Vortex wrap with variable wall thickness based on logarithmic spiral and molded line design method thereof

Abstract

The invention relates to the technical field of compressors. The invention provides a logarithmic spiral-based variable-wall-thickness scroll wrap. A logarithmic spiral is adopted to construct a new gradient-wall-thickness molded line. Meanwhile, the invention provides a molded line design method of the variable-wall-thickness scroll wrap, a new variable-wall-thickness molded line is designed by adopting the combination of three sections of logarithmic spirals, and a scroll wrap head formed by an equal-wall-thickness molded line and a non-equal-wall-thickness molded line is reconstructed. According to the reconfiguration method, the circle involute is used as a reconfiguration curve, reconfiguration is conducted on the newly-designed vortex tooth with the gradually-changed wall thickness and the tooth head of the vortex tooth with the variable wall thickness, and it is guaranteed that the vortex tooth with the non-equal wall thickness can be correctly meshed during operation.

Description

Technical Field

[0001] The invention relates to the technical field of compressors, and in particular to a variable-wall-thickness scroll tooth based on a logarithmic spiral and a profile design method thereof. Background Art

[0002] The scroll compressor is a new type of positive displacement fluid machinery with significant advantages such as compact structure, high efficiency and energy saving, and low noise. It is widely used in air conditioning, new energy vehicles, booster pumps, refrigeration and other fields. The core component of the scroll compressor is a pair of meshing dynamic and static scroll teeth, which are constructed by profiles. Therefore, the design of the scroll profile is the key to determining the performance of the compressor.

[0003] At present, the profiles are mainly divided into two categories: equal wall thickness profiles and non-equal wall thickness profiles. Among them, non-equal wall thickness profiles are further divided into two types: gradient wall thickness profiles and variable wall thickness profiles. Compared with equal wall thickness profiles, non-equal wall thickness profiles have more obvious advantages. For example, gradient wall thickness profiles can make the cross-section of the vortex teeth meet the principle of equal strength. For example, variable wall thickness profiles have the advantages of fewer turns, short leakage lines, and high compression ratios. However, non-equal wall thickness profiles have the following shortcomings: First, gradient wall thickness profiles can only be constructed using two types of curves: variable diameter base circle involutes and algebraic spirals. No new curves have been found to construct gradient wall thickness profiles, that is, there are few types of curves to choose from; second, in the design process of variable wall thickness profiles, the design and processing of the profiles become complicated due to the different types of curves. Summary of the invention

[0004] In view of the problems existing in the above-mentioned non-equal wall thickness profile, the present invention provides a variable wall thickness scroll tooth based on a logarithmic spiral, and uses the logarithmic spiral to construct a new gradually changing wall thickness profile. At the same time, a profile design method for a variable wall thickness scroll tooth is provided, and a new variable wall thickness profile is designed by combining three sections of logarithmic spirals, and the scroll tooth head composed of the equal wall thickness profile and the non-equal wall thickness profile is reconstructed.

[0005] A variable wall thickness scroll tooth based on logarithmic spiral, the profile equation is:

[0006] The equation of the inner wall profile of the moving scroll gear is:

[0007]

[0008] The profile equation of the outer wall of the moving scroll tooth is:

[0009]

[0010] The equation of the inner wall profile of the static scroll tooth is:

[0011]

[0012] The equation of the outer wall profile of the static scroll tooth is:

[0013]

[0014] Wherein, subscript m represents the orbiting scroll tooth; subscript f represents the stationary scroll tooth; j (j=1, 2, 3) represents the first, second and third sections of the logarithmic spiral respectively; ω1 and ω2 are the wall thickness coefficients, and satisfy ω1+ω2=1.

