Variable cross-section scroll wrap of asymmetric scroll expander and design method of variable cross-section scroll wrap

Abstract

The invention discloses a variable cross-section scroll wrap of an asymmetric scroll expander and a design method of the variable cross-section scroll wrap. A movable scroll wrap is composed of a first molded line PQ obtained after a base circle combination generatrix pq rotates anticlockwise, a second molded line MN obtained after a variable-diameter base circle combination generatrix mn is intercepted, a right side correction inner equidistant arc AiEi and a left side correction inner equidistant arc BiEi; the static scroll wrap is composed of a third molded line P 'Q', a fourth molded line M 'N', a right side correction outer equidistant arc AoEo and a left side correction outer equidistant arc BoEo; in the working process, the movable scroll wrap and the static scroll wrap can be correctly meshed. The asymmetric variable cross-section scroll wrap profile is simple in design, and the thickness of the static scroll wrap is firstly reduced, then increased and then reduced from the center to the outer ring, so that the number of scroll turns and the length of a leakage line are reduced and the leakage rate is reduced under the requirements of a scroll expander on a large expansion ratio and high output work; and the thickness of the movable scroll wrap is gradually reduced from the center to the outer ring, so that the strain of the scroll wrap is reduced, and the dynamic characteristic of the scroll wrap is improved.

Description

Technical Field

[0001] This invention belongs to the field of expander engineering technology, and specifically relates to a vortex expander with asymmetric variable cross-section vortex teeth. Background Technology

[0002] The scroll expander is a highly efficient energy conversion device. Due to its simple structure, few parts, small size, low noise, and high energy conversion efficiency, it has been widely used in organic Rankine cycles, compressed air energy storage, and combined cooling, heating, and power (CCHP) applications. Its working principle relies on the meshing of moving and stationary scroll plates to form multiple closed chambers. When high-pressure gas enters the scroll expander, it drives the moving scroll plate to revolve and translate, causing periodic changes in the volume of the closed chambers, thus achieving gas expansion and work. Since the profile of the scroll teeth directly determines the performance of the scroll expander, its design is crucial.

[0003] Currently, the operating conditions applicable to scroll expanders generally require a high expansion ratio. Using a scroll tooth structure with uniform wall thickness results in an increase in the size of the scroll disk and the length of the leakage line, reducing the efficiency of the scroll expander. Chinese Patent, Publication No. CN107939681B, discloses a fully meshing variable wall thickness scroll profile design method. This method uses a combined profile as the generatrix to construct dynamic and static scroll teeth with varying wall thicknesses, increasing the intake volume. However, this variable wall thickness scroll tooth uses a symmetrical design, meaning the tooth profiles of the dynamic and static scroll teeth are consistent, leading to problems such as large mass of the dynamic scroll teeth and poor dynamic characteristics. Therefore, to improve the expansion ratio, increase output power, and enhance the operational stability of the expander, researching the application of asymmetric variable wall thickness scroll tooth structures in scroll expanders is of great significance. Summary of the Invention

[0004] To address the issues of numerous vortex tooth rotations, long leakage lines, and the symmetrical design of existing variable wall thickness vortex teeth with complex profiles and large moving vortex tooth mass resulting in poor dynamic characteristics under high expansion ratios, this invention proposes an asymmetric variable cross-section vortex tooth for an expander and its design method. The vortex tooth profile consists of an involute base circle, a variable diameter involute base circle, higher-order curves, and circular arcs, enabling perfectly correct meshing. The profile design is simple, with the static vortex tooth thickness decreasing, increasing, and then decreasing again from the center outwards, reducing the number of vortex rotations and the length of the leakage line, effectively reducing leakage. Simultaneously, the moving vortex tooth thickness gradually decreases from the center outwards, improving vortex tooth strain and reducing rotational inertia. The proposed asymmetric variable cross-section vortex tooth is significant for enriching vortex tooth profile design methods and improving the working performance of expanders.

