Carbon fiber joint non-contact detection method and system

Abstract

The invention relates to the technical field of carbon fiber joint detection, in particular to a carbon fiber joint non-contact detection method and system.The method comprises the steps that S10, a detection system is installed on a carbon fiber production line, and the production line is started to start conveying carbon fiber yarn; the production line conveying speed V and the yarn standard thickness Db are recorded; s20, the real-time thickness Ds of the carbon fiber yarn is detected; recording the starting time tk when the real-time thickness Ds is inconsistent with the standard thickness Db at each time and the ending time tj when the real-time thickness Ds is continuously changed at the time; and S30, generating a detection result according to the thickness Ds and the change time period t = tj-tk. According to the invention, the detection accuracy of the carbon fiber joint under non-contact detection is effectively improved.

Description

Technical Field

[0001] The present invention relates to the technical field of carbon fiber joint detection, and in particular to a non-contact detection method and system for carbon fiber joints. Background Art

[0002] As an advanced material with high strength, high modulus and light weight, carbon fiber is widely used in the field of automobile manufacturing. During the forming process of automobile carbon fiber parts, the yarn joint is one of the key factors affecting product quality. Due to the limitation of the original yarn length or broken yarn problem during the production of carbon fiber, it is necessary to splice the joints to achieve continuous production; such joints are usually formed by knotting or bonding two sections of yarn by manual or automatic equipment, but their local thickness, density and mechanical properties are significantly different from those of normal yarns; if not detected and removed in time, during the forming process of automobile carbon fiber parts, the joints will become the weak points of composite products, resulting in defects such as a decrease in structural strength.

[0003] In the existing carbon fiber joint detection technology, although the contact detection means can directly obtain the yarn parameters, the continuous friction between the mechanical probe and the high-speed running fiber is likely to cause broken filaments and fuzzing, significantly reducing the material strength. Although the non-contact scheme avoids physical contact, due to relying on a single yarn parameter for determination and not considering the influence of environmental factors on the yarn, it is difficult to distinguish real joints from other abnormal situations such as twisting and tail yarn interference, resulting in a high false positive rate. Therefore, in non-contact detection, there is an urgent need for a detection method and system to improve the accuracy of carbon fiber joint detection. Summary of the Invention

[0004] In view of at least one of the above technical problems, the present invention provides a non-contact detection method and system for carbon fiber joints, which accurately identify joints while avoiding physical damage to the yarn by combining the real-time thickness change and the change time period.

[0005] The present invention provides a non-contact detection method for carbon fiber joints, including the following steps: S10: Install the detection system on the carbon fiber production line, start the production line to start conveying the carbon fiber yarn; record the standard thickness Db of the yarn; S20: Detect the real-time thickness Ds of the carbon fiber yarn; record the start time tk when the real-time thickness Ds is inconsistent with the standard thickness Db each time, and the end time tj of this continuous change; S30: Generate a detection result according to the thickness Ds and the change time period t = tj - tk.

[0006] In some embodiments of the present invention, it further includes: S40: Record the conveying speed V of the production line, and establish a dynamic threshold Td according to the conveying speed V of the production line and the standard thickness Db of the yarn; S50: Detect the change rate of yarn density Δρ, and calculate the variance of yarn tension fluctuation σ 2 ; Based on the detection results, dynamic threshold Td, change rate of density Δρ, and variance of tension fluctuation σ 2 Construct a judgment formula to judge the joint.

[0007] In some embodiments of the present invention, the specific process of establishing the dynamic threshold Td in step S40 is as follows: Establish Td = a·Db + b·V + c; Wherein, a, b, and c are artificially set threshold coefficients and are constants.

[0008] In some embodiments of the present invention, step S40 further includes calculating the time window Δt: Δt = (Lj + Lw + Lb) / V; Wherein, Lj is the length of the joint itself and is a constant controlled by humans; Lw is the length of the trailing yarn after the joint and is a constant controlled by humans; Lb is the compensation length and is a constant.