[0015] A method for designing a profile of a logarithmic spiral scroll with variable wall thickness comprises the following steps:

[0016] Step S1: Construct the logarithmic spiral line equation:

[0017]

[0018] Where: r0 is the radius of the starting circle, is the spiral polar angle, is the terminal polar angle;

[0019] Step S2: Construct the envelope equation, the inner or outer side of the logarithmic spiral with the radius of gyration R or The envelope is formed by revolution and translation, and the envelope equation is obtained:

[0020]

[0021] Where ζ is the envelope parameter;

[0022] Step S3: According to the envelope equation, the inner and outer wall profile equations of the dynamic and static scroll teeth composed of logarithmic spirals are constructed:

[0023]

[0024] In the formula, "+" represents the orbiting scroll gear, and "-" represents the static scroll gear; i and o represent the inner and outer walls of the scroll gear respectively; λ is a constant, when the subscript is i, λ is 2; when the subscript is o, λ is 1;

[0025] Step S4: constructing a variable wall thickness vortex profile by combining three sections of logarithmic spirals, wherein:

[0026] when When , the curve equation of the first logarithmic spiral is:

[0027]

[0028] In the formula,

[0029] when When , the curve equation of the second logarithmic spiral is:

[0030]

[0031] In the formula,

[0032] when When , the curve equation of the third logarithmic spiral is:

[0033]

[0034] In the formula,

[0035] Step S5: reconstructing the scroll tooth head profile;

[0036] Step S6: construct the inner and outer wall profile equations of the variable wall thickness dynamic and static scroll teeth using the normal isometric method, where:

[0037] The equation of the inner wall profile of the moving scroll gear is:

[0038]

[0039] The profile equation of the outer wall of the moving scroll tooth is:

[0040]

[0041] The equation of the inner wall profile of the static scroll tooth is:

[0042]

[0043] The equation of the outer wall profile of the static scroll tooth is:

[0044]

[0045] Wherein, subscript m represents the orbiting scroll tooth; subscript f represents the stationary scroll tooth; j (j=1, 2, 3) represents the first, second and third sections of the logarithmic spiral respectively; ω1 and ω2 are the wall thickness coefficients, and satisfy ω1+ω2=1.

[0046] Furthermore, in step S2, the envelope parameter is obtained by the following formula:

[0047]

[0048] Substituting the logarithmic spiral line equation into equation (11), we obtain:

[0049]

[0050] Furthermore, in step S5, reconstructing the scroll tooth head profile includes the following steps:

[0051] Step S51: Make an auxiliary involute OA, find a point D on the auxiliary involute, connect OD, and make an auxiliary circle R with OD as the radius and O as the center. O ;

[0052] Step S52: Draw a common tangent line between the logarithmic spiral and the auxiliary circle through point D, which intersects the first section of the logarithmic spiral. The intersection point is B, where point B is the common tangent point between the reconstructed circle involute and the first section of the logarithmic spiral. BD is the normal of the tangent line, and the base circle O1 of the reconstructed base circle involute is above the normal line and tangent to the normal line, and the tangent point is C;

[0053] Step S53: Set L CD With L BD The proportional relationship between them is μ, and the coordinates of the center of the base circle of the reconstructed base circle involute are:

[0054]

[0055] Where σ is the correction angle of the logarithmic spiral; L BD is the distance between point B and point D;

[0056] Step S54: Obtain the occurrence angle α of the base circle involute:

[0057] α=π-(∠ECF+∠EO1F+∠EO1O) (14)

[0058] in,

[0059]

[0060] Step S54: reconstruct the involute equation of the curve base circle as:

[0061]

[0062] Beneficial effects:

[0063] The present invention adopts logarithmic spiral to design a vortex profile with a gradual wall thickness, breaking the barrier that the profile can only be constructed with a variable diameter base circle involute and an algebraic spiral, and enriching the types of existing gradual variable wall thickness profiles. At the same time, the wall thickness variation law of the gradual wall thickness vortex tooth formed by the logarithmic spiral is consistent with the variation law of the medium pressure in the vortex compression chamber, effectively reducing the stress on the vortex tooth.

