CN109029318A - A kind of calculation method of spur gear planetary gear train volume - Google Patents
A kind of calculation method of spur gear planetary gear train volume Download PDFInfo
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- CN109029318A CN109029318A CN201811144734.1A CN201811144734A CN109029318A CN 109029318 A CN109029318 A CN 109029318A CN 201811144734 A CN201811144734 A CN 201811144734A CN 109029318 A CN109029318 A CN 109029318A
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- 241001269238 Data Species 0.000 claims abstract description 7
- 238000000034 method Methods 0.000 claims description 14
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- 238000012986 modification Methods 0.000 description 2
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Classifications
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
- G01B21/00—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant
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- F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
- F16—ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
- F16H—GEARING
- F16H1/00—Toothed gearings for conveying rotary motion
- F16H1/28—Toothed gearings for conveying rotary motion with gears having orbital motion
- F16H1/32—Toothed gearings for conveying rotary motion with gears having orbital motion in which the central axis of the gearing lies inside the periphery of an orbital gear
-
- F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
- F16—ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
- F16H—GEARING
- F16H57/00—General details of gearing
- F16H2057/0087—Computer aided design [CAD] specially adapted for gearing features; Analysis of gear systems
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- General Engineering & Computer Science (AREA)
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- General Physics & Mathematics (AREA)
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Abstract
The invention discloses a kind of calculation methods of spur gear planetary gear train volume, it obtains the number of teeth of any three gears and other related datas in spur gear planetary gear train the following steps are included: S1；S2 calculates the number of teeth of a remaining gear in spur gear planetary gear train；S3 calculates the tip diameter of all spur gears in spur gear planetary gear train；S4 calculates the volume of all spur gears in spur gear planetary gear train；S5 calculates the volume of spur gear planetary gear train.The present invention can it is fast and convenient calculate spur gear planetary gear train volume, calculation method is simple, substantially increases the computational accuracy of spur gear planetary gear train volume.
Description
Technical field
The present invention relates to gear wheel-train art drive systems field, specifically a kind of spur gear planetary gear train volume
Calculation method.
Background technique
Planetary gear train have compact-sized, small in size, large carrying capacity, transmitting power bracket it is big, running noises are small, efficiency
The advantages that high and service life is long, in the mechanical equipment of the departments such as national defence, metallurgy, lifting transport, mine, chemical industry, light textile, building industry
In, it has been more and more widely used.All gears are all made of spur gear in spur gear planetary gear train, have the processing is simple Deng spies
Point.Spur gear planetary gear train stereometer is the basis of spur gear planetary gear train volume optimization.Therefore, carry out spur gear planetary gear
It is that volume calculates research with important engineering significance.
The calculating of train volume mostly uses simplified method at present, greatly reduces the precision of train volume-based model.
Summary of the invention
In view of the deficiencies of the prior art, the invention proposes a kind of calculation methods of spur gear planetary gear train volume, significantly
Improve the computational accuracy of spur gear planetary gear train volume.
The present invention solves its technical problem and adopts the technical scheme that:
A kind of calculation method of spur gear planetary gear train volume provided in an embodiment of the present invention, the spur gear planetary gear train
Structure mainly include rack, centre wheel one, planetary gear one, planetary gear two, centre wheel two, planet carrier, centre wheel one and planet
One engagement of wheel, planetary gear two are engaged with centre wheel two, and planetary gear one and planetary gear two are connected on the same axis, centre wheel two and machine
Frame is fixed together, and the facewidth of intermeshing spur gear is equal, and all spur gears are master gear, ignores the body of planet carrier
Product, characterized in that the calculation method the following steps are included:
S1 obtains the number of teeth of any three gears and other related datas in spur gear planetary gear train；
S2 calculates the number of teeth of a remaining gear in spur gear planetary gear train；
S3 calculates the tip diameter of all spur gears in spur gear planetary gear train；
S4 calculates the volume of all spur gears in spur gear planetary gear train；
S5 calculates the volume of spur gear planetary gear train.
