A fuzzy optimization design method for special-shaped guide plates of toothed chains

Abstract

The present invention discloses a fuzzy optimization design method for a toothed chain special-shaped guide plate, which belongs to the technical field of toothed chains. The toothed chain special-shaped guide plate must have a certain strength to meet the requirement of lightweight, and in order to ensure that all chain plates bear the load, the elongation of the guide plate must make up for the assembly gap. The present invention establishes a maximum volume reduction of the guide plate as the objective function, and takes the middle longitudinal height of the waist, the radius of the concave arc and the thickness of the guide plate, the main design parameters of the guide plate, as the design variables. The bounded search method and the penalty function method are used for optimization to obtain two optimization solutions, and then combined with the strict restriction conditions of the elongation, the optimal solution is obtained. The present invention is suitable for the geometric parameter optimization design of most toothed chain special-shaped guide plates. Based on certain design goals and usage requirements, combined with relevant optimization algorithms, the optimization design parameters are quickly obtained through computer programming. It is a purely parametric scientific design process.

Description

Technical Field

[0001] The invention relates to the technical field of toothed chains, and in particular to a fuzzy optimization design method for a toothed chain special-shaped guide plate. Background Art

[0002] Toothed chain is an important basic mechanical part and is widely used. Especially under working conditions such as high speed, heavy load, and large center distance, its transmission performance is better than that of toothed belt drive, gear drive, and roller chain drive. However, the guide plate, as an important component of the toothed chain, has not received enough attention in the chain industry for a long time.

[0003] For the entire toothed chain transmission system, the rationality of the guide plate design directly affects the power and stability of the chain during operation. The special-shaped guide plate involves many variables, and each variable restricts each other. It is difficult for general designers to coordinate the design of various parameters to achieve the optimal overall. On the other hand, it is difficult to continue to improve the chain performance by improving the tooth shape and structure at this stage. Therefore, mastering the correct and effective optimization design method of special-shaped guide plates has gradually become one of the core technical demands of various chain manufacturers.

[0004] In the past, there was a lack of systematic and scientific design methods for the design of special-shaped guide plates. The longitudinal height of the middle waist, the radius of the concave arc and the corresponding parameters were selected based on experience. Through a large number of experiments and continuous corrections, the design goals were slowly approached and finally met the work requirements. However, this empirical design method has many shortcomings: first, this design method has a certain blindness in parameter selection, does not consider the coupling relationship between various parameters, requires high experience for designers, and lacks scientific theoretical support for the selection and matching of parameters; second, there are many uncertain phenomena in the design process of special-shaped guide plates, mainly because there are many design parameters, the relationship between various variables is complex, and the parameters show a certain randomness and ambiguity. In the past, empirical design lacked methods and means to deal with fuzzy concepts, often ignoring these situations, and artificially determining parameters, resulting in missing the real optimization plan. Third, the traditional empirical design method has a long design cycle, a large workload, consumes a lot of manpower and material resources, lacks a fast and accurate optimization algorithm for matching design, and no patent application for the fuzzy optimization design method of toothed chain special-shaped guide plates was found after searching. Summary of the invention

[0005] The present invention provides a fuzzy optimization design method for a toothed chain special-shaped guide plate. The entire design process is purely parametric, more systematic and scientific, and a mathematical model of fuzzy optimization design is established from actual design problems. While ensuring that the guide plate has a certain strength and the elongation makes up for the assembly gap, the volume of the guide plate is reduced as much as possible to better meet the lightweight requirements. The core of solving the fuzzy optimization problem is the transformation from fuzzy to non-fuzzy, and different conversion methods produce different fuzzy optimization solutions.

[0006] The present invention improves on the traditional fuzzy optimization design method and uses two different optimization methods, the bounded search method and the penalty function method, to obtain two optimization solutions. The constraint condition that the elongation makes up for the assembly gap is the most stringent and important. The elongation in the two optimization solutions is compared with the assembly gap to obtain the optimal solution that best meets the design requirements.

[0007] A fuzzy optimization design method for a toothed chain special-shaped guide plate, the design method comprising the following steps:

[0008] Step 1: Take the main design parameters of the guide plate as the middle longitudinal height H of the waist G , radius of the concave arc R G and guide plate thickness b D As the design variable, the objective function is established by maximizing the volume reduction of the guide plate;

[0009] Step 2: Establish constraint conditions based on the strength limit and elongation requirements of the special-shaped guide plate, determine the value range of the design variables, and obtain the mathematical model of the fuzzy optimization design;

[0010] Step 3: Establish the membership function of the fuzzy constraint, determine the upper and lower limits of the fuzzy constraint transition interval, transform the fuzzy constraint problem into a non-fuzzy constraint problem, and then use the bounded search method and penalty function method for optimization to obtain two optimal solutions. Combined with the strict restrictions on the elongation, the optimal solution is obtained.