[0009] In some embodiments of the present invention, the specific process of constructing a judgment formula to judge the joint in step S50 is as follows: Construct P = (w1·ΔD + w2·Δρ + w3·σ 2 ) / Td·(t / Δt); If P≥P2, there is a joint in the carbon fiber yarn; if P≤P1, the carbon fiber yarn is normal; Wherein, w1, w2, and w3 are artificially set weight coefficients and are constants; and w1 + w2 + w3 = 1; the thickness change ΔD = Ds - Db; P2 is an artificially set joint threshold and is a constant; P1 is an artificially set normal threshold and is a constant.

[0010] In some embodiments of the present invention, it further includes that in step S50, when P1 < P < P2, judgment correction is required: Calculate the time-domain integral of the change rate of density ; When Sp > Ss, correct it to that there is a joint in the carbon fiber; Wherein, Ss is an artificially set time-domain threshold and is a constant.

[0011] In some embodiments of the present invention, the specific process of artificially setting w1, w2, and w3 in step S50 is as follows: Establish a preset weight combination table; Initial setting stage: According to the type of carbon fiber yarn, select the initial weight group from the preset weight combination table; Adjustment stage: Collect the misjudgment rates of historical detection results, and distinguish misjudgments related to thickness, density or tension from them; if it is a misjudgment related to thickness, reduce the weight coefficient w1 and increase the weight coefficients w2 and w3; if it is a misjudgment related to density or tension, reduce the corresponding weight coefficient and increase the other weight coefficients; Constraint stage: Fine-tune w1, w2, and w3 so that the final weight coefficients satisfy w1 + w2 + w3 = 1.

[0012] The present invention also provides a non-contact detection system for carbon fiber joints, including: A bracket fixed on the production line frame; A detection mechanism installed on the bracket for detecting the real-time thickness Ds of carbon fiber yarns and collecting the conveying speed V of the production line; A control mechanism connected to the detection mechanism; including a storage module for recording the standard thickness Db of the yarn; A timing module for recording the start time tk when the real-time thickness Ds is inconsistent with the standard thickness Db each time, and the end time tj of this continuous change; An analysis module for generating a detection result according to the thickness Ds and the change time period t = tj - tk.

[0013] In some embodiments of the present invention, the detection mechanism includes: A non-contact thickness gauge fixed on the bracket, facing the carbon fiber production line, for detecting the real-time thickness Ds of carbon fiber yarns; A speed sensor for collecting the conveying speed V of the production line; A timing module for recording the start time tk and the end time tj.

[0014] In some embodiments of the present invention, it further includes: A density sensor for detecting the yarn density; A tension sensor for detecting the yarn tension; The analysis module also establishes a dynamic threshold Td, calculates the yarn density change rate Δρ and the yarn tension fluctuation variance σ²; constructs a judgment formula to judge the joint.

[0015] The beneficial effects of the present invention are as follows: Through non-contact sensing technology, the present invention achieves zero physical damage detection and improves the integrity retention rate of carbon fiber yarns; through the adjustment of dynamic thresholds and time windows, it adapts to the production conditions of different production lines and improves the working condition compatibility; by combining multiple parameters to determine the joint and making judgment corrections in difficult-to-distinguish states, the detection accuracy is effectively improved, and the anti-interference ability of the entire detection system is improved. Description of the Drawings

[0016] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for use in the description of the embodiments or the prior art. Obviously, the drawings in the following description are only some embodiments recorded in the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can also be obtained based on these drawings.

[0017] Figure 1 It is a step flow chart of the non-contact detection method for carbon fiber joints in the embodiments of the present invention; Figure 2 It is a structural schematic diagram of the non-contact detection system for carbon fiber joints in the embodiments of the present invention; Figure 3 It is a sectional structural schematic diagram of the non-contact detection system for carbon fiber joints in the embodiments of the present invention.

[0018] Reference numerals: 1, support; 2, detection mechanism; 21, non-contact thickness gauge. Specific embodiments

[0019] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments.

[0020] It should be noted that when an element is referred to as being "fixed to" another element, it can be directly on the other element or there can also be an intermediate element. When an element is considered to be "connected" to another element, it can be directly connected to the other element or there may be an intermediate element at the same time. The terms "vertical", "horizontal", "left", "right" and similar expressions used herein are only for the purpose of illustration and do not represent the only implementation manner.

[0021] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by those skilled in the technical field to which the present invention belongs. The terms used in the description of the present invention are only for the purpose of describing specific embodiments and are not intended to limit the present invention. The term "and / or" used herein includes any and all combinations of one or more of the related listed items.

