CN105893710B - NGWN planetary gear train geometric lost motion calculation method - Google Patents
NGWN planetary gear train geometric lost motion calculation method Download PDFInfo
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Abstract
Present invention firstly provides a kind of geometric lost motion calculation methods of NGWN planetary gear train.This method is established on the basis of the geometric lost motion of NGW planetary gear train calculates, by the number of teeth for obtaining gear, pressure angle, the practical angle of engagement, lower deviation in the common normal of each gear, runout tolerance, and the parameters such as limit deviation of centre distance between gear pair, it determines the sideshake between gear pair, using transmission ratio, and then obtains the size of its geometric lost motion.This method is the combination calculated by the calculating of NGW train geometric lost motion and single gear return difference, and the puzzlement of structure precision can not be determined in the design phase by largely solving people for a long time, provide foundation for the careful design of train.This return difference calculation method form is simple, and required parameter is easy to get, and as a result close to reality, saves time, energy and cost for designer, and improve reliability and the service life of system.
Description
Technical field
The present invention relates to STRUCTURAL SENSITIVITY ANALYSIS INDESIGN computing technique fields, are a kind of calculation methods of train return difference, specially
It is all using NGWN planetary gear train to can be applied to aerospace etc. for a kind of NGWN planetary gear train geometric lost motion calculation method
Occasion.
Background technique
Currently, NGWN train (N- inside engaged gear；W- external gear pump；Public tooth among two gear Meshing Pairs of G-
Wheel) by its transmission ratio it is big, it is compact-sized the advantages that, in the every field of machinery industry, especially aerospace field application is cured
Add extensively.With the development of China's aeronautical and space technology, the high lift device of aircraft, such as drive mechanism of wing flap slat are proposed
Higher requirement.We not only require train therein to be normally driven, and more require it each to ensure with good sensitivity
The synchronism and stability of a mechanism kinematic, and then improve its transmission accuracy.As a part of entire transmission mechanism, NGWN wheel
Be geometric lost motion calculating be exactly the breach solved these problems.Just because of this, each developed country starts the train geometry time
The research of poor calculation method.It is much to the research of geometric lost motion calculation method in the research of China in recent years, but only
It stays in the calculating research of single gear pair and NGW planetary gear train (structure is as shown in Fig. 2).NGWN gear train ratio NGW
The stationarity of gear train is higher, and overall structure is rigidly more preferable, ought to be favored and be paid attention in terms of geometric lost motion calculation method.
In order to preferably analyze and research and improve the precision of wheel train structure, the exploitation of the geometric lost motion calculation method of NGWN train becomes outstanding
It is important.
Summary of the invention
In order to preferably study the stationarity of transmission mechanism, the precision of structure is improved, the present invention provides a kind of NGWN planet
The geometric lost motion calculation method of train, this method comprehensively consider several factors mainly influenced on geometric lost motion generation, ignore shadow
Lesser secondary cause is rung, obtained calculation method is more succinct understandable, and obtained result is more accurate, can instruct practical work
Make.
The technical solution adopted in the present invention:
Carried out by the sideshake size of each gear being meshed carry out train geometric lost motion calculate, consideration it is several
Major influence factors are respectively 1) gear backlash caused by common normal average length deviation；2) caused by gear run-out error
Gear backlash；3) gear backlash caused by limit deviation of centre distance between gear pair.
The NGWN gear train geometric lost motion calculation method established herein is built upon what existing NGW gear train return difference calculated
On the basis of, attached drawing 1 is NGWN wheel train structure form, and composite gear N2 and N5 is coaxial, does not consider the geometric lost motion that N5 itself is generated
When, the geometric lost motion of N5 and N2 are identical, that is, the return differences of NGW train output end.It will be by sun gear N1, composite gear N2
The return difference that composite gear N2 output end is generated with output gear N4 is tied up to the N1N2N3 wheel of internal gear N3 composition to be all folded to
It is calculated on composite gear N5, then again with transmission ratio i45Output gear N4 output end is converted into back, core of the invention has just been obtained:
The return difference calculation formula of NGWN train, in the formula, the calculating of return difference and the parameter value of gear are related.In practical implementation
, can be by tabling look-up or measuring base tangent length deviation or in design, gear run-out error, between gear pair center away from
These parameters of limit deviation to determine the backlash values between gear, and then obtain geometric lost motion result.