[0005] The technical solution adopted by this invention to solve its technical problem is:

[0006] A design method for variable wall thickness vortex teeth of an asymmetric vortex expander includes: a base circle combined generatrix pq, a variable diameter base circle combined generatrix mn, and a double circular arc correction generatrix AB;

[0007] The base circle combination generatrix pq is composed of 3 curve segments, namely: the involute ab of the center circle, the higher-order curve bc, and the involute cd of the outer circle.

[0008] The variable diameter base circle combination generatrix mn consists of 3 curve segments, namely: the involute a'b' of the center variable diameter base circle, the higher-order curve b'c', and the involute c'd' of the outer variable diameter base circle;

[0009] The double-circular-arc correction generatrix AB consists of two curve segments, namely: the right correction circular arc AE and the left correction circular arc BE.

[0010] The moving vortex tooth (1) consists of the first profile PQ after the base circle combination generatrix pq is rotated counterclockwise, the second profile MN after being cut from the variable diameter base circle combination generatrix mn, and the right-side corrected inner equidistant circular arc A. i E i Left side correction inner equidistant arc B i E i Composition; the thickness of the moving vortex tooth (1) gradually decreases from the center to the outer ring; the stationary vortex tooth (2) is composed of the third type line P'Q', the fourth type line M'N', and the right-side corrected outer equidistant circular arc A. o E o Left-side corrected outer equidistant arc B o E o Composition; The thickness of the static vortex tooth (2) decreases, then increases, and then decreases again from the center to the outer ring;

[0011] The third type line P'Q' is equidistant from the first type line PQ inwards along a normal radius R. or The fourth type line M'N' is then obtained; its radius of gyration R is equidistant from the second type line MN in the outward normal direction. or get;

[0012] The right-side corrected inner equidistant circular arc A i E i Left side correction inner equidistant arc B i E i The right-side corrected arc AE and the left-side corrected arc BE are equidistant from each other by a distance R. or / 2 obtained; the right-side corrected outer equidistant circular arc A o E o Left-side corrected outer equidistant arc B o E o From the right-side corrected arc AE and the left-side corrected arc BE, respectively, extend outwards at equal distances R. or / 2 is obtained; the right-side corrected circular arc AE and the left-side corrected circular arc BE are smoothly connected at the connection point E to obtain the double circular arc corrected generatrix AB;

[0013] The ratio of the axial projected area of ​​the moving vortex tooth (1) to the stationary vortex tooth (2) is 22% to 36%; when the number of vortex tooth turns is 1.85 to 2.35, the ratio of the volume of the maximum intake chamber to the volume of the minimum exhaust chamber formed by the meshing of the moving vortex tooth (1) and the stationary vortex tooth (2), i.e., the internal volume ratio, reaches 3.21 to 3.76.

[0014] During the revolution and translation process, the moving volute (1) and the stationary volute (2) can achieve correct meshing, that is, the first profile PQ after the base circle combination generatrix pq of the moving volute (1) is rotated counterclockwise by α, the second profile MN in the variable diameter base circle combination generatrix mn, and the right-side corrected inner equidistant circular arc A. i E i Left side correction inner equidistant arc B i E i ; respectively with the third profile P'Q', the fourth profile M'N', and the right-side corrected outer equidistant circular arc A of the static vortex tooth (2) o E o Left-side corrected outer equidistant arc B o E o To achieve proper meshing.

