Establishment method of suction curve mathematical model of smoking machine for conventional analysis and mathematical model

Abstract

The invention provides a method for establishing a mathematical model of a suction curve of a smoking machine for conventional analysis and the mathematical model, and the method comprises the following steps: firstly, according to the geometrical relationship of a suction mechanism, establishing geometrical relationships between a piston movement distance x and a connecting rod length l, a crankshaft radius r, a distance h between a fulcrum and a crankshaft center, and a crank angular displacement theta; according to the principle of piston movement, an expression of the suction flow phi based on the geometrical relationship of the suction mechanism is established; simplifying and unifying the expression of the suction flow phi; and finally, converting the expression of the suction flow phi according to the corresponding relation of the piston motion, the ventilation capacity and the suction duration to obtain a mathematical model. According to the method and the obtained mathematical model, the suction curve of the smoking machine for conventional analysis is summarized, and a unified suction curve mathematical model is formed, so that a research basis is provided for research and design of a smoking mechanism.

Description

Technical Field

[0001] This invention relates to the field of tobacco detection technology, and more specifically, to a method and mathematical model for establishing a mathematical model of the smoking curve of a conventional analytical smoking machine. Background Technology

[0002] Smoke gas analysis is of paramount importance in the tobacco industry's quality inspection and a key focus of global tobacco technology. It not only relates to the development of the tobacco industry itself but also attracts the attention of the entire society.

[0003] In conventional analysis, the smoking machine, used as a tool in the testing process, does not measure data itself; its main function is to capture smoke generated during cigarette combustion. Numerous studies have shown that the technical conditions of the smoking machine affect the smoke capture process, thus influencing the results of smoke analysis. International and domestic joint experiments have also demonstrated differences in test results between different laboratories and between different brands and models of smoking machines. Therefore, the characteristics of the smoking machine itself can affect the conclusions of smoke analysis.

[0004] The suction curve is a crucial parameter affecting the collection effect of a fumigation machine. GB16450-2004, "Definition and Standard Conditions for Fumigation Machines for Routine Analysis," stipulates that the suction curve of a fumigation machine should be bell-shaped. The standard provides three types of crankshaft piston-type suction mechanisms, such as... Figure 1 As shown.

[0005] How to summarize the three types of suction curves and form a mathematical model for analysis is a technical problem that urgently needs to be solved.

[0006] In order to solve the above problems, people have been seeking an ideal technological solution. Summary of the Invention

[0007] The purpose of this invention is to address the shortcomings of existing technologies by providing a method and mathematical model for establishing a mathematical model of the suction curve of a conventional analytical smoking machine, which summarizes and generalizes the suction curve of the smoking machine to form a unified mathematical model of the suction curve, so as to provide a research basis for the research and design of smoking institutions.

[0008] To achieve the above objectives, the technical solution adopted by this invention is: a method for establishing a mathematical model of the suction curve of a conventional analytical smoking machine, wherein the conventional analytical smoking machine is a piston-type smoking machine, and the suction mechanism of the piston-type smoking machine includes a crankshaft, a crank, a connecting rod, and a piston, wherein the crankshaft drives the piston to move through the crank and the connecting rod, comprising the following steps:

[0009] Step 1) Based on the geometric relationship of the suction mechanism, establish the geometric relationship between the piston movement distance x and the connecting rod length l, crankshaft radius r, distance h between the fulcrum and the crankshaft center, and crank angular displacement θ;

[0010] Step 2) Based on the principle of piston motion, establish an expression for the suction flow rate φ based on the geometric relationship of the suction mechanism;

[0011] Step 3) Since the distance h between the fulcrum and the center of the crankshaft is more than ten times the crankshaft radius r, the approximate values ​​in the calculation of the distance h between the fulcrum and the center of the crankshaft and the crankshaft radius r in the expression for the suction flow rate φ are simplified to obtain a simplified expression for the suction flow rate φ.

[0012] Step 4) Based on the correspondence between piston motion, gas exchange capacity, and suction duration, the expression for suction flow rate φ is transformed to obtain a mathematical model that only includes gas exchange capacity, suction duration, and crank rotation time as factors.