A kind of NGWN planetary gear train geometric lost motion calculation method, it is characterised in that:
One, according to formula
Calculate the geometric lost motion mean value of the output gear N4 of NGWN planetary gear train
Wherein:
For composite gear N5 input terminal geometric lost motion mean value in NGWN planetary gear train；
For the geometric lost motion mean value of composite gear N2 output end in NGWN planetary gear train；
M is modulus, z2For the number of teeth of composite gear N2；
∑jw,N1N2=jw1,N1N2+jw2,N1N2+jw3,N1N2
jw1,N1N2=jw1dan,N1+jw1dan,N2
jw2,N1N2=jw2dan,N1+jw2dan,N2
∑jw,N2N3=jw1,N2N3+jw2,N2N3+jw3,N2N3
jw1,N2N3=jw1dan,N2+jw1dan,N3
jw2,N2N3=jw2dan,N2+jw2dan,N3
jw1dan,N1、jw1dan,N2、jw1dan,N3Sun gear N1, composite gear N2 and internal tooth respectively in NGWN planetary gear train
Take turns N3 on business gear backlash caused by normal average length variation, jw2dan,N1、jw2dan,N2、jw2dan,N3Respectively sun gear N1, public affairs
With gear N2 and internal gear N3 because of gear backlash caused by gear run-out error, jw3,N1N2And jw3,N2N3Respectively gear pair
Tooth caused by limit deviation of centre distance between gear backlash caused by limit deviation of centre distance and gear pair N2N3 between N1N2
Take turns sideshake；
The geometric lost motion mean value generated for composite gear N5 itself:
z5For the number of teeth of composite gear N5；jw1dan,N5For gear caused by composite gear N5 on business normal average length variation
Sideshake, jw2dan,N5It is composite gear N5 because of gear backlash caused by gear run-out error；
The geometric lost motion mean value generated for output gear N4 itself:
z4For the number of teeth of output gear N4；jw1dan,N4For gear caused by output gear N4 on business normal average length variation
Sideshake, jw2dan,N4It is output gear N4 because of gear backlash caused by gear run-out error；
i54For the transmission ratio of composite gear N5 and output gear N4；
Two, according to formula
Calculate the geometric lost motion tolerance T Δ φ of the output gear N4 of NGWN planetary gear train4；
Wherein:
TΔφ5startFor composite gear N5 input terminal geometric lost motion tolerance in NGWN planetary gear train；
TΔφ5start=T Δ φ2, T Δ φ2It is public for the geometric lost motion of composite gear N2 output end in NGWN planetary gear train
Difference；
∑D(jw,N1N2)=D (jw1,N1N2)+D(jw2,N1N2)+D(jw3,N1N2)
D(jw1,N1N2)=D (jw1dan,N1)+D(jw1dan,N2)
D(jw2,N1N2)=D (jw2dan,N1)+D(jw2dan,N2)
∑D(jw,N2N3)=D (jw1,N2N3)+D(jw2,N2N3)+D(jw3,N2N3)
D(jw1,N2N3)=D (jw1dan,N2)+D(jw1dan,N3)
D(jw2,N2N3)=D (jw2dan,N2)+D(jw2dan,N3)
D(jw1dan,N1)、D(jw1dan,N2)、D(jw1dan,N3) it is respectively sun gear N1, composite gear in NGWN planetary gear train
N2 and internal gear N3 on business gear backlash tolerance caused by normal average length variation, D (jw2dan,N1)、D(jw2dan,N2)、D
(jw2dan,N3) it is respectively sun gear N1, composite gear N2 and internal gear N3 because gear backlash caused by gear run-out error is public
Difference, D (jw3,N1N2) and D (jw3,N2N3) be respectively between gear pair N1N2 gear backlash tolerance caused by limit deviation of centre distance with
And gear backlash tolerance caused by limit deviation of centre distance between gear pair N2N3；
TΔφ5selfThe geometric lost motion tolerance generated for composite gear N5 itself:
D(jw1dan,N5) it is composite gear N5 on business gear backlash tolerance caused by normal average length variation, D
(jw2dan,N5) it is composite gear N5 because of gear backlash tolerance caused by gear run-out error；
TΔφ4selfThe geometric lost motion tolerance generated for output gear N4 itself:
D(jw1dan,N4) it is output gear N4 on business gear backlash tolerance caused by normal average length variation, D
(jw2dan,N4) it is output gear N4 because of gear backlash tolerance caused by gear run-out error；
Three, according to formula
Obtain the output gear N4 geometric lost motion maximum value φ of NGWN planetary gear train4maxWith minimum value φ4min。
Further preferred embodiment, a kind of NGWN planetary gear train geometric lost motion calculation method, it is characterised in that:
A certain gear N on business gear backlash j caused by normal average length variationw1dan,NAccording to formula
It obtains；Wherein, α is pressure angle, wEs,NFor the gear N common normal upper deviation, wEi,NIt is inclined under gear N common normal
Difference；
A certain gear N on business gear backlash tolerance D (j caused by normal average length variationw1dan,N) according to formula
It obtains；
A certain gear N is because of gear backlash tolerance D (j caused by gear run-out errorw2dan,N) according to formula
It obtains；Wherein, Fr,NFor gear N run-out error,α ' is the gear angle of engagement；
A certain gear pair NN ' is because of gear backlash tolerance D (j caused by limit deviation of centre distancew3,NN′) according to formula
It obtains；Wherein, Fa,NN′For gear pair NN ' limit deviation of centre distance.