[0015] The base circle combination generatrix pq includes the central circle involute ab, the higher order curve bc, and the outer circle involute cd;

[0016] The equations of the central involute ab and the outer involute cd are as follows:

[0017]

[0018] The equation of the higher-order curve bc is:

[0019]

[0020] Where t is the angle parameter, R b The radius of the base circle, As the starting angle, The initial development angle of the replacement segment of the involute curve. The termination angle of the replacement segment of the involute curve. Let be the termination angle of the higher-order curve bc. For the final development angle, C0, C1, C2, and C3 are the parameters of the power series high-order curve;

[0021] The variable diameter base circle combination generatrix mn includes the central variable diameter base circle involute a'b', the higher order curve b'c', and the outer variable diameter base circle involute c'd';

[0022] The equations for the involute a'b' of the center variable base circle and the involute c'd' of the outer variable base circle are as follows:

[0023]

[0024] The equation of the higher-order curve b'c' is:

[0025]

[0026] Where t is the angle parameter, R b (1-D1t) is the radius of the variable-diameter base circle. The initial development angle of the replacement segment of the involute of the base circle with varying diameter. The termination angle of the replacement segment of the involute on the base circle with a variable diameter. C is the termination angle of the higher-order curve b'c', and C4, C5, C6, and C7 are the parameters of the power series higher-order curve;

[0027] The equation of the right-side corrected circular arc AE is:

[0028]

[0029]

[0030] The equation for the left-side corrected circular arc BE is:

[0031]

[0032] Among them, R m1 To correct the radius of the arc AE on the right, x F y F R is the coordinate of the center of the right-side corrected arc. m2 To correct the radius of the arc BE on the left, x G y G Let λ be the coordinates of the center of the left-side correction arc, λ be the central angle of the correction arc, and γ be the exhaust angle.

[0033] An asymmetric scroll compressor using the aforementioned variable cross-section scroll gear.

[0034] An asymmetric vortex vacuum pump using the aforementioned variable cross-section vortex gear.

[0035] The beneficial results of this invention are as follows:

[0036] ① The inner and outer profiles of the variable wall thickness moving vortex teeth of the proposed asymmetric vortex expander are respectively composed of the base circle combination profile and the variable diameter base circle combination profile. The outer and inner profiles of the variable wall thickness static vortex teeth are obtained by the normal equidistant method. The vortex tooth profile design is simple, which simplifies the generation process of the moving and static vortex teeth.

[0037] ② The proposed asymmetric variable wall thickness vortex tooth profile is composed of a combination profile containing high-order continuous curves. The static vortex tooth thickness decreases first, then increases, and then decreases again from the center to the outer ring. This reduces the number of vortex turns required for the vortex expander under the requirements of large expansion ratio and high output power, shortens the leakage line length, and reduces the leakage amount.

[0038] ③ The proposed asymmetric variable wall thickness vortex expander has a dynamic vortex tooth thickness that gradually decreases from the center to the outer ring, and the tooth thickness is relatively small. The tooth thickness increases at the vortex tooth head, which improves the strength of the vortex tooth under high pressure conditions. In addition, the dynamic vortex tooth has a small mass, small rotational inertia force, and good dynamic characteristics. Attached Figure Description

[0039] Figure 1 This is a diagram of the base circle combination busbar.

[0040] Figure 2 It is a diagram of the combined generatrix of the base circle with varying diameter.

[0041] Figure 3 This is a schematic diagram of the positional relationship of the vortex profile.

[0042] Figure 4 It is a correction diagram of the asymmetric double circular arc of the vortex tooth.

[0043] Figure 5 The diagram shows the moving vortex tooth (1) and the stationary vortex tooth (2) at the center of revolution.

[0044] Figure 6 This is a structural diagram of the moving vortex gear (1).

[0045] Figure 7 This is a structural diagram of the static vortex gear (2).

[0046] In the figure: 1—moving vortex tooth (1), 2—stationary vortex tooth (2), pq—base circle combination generatrix, mn—variable diameter base circle combination generatrix, p'q'—inner equidistant curve of base circle combination generatrix, m'n'—outer equidistant curve of variable diameter base circle combination generatrix, PQ—first type line, MN—second type line, P'Q'—third type line, M'N'—fourth type line, AE—right correction arc, BE—left correction arc, O—revolution center, O1—center of moving vortex tooth (1), O2—center of stationary vortex tooth (2). Detailed Implementation

[0047] The invention will now be further described with reference to the accompanying drawings.

