CN101956793A - Six-drive and three-reverse planet speed changer - Google Patents

Abstract

The invention belongs to a planet speed changer, in particular relates to a six-drive and three-reverse planet speed changer for an automatic gearbox, which aims to realize six drive gears by utilizing few planet rows, wherein the speed changer consists of two simple planet rows and a complex planet row, and is provided with six manipulating pieces; a first simple planet row consists of one row of gear rings R1, one row of planet carriers PC1, one row of sun wheels S1 and one row of planet wheels P1; a second simple planet row consists of two rows of gear rings R2, two rows of planet carriers PC2, two rows of sun wheels S2 and two rows of planet wheels P2; and the complex planet row consists of a complex row sun wheel S3, a complex row planet carrier PC3, a complex row minor gear ring R3, a complex row major gear ring R4, a complex row long planet wheel P3 and a complex row short planet wheel P4. The six-drive and three-reverse planet speed changer has the advantages that the three planet rows realize six drive gears and three reverse gears, gears are switched by only one manipulating piece, and the rotation speed of the planet wheels of the speed changer is low.

Description

Six first three the backward star speed changers that are used for automatic transmission case

Technical field

The invention belongs to a kind of planetary transmission that is used for automatic transmission case, specifically is a kind of planetary transmission with six forward gearss and three reverse gears.

Background technique

The gear of automatic transmission case changes the rotating speed and the moment of torsion of fluid torque converter output, and rotating speed and moment of torsion after changing are exported by output shaft.As everyone knows, for manual transmission, gear too much can cause the driver tired in buty shifting, but the gear shift of automatic transmission case does not need the driver manually to operate, and therefore, the gear of automatic transmission case is many more, velocity ratio series is easy more optimised, its power performance and fuel economy are good more, so, utilize investment cost to realize more gear as far as possible.

When having determined velocity ratio series, the transmission sketch that chooses is a very important job, and this is because efficient, size and the reliability of speed changer depend on the transmission sketch to a great extent.

The planetary transmission of present four forward gearss and five forward gearss has been applied among the vehicle, recently domestic and international scientific worker is studying the planetary transmission of six forward gearss, for example the patent of U.S.'s issue on March 23rd, 2006: US2006/0063635A1.Planetary transmission in this patent is realized 1 grade in conjunction with C3 and B1, realizes 2 grades in conjunction with C3 and B2, realizes 3 grades in conjunction with C3 and C1, realizes 4 grades in conjunction with C3 and C2, realizes 5 grades in conjunction with C1 and C2, realizes 6 grades in conjunction with C2 and B2, realizes reverse gear in conjunction with C1 and B1; Add up to and used 4 planet rows and 6 operator; Its shortcoming is: planet row quantity is more, makes that the speed changer overall dimensions is big, oil consumption, and mechanical efficiency is low; The planet wheel relative rotation speed is higher simultaneously, makes that price is more expensive to the requirement height of structural design and material.

Summary of the invention

The purpose of this invention is to provide a kind of six first three backward star speed changers that are used for automatic transmission case, can utilize less planet to arrange and realize six forward gears, and make the planet wheel relative rotation speed lower.

The present invention is achieved in that a kind of six first three backward star speed changers that are used for automatic transmission case, and wherein, described speed changer is made up of two simple planet rows and a compound planetary row, has 6 operator;

First simple planet row is made up of a toothrow circle R1, a rows of planetary frame PC1, a row sun gear S1 and a seniority among brothers and sisters star-wheel P1, a seniority among brothers and sisters star-wheel P1 while and a toothrow circle R1, row's sun gear S1 engagement, and a rows of planetary frame PC1 supports a seniority among brothers and sisters star-wheel P1;

Second simple planet row is made up of two toothrow circle R2, two-row planetary frame PC2, two row sun gear S2 and two-row planetary wheel P2, two-row planetary wheel P2 while and two toothrow circle R2, two row's sun gear S2 engagements, and two-row planetary frame PC2 supports two-row planetary wheel P2;

Compound row is made up of compound row's sun gear S3, compound rows of planetary frame PC3, the little gear ring R3 of compound row, compound row's bull gear R4, compound platoon leader's planet wheel P3, compound row weak point planet wheel P4, planet carrier PC3 supports planet wheel P3 and planet wheel P4, and planet wheel P3 and planet wheel P4 are meshing with each other;