Beneficial effect
The beneficial effects of the present invention are:
Present invention firstly provides a kind of geometric lost motion calculation methods of NGWN planetary gear train.This method is taken turns by NGW
Be geometric lost motion calculating with single gear return difference calculating combination, largely solve people for a long time the design phase without
Method determines the puzzlement of structure precision, provides foundation for the careful design of train.This return difference calculation method form is simple, required
Parameter is easy to get, and as a result close to reality, saves time, energy and cost for designer, and improve system
Reliability and service life.
Additional aspect and advantage of the invention will be set forth in part in the description, and will partially become from the following description
Obviously, or practice through the invention is recognized.
Detailed description of the invention
Fig. 1: NGWN planetary gear train schematic diagram；
Fig. 2: NGW train schematic diagram.
Specific embodiment
The embodiment of the present invention is described below in detail, the embodiment of description is exemplary, it is intended to it is used to explain the present invention,
And it is not considered as limiting the invention.
In order to preferably study the stationarity of transmission mechanism, the precision of structure is improved, a kind of NGWN planet is provided below
The geometric lost motion calculation method of train, this method comprehensively consider several factors mainly influenced on geometric lost motion generation, ignore shadow
Lesser secondary cause is rung, obtained calculation method is more succinct understandable, and obtained result is more accurate, can instruct practical work
Make.
Carried out by the sideshake size of each gear being meshed carry out train geometric lost motion calculate, consideration it is several
Major influence factors are respectively 1) gear backlash caused by common normal average length deviation；2) caused by gear run-out error
Gear backlash；3) gear backlash caused by limit deviation of centre distance between gear pair.
The NGWN gear train geometric lost motion calculation method established herein is built upon what existing NGW gear train return difference calculated
On the basis of, attached drawing 1 is NGWN wheel train structure form, and composite gear N2 and N5 is coaxial, does not consider the geometric lost motion that N5 itself is generated
When, the geometric lost motion of N5 and N2 are identical, that is, the return differences of NGW train output end.It will be by sun gear N1, composite gear N2
The return difference that composite gear N2 output end is generated with output gear N4 is tied up to the N1N2N3 wheel of internal gear N3 composition to be all folded to
It is calculated on composite gear N5, then again with transmission ratio i45Output gear N4 output end is converted into back, core of the invention has just been obtained:
The return difference calculation formula of NGWN train, in the formula, the calculating of return difference and the parameter value of gear are related.In practical implementation
, can be by tabling look-up or measuring base tangent length deviation or in design, gear run-out error, between gear pair center away from
These parameters of limit deviation to determine the backlash values between gear, and then obtain geometric lost motion result.