As a kind of possible implementation of the present embodiment, in step sl, any three in the spur gear planetary gear train
The number of teeth of a gear and other related datas include: the number of teeth z of any three gearsa、zb、zc, number of teeth zaGear and tooth
Number is zbGear engagement, addendum coefficient ha *, tip clearance coefficient c*, number of teeth zaGear modulus ma, number of teeth zcGear
Modulus mc, number of teeth zaGear facewidth ba, number of teeth zcGear facewidth bcAnd the number of teeth is zaGear cooperation axis
Diameter dzhaAnd the number of teeth is zbGear cooperation diameter of axle dzhbAnd the number of teeth is zcGear cooperation diameter of axle dzhcAn and remaining tooth
Take turns the diameter of axle d of cooperationzhd。
As a kind of possible implementation of the present embodiment, in step s 2, residue one in spur gear planetary gear train is calculated
The detailed process of the number of teeth of a gear are as follows:
The number of teeth z of a remaining gear is calculated by the concentric condition calculation formula of planetary gear traind.V is as this reality
Apply a kind of possible implementation of example, the concentric condition calculation formula of the planetary gear train are as follows:
In formula, zdFor the number of teeth of a remaining gear, za、zb、zcFor the tooth of three gears any in spur gear planetary gear train
Number, maIt is z for the number of teethaGear modulus, mcIt is z for the number of teethcGear modulus.
As a kind of possible implementation of the present embodiment, in step s3, calculate all straight in spur gear planetary gear train
The detailed process of the tip diameter of gear are as follows:
It is z that the number of teeth, which is calculated, by the tip diameter calculation formula of spur gearaGear tip diameter daa, tooth
Number is zbGear tip diameter dab, number of teeth zcGear tip diameter dac, number of teeth zdGear tooth top
Circular diameter dad。
As a kind of possible implementation of the present embodiment, the tip diameter calculation formula of the spur gear are as follows:
In formula, daFor the tip diameter of spur gear, m is the modulus of spur gear, and z is the number of teeth of spur gear, ha *For tooth top
High coefficient.
As a kind of possible implementation of the present embodiment, in step s 4, calculate all straight in spur gear planetary gear train
The detailed process of the volume of gear are as follows:
According to the tip diameter of spur gear, the volume calculation formula of spur gear is reasonably selected, the volume of spur gear is passed through
It is z that the number of teeth, which is calculated, in calculation formulaaGear volume Va, number of teeth zbGear volume Vb, number of teeth zcGear
Volume Vc, number of teeth zdGear volume Vd。
As a kind of possible implementation of the present embodiment, when the tip diameter of spur gear is less than or equal to 160mm, institute
State the volume calculation formula of spur gear are as follows:
In formula, V is the volume of spur gear, and b is the facewidth of spur gear, and z is the number of teeth of spur gear, and m is the modulus of spur gear,
dzhFor the diameter of axle cooperated with spur gear；
When the tip diameter of spur gear is greater than 160mm and is less than or equal to 500mm, the volume of the spur gear is calculated
Formula are as follows:
In formula, V is the volume of spur gear, and b is the facewidth of spur gear, and m is the modulus of spur gear, and z is the number of teeth of spur gear,
daFor the tip diameter of spur gear, dzhFor the diameter of axle cooperated with spur gear；
When the tip diameter of spur gear is greater than 500mm and is less than 1000mm, the volume of the spur gear calculates public
Formula are as follows:
In formula, V is the volume of spur gear, and b is the facewidth of spur gear, and m is the modulus of spur gear, and z is the number of teeth of spur gear,
daFor the tip diameter of spur gear, ha *For addendum coefficient, c*For tip clearance coefficient, dzhFor the diameter of axle cooperated with spur gear；
When the tip diameter of spur gear is more than or equal to 1000mm, the volume calculation formula of the spur gear are as follows:
In formula, V is the volume of spur gear, and b is the facewidth of spur gear, and m is the modulus of spur gear, and z is the number of teeth of spur gear,
daFor the tip diameter of spur gear, ha *For addendum coefficient, c*For tip clearance coefficient, dzhFor the diameter of axle cooperated with spur gear.