[0022] As Figure 1 shown, the present invention provides a non-contact detection method for carbon fiber joints, including the following steps: S10: Install the detection system on the carbon fiber production line, start the production line to convey carbon fiber yarn; record the standard thickness Db of the yarn; S20: Detect the real-time thickness Ds of the carbon fiber yarn; record the start time tk when the real-time thickness Ds is inconsistent with the standard thickness Db each time, and the end time tj of this continuous change. S30: Generate a detection result based on the thickness Ds and the change time period t = tj - tk.

[0023] The specific working principle of the present invention is as follows: Detect the thickness of the carbon fiber yarn on the carbon fiber production line through a non-contact detection tool to obtain the real-time thickness Ds of the yarn passing through the detection area of the detection tool. When the real-time thickness Ds of the yarn is greater than the standard thickness Db of the yarn, it can already be preliminarily determined as a joint at this time. However, due to the twisted yarn, the yarn will be flipped and folded, and there will be a gap in the middle of the folded yarn, increasing the overall thickness and being easily misjudged as a joint. Therefore, further judgment is needed.

[0024] There is a tail yarn after the joint. Because twisting exists periodically at intervals from one end to the other end of the yarn, the joint and the tail yarn only exist locally on the yarn and are short-term anomalies that occur irregularly and once. The joint length and tail yarn length corresponding to different yarn types can be obtained according to different yarn types. Then, considering the joint length and tail yarn length under the production line speed, within what time period they will be detected. Therefore, when the real-time thickness Ds of the yarn is greater than the standard thickness Db of the yarn, record the start time tk of this thickness change and the end time tj of this continuous change to obtain the change time period t = tj - tk. Then, combined with the continuous change time period t brought about by the change in the real-time thickness Ds of the yarn when the joint and the tail yarn pass through the detection area, it can be determined that there is a joint in the yarn with a thickness change within the specified time period.

[0025] Taking the yarn type of 50k and the production line speed of 12.7 m / min as an example, in the case of no twisting interference, when the thickness is within 3 mm, it is normal, and when it is above 3 mm, it is judged as a joint. When there is twisting, the joint length of this type of yarn is about 1 cm, and there is about 15 cm of tail yarn after the joint. The two together are 16 cm. The expected detection time through the non-contact detection system is 760 ms. The detection time for the twisted, flipped, and folded part is about 20 seconds. Therefore, during the detection of 50k yarn, it can be judged that the joint is the one with a thickness exceeding 3 mm within 1 second.

[0026] In some embodiments of the present invention, it further includes: S40: Record the production line conveying speed V, and establish a dynamic threshold Td based on the production line conveying speed V and the standard thickness Db of the yarn. By establishing the dynamic threshold Td, the judgment of the joint can vary with the production line conveying speed V and different types of yarns, solving the problem of the failure of the traditional fixed threshold under complex working conditions.

[0027] S50: Detect the yarn density change rate Δρ and calculate the variance σ of the yarn tension fluctuation 2 ; Based on the detection results, the dynamic threshold Td, the density change rate Δρ, and the variance σ of the tension fluctuation 2 Construct a judgment formula to judge the joint.

[0028] In the joint area, knotting or bonding will cause uneven internal density distribution of the yarn (such as local accumulation or voids). Twisting or surface fuzz may cause a sudden increase in thickness, but the internal density change is small; while a real joint will simultaneously cause a sudden increase in thickness and internal density variation; using the density change rate Δρ can obtain additional internal information and reduce misjudgment of the detection system. The density change rate Δρ can be calculated from the peak value, valley value, and average value of the yarn density within the change time period t; the mechanical discontinuity in the joint area will cause the tension value to fluctuate violently in a short time, and the variance σ of the tension fluctuation 2 quantifies the intensity of this fluctuation and can be calculated using the instantaneous tension values recorded by the tension sensor; by introducing the density change rate Δρ and the variance σ of the tension fluctuation 2 , construct a multi-dimensional judgment logic to solve the limitation of a single thickness parameter.

[0029] Preferably, in step S40, establishing the dynamic threshold Td specifically is:[[]] Establish Td = a·Db + b·V + c; where a, b, and c are artificially set threshold coefficients and are constants.