Method particularly includes:
One, according to formula
Calculate the geometric lost motion mean value of the output gear N4 of NGWN planetary gear train
Wherein:
For composite gear N5 input terminal geometric lost motion mean value in NGWN planetary gear train；
For the geometric lost motion mean value of composite gear N2 output end in NGWN planetary gear train；
M is modulus, z2For the number of teeth of composite gear N2；
∑jw,N1N2=jw1,N1N2+jw2,N1N2+jw3,N1N2
jw1,N1N2=jw1dan,N1+jw1dan,N2
jw2,N1N2=jw2dan,N1+jw2dan,N2
∑jw,N2N3=jw1,N2N3+jw2,N2N3+jw3,N2N3
jw1,N2N3=jw1dan,N2+jw1dan,N3
jw2,N2N3=jw2dan,N2+jw2dan,N3
jw1dan,N1、jw1dan,N2、jw1dan,N3Sun gear N1, composite gear N2 and internal tooth respectively in NGWN planetary gear train
Take turns N3 on business gear backlash caused by normal average length variation, jw2dan,N1、jw2dan,N2、jw2dan,N3Respectively sun gear N1, public affairs
With gear N2 and internal gear N3 because of gear backlash caused by gear run-out error, jw3,N1N2And jw3,N2N3Respectively gear pair
Tooth caused by limit deviation of centre distance between gear backlash caused by limit deviation of centre distance and gear pair N2N3 between N1N2
Take turns sideshake；
The geometric lost motion mean value generated for composite gear N5 itself:
z5For the number of teeth of composite gear N5；jw1dan,N5For gear caused by composite gear N5 on business normal average length variation
Sideshake, jw2dan,N5It is composite gear N5 because of gear backlash caused by gear run-out error；
The geometric lost motion mean value generated for output gear N4 itself:
z4For the number of teeth of output gear N4；jw1dan,N4For gear caused by output gear N4 on business normal average length variation
Sideshake, jw2dan,N4It is output gear N4 because of gear backlash caused by gear run-out error；
i54For the transmission ratio of composite gear N5 and output gear N4.
For a certain gear N, on business gear backlash j caused by normal average length variationw1dan,NAccording to formula
It obtains；Wherein, α is pressure angle, wEs,NFor the gear N common normal upper deviation, wEi,NIt is inclined under gear N common normal
Difference.
And in the design phase, for a certain gear N, gear backlash caused by gear run-out error can take 0, right
In a certain gear pair NN ', because gear backlash caused by limit deviation of centre distance can take 0.
Two, according to formula
Calculate the geometric lost motion tolerance T Δ φ of the output gear N4 of NGWN planetary gear train4；
Wherein:
TΔφ5startFor composite gear N5 input terminal geometric lost motion tolerance in NGWN planetary gear train；
TΔφ5start=T Δ φ2, T Δ φ2It is public for the geometric lost motion of composite gear N2 output end in NGWN planetary gear train
Difference；
∑D(jw,N1N2)=D (jw1,N1N2)+D(jw2,N1N2)+D(jw3,N1N2)
D(jw1,N1N2)=D (jw1dan,N1)+D(jw1dan,N2)
D(jw2,N1N2)=D (jw2dan,N1)+D(jw2dan,N2)
∑D(jw,N2N3)=D (jw1,N2N3)+D(jw2,N2N3)+D(jw3,N2N3)
D(jw1,N2N3)=D (jw1dan,N2)+D(jw1dan,N3)
D(jw2,N2N3)=D (jw2dan,N2)+D(jw2dan,N3)
D(jw1dan,N1)、D(jw1dan,N2)、D(jw1dan,N3) it is respectively sun gear N1, composite gear in NGWN planetary gear train
N2 and internal gear N3 on business gear backlash tolerance caused by normal average length variation, D (jw2dan,N1)、D(jw2dan,N2)、D
(jw2dan,N3) it is respectively sun gear N1, composite gear N2 and internal gear N3 because gear backlash caused by gear run-out error is public
Difference, D (jw3,N1N2) and D (jw3,N2N3) be respectively between gear pair N1N2 gear backlash tolerance caused by limit deviation of centre distance with
And gear backlash tolerance caused by limit deviation of centre distance between gear pair N2N3；
TΔφ5selfThe geometric lost motion tolerance generated for composite gear N5 itself:
D(jw1dan,N5) it is composite gear N5 on business gear backlash tolerance caused by normal average length variation, D
(jw2dan,N5) it is composite gear N5 because of gear backlash tolerance caused by gear run-out error；
TΔφ4selfThe geometric lost motion tolerance generated for output gear N4 itself:
D(jw1dan,N4) it is output gear N4 on business gear backlash tolerance caused by normal average length variation, D
(jw2dan,N4) it is output gear N4 because of gear backlash tolerance caused by gear run-out error；
Three, according to formula
Obtain the output gear N4 geometric lost motion maximum value φ of NGWN planetary gear train4maxWith minimum value φ4min。
For a certain gear N, on business gear backlash j caused by normal average length variationw1dan,NAccording to formula
It obtains；Wherein, α is pressure angle, wEs,NFor the gear N common normal upper deviation, wEi,NIt is inclined under gear N common normal
Difference；
A certain gear N on business gear backlash tolerance D (j caused by normal average length variationw1dan,N) according to formula
It obtains；
A certain gear N is because of gear backlash tolerance D (j caused by gear run-out errorw2dan,N) according to formula
It obtains；Wherein, Fr,NFor gear N run-out error,α ' is the gear angle of engagement；
A certain gear pair NN ' is because of gear backlash tolerance D (j caused by limit deviation of centre distancew3,NN′) according to formula
It obtains；Wherein, Fa,NN′For gear pair NN ' limit deviation of centre distance.