As a kind of possible implementation of the present embodiment, the detailed process of the step S5 are as follows:
The body of spur gear planetary gear train is calculated by the volume calculation formula of spur gear planetary gear train shown in formula (7)
Product Vz,
Vz=Va+Vb+Vc+Vd (7)
In formula, VzFor the volume of spur gear planetary gear train, VaIt is z for the number of teethaGear volume, VbIt is z for the number of teethbTooth
The volume of wheel, VcIt is z for the number of teethcGear volume, VdIt is z for the number of teethdGear volume.
What the technical solution of the embodiment of the present invention can have has the beneficial effect that:
The calculation method of a kind of spur gear planetary gear train volume of technical solution of the embodiment of the present invention, according to spur gear planet
The structure of train obtains the number of teeth of any three gears and other related datas in spur gear planetary gear train, calculates spur gear
The number of teeth of a remaining gear, calculates the tip diameter of all spur gears in spur gear planetary gear train in planetary gear train, calculates
The volume of all spur gears in spur gear planetary gear train calculates the volume of spur gear planetary gear train.The present invention fast and convenient can count
The volume of spur gear planetary gear train is calculated, calculation method is simple, substantially increases the computational accuracy of spur gear planetary gear train volume.
Detailed description of the invention
Fig. 1 is a kind of process of the calculation method of spur gear planetary gear train volume shown according to an exemplary embodiment
Figure；
Fig. 2 is a kind of transmission principle figure of spur gear planetary gear train shown according to an exemplary embodiment；
Symbol indicates in Fig. 2: 1, rack, 2, centre wheel one, 3, planetary gear one, 4, planetary gear two, 5, centre wheel two, H, row
Carrier.
Specific embodiment
In order to clarify the technical characteristics of the invention, below by specific embodiment, and its attached drawing is combined, to this hair
It is bright to be described in detail.In order to simplify disclosure of the invention, hereinafter the component of specific examples and setting are described.This
Outside, the present invention can in different examples repeat reference numerals and/or letter.This repetition is for simplified and clear mesh
, the relationship between discussed various embodiments and/or setting itself is not indicated.It should be noted that illustrated in the accompanying drawings
Component is not drawn necessarily to scale.Present invention omits the descriptions to known assemblies and treatment technology and process to avoid unnecessary
The ground limitation present invention.
As shown in Fig. 2, the structure of spur gear planetary gear train mainly includes rack 1, centre wheel 1, planetary gear 1, planet
24, centre wheel 25, planet carrier H are taken turns, centre wheel 1 is engaged with planetary gear 1, and planetary gear 24 is engaged with centre wheel 25, row
Star-wheel 1 and planetary gear 23 are connected on the same axis, and centre wheel 25 is fixed together with rack 1, intermeshing spur gear
The facewidth it is equal, all spur gears are master gear, ignore the volume of planet carrier.
For the structure of above-mentioned spur gear planetary gear train, the present invention provides a kind of calculating of spur gear planetary gear train volume
Method obtains in spur gear planetary gear train the number of teeth of any three gears and other as shown in Figure 1, it is the following steps are included: S1
Related data；S2 calculates the number of teeth of a remaining gear in spur gear planetary gear train；S3 is calculated in spur gear planetary gear train
The tip diameter of all spur gears；S4 calculates the volume of all spur gears in spur gear planetary gear train；S5 calculates spur gear
The volume of planetary gear train.
A kind of calculation method of spur gear planetary gear train volume provided in an embodiment of the present invention, specific implementation process include
Following steps:
Step 1: obtaining the related data of spur gear planetary gear train: the number of teeth z of centre wheel 1 in the present embodimenta, planetary gear
One 3 number of teeth zb, planetary gear 24 number of teeth zc, addendum coefficient ha *, tip clearance coefficient c*, centre wheel 1 modulus ma, planetary gear
24 modulus mc, as shown in table 1；The facewidth b of centre wheel 1a, planetary gear 24 facewidth bcAnd the axis that centre wheel 1 cooperates
Diameter dzhaAnd the diameter of axle d that planetary gear 1 cooperateszhbAnd the diameter of axle d that planetary gear 24 cooperateszhcAnd the diameter of axle that centre wheel 25 cooperates
dzhd, as shown in table 2.