[0013] Based on the above, there are three standard composition forms of the suction mechanism in the piston-type smoking machine. In steps 1) and 2), the suction mechanisms of different composition forms are processed separately. In step 3), the expression of the suction flow rate φ of the three suction mechanisms is unified through simplification processing with reduction as the main method.

[0014] Based on the above, in the first structure, the piston reciprocates in a fixed direction, the front end of the connecting rod is hinged to the rear end of the piston, and the rear end of the connecting rod is hinged to the crank.

[0015] Under this structure, the expression for the suction flow rate φ is: Φ=Aωr sinωt-----(1);

[0016] in,

[0017] A—Piston cross-sectional area;

[0018] ω — the angular velocity of the crank;

[0019] t — crank rotation time.

[0020] Based on the above, in the second structure, the tail end of the piston is fixed to the front end of the connecting rod, the front end of the piston cylinder is provided with a hinge point, and the tail end of the connecting rod is hinged to the crank.

[0021] Under this structure, the expression for the suction flow rate φ is:

[0022]

[0023] Based on the above, since the distance h between the fulcrum and the crankshaft center is more than ten times the crankshaft radius r, in formula (2), the approximate denominator is denoted as h. After simplification, formula (2) is simplified to:

[0024] Φ = Aωrsinωt.

[0025] Based on the above, in the third structure, the piston reciprocates in a fixed direction, the front end of the connecting rod is fixed to the rear end of the piston, and the rear end of the connecting rod is hinged to the crank.

[0026] Under this structure, the expression for the suction flow rate φ is:

[0027]

[0028] Based on the above, in step 4), among the three structures, the piston travels the longest distance when the crank rotates 180°, the gas exchange capacity of the piston in one cycle is 2Ar, and the time for the crank to rotate 180° is the pumping duration. Therefore, the mathematical model can be converted to:

[0029]

[0030] This yields a general mathematical model for the suction curve of the smoking machine, where Q represents the air exchange capacity and T represents the suction duration.

[0031] A mathematical model for analyzing the suction curve of a conventional smoking machine is obtained through the aforementioned method.

[0032] The mathematical model is as follows:

[0033]

[0034] Wherein, φ -- suction flow rate;

[0035] Q – Ventilation capacity;

[0036] T – Duration of suction;

[0037] t — crank rotation time.

[0038] This invention has significant substantive features and remarkable progress compared to existing technologies. Specifically, this invention utilizes the basic structural form of the suction mechanism in conventional analytical smoking machines, approaches the problem from the perspective of its geometric relationships, establishes a multi-parameter expression with suction flow rate as the target, and can unify the suction flow rate expression for three different structural forms of suction mechanisms. After unification, by leveraging the characteristics of piston motion and the relationship between air exchange capacity, suction duration, and crank rotation time, the expression can be converted into a form that only includes air exchange capacity, suction duration, and crank rotation time parameters. These parameters further eliminate geometric parameters, retaining only the parameters that need to be monitored during the use of the smoking machine, thus forming a universal mathematical model. This provides a theoretical basis for in-depth analysis of the suction mechanism of smoking machines and the design of smoking mechanisms. Attached Figure Description

[0039] Figure 1 This is a schematic diagram of the suction mechanism in a conventional analytical smoking machine of the present invention. Detailed Implementation

[0040] The technical solution of the present invention will be further described in detail below through specific embodiments.

[0041] like Figure 1 As shown, a method for establishing a mathematical model of the suction curve of a conventional analytical smoking machine is presented. The conventional analytical smoking machine is a piston-type smoking machine. The suction mechanism of the piston-type smoking machine includes a crankshaft, a crank, a connecting rod, and a piston. The crankshaft drives the piston through the crank and connecting rod. According to standard GB16450-2004 "Definition and Standard Conditions for Smoking Machines for Conventional Analysis," the suction curve of the smoking machine should be bell-shaped. The standard provides three types of crankshaft-piston suction mechanisms, such as... Figure 1 As shown.

[0042] Where A represents the cross-sectional area of ​​the piston, i.e., the effective working area of ​​the piston; points P and H are the fulcrum; l is the length of the connecting rod; h is the distance between the fulcrum and the center of the crankshaft; r is the crankshaft radius; and θ is the crank angular displacement. In the first structure, point P is the hinge point; in the second structure, point H is the hinge point and point P is the fixed point; and in the third structure, point P is the fixed point.

