A design method for leaf spring of Stirling generator

Abstract

A design method for a leaf spring of a Stirling generator comprises the following steps: Step S1: constructing a leaf spring optimization model: S and K The ratio of Z The leaf spring optimization model is built with the minimum value as the goal, step S2: generating an initial population under the constraint conditions; step S3: optimizing the initial population that meets the constraint conditions using a chaos algorithm, and step S4: solving the optimal parameters of the leaf spring using a particle swarm algorithm. The present invention can ensure both the performance of the leaf spring and the lightweight of the leaf spring.

Description

Technical Field

[0001] The invention relates to a Stirling generator leaf spring, and in particular to a design method for a Stirling generator leaf spring. Background Art

[0002] The free piston Stirling engine is an external combustion, closed cycle, reciprocating piston type energy conversion device, which eliminates the complex traditional crank-connecting rod structure and has the advantages of simple structure, low vibration, low noise and long life. The Stirling generator can convert various new alternative energy and low-grade energy into a power or electrical mechanical device, with a wide range of energy sources, and can utilize almost all existing heat sources.

[0003] Stirling engines can be divided into crank-connecting rod type and free piston type, which are further divided into α type, β type and γ type. In the β type free piston Stirling engine, the leaf spring not only provides radial support for the moving parts (valve piston and power piston), maintains the sealing gap between the piston and the cylinder during the movement, but also provides sufficient axial stiffness for the reciprocating vibration of the piston. Therefore, the leaf spring plays an important role in ensuring the gap sealing of the generator, reducing friction loss, and improving the reliability and service life of the whole machine.

[0004] When designing a leaf spring, it should be ensured that it has a small mass, is simple to manufacture, easy to assemble, and has a certain service life. Not only that, it is also necessary to ensure that the leaf spring does not break during the operation of the Stirling. A large leaf spring mass will reduce the power of the entire Stirling generator system, affect the operation of the Stirling generator, and reduce the reliability of the Stirling generator. Therefore, it is required that the mass of the leaf spring should be as light as possible while ensuring the spring stiffness and fatigue life. The lightweighting of the leaf spring means that the overall mass of the leaf spring is reduced as much as possible while ensuring the performance of the leaf spring, making the Stirling engine lighter as a whole. While improving the economy and portability of the device, it also improves the overall performance of the Stirling engine, which is of great significance to the application of Stirling in the aerospace field.

[0005] The leaf springs widely used nowadays are mostly cantilever type, and the design form is mostly involute type, using the slow wire cutting process to cut the required shape of the involute on a whole frame of steel sheets. The involute design is very helpful in improving the radial-axial stiffness ratio of the leaf spring, optimizing the stress distribution, adapting to high-frequency working conditions, and improving the overall reliability of the Stirling system. How to ensure the performance of the leaf spring while ensuring the lightweight of the leaf spring is a problem that the Stirling generator needs to solve at present. Summary of the invention

[0006] The technical problem to be solved by the present invention is to overcome the deficiencies of the above-mentioned background technology and provide a design method for a Stirling generator leaf spring, which can ensure both the performance of the leaf spring and the lightness of the leaf spring.

[0007] The technical solution adopted by the present invention to solve the technical problem is a design method of a Stirling generator leaf spring, comprising the following steps:

[0008] Step S1: Building a leaf spring optimization model:

[0009] by S and K The ratio of Z The leaf spring optimization model is built with the minimum value as the goal. The specific optimization model expression is as follows:

[0010]