1. input shaft uses 1 bearings on case of transmission, and a rows of planetary frame PC 1 and two-row planetary frame PC2 adopt 2 bearings 1. to go up at input shaft, and 1. input shaft also is fastenedly connected with row's sun gear S1, two row sun gear S2 and clutch CH De Wai Grains;

Clutch CH De Nei Grains is connected with a break CR De Nei Grains and a rows of planetary frame PC1 simultaneously, and break CR De Wai Grains is fixedly mounted on the case of transmission;

One seniority among brothers and sisters star-wheel P1 is installed among the rows of planetary frame PC1, and a row sun gear S1 and a seniority among brothers and sisters star-wheel P1 are meshed, a seniority among brothers and sisters star-wheel P1 and row's bull gear R1 engagement, and row's bull gear R1 is fixedlyed connected with two-row planetary frame PC2,

Two-row planetary wheel P2 is installed among the two-row planetary frame PC2, two row sun gear S2 and two-row planetary wheel P2 are meshed, two-row planetary wheel P2 and two row's bull gear R2 engagements, two row bull gear R2 and break CL De Nei Grains are one, break CL De Wai Grains is fixedly mounted on the case of transmission;

Two-row planetary frame PC2 is fixedlyed connected with the little gear ring R3 of compound row by drive plate, and drive plate adopts two splines to connect and realizes, the support arm that is connected on the case of transmission is realized supporting to drive plate;

The little gear ring R3 of compound row and compound platoon leader's planet wheel P3 engagement; The short planet wheel P4 engagement of compound row's bull gear R4 and compound row, compound row's bull gear R4 is fixedlyed connected with break C1 De Nei Grains, and compound platoon leader's planet wheel P3, compound row weak point planet wheel P4 are installed among the compound rows of planetary frame PC3,

Compound row's sun gear S3 and compound platoon leader's planet wheel P3 are meshed, and compound row's sun gear S3 and clutch C3 De Wai Grains are connected, and by bearings on housing; Compound rows of planetary frame PC3 and clutch C3 De Nei Grains are connected, and by bearings on housing,

Break C2 De Wai Grains and housing are connected, and break C2 De Nei Grains and clutch C3 De Wai Grains are one;

2. output shaft is fastenedly connected with compound rows of planetary frame PC3.

Aforesaid a kind of six first three backward star speed changers that are used for automatic transmission case, wherein,

Each planet row's interior velocity ratio, the gear ratio of the gear that promptly is meshed is respectively:

The little gear ring R3:Z of compound row's bull gear R4 and compound row _R4/ Z _R3=1.065,

The little gear ring R3 of compound row and compound row's sun gear S3:Z _R3/ Z _S3=2.265,

Two toothrow circle R2 and two row's sun gear S2: ${\mathrm{<figure-callout\; id="2"\; label="Z\; R"\; filenames="H2009101613191E0000011.png,H2009101613191E0000012.png"\; state="\{\{state\}\}">Z</figure-callout>}}_R/{\mathrm{<figure-callout\; id="2"\; label="Z\; S"\; filenames="H2009101613191E0000011.png,H2009101613191E0000012.png"\; state="\{\{state\}\}">Z</figure-callout>}}_{S_{}}=2.111,$

One toothrow circle R1 and two row's sun gear S1:Z _R1/ Z _S1=2.852.

Advantage of the present invention has been simplified the transmission sketch, has reduced the size of automatic transmission case, has alleviated the weight of gearbox, has reduced manufacturing expense.

The present invention can realize six forward gearss and three reverse gears with 3 planet rows.This planet speed changer is made up of two simple rows and a compound row, directly or indirectly is connected with input and output shaft (or casing) with the basic building block (gear ring, planet carrier and sun gear) of six operator (two clutches, four breaks) with each row.

Simultaneously, forward gear D1 to forward gear D2, forward gear D2 to forward gear D3, the switching of forward gear D4 to forward gear D5, forward gear D5 to forward gear D6 only need move an operator, is easy to design controller for shifting.

Speed changer planet wheel relative rotation speed provided by the present invention is lower, is easy to structural design.

Description of drawings

Fig. 1 is the sketch that is used for the planetary transmission of automatic transmission case;

Fig. 2 is the relative rotation speed planimetric map of each basic building block in the planetary transmission;

Fig. 3 is a kind of practical structures figure that is used for six first three backward star speed changers of automatic transmission case.

