A design method for constructing variable cross-section scroll tooth profile using accelerating spiral line

Abstract

The present invention discloses a design method for constructing a variable cross-section scroll tooth profile using an accelerating spiral line, so as to solve the problem that the conventional variable cross-section profile uses a high-order curve, which causes the design and processing to be complicated and is not conducive to technical implementation. The method comprises: S01, drawing an accelerating spiral line with ρ as the polar diameter; S02, taking the polar diameter as ρ * The accelerating spiral B * C * The curve obtained after rotation is #imgabs0#, which replaces the BC segment in the acceleration spiral with a polar diameter of ρ; S03, after the S02 profile is replaced, the newly constructed variable cross-section profile mother line is a three-segment acceleration spiral, that is, the curves #imgabs1# and #imgabs2# are connected in sequence to obtain the variable cross-section profile mother line profile equation; S04, S03 variable cross-section profile mother line profile, after the envelope of the spiral profile is used to construct the symmetrical dynamic and static scroll teeth.

Description

Technical Field

[0001] The invention relates to the field of scroll compressors, and in particular to a design method for constructing a scroll tooth profile with a variable cross-section by using an accelerating spiral line. Background Art

[0002] The scroll compressor, which works on the principle of conjugate profile meshing and cavity volume change, has many advantages such as compact structure, low vibration and low noise, and high efficiency and energy saving. It can not only ensure energy saving but also meet environmental protection requirements. It is widely used in air conditioning, industry, medical treatment, various gas compression, refrigeration, food, medium and low temperature waste heat recovery and utilization and other fields. In recent years, the relevant research on automotive scroll compressors is in full swing. Especially with the rise and vigorous development of new energy vehicles, the application prospects of scroll compressors are even broader. The scroll compressor is mainly composed of moving scroll teeth, static scroll teeth, brackets, anti-rotation mechanisms and crankshafts. It is a fluid machine that uses the "crescent-shaped" cavity volume change to achieve gas compression. During the working process, most of the energy loss occurs on the moving and static scroll teeth, and the tooth profiles of the moving and static scroll teeth are composed of profiles. Therefore, the design of the profile is a key factor in determining the performance of the scroll compressor.

[0003] The existing profiles are divided into two categories: constant-section and variable-section profiles. Compared with constant-section profiles, variable-section profiles have the advantages of fewer turns, shorter leakage lines, and shorter residence time of the working fluid in the cavity. However, there are two shortcomings in the current variable-section profiles: one is the different types of curves, and the other is the introduction of higher-order curves. Different curve types will make the design and processing of profiles more complicated, and the introduction of higher-order curves will make the variable-section profiles difficult in practical applications. Summary of the invention

[0004] The embodiment of the present invention provides a design method for constructing a variable-section scroll tooth profile using an accelerating spiral line, so as to solve the problem that the traditional variable-section profile uses high-order curves, which causes complex design and processing and is not conducive to technical implementation.

[0005] In a first aspect, in order to solve the above technical problems, an embodiment of the present invention provides a design method for constructing a variable cross-section scroll tooth profile using an accelerating spiral line, characterized in that the method comprises:

[0006] S01. Draw an accelerating spiral with ρ as the polar diameter;

[0007] The curve equation of the accelerating helix is:

[0008]

[0009] In the formula, k is the acceleration index, a is the helical coefficient, The terminal angle.

[0010] Among them, the interval where the acceleration spiral line AB segment with ρ as the polar diameter is located is The BC segment is The CD segment interval is n 1 is the number of spiral coils;

[0011] S02, take the pole diameter as ρ * The accelerating spiral B * C * The curve obtained after rotation is To replace the BC segment in the accelerating spiral with a polar diameter of ρ;

[0012] Curve B * C * The line equation is:

[0013]

[0014] In the formula, is the starting angle, n 2 is the number of spiral coils.

[0015] Among them, use ρ * The accelerating spiral B in the interval * C * segment to replace the ρ accelerating spiral in The BC segment in the interval, so to ensure curve B * C * Rotate clockwise After the angle is adjusted, the BC segment can be replaced with fewer circles, and B * Point, C * Point coincides with point B and point C. The following constraints must be satisfied between the parameters: 1.