[0011] In the formula, S represents the ratio of maximum stress to axial stiffness, K represents the ratio of radial stiffness to axial stiffness, Z represents the lightweight factor, represents the maximum stress of the leaf spring, f represents the natural frequency of the leaf spring, The ratio of maximum stress to axial stiffness is The function of The ratio of radial stiffness to axial stiffness is The function of The lightweight factor is about The function of The maximum stress of the leaf spring is about The function of The leaf spring natural frequency is about The function of l 1 represents the penalty factor for the maximum stress, l 2 represents the penalty factor for the leaf spring natural frequency, l 3 represents the cantilever slot width penalty factor, l 4 represents the leaf spring thickness penalty factor, α represents the leaf spring performance weight factor, β represents the leaf spring lightweight weight factor, and α + β =1, α >0, β >0; s lim represents the maximum stress limit value, flim Indicates the leaf spring natural frequency limit value, Indicates the cantilever slot width limit value, Indicates the thickness limit of the leaf spring; n =13, x 1 Indicates the leaf spring thickness, x 2 represents the eccentricity of the involute, x 3 represents the involute radius, x 4 represents the cantilever slot width, x 5 represents the inner arc radius of the outer water droplet, x 6 Indicates the outer arc radius of the outer water droplet, x 7 Indicates the radius of the arc at the end of the outer water droplet, x 8 Indicates the inner arc radius of the inner water droplet, x 9 Indicates the radius of the outer arc of the inner water droplet, x 10 Indicates the arc radius of the inner water droplet end, x 11 represents the leaf spring material density, x 12 Indicates the threaded hole radius, x 13 Indicates the rod through hole radius;

[0012] Step S2: Generate an initial population under the constraints;

[0013] Step S3: Use the chaos algorithm to optimize the initial population that meets the constraints.

[0014] Step S4: Using the particle swarm algorithm to solve the optimal parameters of the leaf spring.

[0015] Further, in step S1, the maximum stress limit value s lim It is expressed as:

[0016]

[0017] In the formula, s -1 represents the fatigue limit value of the leaf spring material, m Represents the safety factor, which is in the range of (0,1).

[0018] Further, in step S1, the leaf spring natural frequency limit value f lim It is expressed as:

[0019] .

[0020] Further, in step S1, the cantilever slot width limit value It is expressed as:

[0021]

[0022] In the formula, d min Indicates the lower limit of the cantilever slot width empirical interval, d max Indicates the upper limit of the cantilever slot width experience range.

[0023] Further, in step S1, the leaf spring thickness limit value It is expressed as:

[0024]

[0025] In the formula, t max Indicates the upper limit of the empirical interval of leaf spring thickness, t min Indicates the lower limit of the empirical range of leaf spring thickness.

[0026] Furthermore, in step S1, the leaf spring is lightweighted in two dimensions, namely, structural lightweighting and material lightweighting. The structural lightweighting is measured by the ratio of the axial stiffness to the mass of the leaf spring, and the material lightweighting is measured by the density of the material used to make the leaf spring. Z The calculation formula is as follows:

[0027]

[0028] In the formula, represents the axial stiffness, represents the mass of the leaf spring, The axial stiffness is about The function of Indicates the mass of the leaf spring with respect to The function of Indicates the density of the material used to make the leaf spring. m 1 represents the weight factor of the lightweight structure, m 2 represents the weight factor for material lightweighting, and m 1 + m 2 =1, m 1 >0, m 2 >0.

[0029] Further, in step S1, the maximum stress and axial stiffness ratio S The calculation formula is as follows:

[0030]

[0031] In the formula, k z represents the axial stiffness, The axial stiffness is about function.

[0032] Further, in step S1, the ratio of radial stiffness to axial stiffness is K The calculation formula is as follows:

[0033] In the formula, k r represents the radial stiffness, The radial stiffness is about The function of k z represents the axial stiffness, The axial stiffness is about function.

[0034] Further, in step S1, the leaf spring natural frequency f The calculation formula is as follows:

[0035]

[0036] In the formula, k z represents the axial stiffness, m represents the mass of the leaf spring, The axial stiffness is about The function of Indicates the mass of the leaf spring with respect to function.

[0037] Furthermore, the leaf spring includes a leaf spring body, which is a flat disc structure. A rod through hole is opened in the center of the leaf spring body, and three cantilevers are symmetrically arranged with the rod through hole as the center. The cantilever adopts a hollow spiral structure, and the spiral line of the spiral structure is an involute. An inner water drop structure is provided at the center starting end of the spiral line structure, and an outer water drop structure is provided at the end end. The inner water drop structure, the spiral structure, and the outer water drop structure are connected to each other to form the cantilever of the leaf spring; the inner water drop structure is the same as the outer water drop structure, and both are composed of three arcs, namely, an inner arc, an end arc, and an outer arc. The inner arc is connected and tangent to the end arc, and the end arc is connected and tangent to the outer arc; a plurality of threaded holes are evenly distributed on the circumferential edge of the leaf spring body.