Wherein, R1 one toothrow circle, PC1 one rows of planetary frame, S1 one row's sun gear, P1 one seniority among brothers and sisters star-wheel, R2 two toothrow circles, PC2 two-row planetary frame, S2 two row's sun gears, P2 two-row planetary wheel, the compound row's sun gear of S3, the compound rows of planetary frame of PC3, the little gear ring of the compound row of R3, the compound row's bull gear of R4, the compound platoon leader's planet wheel of P3, the short planet wheel of the compound row of P4, operator CL, C1, C2 and CR are break, and operator CH and C3 are clutch;

1. input shaft, 2. output shaft, 3. two toothrow circle R2 and break CL, 4. a rows of planetary frame PC1 and break CR, 5. compound row's sun gear S3,6. compound row's bull gear R4 and break C1,7. little gear ring R3 of compound row and two-row planetary frame PC2,8. clutch CH, 9. clutch C3;

Among Fig. 31,2,4,8 be among Fig. 1 1., 2., 4., 8..

Embodiment

The present invention is described further below in conjunction with the drawings and specific embodiments:

As shown in Figure 1, this figure has described the concrete scheme of planetary transmission, and it is made up of two simple planet rows and a compound planetary row, has 6 operator, and this planet speed changer can be realized 6 forward gearss and 3 reverse gears.

First simple planet row is made up of a toothrow circle R1, a rows of planetary frame PC1, a row sun gear S1 and a seniority among brothers and sisters star-wheel P1, a seniority among brothers and sisters star-wheel P1 while and a toothrow circle R1, row's sun gear S1 engagement, and a rows of planetary frame PC1 supports a seniority among brothers and sisters star-wheel P1.

Second simple planet row is made up of two toothrow circle R2, two-row planetary frame PC2, two row sun gear S2 and two-row planetary wheel P2, two-row planetary wheel P2 while and two toothrow circle R2, two row's sun gear S2 engagements, and two-row planetary frame PC2 supports two-row planetary wheel P2.

Compound row is made up of compound row's sun gear S3, compound rows of planetary frame PC3, the little gear ring R3 of compound row, compound row's bull gear R4, compound platoon leader's planet wheel P3, compound row weak point planet wheel P4, planet carrier PC3 supports planet wheel P3 and planet wheel P4, and planet wheel P3 and planet wheel P4 are meshing with each other.

In this planet speed changer, operator CL, C1, C2 and CR are break, and operator CH and C3 are clutch;

For convenience of description, rotatable parts are defined as successively: input shaft 1., output shaft 2., two toothrow circle R2 and break CL 3., a rows of planetary frame PC1 and break CR 4., compound row's sun gear S3 is 5., compound row's bull gear R3 and break C1 are 6., little gear ring R4 of compound row and two-row planetary frame PC2 7., clutch CH 8., clutch C3 is 9..

1. input shaft uses 1 bearings on case of transmission, and a rows of planetary frame PC 1 and two-row planetary frame PC2 adopt 2 bearings 1. to go up at input shaft, and 1. input shaft also is fastenedly connected with row's sun gear S1, two row sun gear S2 and clutch CH De Wai Grains;

Clutch CH De Nei Grains is connected with a break CR De Nei Grains and a rows of planetary frame PC1 simultaneously, and break CR De Wai Grains is fixedly mounted on the case of transmission;

One seniority among brothers and sisters star-wheel P1 is installed among the rows of planetary frame PC1, and a row sun gear S1 and a seniority among brothers and sisters star-wheel P1 are meshed, a seniority among brothers and sisters star-wheel P1 and row's bull gear R1 engagement, and row's bull gear R1 is fixedlyed connected with two-row planetary frame PC2,

Two-row planetary wheel P2 is installed among the two-row planetary frame PC2, two row sun gear S2 and two-row planetary wheel P2 are meshed, two-row planetary wheel P2 and two row's bull gear R2 engagements, two row bull gear R2 and break CL De Nei Grains are one, break CL De Wai Grains is fixedly mounted on the case of transmission;

Two-row planetary frame PC2 is fixedlyed connected with the little gear ring R3 of compound row by drive plate, and drive plate adopts two splines to connect and realizes, the support arm that is connected on the case of transmission is realized supporting to drive plate;