[0016] Constraint 1:

[0017]

[0018] Curve B * C * The curve obtained after rotation is Use this curve to replace the curve BC with more circles, so The line equation is:

[0019]

[0020] In order to make the three acceleration spiral lines connect smoothly at the connection point, Point and The points are processed so that they have a common normal. exist The slope of the tangent line at point K 1 ,curve exist The slope of the tangent line at point K 2 , the two curves are connected at the point The tangent angle is Φ 1 . Note the curve exist The slope of the tangent line at point K 3 ,curve D The slope of the tangent line at point K 4 , the two curves are connected at the point The tangent angle is Φ 2 , then the following constraint 2 must be satisfied:

[0021] Constraint 2:

[0022]

[0023]

[0024] Φ 1 =arctan|(K 1 -K 2 ) / (1+K 1 K 2 )| (7)

[0025]

[0026]

[0027]

[0028] In the formula, Respectively Point horizontal and vertical coordinate values;

[0029] S03, after the S02 profile is replaced, the newly constructed variable cross-section profile generatrix is ​​a 3-segment accelerating spiral line, i.e., the curve and Sequentially, the equations of the variable cross-section profile generatrix are:

[0030]

[0031]

[0032]

[0033] In the formula, B x , B yRespectively represent the horizontal and vertical coordinate values ​​of point B, Respectively Point horizontal and vertical coordinate values;

[0034] After the design of the S04 and S03 variable-section profile busbars is completed, the envelope of the spiral profile is used to construct symmetrical dynamic and static scroll teeth.

[0035] Optionally, the above step S04 includes:

[0036] S041. Take the point on the spiral as the center and make a circle with a radius of gyration R on the inside (or outside) of the spiral. or The envelope curve is formed by orbital and translational motion, and its envelope equation is:

[0037]

[0038] The unknown variable β can be solved according to the envelope theory. According to differential geometry theory, in order for the envelope of a plane curve family to exist, the Jacobian determinant must be equal to zero, that is,

[0039]

[0040] Substitute equations (11) to (13) into equation (15) to eliminate the parameters and obtain

[0041]

[0042] S042. According to S041, for the symmetrical dynamic and static scroll teeth formed by the accelerating spiral line, the inner and outer wall line equations are:

[0043]

[0044]

[0045]

[0046] In the formula, “+” represents the orbiting scroll tooth, and “-” represents the static scroll tooth; i and o represent the inner and outer walls of the scroll tooth, respectively; λ is a constant, when the subscript is i, λ is 2; when the subscript is o, λ is 1.

[0047] Optionally, after the above step S04, the method further includes step S05 and step S06;

[0048] S05. After the design of the variable cross-section profile generatrix of the three-segment accelerating spiral is completed, the generatrix of the three-segment accelerating spiral is used as the outer wall profile of the static scroll tooth, and its profile equation is:

[0049]

[0050]

[0051]

[0052] In the formula, subscript f represents the static scroll tooth, and subscript o represents the outer wall profile;

[0053] S06. According to the outer wall profile of the static scroll gear and the inner wall profile of the moving scroll gear, the normal distance must be R or The equation of the inner wall profile of the movable scroll tooth is obtained by using two equidistant lines:

[0054]

[0055]

[0056]

[0057] In the formula, R or is the radius of gyration, subscript m represents the orbiting scroll tooth, and i represents the inner wall profile.

[0058] Optionally, after the above step S04, the method further includes steps S07 and S08;

[0059] S07. Since the movable scroll has a constant cross section, the wall thickness of the movable scroll is set to a constant t, and the outer wall profile equation of the movable scroll is:

[0060]

[0061]

[0062]

[0063] S08. Since the static scroll has a variable cross-section, and the inner wall profile of the static scroll and the outer wall profile of the moving scroll must also be at a normal distance of R. or The two equidistant lines of the static scroll tooth are obtained by the same logic:

[0064]

[0065]

[0066]

[0067] Wherein, subscript f represents the static scroll tooth, subscript o represents the outer wall profile; R or is the radius of gyration, subscript m represents the orbiting scroll tooth, and subscript i represents the inner wall profile.

[0068] In a second aspect, an embodiment of the present application provides a scroll tooth designed by a design method of constructing a scroll tooth profile with a variable cross-section using an accelerating spiral line. The scroll tooth is obtained based on the method of the first aspect described above.

[0069] In a third aspect, an embodiment of the present application provides a scroll compressor or a scroll expander, which uses the scroll tooth of the second aspect mentioned above.