[0038] Compared with the prior art, the advantages of the present invention are as follows:

[0039] The present invention stipulates various parameters of the leaf spring within an appropriate range, unifies the various parameters of the leaf spring with a single-valued function, and adds parameters for measuring lightweight. The lightweight of the leaf spring is divided into two dimensions, namely structural lightweight and material lightweight. The structural lightweight is measured by the ratio of axial stiffness to the mass of the leaf spring, and the material lightweight is measured by the density of the material used to make the leaf spring. The multivariate parameter optimization of the leaf spring is completed by a particle swarm algorithm based on chaotic mapping, and the optimal parameters of the leaf spring are obtained, which can ensure both the performance of the leaf spring and the lightweight of the leaf spring. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] Figure 1 It is a schematic diagram of the three-dimensional structure of the leaf spring according to an embodiment of the present invention.

[0041] Figure 2 It is a schematic diagram of the planar structure of the leaf spring according to an embodiment of the present invention.

[0042] Figure 3 yes Figure 1 A schematic structural diagram of the inner / outer water droplet structure of the illustrated embodiment.

[0043] Figure 4 4 is a flow chart of a leaf spring design method according to an embodiment of the present invention.

[0044] 1—leaf spring body, 2—cantilever, 3—inner water drop structure, 4—outer water drop structure, 5—rod through hole, 6—threaded hole, 7—inner arc, 8—end arc, 9—outer arc. DETAILED DESCRIPTION

[0045] The present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0046] Reference Figure 1-3 The leaf spring of this embodiment is a flexible leaf spring, including a leaf spring body 1. The leaf spring body 1 is a flat disc structure. A rod through hole 5 is opened in the center of the leaf spring body 1. Three cantilevers 2 are symmetrically arranged around the rod through hole 5. The cantilever 2 adopts a hollow spiral structure. The spiral line of the spiral structure is an involute. An inner water drop structure 3 is provided at the center starting end of the spiral line structure, and an outer water drop structure 4 is provided at the end end. The inner water drop structure 3, the spiral structure, and the outer water drop structure 4 are interconnected to form the cantilever 2 of the flexible leaf spring.

[0047] The inner water drop structure 3 is the same as the outer water drop structure 4, and is composed of three arcs, namely an inner arc 7, an end arc 8, and an outer arc 9. The inner arc 7 is connected to and tangent to the end arc 8, and the end arc 8 is connected to and tangent to the outer arc 9.

[0048] Six threaded holes 6 are evenly distributed on the circumferential edge of the leaf spring body 1. The threaded holes 6 and the rod through hole 5 are independent of other structures.

[0049] Reference Figure 4 This embodiment proposes a design method for a Stirling generator leaf spring, comprising the following steps:

[0050] Step S1: building a leaf spring optimization model;

[0051] In order to ensure the gap sealing and oil-free lubrication of the Stirling generator, increase the service life of the leaf spring and achieve the lightweight of the leaf spring, various parameters of the leaf spring are changed to S and K The ratio of Z The leaf spring optimization model is built with the minimum value as the goal. The specific optimization model expression is as follows:

[0052]

[0053] In the formula, S represents the ratio of maximum stress to axial stiffness, K represents the ratio of radial stiffness to axial stiffness, Z represents the lightweight factor, represents the maximum stress of the leaf spring, f represents the natural frequency of the leaf spring, x 4 represents the cantilever slot width, x 1 Indicates the leaf spring thickness, The maximum stress and axial stiffness ratio is about The function of The ratio of radial stiffness to axial stiffness is The function of The lightweight factor is about The function of The maximum stress of the leaf spring is about The function of The leaf spring natural frequency is about The function of l 1 represents the penalty factor for the maximum stress, l 2 represents the penalty factor for the leaf spring natural frequency, l 3 represents the cantilever slot width penalty factor, l 4 represents the leaf spring thickness penalty factor, α represents the leaf spring performance weight factor, β represents the leaf spring lightweight weight factor, and α +β =1, α >0, β >0; s lim represents the maximum stress limit value, f lim Indicates the leaf spring natural frequency limit value, Indicates the cantilever slot width limit value, Indicates the leaf spring thickness limit value.