The little gear ring R3 of compound row and compound platoon leader's planet wheel P3 engagement; The short planet wheel P4 engagement of compound row's bull gear R4 and compound row, compound row's bull gear R4 is fixedlyed connected with break C1 De Nei Grains, and compound platoon leader's planet wheel P3, compound row weak point planet wheel P4 are installed among the compound rows of planetary frame PC3,

Compound row's sun gear S3 and compound platoon leader's planet wheel P3 are meshed, and compound row's sun gear S3 and clutch C3 De Wai Grains are connected, and by bearings on housing; Compound rows of planetary frame PC3 and clutch C3 De Nei Grains are connected, and by bearings on housing,

Break C2 De Wai Grains and housing are connected, and break C2 De Nei Grains and clutch C3 De Wai Grains are one;

2. output shaft is fastenedly connected with compound rows of planetary frame PC3,

Each planet row's interior velocity ratio among Fig. 1, the gear ratio of the gear that promptly is meshed is respectively:

The little gear ring R3:Z of compound row's bull gear R4 and compound row _R4/ Z _R3=1.065,

The little gear ring R3 of compound row and compound row's sun gear S3:Z _R3/ Z _S3=2.265,

Two toothrow circle R2 and two row's sun gear S2: ${\mathrm{<figure-callout\; id="2"\; label="Z\; R"\; filenames="H2009101613191E0000011.png,H2009101613191E0000012.png"\; state="\{\{state\}\}">Z</figure-callout>}}_R/{\mathrm{<figure-callout\; id="2"\; label="Z\; S"\; filenames="H2009101613191E0000011.png,H2009101613191E0000012.png"\; state="\{\{state\}\}">Z</figure-callout>}}_{S_{}}=2.111,$

One toothrow circle R1 and two row's sun gear S1:Z _R1/ Z _S1=2.852.

Below be the explanation that each gear is realized, D1～D6 is a forward gears, and R1～R3 is for retreating shelves:

(1) realize the D1 shelves in conjunction with operator break CL and break C1,

1. power imported by input shaft, sends power to two-row planetary frame PC2 by two row's sun gear S2 then, and the little gear ring R3 of two-row planetary frame PC2 and compound row is an one; The little gear ring R3 of compound row is sent to short planet wheel P4 of compound row and compound rows of planetary frame PC3 with power, at last by 2. outputting power of output shaft;

(2) realize the D2 shelves in conjunction with operator break CL and break C2,

1. power imported by input shaft, sends power to two-row planetary frame PC2 by two row's sun gear S2 then, and the little gear ring R3 of two-row planetary frame PC2 and compound row is an one; The little gear ring R3 of compound row is sent to compound platoon leader's planet wheel P3 and compound rows of planetary frame PC3 successively with power, at last by 2. outputting power of output shaft; At this moment, under the effect of break C2, compound row's sun gear S3 fixes, and does not rotate;

(3) realize the D3 shelves in conjunction with operator break CL and clutch C3,

1. power imported by input shaft, send power to two-row planetary frame PC2 by two row's sun gear S2 then, the little gear ring R3 of two-row planetary frame PC2 and compound row is an one, this moment, clutch C3 connected as one compound row's sun gear S3 and compound rows of planetary frame PC3, the little gear ring R3 of compound row is sent to compound row's sun gear S3 and compound rows of planetary frame PC3 with power, at last by 2. outputting power of output shaft;

(4) realize the D4 shelves in conjunction with operator clutch CH and break C1,

1. power imported by input shaft, then by row's sun gear S1, a rows of planetary frame PC1, this moment, clutch CH connected as one S1 and PC1, power is sent to a seniority among brothers and sisters star-wheel P1, a toothrow circle R1, two-row planetary frame PC2, the little gear ring R3 of compound row by a rows of planetary frame PC1, the little gear ring R3 of compound row is sent to short planet wheel P4 of compound row and compound rows of planetary frame PC3 with power, at last by 2. outputting power of output shaft;

(5) realize the D5 shelves in conjunction with operator clutch CH and break C2,

1. power imported by input shaft, then by row's sun gear S1, a rows of planetary frame PC1, this moment, clutch CH connected as one a row sun gear S1 and a rows of planetary frame PC1, power is sent to a seniority among brothers and sisters star-wheel P1, a toothrow circle R1, two-row planetary frame PC2, the little gear ring R3 of compound row by a rows of planetary frame PC1, the little gear ring R3 of compound row is sent to compound platoon leader's planet wheel P3 and compound rows of planetary frame PC3 successively with power, at last by 2. outputting power of output shaft; At this moment, under the effect of break C2, compound row's sun gear S3 fixes, and does not rotate;