[0064] The present invention adopts three sections of curves of the same type to construct a new variable wall thickness scroll profile, and also uses the profile to design two tooth shapes of dynamic and static scroll teeth, which greatly meets the needs of the scroll compressor for different tooth shapes, especially the dynamic scroll teeth with smaller wall thickness. It can not only reduce the mass of the dynamic scroll teeth to the greatest extent and realize lightweight design, but also can well reduce the inertia force during the process of the dynamic scroll teeth orbiting and translating around the static scroll teeth.

[0065] The present invention utilizes a circular involute as a reconstruction curve to reconstruct a newly designed volute with a gradually variable wall thickness and a volute tooth head with a variable wall thickness, thereby ensuring that the volute with non-uniform wall thickness can maintain correct meshing during operation. BRIEF DESCRIPTION OF THE DRAWINGS

[0066] Figure 1 Schematic diagram of the generatrix of variable wall thickness vortex profile.

[0067] Figure 2 Schematic diagram of the reconstruction of the tooth head profile.

[0068] Figure 3 Schematic diagram of the moving scroll with gradual wall thickness.

[0069] Figure 4 Schematic diagram of a static scroll tooth with gradient wall thickness.

[0070] Figure 5 Schematic diagram of meshing of dynamic and static scroll gears with gradually varying wall thickness, in which 11 is the dynamic scroll gear and 21 is the static scroll gear.

[0071] Figure 6 This is a schematic diagram of the meshing of the variable wall thickness dynamic and static scroll teeth when ω1=ω2.

[0072] Figure 7 It is a schematic diagram of the variable wall thickness movable scroll tooth when ω1≠ω2.

[0073] Figure 8 It is a schematic diagram of the static scroll tooth with variable wall thickness when ω1≠ω2.

[0074] Fig. 9 This is a schematic diagram of the meshing of the variable wall thickness dynamic and static scroll teeth when ω1≠ω2. DETAILED DESCRIPTION

[0075] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the solutions of the embodiments will be introduced below. Obviously, the solutions described below are some embodiments of the present invention. For ordinary technicians in this field, other solutions can be obtained based on these solutions without paying creative work.

[0076] A method for designing a profile of a logarithmic spiral scroll with variable wall thickness comprises the following steps:

[0077] Step S1: Construct the logarithmic spiral line equation:

[0078]

[0079] Where: r0 is the radius of the starting circle, is the spiral polar angle, is the terminal polar angle;

[0080] Step S2: Construct the envelope equation, the inner or outer side of the logarithmic spiral with the radius of gyration R or The envelope is formed by revolution and translation, and the envelope equation is obtained:

[0081]

[0082] In the formula, ζ is the envelope parameter, which can be obtained by solving the following formula:

[0083]

[0084] Substituting the line equation of the logarithmic spiral into the above formula, we get:

[0085]

[0086] Step S3: According to the envelope equation, the inner and outer wall profile equations of the dynamic and static scroll teeth composed of logarithmic spirals are constructed:

[0087]

[0088] In the formula, "+" represents the orbiting scroll gear, and "-" represents the static scroll gear; i and o represent the inner and outer walls of the scroll gear respectively; λ is a constant, when the subscript is i, λ is 2; when the subscript is o, λ is 1;

[0089] Step S4: construct a variable wall thickness vortex profile by combining three sections of logarithmic spirals, wherein:

[0090] when When , the curve equation of the first segment of the logarithmic spiral is:

[0091]

[0092] In the formula,

[0093] when When , the curve equation of the second logarithmic spiral is:

[0094]

[0095] In the formula,

[0096] when When , the curve equation of the third logarithmic spiral is:

[0097]

[0098] In the formula,

[0099] According to equations (8), (9) and (10), the generatrix of the variable wall thickness profile is obtained, as follows: Figure 1 As shown, AB represents the first section of the logarithmic spiral; BC represents the second section of the logarithmic spiral; CD represents the third section of the logarithmic spiral.

[0100] In order to enable the volute to mesh correctly, after the generatrix of the three-segment logarithmic spiral combination is constructed, the volute head is reconstructed in the following manner.