[0030] Starting from the physical properties of the yarn itself, the standard thickness Db of different specifications of yarns varies significantly, which directly affects the detection threshold of the joint; the faster the production line conveying speed V, the shorter the time for the yarn to pass through the detection area, and a higher threshold is required to avoid misjudgment in a high-speed environment; the threshold coefficients a, d, and c can be obtained by fitting historical data and are used to balance the influence of yarn thickness and speed on the threshold; the threshold coefficient a is used to adjust the contribution of yarn thickness to the threshold, the threshold coefficient b is used to adjust the contribution of the production line speed to the threshold, and the threshold coefficient c is used to correct the interference of the environment on the detected yarn, such as the influence of temperature, humidity, etc. on the detection system; such a design realizes the dynamic adjustment of the threshold, adapts to different specifications of yarns and production line speeds according to specific situations, and improves the detection accuracy of yarn joints.

[0031] In some embodiments of the present invention, step S40 further includes calculating the time window Δt: Δt = (Lj + Lw + Lb) / V; where Lj is the length of the joint itself, which is a constant controlled by humans; Lw is the length of the tail yarn after the joint, which is a constant controlled by humans; Lb is the compensation length, which is a constant.

[0032] As mentioned above, the presence of joints in the yarn is detected by combining the change in time period and the change in thickness, but the influence brought by the production line speed is not considered. When the conveying speed V of the production line is high, the yarn passes through the detection area quickly. If the time window Δt is fixed, the joint characteristics may not be fully captured, resulting in missed detection. When the conveying speed V of the production line is low, the joint passes through the detection area for a long time. If the time window Δt is too short, the twist may be misjudged as a joint. Therefore, designing this time window Δt not only compensates for the length to avoid calculation deviations caused by external interference, but also eliminates the influence of high-speed or slow-speed production lines on the thickness change time period by taking the ratio with the production line conveying speed V, ensuring that the detection time is synchronized with the actual production rhythm and avoiding missed detection and misjudgment caused by speed differences.

[0033] In some embodiments of the present invention, in step S50, the judgment formula for judging the joint is specifically as follows: Construct P = (w1·ΔD + w2·Δρ + w3·σ 2 ) / Td·(t / Δt); If P ≥ P2, there is a joint in the carbon fiber yarn; if P ≤ P1, the carbon fiber yarn is normal; Among them, w1, w2, and w3 are artificially set weight coefficients, which are constants; and w1 + w2 + w3 = 1; the thickness change ΔD = Ds - Db; P2 is an artificially set joint threshold, which is a constant; P1 is an artificially set normal threshold, which is a constant.

[0034] Combining the thickness change ΔD, density change rate Δρ, and tension fluctuation variance σ in the joint area 2 , the joint characteristics on the yarn are captured from three dimensions of physical size, material properties, and mechanical behavior, reducing the risk of misjudgment caused by a single parameter; through the neutralization of the weight coefficients w1, w2, and w3, the overinfluence of a certain parameter on the judgment result is avoided. And the above whole is divided by the dynamic threshold Td, and the multiple parameters of the numerator are dynamically scaled according to the specific actual working conditions (production line conveying speed V and yarn standard thickness Db), so that the judgment formula P is comparable under different production conditions.

[0035] t represents the actual continuous change time period from the start to the end of the detected thickness change, and Δt is the calculated theoretical time window. By comparing these two, the conformity between the actual and the theoretical in detecting the thickness change is quantified. If the ratio t / Δt is close to 1, it indicates that the change time period t is consistent with the time window Δt, and the probability that the detected thickness change is caused by a joint is greater. If the ratio t / Δt is greater than 1, it indicates that the change time period t is much larger than the time window Δt, and at this time, the detected thickness change may be twist or other interferences.

[0036] Therefore, the judgment formula is designed in this way, starting from multiple parameters, which improves the accuracy and stability of non-contact carbon fiber joint detection and reduces the false judgment rate caused by twisting or other interferences.

[0037] Preferably, it also includes that in step S50, when P1 < P < P2, judgment correction is required: Calculate the time-domain integral of the density change rate ; When Sp > Ss, it is corrected to indicate the existence of a joint in the carbon fiber; where Ss is a manually set time-domain threshold and is a constant.