[0054] In this embodiment, the parameters of the leaf spring include the leaf spring thickness x 1 , involute eccentricity x 2 , involute radius x 3 , cantilever slot width x 4 、Inner arc radius of outer water drop x 5 , the outer arc radius of the outer water drop x 6 , the arc radius of the outer water drop end x 7 、Inner arc radius of inner water drop x 8 、Radius of the outer arc of the inner water drop x 9 , the arc radius of the inner water drop end x 10 , Leaf spring material density x 11 , threaded hole radius x 12 , Rod hole radius x 13 There are 13 parameters in total. In this embodiment, a small round gasket is added to bear the force during the ANSYS stress simulation. The small gasket also has two parameters: gasket radius x 14 , Gasket thickness x 15 , so these two parameters can be added, a total of 18 parameters, so here x n Subscript n It should be 15. l 1 , 2 , l 3 , l 4 The corresponding term is a constraint term, which converts the optimization constraint into a penalty term in the function, making g an unconstrained single-value optimization function.

[0055] The involute eccentricity refers to the distance that the involute deviates from the base circle center, that is, the distance between the actual base circle center of the involute and the theoretical base circle center. The involute radius refers to the radius of the involute base circle.

[0056] In order to prevent the maximum stress of the spring from exceeding 60% of the fatigue limit of the spring, a penalty factor is used to limit the maximum stress and the natural frequency of the leaf spring.

[0057] Maximum stress limit s lim It is expressed as:

[0058] In the formula, s -1 represents the fatigue limit value of the leaf spring material, m Represents the safety factor, which is in the range of (0,1).

[0059] Leaf spring natural frequency limit value It is expressed as:

[0060] .

[0061] Cantilever slot width limit It is expressed as:

[0062] In the formula, d min Indicates the lower limit of the cantilever slot width empirical interval, d max Indicates the upper limit of the cantilever slot width experience range.

[0063] Leaf spring thickness limit It is expressed as:

[0064] In the formula, t max Indicates the upper limit of the empirical interval of leaf spring thickness, t min Indicates the lower limit of the empirical range of leaf spring thickness.

[0065] The lightweighting of leaf springs can be divided into two dimensions: structural lightweighting and material lightweighting. Structural lightweighting is measured by the ratio of axial stiffness to the mass of leaf springs, and material lightweighting is measured by the density of the material used to make leaf springs. Therefore, the lightweight coefficient Z is proposed as a measure of leaf spring lightweighting. Z The calculation formula is as follows:

[0066] In the formula, represents the axial stiffness, represents the mass of the leaf spring, The axial stiffness is about The function of Indicates the mass of the leaf spring with respect to The function of Indicates the density of the material used to make the leaf spring. m 1 It represents the weight factor of structural lightweighting, that is, the weight ratio of the influence of leaf spring structure on leaf spring lightweight index. m 2 represents the weight factor of material lightweighting, that is, the weight ratio of the influence of the leaf spring material itself on the leaf spring lightweight parameters, and m 1 + m 2 =1, m 1 >0, m 2 >0.

[0067] In the process of leaf spring optimization, the radial stiffness of the spring should be increased as much as possible to reduce the stress distribution while satisfying the axial stiffness. K、 Ratio of maximum stress to axial stiffness S , as the optimization parameter of the leaf spring. K The larger the diameter, the greater the radial rigidity under the same axial rigidity, which can better support the power piston and ensure gap sealing and oil-free lubrication; S The smaller the radial stiffness is, the smaller the stress distribution is when the same axial stiffness and axial displacement are met, which is beneficial to prolonging the service life of the leaf spring. K , maximum stress to axial stiffness ratio S The leaf spring natural frequency f The calculation formula is as follows:

[0068] In the formula, represents the maximum stress of the leaf spring, k z represents the axial stiffness, k r represents the radial stiffness, m represents the mass of the leaf spring, The maximum stress of the leaf spring is about The function of The axial stiffness is about The function of The radial stiffness is about The function of Indicates the mass of the leaf spring with respect to Function of

[0069] Furthermore, in order to ensure the accuracy and effectiveness of the optimization results, the following constraints need to be imposed on the optimization model:

[0070] (1) The maximum stress of the leaf spring is less than the fatigue limit of the leaf spring.