After obtaining above method, according to the different phase used, such as the design phase and safeguard or the maintenance stage, by not
Relevant parameter (is tabled look-up or measured) to same mode, is calculated, and obtains output end geometric lost motion, and be compared with national standard,
It can be used for determining or prioritization scheme in the design phase, can be used for considering in maintenance or maintenance stage steady to other component, system
Qualitative and sensitivity influence, preferably guidance maintenance and maintenance, and then increase train reliability and service life.
Although the embodiments of the present invention has been shown and described above, it is to be understood that above-described embodiment is example
Property, it is not considered as limiting the invention, those skilled in the art are not departing from the principle of the present invention and objective
In the case where can make changes, modifications, alterations, and variations to the above described embodiments within the scope of the invention.
Claims (2)
1. a kind of NGWN planetary gear train geometric lost motion calculation method, it is characterised in that:
One, according to formula
Calculate the geometric lost motion mean value of the output gear N4 of NGWN planetary gear train
Wherein:
For composite gear N5 input terminal geometric lost motion mean value in NGWN planetary gear train；
For the geometric lost motion mean value of composite gear N2 output end in NGWN planetary gear train；
M is modulus, z2For the number of teeth of composite gear N2；
∑jw,N1N2=jw1,N1N2+jw2,N1N2+jw3,N1N2
jw1,N1N2=jw1dan,N1+jw1dan,N2
jw2,N1N2=jw2dan,N1+jw2dan,N2
∑jw,N2N3=jw1,N2N3+jw2,N2N3+jw3,N2N3
jw1,N2N3=jw1dan,N2+jw1dan,N3
jw2,N2N3=jw2dan,N2+jw2dan,N3
jw1dan,N1、jw1dan,N2、jw1dan,N3Sun gear N1, composite gear N2 and internal gear N3 respectively in NGWN planetary gear train
On business gear backlash caused by normal average length variation, jw2dan,N1、jw2dan,N2、jw2dan,N3Respectively sun gear N1, public tooth
N2 and internal gear N3 is taken turns because of gear backlash caused by gear run-out error, jw3,N1N2And jw3,N2N3Respectively gear pair N1N2
Between gear side caused by limit deviation of centre distance between gear backlash and gear pair N2N3 caused by limit deviation of centre distance
Gap；
The geometric lost motion mean value generated for composite gear N5 itself:
z5For the number of teeth of composite gear N5；jw1dan,N5For gear side caused by composite gear N5 on business normal average length variation
Gap, jw2dan,N5It is composite gear N5 because of gear backlash caused by gear run-out error；
The geometric lost motion mean value generated for output gear N4 itself:
z4For the number of teeth of output gear N4；jw1dan,N4For gear side caused by output gear N4 on business normal average length variation
Gap, jw2dan,N4It is output gear N4 because of gear backlash caused by gear run-out error；
i54For the transmission ratio of composite gear N5 and output gear N4；
Two, according to formula
Calculate the geometric lost motion tolerance T Δ φ of the output gear N4 of NGWN planetary gear train4；
Wherein:
TΔφ5startFor composite gear N5 input terminal geometric lost motion tolerance in NGWN planetary gear train；
TΔφ5start=T Δ φ2, T Δ φ2For the geometric lost motion tolerance of composite gear N2 output end in NGWN planetary gear train；
ΣD(jw,N1N2)=D (jw1,N1N2)+D(jw2,N1N2)+D(jw3,N1N2)
D(jw1,N1N2)=D (jw1dan,N1)+D(jw1dan,N2)
D(jw2,N1N2)=D (jw2dan,N1)+D(jw2dan,N2)
ΣD(jw,N2N3)=D (jw1,N2N3)+D(jw2,N2N3)+D(jw3,N2N3)
D(jw1,N2N3)=D (jw1dan,N2)+D(jw1dan,N3)
D(jw2,N2N3)=D (jw2dan,N2)+D(jw2dan,N3)