Table 1
Table 2
Step 2: using the number of teeth z of the centre wheel 1 in step 1a, the number of teeth z of planetary gear 1b, the number of teeth of planetary gear 24
zc, the modulus m of centre wheel 1a, the modulus m of planetary gear 24c, calculated by the concentric condition of planetary gear train shown in formula (8) public
The number of teeth z of centre wheel 25 is calculated in formulad。
In formula, zdCentered on wheel 25 the number of teeth, zaCentered on wheel 1 the number of teeth, zbFor the number of teeth of planetary gear 1, zcFor
The number of teeth of planetary gear 24, maCentered on wheel 1 modulus, mcFor the modulus of planetary gear 24.
Step 3: using the number of teeth z of the centre wheel 1 in step 1a, the modulus m of centre wheel 1a, addendum coefficient ha *,
The tip diameter d of centre wheel 1 is calculated by the tip diameter calculation formula of spur gear shown in formula (9)aa；It uses
The number of teeth z of planetary gear 1 in step 1b, the modulus m of centre wheel 1a, addendum coefficient ha *, pass through straight-tooth shown in formula (9)
The tip diameter d of planetary gear 1 is calculated in the tip diameter calculation formula of wheelab；Use the planetary gear 24 in step 1
Number of teeth zc, the modulus m of planetary gear 24c, addendum coefficient ha *, calculated by the tip diameter of spur gear shown in formula (9)
The tip diameter d of planetary gear 24 is calculated in formulaac；Use the modulus m of the planetary gear 24 in step 1c, addendum coefficient
ha *, the number of teeth z of the centre wheel 25 calculated in step 2d, pass through the tip diameter calculation formula meter of spur gear shown in formula (9)
Calculation obtains the tip diameter d of centre wheel 25ad,
In formula, daFor the tip diameter of spur gear, m is the modulus of spur gear, and z is the number of teeth of spur gear, ha *For tooth top
High coefficient.
Step 4: using the tip diameter d of the centre wheel 1 calculated in step 3aa, the tooth of the centre wheel 1 in step 1
Number za, the facewidth b of centre wheel 1a, the modulus m of centre wheel 1a, with centre wheel 1 cooperate diameter of axle dzha, pass through formula (10) institute
The volume V of centre wheel 1 is calculated in the volume calculation formula of the spur gear showna,
In formula, V is the volume of spur gear, and b is the facewidth of spur gear, and z is the number of teeth of spur gear, and m is the modulus of spur gear,
dzhFor the diameter of axle cooperated with spur gear.
Use the tip diameter d of the planetary gear 1 calculated in step 3ab, the modulus m of the centre wheel 1 in step 1a,
The number of teeth z of planetary gear 1b, the facewidth b of centre wheel 1a, addendum coefficient ha *, tip clearance coefficient c*, cooperate with planetary gear 1
Diameter of axle dzhb, the volume V of planetary gear 1 is calculated by the volume calculation formula of spur gear shown in formula (11)b,
In formula, V is the volume of spur gear, and b is the facewidth of spur gear, and m is the modulus of spur gear, and z is the number of teeth of spur gear,
daFor the tip diameter of spur gear, ha *For addendum coefficient, c*For tip clearance coefficient, dzhFor the diameter of axle cooperated with spur gear.
Use the tip diameter d of the planetary gear 24 calculated in step 3ac, the facewidth b of the planetary gear 24 in step 1c,
The modulus m of planetary gear 24c, the number of teeth z of planetary gear 24c, addendum coefficient ha *, tip clearance coefficient c*, cooperate with planetary gear 24
Diameter of axle dzhc, the volume V of planetary gear 24 is calculated by the volume calculation formula of spur gear shown in formula (12)c,
In formula, V is the volume of spur gear, and b is the facewidth of spur gear, and m is the modulus of spur gear, and z is the number of teeth of spur gear,
daFor the tip diameter of spur gear, ha *For addendum coefficient, c*For tip clearance coefficient, dzhFor the diameter of axle cooperated with spur gear.