[0070] Beneficial effects of the present invention:

[0071] 1. When constructing traditional variable cross-section profiles, higher-order curves are often introduced. However, the introduction of such curves has the following disadvantages: (1) When processing higher-order curves, it is necessary to design the tool path and tool path, so the processing difficulty is relatively high; (2) When the parameters partially or completely change during profile design, the undetermined coefficients in the higher-order curves need to be recalculated, which can easily lead to a complicated profile design process and poor connection at the connection points. The present invention proposes a new combination method of variable cross-section vortex profiles, namely a combination of three accelerating spiral lines. This profile not only takes into account the advantages of traditional variable cross-section profiles, and makes up for the shortcomings of introducing higher-order curves as vortex profiles during profile design and processing, but also provides a new idea for not using higher-order curves in variable cross-section profile design.

[0072] 2. The three-segment accelerating spiral generatrix constructed by the present invention can be designed with two different cross-sectional tooth shapes: symmetrical and asymmetrical. For the symmetrical cross-sectional tooth shape, the shape of the vortex tooth can be adjusted by adjusting the acceleration index of the accelerating spiral line, so that the cross section of the vortex tooth conforms to the principle of equal strength, that is, the change law of the cross section of the vortex tooth is consistent with the change law of the medium pressure in the working chamber, which can effectively reduce the stress on the vortex tooth. For the asymmetrical cross-sectional tooth shape, it can not only minimize the mass of the moving scroll tooth and achieve the goal of lightweight, but also can well reduce the inertial force during the orbital and translational motion of the moving scroll tooth around the static scroll tooth, providing an effective way to improve the overall performance of the scroll compressor. In addition, the newly constructed variable cross-sectional profile is composed of the same type of curves, which has the advantages of simple mathematical description, easy design, and can be used directly without modification at the tooth head. BRIEF DESCRIPTION OF THE DRAWINGS

[0073] Figure 1 Schematic diagram of the acceleration spiral provided for this application;

[0074] Figure 2 One of the profile replacement schematics provided for this application;

[0075] Figure 3 The second schematic diagram of the replacement of the profile provided for this application;

[0076] Figure 4 A schematic diagram of a variable cross-section vortex profile provided in this application;

[0077] Figure 5 A schematic diagram of the meshing of the symmetrical moving and stationary scroll teeth provided in this application;

[0078] Figure 6 The asymmetric dynamic and static scroll gear provided in this application;

[0079] Figure 7 A schematic diagram of the meshing of the asymmetric moving and stationary scroll teeth provided in this application. DETAILED DESCRIPTION

[0080] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0081] Example 1

[0082] like Figures 1 to 7 As shown, an embodiment of the present invention provides a method for designing a variable cross-section scroll tooth and profile of a scroll compressor, the method comprising:

[0083] S01. Draw an accelerating spiral with ρ as the polar diameter.

[0084] The curve equation of the accelerating helix is:

[0085]

[0086] In the formula, k is the acceleration index, a is the helical coefficient, The terminal angle.

[0087] The present invention adopts three sections of accelerating spiral (ρ accelerating spiral + ρ * Accelerating spiral line + ρ accelerating spiral line) combination to construct variable cross-section vortex profile, such as Figure 1 The figure shows a complete accelerating spiral with ρ as the polar radius, where the interval of segment AB is The BC segment is The CD segment interval is n 1 is the number of spiral coils.

[0088] S02, take the pole diameter as ρ * The accelerating spiral B * C * The curve obtained after rotation is To replace the BC segment in the acceleration spiral with a polar diameter of ρ.

[0089] In order to construct the variable cross-section vortex profile, the polar diameter is taken as ρ * The accelerating spiral B * C * To replace the BC segment in the accelerating spiral with a polar diameter of ρ, Figure 2 Curve B * C * The line equation is:

[0090]

[0091] In the formula, is the starting angle, n 2 is the number of spiral coils.

[0092] Since it is ρ * The accelerating spiral B in the interval * C * segment to replace the ρ accelerating spiral in The BC segment in the interval, so to ensure curve B * C * Rotate clockwise After the angle is adjusted, the BC segment can be replaced with fewer circles, and B * Point, C * Point coincides with point B and point C. The following constraints must be satisfied between the parameters: 1.