D(jw1dan,N1)、D(jw1dan,N2)、D(jw1dan,N3) be respectively sun gear N1 in NGWN planetary gear train, composite gear N2 and
Internal gear N3 on business gear backlash tolerance caused by normal average length variation, D (jw2dan,N1)、D(jw2dan,N2)、D(jw2dan,N3)
Respectively sun gear N1, composite gear N2 and internal gear N3 are because of gear backlash tolerance caused by gear run-out error, D
(jw3,N1N2) and D (jw3,N2N3) it is respectively gear backlash tolerance and tooth caused by limit deviation of centre distance between gear pair N1N2
Gear backlash tolerance caused by limit deviation of centre distance between wheel set N2N3；
TΔφ5selfThe geometric lost motion tolerance generated for composite gear N5 itself:
D(jw1dan,N5) it is composite gear N5 on business gear backlash tolerance caused by normal average length variation, D (jw2dan,N5) it is public affairs
With gear N5 because of gear backlash tolerance caused by gear run-out error；
TΔφ4selfThe geometric lost motion tolerance generated for output gear N4 itself:
D(jw1dan,N4) it is output gear N4 on business gear backlash tolerance caused by normal average length variation, D (jw2dan,N4) it is defeated
Gear N4 is because of gear backlash tolerance caused by gear run-out error out；
Three, according to formula
Obtain the output gear N4 geometric lost motion maximum value φ of NGWN planetary gear train4maxWith minimum value φ4min。
2. a kind of NGWN planetary gear train geometric lost motion calculation method according to claim 1, it is characterised in that:
A certain gear N on business gear backlash j caused by normal average length variationw1dan,NAccording to formula
It obtains；Wherein, α is pressure angle, wEs,NFor the gear N common normal upper deviation, wEi,NFor gear N common normal lower deviation；
A certain gear N on business gear backlash tolerance D (j caused by normal average length variationw1dan,N) according to formula
It obtains；
A certain gear N is because of gear backlash tolerance D (j caused by gear run-out errorw2dan,N) according to formula
It obtains；Wherein, Fr,NFor gear N run-out error,α ' is the gear angle of engagement；
A certain gear pair NN ' is because of gear backlash tolerance D (j caused by limit deviation of centre distancew3,NN′) according to formula
It obtains；Wherein, Fa,NN′For gear pair NN ' limit deviation of centre distance.
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| CN201818728U (en) * | 2010-06-12 | 2011-05-04 | 吴长敏 | NGWN single-element type planetary gear speed reducer |
| CN104214281A (en) * | 2014-09-15 | 2014-12-17 | 北京卫星制造厂 | Modification method for planetary gear trains with positive addendum modification |
| CN104504196A (en) * | 2014-12-22 | 2015-04-08 | 湘潭电机股份有限公司 | Method for optimizing efficiency of NW type fixed-axle gear system |
| CN204828542U (en) * | 2015-08-03 | 2015-12-02 | 许奉成 | Differential planet gear |
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| Publication number | Priority date | Publication date | Assignee | Title |
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| US6682456B2 (en) * | 2001-12-10 | 2004-01-27 | Axicon Technologies, Inc. | Multi-mesh gear system |
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| CN201818728U (en) * | 2010-06-12 | 2011-05-04 | 吴长敏 | NGWN single-element type planetary gear speed reducer |
| CN104214281A (en) * | 2014-09-15 | 2014-12-17 | 北京卫星制造厂 | Modification method for planetary gear trains with positive addendum modification |
| CN104504196A (en) * | 2014-12-22 | 2015-04-08 | 湘潭电机股份有限公司 | Method for optimizing efficiency of NW type fixed-axle gear system |
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