Use the tip diameter d of the centre wheel 25 calculated in step 3ad, the modulus m of the planetary gear 24 in step 1c,
The number of teeth z of centre wheel 25d, the facewidth b of planetary gear 24c, with centre wheel 25 cooperate diameter of axle dzhd, by shown in formula (13)
The volume V of centre wheel two is calculated in the volume calculation formula of spur geard,
In formula, V is the volume of spur gear, and b is the facewidth of spur gear, and m is the modulus of spur gear, and z is the number of teeth of spur gear,
daFor the tip diameter of spur gear, dzhFor the diameter of axle cooperated with spur gear.
Step 5: using the volume V of the centre wheel 1 calculated in step 4a, planetary gear 1 volume Vb, planetary gear 24
Volume Vc, centre wheel 25 volume Vd, it is calculated by the volume calculation formula of spur gear planetary gear train shown in formula (14)
The volume V of spur gear planetary gear trainz,
Vz=Va+Vb+Vc+Vd (14)
In formula, VzFor the volume of spur gear planetary gear train, VaCentered on wheel 1 volume, VbFor the volume of planetary gear 1,
VcFor the volume of planetary gear 24, VdCentered on wheel 25 volume.
The number of teeth z of centre wheel 25d, centre wheel 1 tip diameter daa, planetary gear 1 tip diameter dab, row
The tip diameter d of star-wheel 24ac, centre wheel 25 tip diameter dadCalculated result it is as shown in table 3；Centre wheel 1
Volume Va, planetary gear 1 volume Vb, planetary gear 24 volume Vc, centre wheel 25 volume Vd, spur gear planetary gear train
Volume VzCalculated result it is as shown in table 4.
Table 3
Table 4
The present invention obtains the number of teeth of any three gears in spur gear planetary gear train according to the structure of spur gear planetary gear train
And other related datas, the number of teeth of a remaining gear in spur gear planetary gear train is calculated, is calculated in spur gear planetary gear train
The tip diameter of all spur gears calculates the volume of all spur gears in spur gear planetary gear train, calculates spur gear planetary gear
The volume of system.The present invention can it is fast and convenient calculate spur gear planetary gear train volume, calculation method is simple, substantially increases straight-tooth
The computational accuracy of planetary gear train volume is taken turns, beneficial effects of its implementation are also obvious.
The above is the preferred embodiment of the present invention, for those skilled in the art,
Without departing from the principles of the invention, several improvements and modifications can also be made, these improvements and modifications are also regarded as this hair
Bright protection scope.
Claims (9)
1. a kind of calculation method of spur gear planetary gear train volume, the structure of the spur gear planetary gear train mainly include rack,
Centre wheel one, planetary gear one, planetary gear two, centre wheel two, planet carrier, centre wheel one are engaged with planetary gear one, planetary gear two with
Centre wheel two engages, and planetary gear one and planetary gear two are connected on the same axis, and centre wheel two is fixed together with rack, mutually nibbles
The facewidth of the spur gear of conjunction is equal, and all spur gears are master gear, ignores the volume of planet carrier, characterized in that the meter
Calculation method the following steps are included:
S1 obtains the number of teeth of any three gears and other related datas in spur gear planetary gear train；
S2 calculates the number of teeth of a remaining gear in spur gear planetary gear train；
S3 calculates the tip diameter of all spur gears in spur gear planetary gear train；
S4 calculates the volume of all spur gears in spur gear planetary gear train；
S5 calculates the volume of spur gear planetary gear train.
2. a kind of calculation method of spur gear planetary gear train volume as described in claim 1, characterized in that in step sl,
The number of teeth of any three gears and other related datas include in the spur gear planetary gear train: the number of teeth of any three gears
za、zb、zc, number of teeth zaGear and the number of teeth be zbGear engagement, addendum coefficient ha *, tip clearance coefficient c*, number of teeth za's
The modulus m of geara, number of teeth zcGear modulus mc, number of teeth zaGear facewidth ba, number of teeth zcGear the facewidth
bcAnd the number of teeth is zaGear cooperation diameter of axle dzhaAnd the number of teeth is zbGear cooperation diameter of axle dzhbAnd the number of teeth is zcTooth
Take turns the diameter of axle d of cooperationzhcAnd the diameter of axle d of remaining gear cooperationzhd。
3. a kind of calculation method of spur gear planetary gear train volume as described in claim 1, characterized in that
In step s 2, the detailed process of the number of teeth of a remaining gear in spur gear planetary gear train is calculated are as follows:
The number of teeth z of a remaining gear is calculated by the concentric condition calculation formula of planetary gear traind。
4. a kind of calculation method of spur gear planetary gear train volume as claimed in claim 3, characterized in that
The concentric condition calculation formula of the planetary gear train are as follows:
In formula, zdFor the number of teeth of a remaining gear, za、zb、zcFor the number of teeth of three gears any in spur gear planetary gear train, ma
It is z for the number of teethaGear modulus, mcIt is z for the number of teethcGear modulus.