[0093] Constraint 1:

[0094]

[0095] Curve B * C * The curve obtained after rotation is Use this curve to replace the curve BC with more circles, such as Figure 3 Its profile equation is:

[0096]

[0097] In order to make the three acceleration spiral lines connect smoothly at the connection point, Point and The points are processed so that they have a common normal. exist The slope of the tangent line at point K 1 ,curve exist The slope of the tangent line at point K 2 , the two curves are connected at the point The tangent angle is Φ 1 . Note the curve exist The slope of the tangent line at point K 3 ,curve exist The slope of the tangent line at point K 4 , the two curves are connected at the point The tangent angle is Φ 2 , then the following constraint 2 must be satisfied:

[0098] Constraint 2:

[0099]

[0100]

[0101] Φ 1 =arctan|(K 1 -K 2 ) / (1+K 1 K 2 )| (7)

[0102]

[0103]

[0104]

[0105] In the formula, Respectively Point horizontal and vertical coordinate values.

[0106] S03, after the S02 profile is replaced, the newly constructed variable cross-section profile generatrix is ​​a 3-segment accelerating spiral line, i.e., the curve and After the above profile replacement is completed, the newly constructed variable cross-section profile generatrix is ​​a curve and The line equations are:

[0107]

[0108]

[0109]

[0110] In the formula, B x , B y Respectively represent the horizontal and vertical coordinate values ​​of point B, Respectively Point horizontal and vertical coordinate values.

[0111] After the design of the S04 and S03 variable-section profile busbars is completed, the envelope of the spiral profile is used to construct symmetrical dynamic and static scroll teeth.

[0112] Optionally, the above step S04 includes:

[0113] S041. Take the point on the spiral as the center and make a circle with a radius of gyration R on the inside (or outside) of the spiral. or The envelope is formed by orbital and translational motion. After the above-mentioned busbar design is completed, the envelope of the spiral line can be used to construct symmetrical dynamic and static scroll teeth. The specific steps are to take the point on the spiral as the center of the circle, and make a circle with a radius of gyration R on the inside (or outside) of the spiral. or The envelope curve is formed by orbital and translational motion, and its envelope equation is:

[0114]

[0115] The unknown variable β can be solved according to the envelope theory. According to differential geometry theory, in order for the envelope of a plane curve family to exist, the Jacobian determinant must be equal to zero, that is,

[0116]

[0117] Substitute equations (11) to (13) into equation (15) to eliminate the parameters and obtain

[0118]

[0119] S042. According to S041, for the symmetrical dynamic and static scroll teeth formed by the accelerating spiral line, the inner and outer wall line equations are:

[0120]

[0121]

[0122]

[0123] In the formula, “+” represents the orbiting scroll tooth, and “-” represents the static scroll tooth; i and o represent the inner and outer walls of the scroll tooth, respectively; λ is a constant, when the subscript is i, λ is 2; when the subscript is o, λ is 1.

[0124] For example, Figure 4 As shown in the figure, it is a variable cross-section vortex profile composed of three sections of accelerating spiral lines, and the dotted line part in the figure is a profile composed of one section of accelerating spiral lines. By comparison, it can be seen that the number of coils in the newly constructed variable cross-section vortex is significantly reduced, which is more beneficial to shorten the length of the leakage line and reduce the residence time of the compressed medium in the working chamber. Figure 5 The figure shows a schematic diagram of a pair of symmetrical scroll teeth meshing, in which 1 is a stationary scroll tooth and 2 is a movable scroll tooth.

[0125] Optionally, after the above step S04, the method further includes step S05 and step S06;

[0126] S05. After the design of the generatrix of the variable cross-section profile of the three-section accelerating spiral is completed, the generatrix of the three-section accelerating spiral is used as the outer wall profile of the static scroll tooth.

[0127] After the design of the generatrix of the three-segment accelerating spiral is completed, a pair of asymmetric spiral tooth shapes can be constructed using the meshing principle of the dynamic and static spiral teeth, that is, the dynamic spiral tooth shape is a constant cross-section tooth shape, and the static spiral tooth shape is a variable cross-section tooth shape. The specific steps are to use the generatrix of the three-segment accelerating spiral as the outer wall profile of the static spiral tooth, and its profile equation is:

[0128]

[0129]

[0130]

[0131] Wherein, subscript f represents the static scroll tooth, and subscript o represents the outer wall profile.