[0038] The real joint will cause the density to be continuously abnormal during the detected change time period because the internal structure of the joint area is not as uniform as that of the normal yarn; while the judgment formula P may not fully cover all joint characteristics due to parameter weight allocation or dynamic threshold setting. Therefore, judgment correction is introduced. Through the verification of the persistence of density change, the uncertainty false judgment when the calculation result of P is in the middle range is significantly reduced, making up for the deficiency of single formula determination.

[0039] In some embodiments of the present invention, the specific process of manually setting w1, w2, and w3 in step S50 is as follows: Establish a preset weight combination table; the optimal weight combination can be preset for different yarn types according to historical data or experimental calibration.

[0040] Initial setting stage: According to the carbon fiber yarn type, select the initial weight group from the preset weight combination table; when switching the yarn type, directly call the preset weight, shortening the debugging time and reducing the subjectivity and inefficiency of manual parameter adjustment.

[0041] Adjustment stage: Collect the false judgment rate of historical detection results and distinguish thickness-related false judgments, density or tension-related false judgments from them; if it is a thickness-related false judgment, reduce the w1 weight coefficient and increase the w2 and w3 weight coefficients; if it is a density or tension-related false judgment, reduce the corresponding weight coefficient and increase the other weight coefficients; the weights of the corresponding yarn types can be automatically optimized according to the data obtained from historical false judgments, improving the accuracy of the overall judgment formula.

[0042] Constraint stage: Fine-tune w1, w2, and w3 so that the final weight coefficients satisfy w1 + w2 + w3 = 1; prevent a single parameter from overly dominating the judgment result and avoid the influence of parameter weight imbalance on the judgment formula.

[0043] The present invention also provides a non-contact detection system for carbon fiber joints, as Figure 2 and Figure 3 shown, including: Bracket 1 is fixed on the production line frame; it provides a stable installation platform to ensure accurate alignment between the detection mechanism 2 and the yarn.

[0044] Detection mechanism 2 is installed on the bracket 1 and is used to detect the real-time thickness Ds of the carbon fiber yarn and collect the production line conveying speed V; Control mechanism is connected to the detection mechanism 2; it includes a storage module for recording the standard thickness Db of the yarn. Timing module records the start time tk when the real-time thickness Ds is inconsistent with the standard thickness Db each time, and the end time tj of this continuous change. Analysis module generates a detection result based on the thickness Ds and the change time period t = tj - tk.

[0045] The detection system of the present invention detects the yarn thickness through the non-contact detection mechanism 2 In some embodiments of the present invention, the detection mechanism 2 includes: Non-contact thickness gauge 21 is fixed on the bracket 1, facing the carbon fiber production line, and is used to detect the real-time thickness Ds of the carbon fiber yarn; the non-contact thickness gauge 21 can adopt an infrared sensor, a laser thickness gauge, or an ultrasonic thickness gauge, etc. Speed sensor is used to collect the production line conveying speed V; Timing module is used to record the start time tk and the end time tj.

[0046] In some embodiments of the present invention, it further includes: Density sensor is used to detect the yarn density; Tension sensor is used to detect the yarn tension; The analysis module also establishes a dynamic threshold Td, calculates the yarn density change rate Δρ and the yarn tension fluctuation variance σ²; constructs a judgment formula to judge the joint.

[0047] Those skilled in the art of this industry should understand that the present invention is not limited by the above embodiments. What is described in the above embodiments and the specification only illustrates the principle of the present invention. Without departing from the spirit and scope of the present invention, the present invention will have various changes and improvements, and these changes and improvements all fall within the scope of the present invention claimed. The scope of protection claimed by the present invention is defined by the appended claims and their equivalents.

Claims

1. A non-contact detection method for a carbon fiber joint, characterized in that It includes the following steps: S10: Install the detection system on the carbon fiber production line, start the production line to convey the carbon fiber yarn; record the standard thickness Db of the yarn. S20: Detect the real-time thickness Ds of the carbon fiber yarn; record the start time tk when the real-time thickness Ds is inconsistent with the standard thickness Db each time, and the end time tj of this continuous change. S30: Generate a detection result according to the thickness Ds and the change time period t = tj - tk.