5. a kind of calculation method of spur gear planetary gear train volume as described in claim 1, characterized in that
In step s3, the detailed process of the tip diameter of all spur gears in spur gear planetary gear train is calculated are as follows:
It is z that the number of teeth, which is calculated, by the tip diameter calculation formula of spur gearaGear tip diameter daa, the number of teeth be
zbGear tip diameter dab, number of teeth zcGear tip diameter dac, number of teeth zdGear outside circle it is straight
Diameter dad。
6. a kind of calculation method of spur gear planetary gear train volume as claimed in claim 5, characterized in that
The tip diameter calculation formula of the spur gear are as follows:
In formula, daFor the tip diameter of spur gear, m is the modulus of spur gear, and z is the number of teeth of spur gear, ha *For height of teeth top system
Number.
7. a kind of calculation method of spur gear planetary gear train volume as described in claim 1, characterized in that
In step s 4, the detailed process of the volume of all spur gears in spur gear planetary gear train is calculated are as follows:
According to the tip diameter of spur gear, the volume calculation formula of spur gear is reasonably selected, is calculated by the volume of spur gear
It is z that the number of teeth, which is calculated, in formulaaGear volume Va, number of teeth zbGear volume Vb, number of teeth zcGear volume
Vc, number of teeth zdGear volume Vd。
8. a kind of calculation method of spur gear planetary gear train volume as claimed in claim 7, characterized in that
When the tip diameter of spur gear is less than or equal to 160mm, the volume calculation formula of the spur gear are as follows:
In formula, V is the volume of spur gear, and b is the facewidth of spur gear, and z is the number of teeth of spur gear, and m is the modulus of spur gear, dzhFor
With the diameter of axle of spur gear cooperation；
When the tip diameter of spur gear is greater than 160mm and is less than or equal to 500mm, the volume calculation formula of the spur gear
Are as follows:
In formula, V is the volume of spur gear, and b is the facewidth of spur gear, and m is the modulus of spur gear, and z is the number of teeth of spur gear, daFor
The tip diameter of spur gear, dzhFor the diameter of axle cooperated with spur gear；
When the tip diameter of spur gear is greater than 500mm and is less than 1000mm, the volume calculation formula of the spur gear are as follows:
In formula, V is the volume of spur gear, and b is the facewidth of spur gear, and m is the modulus of spur gear, and z is the number of teeth of spur gear, daFor
The tip diameter of spur gear, ha *For addendum coefficient, c*For tip clearance coefficient, dzhFor the diameter of axle cooperated with spur gear；
When the tip diameter of spur gear is more than or equal to 1000mm, the volume calculation formula of the spur gear are as follows:
In formula, V is the volume of spur gear, and b is the facewidth of spur gear, and m is the modulus of spur gear, and z is the number of teeth of spur gear, daFor
The tip diameter of spur gear, ha *For addendum coefficient, c*For tip clearance coefficient, dzhFor the diameter of axle cooperated with spur gear.
9. a kind of calculation method of spur gear planetary gear train volume as described in claim 1, characterized in that the step S5's
Detailed process are as follows:
The volume V of spur gear planetary gear train is calculated by the volume calculation formula of spur gear planetary gear train shown in formula (7)z,
Vz=Va+Vb+Vc+Vd (7)
In formula, VzFor the volume of spur gear planetary gear train, VaIt is z for the number of teethaGear volume, VbIt is z for the number of teethbGear
Volume, VcIt is z for the number of teethcGear volume, VdIt is z for the number of teethdGear volume.
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