(6) realize the D6 shelves in conjunction with operator CH and C3,

1. power imported by input shaft, then by row's sun gear S1, a rows of planetary frame PC1, this moment, clutch CH connected as one a row sun gear S1 and a rows of planetary frame PC1, power is sent to a seniority among brothers and sisters star-wheel P1, a toothrow circle R1, two-row planetary frame PC2, the little gear ring R3 of compound row by a rows of planetary frame PC1, this moment, clutch C3 connected as one compound row's sun gear S3 and compound rows of planetary frame PC3, the little gear ring R3 of compound row is sent to compound row's sun gear S3 and compound rows of planetary frame PC3 with power, at last by 2. outputting power of output shaft;

(7) realize the R1 shelves in conjunction with operator break CR and break C1,

1. power imported by input shaft, then by row's sun gear S1, a seniority among brothers and sisters star-wheel P1, a toothrow circle R1, two-row planetary frame PC2, the little gear ring R3 of compound row, break CR is fixedlyed connected a rows of planetary frame PC1 with case of transmission, the sense of rotation of R1 changes, and realizes reverse gear; The little gear ring R3 of compound row is sent to P4 and planet carrier PC3 with power, at last by 2. outputting power of output shaft;

(8) realize the R2 shelves in conjunction with operator break CR and break C2,

1. power imported by input shaft, then by row's sun gear S1, a seniority among brothers and sisters star-wheel P1, a toothrow circle R1, two-row planetary frame PC2, the little gear ring R3 of compound row, the little gear ring R3 of compound row is sent to compound platoon leader's planet wheel P3 and compound rows of planetary frame PC3 successively with power, at last by 2. outputting power of output shaft; At this moment, compound row's sun gear S3 fixes, and does not rotate;

(9) realize the R3 shelves in conjunction with operator break CR and clutch C3.

Power is imported by input shaft, then by row's sun gear S1, a seniority among brothers and sisters star-wheel P1, a toothrow circle R1, two-row planetary frame PC2, the little gear ring R3 of compound row, this moment, clutch C3 connected as one compound row's sun gear S3 and compound rows of planetary frame PC3, the little gear ring R3 of compound row is sent to compound row's sun gear S3 and compound rows of planetary frame PC3 with power, at last by 2. outputting power of output shaft;

Aforesaid design proposal can obtain the relative rotation speed planimetric map of each basic building block in the planetary transmission shown in Figure 2, can obtain the relative rotation speed of each member in each gear intuitively among Fig. 2, Fig. 2 promptly can obtain according to scheme shown in Figure 1 and above-mentioned interior velocity ratio, and this is the common practise in present technique field;

And can directly design the speed changer with performance as shown in table 1, simultaneously, reach under the situation of this performance, the speed changer that designs has lower relative rotation speed and less relative moment shown in table 2 and table 3.Gear R3 less application when reality is used is not so provide data.

Table 1 is planetary transmission gear and velocity ratio, and this figure has described the operator of realizing the required combination of each gear, has provided the rank ratio between the gear simultaneously.

Table 2 is the planetary transmission relative rotation speed, and this figure has described the relative rotation speed of member when each gear.

Table 3 is the planetary transmission relative moment, and this figure has described the relative moment of member when each gear.

Table 1 planetary transmission gear and velocity ratio

Table 2 member relative rotation speed

Wherein, n ₁～n ₉What represent is 9 rotatable parts that indicate among Fig. 1, n _X1～n _X4That represent is a seniority among brothers and sisters star-wheel P1, two-row planetary wheel P2, compound platoon leader's planet wheel P3, the short planet wheel P4 of compound row.

Table 3 member relative moment

Wherein, when theory was calculated, compound row was considered to two planet rows, and the little gear ring R3 of compound row, compound rows of planetary frame PC3 think fourth line star row's four row's sun gear and four rows of planetary framves simultaneously.

