometric uncertainty, or positional uncertainty, such as: dimensional error, roundness, cylindricity, coaxiality, parallelism, perpendicularity, symmetry, position, flatness, straightness, profile, or, depending on the evaluation requirements, an uncertainty vector composed of multiple uncertainties.

[0047] The genetic processing uncertainty is the Hadamard product of the processing uncertainty of the preceding process and the genetic coefficient.

[0048] The uncertainty of the regeneration process is a combination of the uncertainty of all error sources and the Hadamard product of the corresponding sensitivity.

[0049] The aforementioned error source uncertainty is the sum of the uncertainties of all the uncertainty components of this error source and the Hadamard product of the corresponding sensitivity.

[0050] The error sources include, but are not limited to: workpiece positioning surface error, machine tool positioning surface error, clamping deformation error, machine tool motion error, ambient temperature error, warping deformation caused by cutting force, and residual stress deformation.

[0051] The aforementioned error source sensitivity is the cosine of the angle between the error source direction and the direction of the processing uncertainty.

[0052] When the error source is workpiece temperature, its uncertainty is the product of workpiece size, workpiece thermal expansion coefficient, and temperature uncertainty.

[0053] The invention will be further described in detail below with reference to the accompanying drawings:

[0054] like Figure 1 As shown, a certain process consists of n steps, each step has m uncertainties that need to be evaluated, each step has p error sources, and each error source has q error components.

[0055] Processing uncertainty generation process as follows Figure 2 As shown. The processing uncertainty U(i) of process i is a combination of the reproduction uncertainty R(i) and the inherited uncertainty, and its calculation formula is:

[0056]

[0057] Where, <+> represents the combination of uncertainties, ×. represents the Hadamard product (commonly known as dot product); i is the process number, U(i) is the processing uncertainty of the i-th process, G(i) is the genetic coefficient, and U(i-1) is the processing uncertainty of the previous process.

[0058] The reproduction uncertainty is expressed as:

[0059] R(i)=±ΔR(i) (2)

[0060] The uncertainty of the preceding process is expressed as:

[0061] U(i-1)=±ΔU(i-1) (3)

[0062] Genetic uncertainty is the Hadamard product (commonly known as dot product) of the genetic coefficient G(i) and the processing uncertainty U(i-1) of the preceding process (i-1), and the calculation formula is as follows:

[0063]

[0064] Where m is the number of processing uncertainties being evaluated, g(i,k) is the k-th component of the genetic coefficient G(i), and ΔU(i-1,k) is the k-th component of the processing uncertainty U(i-1) of the preceding process.

[0065] like Figure 3 As shown, the J-th regeneration uncertainty R(i,j) of process i is the synthesis of the Hadamard product (dot product) of the regeneration uncertainties R(i,j,k) of all p error sources and the sensitivity C(i,j,k) of each error source, i.e.

[0066]

[0067] in, This represents the synthesis of regenerated uncertainties from a series of error sources. Each error source in each process has a different impact on the processing uncertainty to be evaluated, so the value of J varies depending on the specific process, but j ≤ m. When the angle between the direction of the regenerated processing uncertainty component R(i, j, k) and the direction of the synthesized regenerated processing uncertainty R(i, j) is α... k At that time, C(i,j,k)=cosα k .

[0068] like Figure 4 As shown, assuming that the error source k of the j-th processing uncertainty component in process i has q error components, then the regenerative processing uncertainty R(i,j,k) generated by this error source is the synthesis of the product of all q error source uncertainty components u(i,j,k,l) ​​and the corresponding sensitivity C(i,j,k,l), that is...

[0069]

[0070] In the formula, when the angle between the direction of the uncertainty component u(i,j,k,l) ​​of the error source q and the uncertainty R(i,j,k) of the combined error source k is β l At that time, C(i,j,k,l)=cosβ l .

[0071] Combining equations (1) to (6), the uncertainty U(i,j) of the j-th process in process i is:

[0072]

[0073] The following section uses the machining of gear rings as an example to further explain this calculation method in detail.

[0074] A certain toothed ring, such as Figure 5 As shown, OD is the tip circle diameter, ID is the inner diameter of the gear ring, H is the gear ring height, and PD is the gear pitch circle diameter. The manufacturing of this gear ring involves 18 processes, i.e., n = 18. The details of these processes are shown in Table 1.

[0075] Table 1. 18 Processes in Gear Ring Machining

[0076]

[0077] Each process has 8 uncertainties to be evaluated, m=8, including: U(i,1) radial fluctuation of the tooth tip circle, U(i,2) axial runout of the tooth tip circle, U(i,3) roundness of the tooth tip circle, U(i,4) concentricity of the tooth tip circle; U(i,5) normal fluctuation of the tooth profile, U(i,6) tooth direction error, U(i,7) roundness of the pitch circle, and U(i,7) concentricity of the pitch circle.

[0078] Each process has 8 error sources, i.e., p=8, including: workpiece positioning surface error u(1), machine tool positioning surface error u(2), clamping deformation error u(3), tool motion error u(4), spindle motion error u(5), and error caused by cutting force.