[0132] S06. According to the outer wall profile of the static scroll gear and the inner wall profile of the moving scroll gear, the normal distance must be R or The equation of the inner wall profile of the movable scroll tooth is obtained by using two equidistant lines:

[0133]

[0134]

[0135]

[0136] In the formula, R or is the radius of gyration, subscript m represents the orbiting scroll tooth, and i represents the inner wall profile.

[0137] Optionally, after the above step S04, the method further includes step S07 and step S08.

[0138] S07. Since the movable scroll has a constant cross section, the wall thickness of the movable scroll is set to a constant t, and the outer wall profile equation of the movable scroll is:

[0139]

[0140]

[0141]

[0142] S08. Since the static scroll has a variable cross-section, and the inner wall profile of the static scroll and the outer wall profile of the moving scroll must also be at a normal distance of R. or The two equidistant lines of the static scroll tooth are obtained by the same logic:

[0143]

[0144]

[0145]

[0146] Wherein, subscript f represents the static scroll tooth, subscript o represents the outer wall profile; R or is the radius of gyration, subscript m represents the orbiting scroll tooth, and subscript i represents the inner wall profile.

[0147] It should be noted that the above steps S05 and S06, as well as steps S07 and S08 are two different tooth shapes, and either one is performed.

[0148] For example, Figure 6 The figure shows a newly designed asymmetric variable cross-section vortex gear. Figure 11 is a variable cross-section static vortex gear obtained according to equations (20) to (22) and equations (29) to (31), and Figure 22 is a uniform cross-section dynamic vortex gear obtained according to equations (23) to (28). Figure 6 and Figure 7 FIG. 1 shows a schematic diagram of the variable cross-section fixed scroll gear 11 and the uniform cross-section movable scroll gear 22 meshing with each other from the center of revolution. Figure 6 and Figure 7 As shown, the variable cross-section fixed scroll gear 11 and the uniform cross-section movable scroll gear 22 are in an asymmetric state. Figure 6 It is a schematic diagram of the stationary scroll gear 11 and the movable scroll gear 22 at the center of revolution; when the movable scroll gear of equal cross section has a radius of gyration R or When the orbital and translational motion of the gear is realized, the movable scroll gear and the stationary scroll gear can achieve correct meshing. Figure 7 It is a schematic diagram of the meshing of the fixed scroll gear 11 and the movable scroll gear 22.

[0149] It can be understood that the present application uses the same type of curve to construct two different variable-section profiles, namely, symmetrical and asymmetrical types. This profile not only realizes the lightweight design of the scroll tooth while taking into account the advantages of traditional variable-section profiles, but also breaks through the constraints of using base circle involutes and higher-order curves as the main scroll line in profile design, thereby effectively improving the overall performance of the scroll compressor.

[0150] Example 2

[0151] The scroll gear designed based on the design method of Example 1 is as follows: Figure 6 and Figure 7As shown, the variable cross-section fixed scroll gear 11 and the uniform cross-section movable scroll gear 22 are in an asymmetric state. Figure 6 It is a schematic diagram of the stationary scroll gear 11 and the movable scroll gear 22 at the center of revolution; when the movable scroll gear of equal cross section has a radius of gyration R or When the orbital and translational motion of the gear is realized, the movable scroll gear and the stationary scroll gear can achieve correct meshing. Figure 7 It is a schematic diagram of the meshing of the fixed scroll gear 11 and the movable scroll gear 22.

[0152] It can be understood that the scroll compressor using the above-mentioned scroll teeth not only realizes the lightweight design of the scroll teeth, but also breaks through the constraints of using base circle involutes and higher-order curves as main scroll lines in profile design, effectively improving the overall performance of the scroll compressor.

[0153] Based on the same inventive concept, the above-mentioned scroll teeth can also be applied to scroll expanders, scroll vacuum pumps and similar devices that require the use of profiled lines.