2. The non-contact detection method for carbon fiber joints according to claim 1, wherein It also includes: S40: Record the conveying speed V of the production line, and establish a dynamic threshold Td according to the conveying speed V of the production line and the standard thickness Db of the yarn. S50: Detect the change rate of yarn density Δρ, and calculate the variance of yarn tension fluctuation σ 2 ; According to the detection results, dynamic threshold Td, density change rate Δρ, and variance of tension fluctuation σ 2 Construct a judgment formula to judge the joint.

3. The non-contact detection method for the carbon fiber joint according to claim 2, characterized in that In step S40, the specific establishment of the dynamic threshold Td is as follows: Establish Td = a·Db + b·V + c; Where, a, b, and c are artificially set threshold coefficients and are constants.

4. The non-contact detection method for carbon fiber joints according to claim 3, characterized in that Step S40 also includes calculating the time window Δt: Δt = (Lj + Lw + Lb) / V; Where, Lj is the length of the joint itself, which is a constant controlled manually; Lw is the length of the tail yarn after the joint, which is a constant controlled manually; Lb is the compensation length and is a constant.

5. The non-contact detection method for carbon fiber joints according to claim 4, characterized in that In step S50, the specific process of constructing a judgment formula to judge the joint is as follows: Construct \(P=(w1\cdot\Delta D + w2\cdot\Delta\rho+w3\cdot\sigma 2 ) / Td\cdot(t / \Delta t)\); If P≥P2, there is a joint in the carbon fiber yarn; if P≤P1, the carbon fiber yarn is normal. Where, w1, w2, and w3 are artificially set weight coefficients and are constants; and w1 + w2 + w3 = 1; the thickness change ΔD = Ds - Db; P2 is an artificially set joint threshold and is a constant; P1 is an artificially set normal threshold and is a constant.

6. The non-contact detection method for carbon fiber joints according to claim 5, characterized in that It also includes that in step S50, when P1 < P < P2, judgment correction is required: Time-domain integration of the density change rate ; When Sp > Ss, it is corrected to that there is a joint in the carbon fiber. Where, Ss is an artificially set time domain threshold and is a constant.

7. The non-contact detection method and system for carbon fiber joints according to claim 5, characterized in that In step S50, the specific process of artificially setting w1, w2, and w3 is as follows: Establish a preset weight combination table. Initial setting stage: According to the type of carbon fiber yarn, select the initial weight group from the preset weight combination table. Adjustment stage: Collect the misjudgment rate of historical detection results, and distinguish misjudgments related to thickness, density or tension from them; if it is a misjudgment related to thickness, reduce the w1 weight coefficient and increase the w2 and w3 weight coefficients; if it is a misjudgment related to density or tension, reduce the corresponding weight coefficient and increase the other weight coefficients. Constraint stage: Fine-tune w1, w2, and w3 so that the final weight coefficients satisfy w1 + w2 + w3 = 1.

8. A non-contact detection system for a carbon fiber joint, characterized in that, It includes: A bracket (1), fixed on the production line frame. A detection mechanism (2), installed on the bracket (1), used to detect the real-time thickness Ds of the carbon fiber yarn and collect the conveying speed V of the production line. A control mechanism, connected to the detection mechanism (2); including a storage module, used to record the standard thickness Db of the yarn. A timing module, recording the start time tk when the real-time thickness Ds is inconsistent with the standard thickness Db each time, and the end time tj of this continuous change. An analysis module, generating a detection result according to the thickness Ds and the change time period t = tj - tk.

9. The non-contact detection system for carbon fiber joints according to claim 8, wherein, The detection mechanism (2) includes: A non-contact thickness gauge (21), fixed on the bracket (1), facing the carbon fiber production line, used to detect the real-time thickness Ds of the carbon fiber yarn. A speed sensor for collecting the production line conveying speed V; A timing module for recording the start time tk and the end time tj.

10. The non-contact detection system for carbon fiber joints according to claim 8, wherein It further includes: A density sensor for detecting the yarn density; A tension sensor for detecting the yarn tension; The analysis module also establishes a dynamic threshold Td, calculates the yarn density change rate Δρ and the yarn tension fluctuation variance σ²; constructs a judgment formula to judge the joint.

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