[0011] Beneficial effects of the present invention:

[0012] The present invention is suitable for the geometric parameter optimization design of most toothed chain special-shaped guide plates. Based on certain design goals and usage requirements, many fuzzy factors are considered in combination with actual conditions, a fuzzy optimization design model is established, and relevant optimization algorithms are used to solve the problem through computer programming to quickly obtain the optimized design parameters, which greatly reduces the time required for design and improves the design accuracy. The entire design process is purely parametric and is a systematic and scientific optimization design method. BRIEF DESCRIPTION OF THE DRAWINGS

[0013] Figure 1 It is a schematic diagram of the structural parameters of the special-shaped guide plate of the present invention;

[0014] Figure 2 This is a flow chart of the fuzzy optimization design method of the present invention;

[0015] Figure 3 It is a flow chart of the bounded search method program called in the fuzzy optimization design method of the present invention;

[0016] Figure 4 This is a program flow chart of the penalty function method called in the fuzzy optimization design method of the present invention. DETAILED DESCRIPTION

[0017] See also Figures 1 to 4 As shown, a fuzzy optimization design method for a toothed chain special-shaped guide plate includes the following steps:

[0018] Step 1: Take the main design parameters of the guide plate as the middle longitudinal height H of the waist G , concave arc radius R G and guide plate thickness b D As the design variable, the objective function is established by maximizing the volume reduction of the guide plate;

[0019] Step 2: Establish constraint conditions based on the strength limit and elongation requirements of the special-shaped guide plate, determine the value range of the design variables, and obtain the mathematical model of the fuzzy optimization design;

[0020] Step 3: Establish the membership function of the fuzzy constraint, determine the upper and lower limits of the fuzzy constraint transition interval, transform the fuzzy constraint problem into a non-fuzzy constraint problem, and then use the bounded search method and penalty function method for optimization to obtain two optimal solutions. Combined with the strict restriction conditions of the elongation, the optimal solution is obtained.

[0021] The specific method of step one is as follows:

[0022] The middle longitudinal height H of the waist has a direct impact on the design of the guide plate parameters G , concave arc radius R G and guide plate thickness b D is the design variable, denoted as:

[0023] X=[H G , R G , b D ] T (1)

[0024] The volume reduced by the guide plate can be approximated as:

[0025] V=2R G b D (HH G ) (2)

[0026] Where:

[0027] H——Longitudinal height of guide plate

[0028] The fuzzy optimization design function F(X) generally takes the minimum value, so it can be expressed as:

[0029] F(X)=2R G b D (H G -H) (3)

[0030] The specific method of step 2 is as follows:

[0031] (1) Limitation of tensile stress σ on the guide plate:

[0032] Corresponding constraint function:

[0033] Where:

[0034] F t - tight edge tension;

[0035] [σ t ]——Allowable tensile stress

[0036] (2) Ideally, the elongation of the guide plate Δl is equal to the assembly gap. However, due to the influence of processing and assembly errors, the actual elongation is often slightly greater than the assembly gap:

[0037]

[0038] Where:

[0039] F——elongation compensation force;

[0040] L——chain plate hole center distance;

[0041] D——chain plate hole diameter;

[0042] E——elastic modulus of guide plate material;

[0043] δ——Assembly unilateral clearance;

[0044] ε——Elongation interference

[0045] Corresponding constraint function:

[0046] (3) Design variable value limits:

[0047]

[0048] The above constraints are all fuzzy constraints, and the mathematical model of fuzzy optimization design of special-shaped guide plates can be obtained:

[0049]

[0050] The specific method of step three is as follows:

[0051] (1) Membership function of fuzzy constraints

[0052] There is a transition interval between the allowable tensile stress value of the guide plate from fully allowed to completely unallowable, so the membership function of formula (4) adopts a descending semi-trapezoidal distribution:

[0053]

[0054] The elongation has a fuzzy range of values, but it cannot be less than the assembly gap. Therefore, the membership function of formula (6) adopts a right-angle trapezoidal distribution, that is, there is no transition interval in the lower bound:

[0055]

[0056] The range of the design variable is also a fuzzy quantity. For the convenience of description, the constraints in formula (7) can be uniformly expressed as:

[0057]

[0058] Where:

[0059] ——x i The upper bound of the value of (i=1, 2, 3);

[0060] k i ——x i The lower bound of the value of (i=1, 2, 3);

[0061] Therefore, the membership function of formula (11) adopts trapezoidal distribution:

[0062]

[0063] The upper and lower limits of the transition interval in the membership function are determined by the expansion coefficient method. Lower amplification factor β =0.7~0.95, we can get Δ l U =Δ l L =2δ; x i L = kβ , x i U =k ;

[0064] According to the decomposition theorem of fuzzy sets, a series of membership λ values ​​are used to intercept the fuzzy sets, and the level intercept sets under different defense levels can be obtained. It is necessary to find an optimal value λ * , transform the fuzzy constraint problem into a non-fuzzy constraint problem:

[0065]

[0066] (2) Optimization process

[0067] ①Using the random direction method, when λ = 0 and λ = 1, solve equation (8) to obtain the minimum value m and the maximum value M, and establish the membership function of the fuzzy objective function: Upper limit The lower limit is by With 1 as the limit, and m and M as the bound, the bounded search method is used to solve, and the optimal solution X can be obtained. *1 ;

[0068] ②Use the two-level fuzzy comprehensive evaluation method to determine the optimal level cut set of λ * , and then call the penalty function method to solve the transformed general optimization problem:

[0069]

[0070]

[0071] The optimized solution X can be obtained *2

[0072] ③ Compare the elongation in the two solutions The closer the assembly gap is to the assembly gap 2δ, the ideal value is the one that is closer to the assembly gap, which is the optimal solution X. * .

[0073] Among them, the flow chart of the bounded search method described in the above design process is as shown in the attached Figure 3 As shown;

[0074] Among them, the penalty function method program flow chart described in the above design process is as shown in the attached Figure 4 As shown;

[0075] According to the above design method, the guide plate is optimized and the main design parameters of the optimal special-shaped guide plate are finally determined.

[0076] Example 1

[0077] Taking a chain as an example, we will optimize the design parameters of the special-shaped guide plate, where δ = 0.0012 mm, H = 6.1 mm, L = 6.35 mm, D = 2.65 mm, E = 2.1 × 10 5 MPa, the ultimate tensile load of the toothed chain is Q = 6.5KN, the load factor is K = 11, the thickness of the chain plate is b = 1.3mm, the guide plate material is 50CrVA, and the allowable tensile stress [σ t ]=637.5MPa.

[0078] Step 1: Establish design variables and objective function:

[0079] The middle longitudinal height H of the waist has a direct impact on the design of the guide plate parameters G , concave arc radius R G and guide plate thickness b D is the design variable, denoted as:

[0080] X=[H G , R G , b D ] T (1)

[0081] The volume reduced by the guide plate can be approximated as:

[0082] V=2R G b D (6.1-H G ) (2)

[0083] The fuzzy optimization design function F(x) generally takes the minimum value, so it can be expressed as:

[0084] F(X)=2R G b D (H G -6.1) (3)

[0085] Step 2: Establish constraints:

[0086] 1. Limitation of tensile stress on the guide plate:

[0087] Corresponding constraint function:

[0088] 2. Ideally, the elongation of the guide plate is equal to the assembly gap, but due to the influence of processing and assembly errors, the actual elongation is often slightly greater than the assembly gap:

[0089]

[0090] in: ε is 0.0004mm

[0091] but

[0092] Corresponding constraint function:

[0093] 3. Design variable value limits:

[0094]

[0095] The above constraints are all fuzzy constraints, and the mathematical model of fuzzy optimization design of special-shaped guide plates can be obtained:

[0096]

[0097]

[0098] Step 3: Optimization solution:

[0099] There is a transition interval between the allowable tensile stress value of the guide plate from fully allowed to fully unallowed, and the membership function adopts a descending semi-trapezoidal distribution:

[0100]

[0101] The elongation has a fuzzy range of values, but it cannot be less than the assembly gap, so the membership function adopts a right-angle trapezoidal distribution, that is, there is no transition interval in the lower bound:

[0102]

[0103] The range of the design variable is also a fuzzy quantity. For the convenience of description, the constraints in formula (7) can be uniformly expressed as:

[0104]

[0105] Where:

[0106] ——x i The upper bound of the value of (i=1, 2, 3);

[0107] k i ——x i The lower bound of the value of (i = 1, 2, 3)

[0108] Therefore, the membership function adopts trapezoidal distribution.