[0043] First, in step 1), it is necessary to establish the geometric relationship between the piston movement distance x and the connecting rod length l, crankshaft radius r, distance h between the fulcrum and the crankshaft center, and crank angular displacement θ based on the geometric relationship of the suction mechanism.

[0044] With the first typical structure, Figure 1 Let's take A as an example for explanation.

[0045] The connecting rod length *l*, the crankshaft radius *r*, and the distance *h* between the fulcrum P and the crankshaft center form a triangle. The angle through which the crank rotates is the angle between the connecting rod length and the crankshaft radius. According to the law of cosines, the relationship is as follows:

[0046] l 2 =r 2 +h 2 -2rhsinθ Where: l——connecting rod length, r——crankshaft radius, h——distance between fulcrum P and crankshaft center, θ——angle of crank rotation.

[0047] Therefore, we can conclude that:

[0048]

[0049] Let x be the distance the piston moves, which can be expressed as:

[0050]

[0051] When θ is 0, h reaches its maximum, which is the sum of the connecting rod length and the crankshaft radius, l+r. This is set as the zero point of x. When θ is 180°, h reaches its minimum, which is lr. At this time, x reaches its maximum value of 2r.

[0052] Step 2) Based on the principle of piston motion, establish an expression for the suction flow rate φ based on the geometric relationship of the suction mechanism;

[0053] The expression for the change of the cylinder volume V over time during the suction process is:

[0054]

[0055] Where A is the piston cross-sectional area, ω is the angular velocity of the crank, and t is the crank rotation time.

[0056] By differentiating the volume with respect to time, the pumping flow rate Φ can be obtained:

[0057] Φ=Aωrsinωt----------------------------------------------(1);

[0058] Using the same method, for the second structure, Figure 1 The calculation of the structure shown in B, omitting the geometric calculations, yields the following expression for its pumping flow rate:

[0059]

[0060] Step 3) Since the distance h between the fulcrum and the crankshaft center is more than ten times the crankshaft radius r, the approximate values ​​in the calculation of the distance h between the fulcrum and the crankshaft center and the crankshaft radius r in the expression for the suction flow rate φ are simplified. In formula (2), the approximate value of the denominator is denoted as h. After simplification, formula (2) is simplified to:

[0061] Φ = Aωr sinωt.

[0062] Using the same method, for the third structure, Figure 1 The calculations are performed on the structure shown in C, with the geometric calculations omitted. The piston movement distance x in structure C can be expressed as:

[0063] x=r|r cosωt

[0064] The expression for its suction flow rate is:

[0065]

[0066] It can be seen that the suction flow curves generated by the three suction mechanisms can all be represented by the same mathematical model, namely, a sine function curve. The shape of this curve is bell-shaped, which meets the standard requirements.

[0067] Step 4) Based on the correspondence between piston motion, gas exchange capacity and pumping duration, the expression for pumping flow rate φ is transformed to obtain a mathematical model that only includes gas exchange capacity, pumping duration and crank rotation time as factors.

[0068] Specifically, among the three structures, the piston travels the longest distance when the crank rotates 180°, the gas exchange capacity in one piston cycle is 2Ar, and the time for the crank to rotate 180° is the pumping duration. Therefore, the mathematical model can be converted to:

[0069]

[0070] This yields a general mathematical model for the suction curve of the smoking machine, where Q represents the air exchange capacity and T represents the suction duration.

[0071] That is, the final mathematical model is:

[0072] Wherein, φ -- suction flow rate;

[0073] Q – Ventilation capacity;

[0074] T – Duration of suction;

[0075] t — crank rotation time.

[0076] This mathematical model provides a theoretical basis for in-depth research on the suction mechanism of smoking machines and for designing the suction mechanism. The air exchange capacity is the parameter data of the piston, and the suction duration and crank rotation time can be obtained through the configured motor parameters. These parameters are easier to obtain and use in research work than geometric parameters, which facilitates the study of suction curves.