[0048] like Figure 1 As shown, the base circle combination generatrix pq is established with the revolution center O as the center point. The outer circles are as follows: the involute ab of the center circle, the higher-order curve bc, and the involute cd of the outer circle.

[0049] The equations of the central involute ab and the outer involute cd are as follows:

[0050]

[0051] Where t is the angle parameter, R b The radius of the base circle, As the starting angle, The initial development angle of the replacement segment of the involute curve. The termination angle of the replacement segment of the involute curve. For the final display corner;

[0052] The equation of the higher-order curve bc is:

[0053]

[0054] Where n is the number of involute coils being replaced. Let be the termination angle of the higher-order curve bc, and C0, C1, C2, and C3 be the parameters of the power series higher-order curve.

[0055] Connection point At this point, the following constraint equations must be satisfied:

[0056]

[0057] Connection point At this point, the following constraint equations must be satisfied:

[0058]

[0059] Based on the above constraint equations, we can obtain:

[0060]

[0061] like Figure 2 As shown, the variable diameter base circle combination generatrix mn is established with the revolution center O as the center point. The outer circle is as follows: the central variable diameter involute a'b', the higher order curve b'c', and the outer variable diameter involute c'd'.

[0062] The equations for the involute a'b' of the center variable base circle and the involute c'd' of the outer variable base circle are as follows:

[0063]

[0064] Where t is the angle parameter, R b (1-D1t) is the radius of the variable-diameter base circle. The initial development angle of the replacement segment of the involute of the base circle with varying diameter. The termination angle of the replacement segment of the involute base circle with varying diameter;

[0065] The equation of the higher-order curve b'c' is:

[0066]

[0067] Where n' is the number of turns of the involute of the base circle being replaced. C is the termination angle of the higher-order curve b'c', and C4, C5, C6, and C7 are the parameters of the power series higher-order curve;

[0068] Connection point At this point, the following constraint equations must be satisfied:

[0069]

[0070] Connection point At this point, the following constraint equations must be satisfied:

[0071]

[0072] Based on the above constraint equations, we can obtain:

[0073]

[0074] like Figure 3 As shown, this is a schematic diagram of the positional relationship of the vortex profile. The base circle assembly generatrix pq is rotated counterclockwise around the center O by an angle α to form the profile of the moving vortex tooth (1); the variable diameter base circle assembly generatrix mn is the profile of the moving vortex tooth (1); after the base circle assembly generatrix pq is rotated counterclockwise around the center O by α, it rotates inward at equal intervals in the normal direction with radius R. or The inner equidistant curve p'q' of the base circle combined generatrix is ​​then obtained as the profile of the static vortex tooth (2); the outer normal equidistant gyration radius R of the variable diameter base circle combined generatrix mn. or Then the outer equidistant curve m'n' of the variable diameter base circle combined generatrix is ​​obtained as the profile of the static vortex tooth (2);

[0075] The equation of the inner equidistant curve p'q' of the base circle combined generatrix is:

[0076]

[0077] The equation of the outer equidistant curve m'n' of the variable diameter base circle combination generatrix is:

[0078]

[0079] like Figure 4 As shown, the asymmetric double circular arc correction diagram of the vortex tooth is as follows: the right centerline gh passes through the revolution center O, and a line segment OC is drawn counterclockwise at an angle φ with the x-axis, intersecting the variable diameter base circle at point C. A tangent CA is drawn to intersect gh at point A. The left centerline ef passes through the center O, and a line segment OD is drawn counterclockwise at an angle φ+π with the x-axis, intersecting the base circle at point D. A tangent DB is drawn to intersect ef at point B. Connect AB to intersect CD at point E. A perpendicular line is drawn through point E, offset along the normal direction by σ, intersecting CA at point F, resulting in the right corrected circular arc EA. A perpendicular line is drawn through point E to intersect DB at point G, resulting in the left corrected circular arc EB. The two corrected circular arcs are smoothly connected at the connection point E.