[0109]

[0110] The upper and lower limits of the transition interval in the membership function are determined by the expansion coefficient method. Lower amplification factor β=0.7~0.95, we can get Δ l U =Δ l L =2δ; x i L = kβ , x i U = k .

[0111] Table 1. Upper and lower limits of fuzzy constraint transition interval

[0112]

[0113] According to the above steps, the objective function, constraint conditions and membership function of fuzzy optimization design are obtained, and the fuzzy optimization mathematical model is transformed into a common optimization model. Figure 2 , 3, 4 are computer programmed, and various parameters are substituted for solving. After the optimal solution is rounded, the main design parameters of the toothed chain special-shaped guide plate are finally determined, including the middle longitudinal height of the waist of the special-shaped guide plate, the radius of the concave arc and the thickness of the guide plate.

[0114] Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions and variations may be made to the embodiments without departing from the principles and spirit of the present invention, and that the scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. A fuzzy optimization design method for a toothed chain special-shaped guide plate, characterized in that: The design method includes the following steps: Step 1: The main design parameters of the guide plate are the middle longitudinal height of the waist H G , radius of the concave arc R G and guide plate thickness b D As the design variable, the objective function is established by maximizing the volume reduction of the guide plate; Step 2: Establish constraint conditions based on the strength limit and elongation requirements of the special-shaped guide plate, determine the value range of the design variables, and obtain the mathematical model of the fuzzy optimization design; Step 3: Establish the membership function of the fuzzy constraint, determine the upper and lower limits of the fuzzy constraint transition interval, transform the fuzzy constraint problem into a non-fuzzy constraint problem, and then use the bounded search method and penalty function method for optimization to obtain two optimal solutions. Combined with the strict restriction conditions of the elongation, the optimal solution is obtained. The specific method of step one is as follows: The middle longitudinal height of the waist has a direct impact on the design of the guide plate parameters H G , radius of the concave arc R G and guide plate thickness b D is the design variable, denoted as: （1） The volume reduced by the guide plate is approximately: （2） Where: H ——Guide plate longitudinal height The fuzzy optimization design function F(X) generally takes the minimum value, which can be expressed as: （3） The specific method of step 2 is as follows: (1) Tensile stress on the guide plate limit: Corresponding constraint function: (4) Where: F t - tight edge tension; —— allowable tensile stress; (2) Elongation of the guide plate Ideally, it is equal to the assembly gap, but due to the influence of processing and assembly errors, the actual elongation is often slightly greater than the assembly gap: （5） Where: F ——elongation compensation force; L ——chain plate hole center distance; D ——chain plate hole diameter; E ——Elastic modulus of the guide plate material; ——Assembly unilateral clearance; ——Extension interference; Corresponding constraint function: (6) (3) Design variable value limits: （7） The above constraints are all fuzzy constraints, and the mathematical model of fuzzy optimization design of special-shaped guide plates can be obtained: （8） The specific method of step three is as follows: (1) Membership function of fuzzy constraints There is a transition interval between the allowable tensile stress value of the guide plate from fully allowed to completely unallowable, so the membership function of formula (4) adopts a descending semi-trapezoidal distribution: （9） The elongation has a fuzzy range of values, but it cannot be less than the assembly gap. Therefore, the membership function of equation (6) adopts a right-angle trapezoidal distribution, that is, there is no transition interval in the lower bound: （10） The range of the design variable is also a fuzzy quantity. For the convenience of description, the constraints in formula (7) are uniformly expressed as: （11） Where: The upper bound of i =1, 2, 3; The lower bound of i =1, 2, 3; Therefore, the membership function of formula (11) adopts trapezoidal distribution: （12） The upper and lower limits of the transition interval in the membership function are determined by the expansion coefficient method. , the lower amplification factor , we can get , ; , ; ; , ; , ; According to the decomposition theorem of fuzzy sets, a series of membership degrees To intercept the fuzzy set with different defense levels, we need to find an optimal value. , transform the fuzzy constraint problem into a non-fuzzy constraint problem: （13） (2) Optimization process ① Using random direction method and When , solve equation (8) to get the minimum value m and maximum value M , establish the membership function of the fuzzy objective function , Upper limit , the lower limit is ,by and 1, m and M As the boundary, the bounded search method is used to solve the problem, and the optimal solution can be obtained. ; ②Use the two-level fuzzy comprehensive evaluation method to determine the optimal level cut set , and then call the penalty function method to solve the transformed general optimization problem: （14） Optimized solution can be obtained ; ③ Compare the elongation in the two solutions , Assembly clearance The closer the assembly clearance is, the ideal value is the optimal solution. .

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