[0101] In a preferred embodiment, the present invention adopts a base circle with a radius of R o1 The circular involute of the tooth head is reconstructed, such as Figure 2 As shown, the specific steps are as follows:

[0102] Draw an auxiliary involute OA, find a point D on the auxiliary involute, connect OD, and draw an auxiliary circle R with OD as the radius and O as the center. o .

[0103] Draw a common tangent line between the logarithmic spiral and the auxiliary circle through point D, which intersects the first logarithmic spiral at point B. At this point, point B is the common tangent point between the reconstructed circle involute and the first logarithmic spiral. BD is the normal line of the tangent line, and the base circle O1 of the reconstructed base circle involute is above the normal line and tangent to it, and the tangent point is C.

[0104] Assume L CD With L BD The proportional relationship between them is μ, then the coordinates of the center of the base circle of the reconstructed base circle involute can be expressed as:

[0105]

[0106] Where, σ is the correction angle of the logarithmic spiral; L BD is the distance between point B and point D.

[0107] After the center of the generating circle of the base circle involute is determined, the generating angle α needs to be obtained to establish the desired base circle involute. According to the properties of the involute, it can be obtained that:

[0108] α=π-(∠ECF+∠EO1F+∠EO1O)

[0109] in,

[0110]

[0111] From the center of the base circle involute and the occurrence angle, we can know that the equation of the reconstructed curve base circle involute is:

[0112]

[0113] According to the inner and outer wall line equations, combined with the above formula, we can get Figures 3 to 5 Gradient wall thickness scroll shown.

[0114] Step S6: The inner and outer wall profile equations of the variable wall thickness dynamic and static scroll teeth can be established by using the normal equidistance method to obtain the scroll tooth profile equation, where:

[0115] The equation of the inner wall profile of the moving scroll gear is:

[0116]

[0117] The profile equation of the outer wall of the moving scroll tooth is:

[0118]

[0119] The equation of the inner wall profile of the static scroll tooth is:

[0120]

[0121] The equation of the outer wall profile of the static scroll tooth is:

[0122]

[0123] Wherein, subscript m represents the orbiting scroll tooth; subscript f represents the stationary scroll tooth; j (j=1, 2, 3) represents the first, second and third sections of the logarithmic spiral respectively; ω1 and ω2 are the wall thickness coefficients, and satisfy ω1+ω2=1.

[0124] When the wall thickness coefficient ω1=ω2, the variable wall thickness orbiting scroll can be obtained according to the equations of the inner and outer wall profiles of the orbiting scroll. Similarly, the variable wall thickness stationary scroll can be obtained according to the equations of the inner and outer wall profiles of the stationary scroll. Figure 6 As shown, the orbiting scroll gear and the stationary scroll gear mesh with each other. Figure 6 It can be seen that when the wall thickness coefficients are equal, the dynamic and static scroll teeth obtained are variable wall thickness scroll teeth with the same shape.

[0125] When the wall thickness coefficient ω1≠ω2 and satisfies ω1<ω2, according to the inner wall profile and outer wall profile equations of the movable scroll gear, the variable wall thickness movable scroll gear can be obtained, such as Figure 7 Similarly, according to the equations of the inner and outer wall profiles of the static scroll gear, the variable wall thickness static scroll gear can be obtained, as shown in Figure 8 As shown. Figure 7 and Figure 8It can be seen that when the wall thickness coefficients are not equal, the shapes of the moving and static scroll teeth are also different, and the wall thickness of the moving scroll tooth is smaller, which greatly reduces the mass of the scroll tooth and effectively improves the stress condition of the scroll compressor. In the figure, 13 is a moving scroll tooth with variable wall thickness, and 23 is a static scroll tooth with variable wall thickness.

[0126] What is disclosed above is only a preferred embodiment of the present invention, which certainly cannot be used to limit the scope of rights of the present invention. A person skilled in the art can understand that all or part of the processes of the above embodiments and equivalent changes made according to the claims of the present invention still fall within the scope of the invention.