[0080] The equation of the right-side corrected circular arc AE is:

[0081]

[0082] Among them, R m1 To correct the radius of the arc AE on the right, x F y F Let λ be the center coordinates of the right-side correction arc, λ be the central angle of the correction arc, and γ be the exhaust angle.

[0083] According to the theory of normal equidistance, the right-side corrected outer equidistant circular arc A is described. o E o Its equation is:

[0084]

[0085] The right-side corrected inner equidistant circular arc A i E i Its equation is:

[0086]

[0087] The equation for the left-side corrected circular arc BE is:

[0088]

[0089] Among them, R m2 To correct the radius of the arc BE on the left, x G y G Set the center coordinates of the left-side correction arc;

[0090] According to the theory of normal equidistance, the left-side corrected outer equidistant circular arc B... o E o Its equation is:

[0091]

[0092] The left-side corrected inner equidistant circular arc B i E i Its equation is:

[0093]

[0094] like Figure 5 The diagram shows the moving vortex tooth (1) and the stationary vortex tooth (2) at the center of revolution. The first profile PQ of the moving vortex tooth (1) is cut off after the base circle assembly generatrix pq is rotated counterclockwise by α. The second profile MN of the moving vortex tooth (1) is cut off on the variable diameter base circle assembly generatrix mn. The third profile P'Q' of the stationary vortex tooth (2) is cut off on the inner equidistant curve p'q' of the base circle assembly generatrix. The fourth profile M'N' of the stationary vortex tooth (2) is cut off on the outer equidistant curve m'n' of the variable diameter base circle assembly generatrix.

[0095] like Figure 6 As shown, this is a diagram of a moving vortex tooth (1), which consists of the first profile PQ after the base circle combination generatrix pq is rotated counterclockwise, the second profile MN after being cut from the variable diameter base circle combination generatrix mn, and the right-side corrected inner equidistant circular arc A. i E i Left side correction inner equidistant arc B i E i Composition; The thickness of the moving vortex tooth (1) gradually decreases from the center to the outer ring;

[0096] like Figure 7 As shown, this is a diagram of a static vortex gear (2), which consists of the third type line P'Q', the fourth type line M'N', and the right-side corrected equidistant circular arc A. o E o Left-side corrected outer equidistant arc B o E o Composition; The thickness of the static vortex tooth (2) decreases, then increases, and then decreases again from the center to the outer ring;

[0097] While the specific embodiments of the present invention have been described above in conjunction with the accompanying drawings, this is not intended to limit the scope of protection of the present invention. Those skilled in the art should understand that various modifications or variations that can be made by those skilled in the art without creative effort based on the technical solutions of the present invention are still within the scope of protection of the present invention.