[0077] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them; although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications can still be made to the specific implementation of the present invention or equivalent substitutions can be made to some technical features without departing from the spirit of the technical solutions of the present invention, and all such modifications and substitutions should be covered within the scope of the technical solutions claimed in the present invention.

Claims

1. A method for establishing a mathematical model of the suction curve of a conventional analytical smoking machine, wherein the conventional analytical smoking machine is a piston-type smoking machine, and the suction mechanism of the piston-type smoking machine includes a crankshaft, a crank, a connecting rod, and a piston, wherein the crankshaft drives the piston to move through the crank and the connecting rod, characterized in that: Includes the following steps: Step 1) Based on the geometric relationship of the suction mechanism, establish the geometric relationship between the piston movement distance x and the connecting rod length l, crankshaft radius r, distance h between the fulcrum and the crankshaft center, and crank angular displacement θ; Step 2) Based on the principle of piston motion, establish an expression for the suction flow rate φ based on the geometric relationship of the suction mechanism; Step 3) Since the distance h between the fulcrum and the center of the crankshaft is more than ten times the crankshaft radius r, the approximate values ​​in the calculation of the distance h between the fulcrum and the center of the crankshaft and the crankshaft radius r in the expression for the suction flow rate φ are simplified to obtain a simplified expression for the suction flow rate φ. Step 4) Based on the correspondence between piston motion, gas exchange capacity, and suction duration, the expression for suction flow rate φ is transformed to obtain a mathematical model that only includes gas exchange capacity, suction duration, and crank rotation time as factors.

2. The method for establishing a mathematical model of the suction curve of a conventional analysis smoking machine according to claim 1, characterized in that: There are three standard composition forms of the suction mechanism in the piston-type smoking machine. In steps 1) and 2), the suction mechanisms of different composition forms are processed separately. In step 3), the expression of the suction flow rate φ of the three suction mechanisms is unified by the simplification process mainly based on reduction.

3. The method for establishing a mathematical model of the suction curve of a conventional analysis smoking machine according to claim 2, characterized in that: In the first structure, the piston reciprocates in a fixed direction, the front end of the connecting rod is hinged to the rear end of the piston, and the rear end of the connecting rod is hinged to the crank. Under this structure, the expression for the suction flow rate φ is: Φ=Aωr sinωt-----(1); in, A—Piston cross-sectional area; ω — the angular velocity of the crank; t — crank rotation time.

4. The method for establishing a mathematical model of the suction curve of a conventional analysis smoking machine according to claim 3, characterized in that: In the second structure, the tail end of the piston is fixed to the front end of the connecting rod, the front end of the piston cylinder is provided with a hinge point, and the tail end of the connecting rod is hinged to the crank. Under this structure, the expression for the suction flow rate φ is:

5. The method for establishing a mathematical model of the suction curve of a conventional analytical smoking machine according to claim 4, characterized in that: Since the distance h between the fulcrum and the crankshaft center is more than ten times the crankshaft radius r, in formula (2), the approximate denominator is denoted as h. After simplification, formula (2) is reduced to: Φ = Aωr sinωt.

6. The method for establishing a mathematical model of the suction curve of a conventional analytical smoking machine according to claim 5, characterized in that: In the third structure, the piston reciprocates in a fixed direction, the front end of the connecting rod is fixed to the rear end of the piston, and the rear end of the connecting rod is hinged to the crank. Under this structure, the expression for the suction flow rate φ is:

7. The method for establishing a mathematical model of the suction curve of a conventional analytical smoking machine according to claim 6, characterized in that: In step 4), among the three structures, the piston travels the longest distance when the crank rotates 180°, the gas exchange capacity of the piston in one cycle is 2Ar, and the time for the crank to rotate 180° is the pumping duration. Therefore, the mathematical model can be converted to: This yields a general mathematical model for the suction curve of the smoking machine, where Q represents the air exchange capacity and T represents the suction duration.

8. A mathematical model for analyzing the suction curve of a conventional smoking machine, characterized in that: Obtained by the method described in any one of claims 1-7; The mathematical model is as follows: Wherein, φ -- suction flow rate; Q – Ventilation capacity; T – Duration of suction; t — crank rotation time.

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