Methods for designing single-lobe and double-lobe rotors

The present invention provides methods for designing single-lobe or double-lobe rotors which enable a defined rotor and a conjugate rotor intermeshing and conjugating to each other and by parameterized sets to generate curve portions of half two lobes of the defined rotor including a curve E, an arc A, an arc B, an arc F, an arc C, an arc G and a horizontal line Y. The main feature is that a radius of the arc C being defined by following equation:in which rF is two times pitch circle radius(Rp) of the defined rotor deducting the maximum radius(R) of the defined rotor(rF=2 Rp−R), and a center of the arc C is located in a straight extension direction from a center of the defined rotor and an end point of an arc F.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to methods for designing single-lobe and double-lobe rotors. By parameterized sets, the methods can profile a defined rotor and a conjugate rotor with single lobe or double lobes which intermesh and conjugate to each other, and effectively evaluate optimum performance in intermeshing and conjugating, whereby to provide higher compression ratio and larger discharge capacity, secure a smooth process while working chamber undergoing compression and expansion, and reduce leakage, thus can reduce noise and vibration while operation of the rotors.

2. Related Art

A large variety of related rotor mechanism are already known, see for example U.S. Pat. Nos. 1,426,820, 4,138,848, 4,224,016, 4,324,538, 4,406,601, 4,430,050 and 5,149,256. Rotors of the prior arts have drawbacks that curves thereof are discontinuity and not smoothly at the joint between each segment and which cause tips of the rotors do not mesh completely with other rotor when they are rotating. Consequently, in applying to machines working as periodical expansion and compression operation, the abnormal situations such as noise and vibration take place in working chamber enclosed by defined rotor, conjugate rotor and inner walls of cylinder. Moreover, inappropriate intermeshing between the rotors increases wear and therefore reduces the durability of operation.

In view of aforesaid disadvantages, U.S. patent application Ser. No. 11/214,876 has disclosed a defined rotor and a conjugate rotor designed by variety of parameters. Such rotors can reduce noise and vibration as operation.

SUMMARY OF THE INVENTION

Accordingly, an object of the present invention is to provide methods for designing single-lobe and double-lobe rotors which is able to generate a defined rotor and a conjugate rotor intermeshing and conjugating to each other by different parameters. Moreover, the methods, as apply to machines working as periodical expansion and compression operation can provide higher compression ratio and larger discharge capacity, secure a smooth process while working chamber undergoing compression and expansion and which reduce leakage as well lessen noise and vibration while operation of the rotors.

To achieve the above-mentioned objects, the methods for designing single-lobe and double-lobe rotors of the present invention comprise: curve portions of half two lobes of the defined rotor including a curve E, an arc A, an arc B, an arc F, an arc C, an arc G and a line Y, wherein the center of the arc C is located in a straight extension direction of the line connected the center of the defined rotor and an end point of an arc F, and a radius of the arc C is defined by following equation:

rC=x+rF=⁢x⁢⁢sin⁢⁢β+D2⁢⇒x=(D/2)-rF1-sin⁢⁢β;⁢rC=(D/2)-rF1-sin⁢⁢β+rF
(in which rCis a radius of the arc C, x is a length between the center of the defined rotor and the center of the arc C, rFis a radius of the arc F, D is a width of the defined rotor)

By the above-mentioned methods, the curve portions of half two lobes of the defined rotor are formed and further symmetrically imaging the curve portions to form a defined rotor with two lobes.

In the manner of generating the curve portions of half two lobes of the defined rotor1, further designating a symmetry point P8which is symmetrical to the fourth point P4against the first center t1, and which is located in an extension direction of a third line h3. A fourth center t4′ located on the third line h3and being symmetrical to the fourth center t4against the first center t1, and defining an arc C′ by drawing around the fourth center t4′ with the radius rCfrom the symmetry point P8to the sixth point P6; therefore the sixth point P6of the arc C′ is tangent to the horizontal line Y; further defining an arc G by drawing around the first center t1with the radius rFfrom the fourth point P4to the symmetry point P8, whereby the arc C′ is smoothly linked with the horizontal line Y and the arc G; consequently, the single-lobe defined rotor is profiled by linking the curve E, the arc A, the arc B, the arc F, the arc C′, the arc G and the horizontal line Y.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

A double-lobe rotor design process in accordance with the present invention designs the curve portions of a defined rotor1by suitable parameters, and then get the curve portions of conjugate rotor2with conjugate theory. Referring toFIGS. 1 to 3, designing process for forming the curve portions of defined rotor1comprises the following steps:1. Designate a maximum radius R and a width D of the defined rotor1, a pitch circle radius Rp of the defined and the conjugate rotor1,2, a first center t1of the defined rotor1and a second center t2of the conjugate rotor2, wherein a distance between the first center t1and the second center t2is 2 Rp, the pitch circle radius Rp is smaller than radius R, and R and Rp are in appropriate ratio R=4 Rp/3.2. Referring toFIG. 1, define a reference horizontal line h1by straight connecting the first center t1and the second center t2, a base point P0located on the reference horizontal line h1and being offset from the first center t1in a length same as the radius R, a conjugate curve E′ generated as the base point P0rotating around the first center t1, a curve E generated by symmetrically imaging the conjugate curve E′ against a tangent point P7of the two pitch circles of the defined and the conjugate rotor, and a first point P1located in an intersection of the curve E and the horizontal line h1.3. Referring toFIG. 2, designate a second point P2which is formed by drawing around the first center t1with the radius R from the point P0in an central angle α (α is 5°), whereby an arc A is generated between the point P0and P2, and is smoothly connected to the curve E.4. Define a second line h2by straight connecting the first center t1and the second point P2and further designating a third center t3thereon, of which a radius is rB.5. The radius rBis defined by following equation:

rB+(R-rB)⁢sin⁢⁢α=D2rB=D/2-R⁢⁢sin⁢⁢α1-sin⁢⁢α(wherein R=the maximum radius of the defined rotor1, that is, a length between the first center t1and the second point P2)6. Define an arc B by drawing around the third center t3with the radius rBfrom the second point P2to a third point P3, wherein the third point P3is vertically located above the third center t3.7. Define an arc F by drawing around the first center t1with a radius rFfrom a first point P1to a fourth point P4wherein the fourth point P4is designated by an central angle β (β is 15°) measured downward from the first point P1according to the first center t1, and the radius rFis defined by following equation rF=2 Rp−R.8. Prior to generating an arc C, define a third line h3which is an extension line with the direction of straight connecting the fourth point P4and the first center t1, and further designate a fourth center t4being located in the third line h3.9. Defining an arc C by drawing around the fourth center t4with a radius rCfrom the fourth point P4to a fifth point P5, wherein the fifth point P5is vertically located under the fourth center t4, and the radius rCis defined by following equation:

rC=x+rF=⁢x⁢⁢sin⁢⁢β+D2⁢⇒x=(D/2)-rF1-sin⁢⁢β;⁢rC=(D/2)-rF1-sin⁢⁢β+rFin which rF=2 Rp−R.10. Define a horizontal line Y by connecting the third point P3and a sixth point P6which is symmetrical to the fifth point P5; whereby curve portions of half two lobes of the defined rotor1are generated by smooth linking the curve E, the arc A, arc B, arc F, arc C, and the horizontal line Y. And further symmetrically imaging each arc and curve of half two lobes of the defined rotor1to form the complete defined rotor1with doublelobes.11. Furthermore, the conjugate rotor2is formed by way of aforesaid curve portions of the defined rotor1and through a conjugate curve profiled respectively from each arc and curve of the double-lobe of the defined rotor1by the above-described steps, the double-lobe defined rotor1and the conjugate rotor2are formed accordingly.

Further referring toFIG. 4, which is a schematic view of various combinations of the double-lobe defined rotor and conjugate rotor, wherein a width D thereof is 55, 60 . . . 80 mm, a central angle α is 5° and a central angel β is 5°; as general characteristics of conjugate intermeshing between two rotors, the defined rotor1(S1) of the minimum width D corresponds to the conjugate rotor2(L1) of the maximum value. Accordingly, depending on practical applications, an appropriate size of the defined rotor1and the conjugate rotor2can be determined by analogy with aforesaid characteristics.

Moreover, referring toFIG. 5for methods for generating curve portions of the single-lobe defined rotor1′; in the manner of generating the curve portions of half two lobes of the defined rotor1, that is, bold parts shown inFIG. 2. Further designating a symmetry point P8which is symmetrical to the fourth point P4against the first center t1, and which is located in an extension direction of a third line h3. A fourth center t4′ located on the third line h3and being symmetrical to the fourth center t4against the first center t1, and defining an arc C′ by drawing around the fourth center t4′ with the radius rCfrom the symmetry point P8to the sixth point P6; therefore the sixth point P6of the arc C′ is tangent to the horizontal line Y; further defining an arc G by drawing around the first center t1with the radius rFfrom the fourth point P4to the symmetry point P8, whereby the arc C′ is smoothly linked with the horizontal line Y and the arc G; consequently, the single-lobe defined rotor1′ is profiled by linking the curve E, arc A, arc B, arc F, arc C′, arc G and horizontal line Y

The single-lobe conjugate rotor2′ is formed (shown inFIG. 6) by way of aforesaid curve portions and through the conjugate curve profiled respectively from each arc and curve of the single-lobe of the defined rotor1by the above-described steps.

By parameterized sets, the methods can profile a single-lobe or double-lobe of a defined rotor and a conjugate rotor which intermesh and conjugate to each other, and effectively evaluate optimum performance in intermeshing and conjugating, whereby to provide higher compression ratio and larger discharge capacity, secure a smooth process while working chamber undergoing compression and expansion, and which reduce leakage, thus lessen noise and vibration while operation of the rotors. Besides, the conjugate curve portions of the conjugate rotor2relatively profiled through the arc F and arc G of the defined rotor1are still arcs, could effectively enhance the sealing ability further.