Claims

1. A variable cross-section vortex tooth for an asymmetric vortex expander, comprising a moving vortex tooth (1) and a stationary vortex tooth (2), characterized in that: The moving vortex tooth (1) consists of four curves: the first profile PQ after the base circle combination generatrix pq is rotated counterclockwise, the second profile MN after the base circle combination generatrix mn is cut off, and the right-side corrected inner equidistant circular arc A. i E i Left side correction inner equidistant arc B i E i Composition; The thickness of the moving vortex tooth (1) gradually decreases from the center to the outer ring; The stationary vortex gear (2) consists of four curves: the third profile P'Q', the fourth profile M'N', and the right-side corrected equidistant circular arc A. o E o Left-side corrected outer equidistant arc B o E o Composition; wherein, the third type line P'Q' is equidistant from the first type line PQ inwards along the normal direction with a radius of gyration R. or The fourth type line M'N' is then obtained; its radius of gyration is R, which is equidistant from the second type line MN in the outward normal direction. or The thickness of the static vortex tooth (2) decreases, increases, and then decreases again from the center to the outer ring. The right-side corrected inner equidistant circular arc A i E i Left side correction inner equidistant arc B i E i The right-side corrected arc AE and the left-side corrected arc BE are equidistant from each other by a distance R. or / 2 obtained; the right-side corrected outer equidistant circular arc A o E o Left-side corrected outer equidistant arc B o E o From the right-side corrected arc AE and the left-side corrected arc BE, respectively, extend outwards at equal distances R. or / 2 is obtained; the right-side corrected circular arc AE and the left-side corrected circular arc BE are smoothly connected at the connection point E to obtain the double circular arc corrected generatrix AB; The ratio of the axial projected area of ​​the moving vortex tooth (1) to the stationary vortex tooth (2) is 22% to 36%; when the number of vortex tooth turns is 1.85 to 2.35, the ratio of the volume of the maximum intake chamber to the volume of the minimum exhaust chamber formed by the meshing of the moving vortex tooth (1) and the stationary vortex tooth (2), i.e., the internal volume ratio, reaches 3.21 to 3.

76. During the revolution and translation process, the moving volute (1) and the stationary volute (2) can achieve correct meshing, that is, the first profile PQ after the base circle combination generatrix pq of the moving volute (1) is rotated counterclockwise by α, the second profile MN in the variable diameter base circle combination generatrix mn, and the right-side corrected inner equidistant circular arc A. i E i Left side correction inner equidistant arc B i E i ; respectively with the third profile P'Q', the fourth profile M'N', and the right-side corrected outer equidistant circular arc A of the static vortex tooth (2) o E o Left-side corrected outer equidistant arc B o E o To achieve proper meshing.

2. A design method for the variable cross-section vortex teeth of the asymmetric vortex expander as described in claim 1, characterized in that: Includes the following steps: 1) Establish a two-dimensional coordinate system with the revolution center O as the center point. The base circle combination generatrix pq is composed of 3 curves, which are: the central circle involute ab, the higher order curve bc, and the outer circle involute cd. The equations of the central involute ab and the outer involute cd are as follows: Where t is the angle parameter, R b The radius of the base circle, As the starting angle, The initial development angle of the replacement segment of the involute curve. The termination angle of the replacement segment of the involute curve. For the final display corner; The equation of the higher-order curve bc is: in, Let be the termination angle of the higher-order curve bc, and C0, C1, C2, and C3 be the parameters of the power series higher-order curve. 2) The variable diameter base circle combination generatrix mn is composed of 3 curve segments, which are: the involute a'b' of the center variable diameter base circle, the higher-order curve b'c', and the involute c'd' of the outer variable diameter base circle; The equations for the involute a'b' of the center variable base circle and the involute c'd' of the outer variable base circle are as follows: Where t is the angle parameter, R b (1-D1t) is the radius of the variable-diameter base circle. The initial development angle of the replacement segment of the involute of the base circle with varying diameter. The termination angle of the replacement segment of the involute base circle with variable diameter; The equation of the higher-order curve b'c' is: in, C is the termination angle of the higher-order curve b'c', and C4, C5, C6, and C7 are the parameters of the power series higher-order curve; 3) The double-circular-arc correction generatrix AB consists of two curve segments: the right correction circular arc AE and the left correction circular arc BE. The equation for the right-side corrected circular arc AE is: Among them, R m1 To correct the radius of the arc AE on the right, x F y F Let λ be the center coordinates of the right-side correction arc, λ be the central angle of the correction arc, and γ be the exhaust angle. The equation for the left-side corrected circular arc BE is: Among them, R m2 To correct the radius of the arc BE on the left, x G y G The coordinates of the center of the left-side correction arc.

3. An asymmetric scroll compressor using the aforementioned variable cross-section scroll gear.

4. An asymmetric vortex vacuum pump using the aforementioned variable cross-section vortex gear.

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