[0071] (2) In order to improve the optimization efficiency, the cantilever groove width of the leaf spring should be within the empirical range and must be greater than the processing accuracy.

[0072] (3) In order to improve the optimization efficiency, the thickness of the leaf spring should be within the empirical range and must be greater than the processing accuracy.

[0073] The fatigue strength of the leaf spring is measured by the fatigue limit of the leaf spring material. In order to increase the service life of the leaf spring, the maximum stress of the leaf spring should not exceed 60% of the fatigue limit. During the operation of the Stirling generator, the frequency is up to 60Hz and generally does not exceed 80Hz. During the operation of the high-frequency Stirling engine, the frequency is generally around 80Hz and does not exceed 100Hz. Therefore, under most working conditions, the natural frequency of the leaf spring should be at least greater than 100Hz.

[0074] Step S2: Generate an initial population under the constraints;

[0075] Step S3: Use the chaos algorithm to optimize the initial population that meets the constraints.

[0076] Step S4: Use the particle swarm algorithm to solve the optimal parameters of the leaf spring, specifically:

[0077] Under a set of leaf spring parameters, determine whether the maximum stress of the leaf spring, the natural frequency of the leaf spring, the thickness of the leaf spring, and the cantilever slot width meet the constraint conditions. If so, the set of parameters is the optimal parameter of the leaf spring; if not, the particles that exceed the limit are penalized and return to step S3.

[0078] The chaos algorithm and particle swarm algorithm used in this example are existing algorithms.

[0079] The present invention stipulates various parameters of the leaf spring within an appropriate range, unifies the various parameters of the leaf spring with a single-valued function, and adds parameters for measuring lightweight. The lightweight of the leaf spring is divided into two dimensions, namely structural lightweight and material lightweight. The structural lightweight is measured by the ratio of axial stiffness to the mass of the leaf spring, and the material lightweight is measured by the density of the material used to make the leaf spring. The multivariate parameter optimization of the leaf spring is completed by a particle swarm algorithm based on chaotic mapping, and the optimal parameters of the leaf spring are obtained, which can ensure both the performance of the leaf spring and the lightweight of the leaf spring.

[0080] Those skilled in the art may make various modifications and variations to the present invention. If these modifications and variations are within the scope of the claims of the present invention and their equivalents, then these modifications and variations are also within the protection scope of the present invention.

[0081] The contents not described in detail in the specification are prior art known to those skilled in the art.

Claims

1. A method for designing a leaf spring of a Stirling generator, characterized in that: The following steps are involved: Step S1: Building a leaf spring optimization model: by S and K The ratio of Z The leaf spring optimization model is built with the minimum value as the goal. The specific optimization model expression is as follows: In the formula, S represents the ratio of maximum stress to axial stiffness, K represents the ratio of radial stiffness to axial stiffness, Z represents the lightweight factor, represents the maximum stress of the leaf spring, f represents the natural frequency of the leaf spring, The ratio of maximum stress to axial stiffness is The function of The ratio of radial stiffness to axial stiffness is The function of The lightweight factor is about The function of The maximum stress of the leaf spring is about The function of The leaf spring natural frequency is about The function of λ 1 represents the penalty factor for the maximum stress, λ 2 represents the penalty factor of the leaf spring natural frequency, λ 3 represents the cantilever slot width penalty factor, λ 4 represents the leaf spring thickness penalty factor, α represents the leaf spring performance weight factor, β represents the leaf spring lightweight weight factor, and α + β =1, α >0, β >0; σ lim represents the maximum stress limit value, f lim Indicates the leaf spring natural frequency limit value, Indicates the cantilever slot width limit value, Indicates the thickness limit of the leaf spring; n =13, x 1 represents the thickness of the leaf spring, x 2 represents the eccentricity of the involute, x 3 represents the involute radius, x 4 represents the cantilever slot width, x 5 represents the inner arc radius of the outer water droplet, x 6 represents the radius of the outer arc of the outer water droplet. x 7 represents the arc radius of the outer water drop end, x 8 represents the radius of the inner arc of the inner water droplet. x 9 represents the radius of the outer arc of the inner water droplet. x 10 Indicates the arc radius of the inner water droplet end, x 11 represents the leaf spring material density, x 12 Indicates the threaded hole radius, x 13 Indicates the rod through hole radius; Step S2: Generate an initial population under the constraints; Step S3: Use the chaos algorithm to optimize the initial population that meets the constraints. Step S4: Using the particle swarm algorithm to solve the optimal parameters of the leaf spring.