Claims

1. A variable wall thickness scroll tooth based on a logarithmic spiral, characterized in that: The line equation is: The equation of the inner wall profile of the moving scroll gear is: The profile equation of the outer wall of the moving scroll tooth is: The equation of the inner wall profile of the static scroll tooth is: The equation of the outer wall profile of the static scroll tooth is: Wherein, subscript m represents the orbiting scroll tooth; subscript f represents the stationary scroll tooth; j (j=1, 2, 3) represents the first, second and third sections of the logarithmic spiral respectively; ω1 and ω2 are the wall thickness coefficients, and satisfy ω1+ω2=1.

2. A method for designing the profile of a logarithmic spiral scroll with variable wall thickness, characterized in that: The following steps are involved: Step S1: Construct the logarithmic spiral line equation: Where: r0 is the radius of the starting circle, is the spiral polar angle, is the terminal polar angle; Step S2: Construct the envelope equation, the inner or outer side of the logarithmic spiral with the radius of gyration R or The envelope is formed by revolution and translation, and the envelope equation is obtained: Where ζ is the envelope parameter; Step S3: According to the envelope equation, the inner and outer wall profile equations of the dynamic and static scroll teeth composed of logarithmic spirals are constructed: In the formula, "+" represents the orbiting scroll gear, and "-" represents the static scroll gear; i and o represent the inner and outer walls of the scroll gear respectively; λ is a constant, when the subscript is i, λ is 2; when the subscript is o, λ is 1; Step S4: constructing a variable wall thickness vortex profile by combining three sections of logarithmic spirals, wherein: when When , the curve equation of the first logarithmic spiral is: In the formula, when When , the curve equation of the second logarithmic spiral is: In the formula, when When , the curve equation of the third logarithmic spiral is: In the formula, Step S5: reconstructing the scroll tooth head profile; Step S6: construct the inner and outer wall profile equations of the variable wall thickness dynamic and static scroll teeth using the normal isometric method, where: The equation of the inner wall profile of the moving scroll gear is: The profile equation of the outer wall of the moving scroll tooth is: The equation of the inner wall profile of the static scroll tooth is: The equation of the outer wall profile of the static scroll tooth is: Wherein, subscript m represents the orbiting scroll tooth; subscript f represents the stationary scroll tooth; j (j=1, 2, 3) represents the first, second and third sections of the logarithmic spiral respectively; ω1 and ω2 are the wall thickness coefficients, and satisfy ω1+ω2=1.

3. The method for designing the profile of a logarithmic spiral scroll with variable wall thickness according to claim 2, characterized in that: In step S2, the envelope parameter is obtained by the following formula: Substituting the logarithmic spiral line equation into equation (11), we obtain:

4. The method for designing the profile of a logarithmic spiral scroll with variable wall thickness according to claim 2, characterized in that: In step S5, reconstructing the scroll tooth head profile includes the following steps: Step S51: Make an auxiliary involute OA, find a point D on the auxiliary involute, connect OD, and make an auxiliary circle R with OD as the radius and O as the center. O ; Step S52: Draw a common tangent line between the logarithmic spiral and the auxiliary circle through point D, which intersects the first section of the logarithmic spiral. The intersection point is B, where point B is the common tangent point between the reconstructed circle involute and the first section of the logarithmic spiral. BD is the normal of the tangent line, and the base circle O1 of the reconstructed base circle involute is above the normal line and tangent to the normal line, and the tangent point is C; Step S53: Set L CD With L BD The proportional relationship between them is μ, and the coordinates of the center of the base circle of the reconstructed base circle involute are: Where σ is the correction angle of the logarithmic spiral; L BD is the distance between point B and point D; Step S54: Obtain the occurrence angle α of the base circle involute: α=π-(∠ECF+∠EO1F+∠EO1O) (14) in, Step S54: reconstruct the involute equation of the curve base circle as:

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