[0079] Geometric error u(6), ambient temperature error u(7), residual stress deformation error u(8). Each error source has two directional error components, q=2, namely radial (represented by l=1, unit μm) and axial (represented by l=2, unit μm).

[0080] The uncertainties of each process error source are shown in Table 2. Here, i and j in u(i,j) do not specifically refer to the preceding process number i, but are general variables representing error source i and its component j. A comparison of the uncertainties of each process error source is shown in Table 2. Figure 6 ,in Figure 6 The numbers 1-16 above represent the error sources for each process.

[0081] Table 2. Uncertainty u(i,j), μm of each process error source component

[0082]

[0083]

[0084] The sensitivities C(i,j,k,l) ​​of each error source are shown in Table 3. Here, i,j,k,l have general meanings, similar to variables in computer editing. That is, i represents the i-th process, j represents the j-th uncertainty to be evaluated, k represents the k-th error source, and l represents the l-th component of the k-th error source, with values ​​ranging from i≤n,j≤m,k≤p,l≤q, respectively. Taking process 8 (i=8) as an example, the comparison of error source sensitivities is shown in Table 3. Figure 7 .

[0085] The heritability coefficients G(i,j) for each process are shown in Table 4, and the comparison of heritability coefficients is shown in Table 4. Figure 8 .

[0086] Substituting the error source uncertainty u(i,j,k,l), sensitivity coefficient C(i,j,k,l), and heredity coefficient G(i,j) into formula (7), the combined uncertainty U(i,j) of each process can be obtained. Table 5 shows the combined uncertainty values. A comparison of the combined uncertainties of each process is shown in Table 5. Figure 9 .

[0087] Table 3. Sensitivity of error sources C(i,j,k,l)

[0088]

[0089]

[0090]

[0091]

[0092]

[0093]

[0094]

[0095] Table 4. Heredity coefficients of process errors G(i,j)

[0096]

[0097] Table 5. Combined uncertainty U(i,j) for each process, in μm

[0098]

[0099]

Claims

1. A method of processing uncertainty calculation, characterized by, The method comprises the following steps: determining the number n of processes in a process flow; the machining uncertainty U(i) of a process i is a combination of a regeneration uncertainty R(i) and a genetic uncertainty G(i), and the calculation formula is: U(i) = R(i) <+> G(i) x U(i-1) (1) Wherein, <+> represents the combination of uncertainties, x represents Hadamard product (also known as dot product); i is the process number, U(i) is the machining uncertainty of the i th process, G(i) is the genetic coefficient, and U(i-1) is the machining uncertainty of the previous process, wherein i≤n.

2. The method of claim 1, wherein, The regeneration uncertainty is represented as: R(i) = ± ΔR(i) (2) Wherein, ΔR(i) is the range estimate of the uncertainty R(i), and when a statistical analysis method is used, the value is the standard deviation of the evaluated quantity; when a non-statistical method is used for evaluation, the value is the estimate of the standard deviation.

3. The method of claim 1, wherein, The machining uncertainty of the previous process is represented as: U(i-1) = ± ΔU(i-1) (3) Wherein, ΔU(i-1) is the range estimate of the uncertainty U(i-1), and when a statistical analysis method is used, the value is the standard deviation of the evaluated quantity; when a non-statistical method is used for evaluation, the value is the estimate of the standard deviation.

4. The method of claim 1, wherein, The genetic uncertainty is the Hadamard product of the genetic coefficient G(i) and the machining uncertainty U(i-1) of the previous process (i-1), and the calculation formula is: Wherein, m is the number of machining uncertainties to be evaluated, g(i,k) is the k th component of the genetic coefficient G(i), and ΔU(i-1,k) is the k th component of the machining uncertainty U(i-1) of the previous process.

5. The method of claim 1, wherein, The calculation formula of the machining uncertainty U(i) of the process i is:

6. The method of claim 5, wherein, The number m of uncertainties to be evaluated for each process, the number p of error sources for each process, and the number q of error components of each error source; the j th regeneration machining uncertainty R(i,j) of the process i is a combination of the Hadamard product of the regeneration machining uncertainty R(i,j,k) of all p error sources and the sensitivity C(i,j,k) of each error source, that is wherein represents a synthesis of the series of error source reproduction uncertainties; j < m; when the reproduction process uncertainty component R(i,j,k) is oriented at an angle a to the direction of the synthesized reproduction process uncertainty R(i,j) k C(i,j,k,) = cos a k .

7. The method of claim 6, wherein, Suppose that the error source k of the j th machining uncertainty component of the process i has q error components, then the regeneration machining uncertainty R(i,j,k) generated by the error source is a combination of the product of all q error source uncertainty components u(i,j,k,l) and the corresponding sensitivity C(i,j,k,l), that is In the formula, when the direction included angle of the uncertainty component u(i,j,k,l) of the error source q and the uncertainty R(i,j,k) of the synthesized error source k is β l , C(i,j,k,l)=cosβ l .

8. The method of claim 7, wherein, The j th machining uncertainty U(i,j) of the process i is:

Images