Fig. 3 has provided a kind of speed changer that designs according to the method described above, its compact structure, planet wheel relative rotation speed are lower, operation conditions and K-theoretic operation K in actual loading test are more or less the same, and have embodied a kind of advantage that is used for six first three backward star speed changers of automatic transmission case of the present invention; Among Fig. 31,2,4,8 be among Fig. 1 1., 2., 4., 8..

Claims (2)

1. six first three backward star speed changers that are used for automatic transmission case is characterized in that: described speed changer is arranged by two simple planets rows and a compound planetary and is formed, and has 6 operator;

First simple planet row is made up of a toothrow circle R1, a rows of planetary frame PC1, a row sun gear S1 and a seniority among brothers and sisters star-wheel P1, a seniority among brothers and sisters star-wheel P1 while and a toothrow circle R1, row's sun gear S1 engagement, and a rows of planetary frame PC1 supports a seniority among brothers and sisters star-wheel P1;

Second simple planet row is made up of two toothrow circle R2, two-row planetary frame PC2, two row sun gear S2 and two-row planetary wheel P2, two-row planetary wheel P2 while and two toothrow circle R2, two row's sun gear S2 engagements, and two-row planetary frame PC2 supports two-row planetary wheel P2;

Compound row is made up of compound row's sun gear S3, compound rows of planetary frame PC3, the little gear ring R3 of compound row, compound row's bull gear R4, compound platoon leader's planet wheel P3, compound row weak point planet wheel P4, planet carrier PC3 supports planet wheel P3 and planet wheel P4, and planet wheel P3 and planet wheel P4 are meshing with each other;

1. input shaft uses 1 bearings on case of transmission, and a rows of planetary frame PC1 and two-row planetary frame PC2 adopt 2 bearings 1. to go up at input shaft, and 1. input shaft also is fastenedly connected with row's sun gear S1, two row sun gear S2 and clutch CH De Wai Grains;

Clutch CH De Nei Grains is connected with a break CR De Nei Grains and a rows of planetary frame PC1 simultaneously, and break CR De Wai Grains is fixedly mounted on the case of transmission;

One seniority among brothers and sisters star-wheel P1 is installed among the rows of planetary frame PC1, and a row sun gear S1 and a seniority among brothers and sisters star-wheel P1 are meshed, a seniority among brothers and sisters star-wheel P1 and row's bull gear R1 engagement, and row's bull gear R1 is fixedlyed connected with two-row planetary frame PC2,

Two-row planetary wheel P2 is installed among the two-row planetary frame PC2, two row sun gear S2 and two-row planetary wheel P2 are meshed, two-row planetary wheel P2 and two row's bull gear R2 engagements, two row bull gear R2 and break CL De Nei Grains are one, break CL De Wai Grains is fixedly mounted on the case of transmission;

Two-row planetary frame PC2 is fixedlyed connected with the little gear ring R3 of compound row by drive plate, and drive plate adopts two splines to connect and realizes, the support arm that is connected on the case of transmission is realized supporting to drive plate;

The little gear ring R3 of compound row and compound platoon leader's planet wheel P3 engagement; The short planet wheel P4 engagement of compound row's bull gear R4 and compound row, compound row's bull gear R4 is fixedlyed connected with break C1 De Nei Grains, and compound platoon leader's planet wheel P3, compound row weak point planet wheel P4 are installed among the compound rows of planetary frame PC3,

Compound row's sun gear S3 and compound platoon leader's planet wheel P3 are meshed, and compound row's sun gear S3 and clutch C3 De Wai Grains are connected, and by bearings on housing; Compound rows of planetary frame PC3 and clutch C3 De Nei Grains are connected, and by bearings on housing,

Break C2 De Wai Grains and housing are connected, and break C2 De Nei Grains and clutch C3 De Wai Grains are one;

2. output shaft is fastenedly connected with compound rows of planetary frame PC3.

2. a kind of six first three backward star speed changers that are used for automatic transmission case as claimed in claim 1 is characterized in that:

Each planet row's interior velocity ratio, the gear ratio of the gear that promptly is meshed is respectively:

The little gear ring R3:Z of compound row's bull gear R4 and compound row _R4/ Z _R3=1.065,

The little gear ring R3 of compound row and compound row's sun gear S3:Z _R3/ Z _S3=2.265,

Two toothrow circle R2 and two row's sun gear S2: $Z_{R2}/Z_{S_2}=2.111,$

One toothrow circle R1 and two row's sun gear S1:Z _R1/ Z _S1=2.852.

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