2. The design method of the Stirling generator leaf spring according to claim 1, characterized in that: In step S1, the maximum stress limit value σ lim It is expressed as: In the formula, σ -1 represents the fatigue limit value of the leaf spring material, μ Represents the safety factor, which is in the range of (0,1).

3. The design method of the Stirling generator leaf spring according to claim 1, characterized in that: In step S1, the leaf spring natural frequency limit value f lim It is expressed as: 。 4. The design method of the Stirling generator leaf spring according to claim 1, characterized in that: In step S1, the cantilever slot width limit value It is expressed as: In the formula, d min Indicates the lower limit of the cantilever slot width empirical interval, d max Indicates the upper limit of the cantilever slot width experience range.

5. The design method of the Stirling generator leaf spring according to claim 1, characterized in that: In step S1, the leaf spring thickness limit value It is expressed as: In the formula, t max Indicates the upper limit of the empirical interval of leaf spring thickness, t min Indicates the lower limit of the empirical range of leaf spring thickness.

6. The design method of a Stirling generator leaf spring according to claim 1, characterized in that: In step S1, the leaf spring is lightweighted in two dimensions, namely, structural lightweighting and material lightweighting. The structural lightweighting is measured by the ratio of the axial stiffness to the mass of the leaf spring, and the material lightweighting is measured by the density of the material used to make the leaf spring. Z The calculation formula is as follows: In the formula, represents the axial stiffness, represents the mass of the leaf spring, The axial stiffness is about The function of Indicates the mass of the leaf spring with respect to The function of Indicates the density of the material used to make the leaf spring. μ 1 represents the weight factor of lightweight structure, μ 2 represents the weight factor of material lightweighting, and μ 1+ μ 2=1, μ 1>0, μ 2>0.

7. The method for designing a Stirling generator leaf spring according to claim 6, characterized in that: In step S1, the maximum stress and axial stiffness ratio S The calculation formula is as follows: In the formula, k z represents the axial stiffness, The axial stiffness is about function.

8. The method for designing a Stirling generator leaf spring according to claim 6, characterized in that: In step S1, the ratio of radial stiffness to axial stiffness is K The calculation formula is as follows: In the formula, k r represents the radial stiffness, The radial stiffness is about The function of k z represents the axial stiffness, The axial stiffness is about function.

9. The method for designing a Stirling generator leaf spring according to claim 6, characterized in that: In step S1, the leaf spring natural frequency f The calculation formula is as follows: In the formula, k z represents the axial stiffness, m represents the mass of the leaf spring, The axial stiffness is about The function of Indicates the mass of the leaf spring with respect to function.

10. The method for designing a Stirling generator leaf spring according to claim 1, characterized in that: The leaf spring comprises a leaf spring body, which is a flat disc structure. A rod through hole is opened in the center of the leaf spring body. Three cantilevers are symmetrically arranged around the rod through hole. The cantilever adopts a hollow spiral structure. The spiral line of the spiral structure is an involute. An inner water drop structure is arranged at the center starting end of the spiral line structure, and an outer water drop structure is arranged at the end end. The inner water drop structure, the spiral structure, and the outer water drop structure are connected to each other to form the cantilever of the leaf spring. The inner water drop structure is the same as the outer water drop structure, and both are composed of three arcs, namely, an inner arc, an end arc, and an outer arc. The inner arc is connected and tangent to the end arc, and the end arc is connected and tangent to the outer arc. A plurality of threaded holes are evenly distributed on the circumferential edge of the leaf spring body.

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