[0154] This article uses specific examples to illustrate the principles and implementation methods of the present invention. The description of the above embodiments is only used to help understand the core idea of ​​the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A design method for constructing a variable cross-section scroll tooth profile using an accelerating spiral line, characterized in that: The method comprises: S01. Draw an accelerating spiral with ρ as the polar diameter; The curve equation of the accelerating helix is: In the formula, k is the acceleration index, a is the helical coefficient, is the terminal extension angle; Among them, the interval where the acceleration spiral line AB segment with ρ as the polar diameter is located is The BC segment is The CD segment interval is n1 is the number of spiral coils; S02, take the pole diameter as ρ * The accelerating spiral B * C * The curve obtained after rotation is To replace the BC segment in the accelerating spiral with a polar diameter of ρ; Curve B * C * The line equation is: In the formula, is the starting angle, n2 is the number of spiral coils; Among them, use ρ * The accelerating spiral B in the interval * C * segment to replace the ρ accelerating spiral in The BC segment in the interval, so to ensure curve B * C * Rotate clockwise After the angle is adjusted, the BC segment can be replaced with fewer circles, and B * Point, C * Point coincides with point B and point C. The following constraints must be satisfied between the parameters:

1. Constraint 1: Curve B * C * The curve obtained after rotation is Use this curve to replace the curve BC with more circles, so The line equation is: In order to make the three acceleration spiral lines connect smoothly at the connection point, Point and The points are processed so that they have a common normal; the curve exist The slope of the tangent line at point is K1, and the curve exist The slope of the tangent line at the point is K2. The two curves are connected at the point The tangent angle is Φ 1； Note the curve exist The slope of the tangent line at point is K3, and the curve exist The slope of the tangent line at the point is K4. The two curves are connected at the point The tangent angle at is Φ2, then the following constraint 2 must be satisfied: Constraint 2: Φ1=arctan|(K1-K2) / (1+K1K2)| (7) In the formula, Respectively Point horizontal and vertical coordinate values; S03, after the S02 profile is replaced, the newly constructed variable cross-section profile generatrix is ​​a 3-segment accelerating spiral line, i.e., the curve and Sequentially, the equations of the variable cross-section profile generatrix are: In the formula, B x , B y Respectively represent the horizontal and vertical coordinate values ​​of point B, Respectively Point horizontal and vertical coordinate values; After S04 and S03 change the cross-section profile to the main profile, the envelope of the spiral profile is used to construct symmetrical dynamic and static scroll teeth.

2. The method according to claim 1, characterized in that The above step S04 includes: S041, take the point on the spiral as the center, and make a circle with a radius of gyration R on the inside or outside of the spiral. or The envelope curve is formed by orbital and translational motion, and its envelope equation is: Among them, the unknown variable β can be solved according to the envelope theory; according to the differential geometry theory, in order for the envelope of the plane curve family to exist, the Jacobian determinant must be equal to zero, that is, Substitute equations (11) to (13) into equation (15) to eliminate the parameters and obtain S042. According to S041, for the symmetrical dynamic and static scroll teeth formed by the accelerating spiral line, the inner and outer wall line equations are: In the formula, "+" represents the orbiting scroll tooth, and "-" represents the static scroll tooth; i and o represent the inner and outer walls of the scroll tooth respectively; λ is a constant, when the subscript is i, λ is 2; when the subscript is o, λ is 1.

3. The method according to claim 1, characterized in that After the above step S04, the method further includes steps S05 and S06; S05. After the design of the variable cross-section profile generatrix of the three-segment accelerating spiral is completed, the generatrix of the three-segment accelerating spiral is used as the outer wall profile of the static scroll tooth, and its profile equation is: In the formula, subscript f represents the static scroll tooth, and subscript o represents the outer wall profile; S06. According to the outer wall profile of the static scroll gear and the inner wall profile of the moving scroll gear, the normal distance must be R or The equation of the inner wall profile of the movable scroll tooth is obtained by using two equidistant lines: In the formula, R or is the radius of gyration, subscript m represents the orbiting scroll tooth, and i represents the inner wall profile.

4. The method according to claim 1, characterized in that: After the above step S04, the method further includes steps S07 and S08; S07. Since the movable scroll has a constant cross section, the wall thickness of the movable scroll is set to a constant t, and the outer wall profile equation of the movable scroll is: S08. Since the static scroll has a variable cross-section, and the inner wall profile of the static scroll and the outer wall profile of the moving scroll must also be at a normal distance of R. or The two equidistant lines of the static scroll tooth are obtained by the same logic: Wherein, subscript f represents the static scroll tooth, subscript o represents the outer wall profile; R or is the radius of gyration, subscript m represents the orbiting scroll tooth, and subscript i represents the inner wall profile.

5. A scroll tooth designed using the design method of constructing a scroll tooth profile with a variable cross-section using an accelerating spiral line as claimed in any one of claims 1 to 4.

6. A scroll compressor using the scroll gear according to claim 5.

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