CN102691773B - Computing method of rotary interference amount of double contact gears - Google Patents

Computing method of rotary interference amount of double contact gears Download PDF

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Publication number
CN102691773B
CN102691773B CN201210183345.6A CN201210183345A CN102691773B CN 102691773 B CN102691773 B CN 102691773B CN 201210183345 A CN201210183345 A CN 201210183345A CN 102691773 B CN102691773 B CN 102691773B
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gear
gears
interference
ydd
xdd
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CN102691773A (en
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文贵华
赵尚吾
厉海祥
刘金生
张金凤
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Zhuzhou Gear Co Ltd
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Zhuzhou Gear Co Ltd
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Abstract

The invention relates to a computing method of a rotary interference amount of double contact gears, which has the essentials that dynamic models for rotatably engaging two gears are established on a computer by parameters of the matched gears; through computing central point dynamic coordinates of the rotary gears, and autorotation and revolution angles of the gears, an interference spot of a gear involute part and a transition curve part of the other gear, which are mutually interfered, is automatically formed on a computer screen when the two gears are rotatably engaged; and the width and the arc length of the interference spot are directly measured so as to obtain the size of the rotary interference amount. The computing method has the advantages that the rotary interference amount of the gears is rapidly and directly obtained, the computing time is short and the accuracy is high; an accurate sinking cutting amount, a shape correcting direction and the size of a shape correcting amount are provided for carrying out finish machining of the double contact gears; the precision of the machined gears is high and the fatigue strength of a gear surface is good; and noises formed by engaging the two gears are small, the abrasion of engaging the two gears is reduced and the service life of the gears is prolonged.

Description

A kind of computational methods of two contact gear turn amount of interference
Technical field
The present invention relates to a kind of computational methods of Gear Processing surplus, be specifically related to a kind of computational methods of two contact gear turn amount of interference.
Background technique
Traditional cylindrical gears is pure involute flank, and its simple in structure, easy processing of the cylindrical gears of this pure involute flank is widely applied in mechanical transmission.But flank of tooth fatigue strength and the flexural strength of the cylindrical gears of pure involute flank are little, when engagement, noise is large, and the flank of tooth easily weares and teares, and working life is short.The gear that the flank of tooth consists of involute and transition curve, flank of tooth fatigue strength and flexural strength be good, noise is little during engagement, has improved the strength of gear teeth and working life.But, there is the interference of transition curve and involute in the flank of tooth consisting of involute and transition curve when gear engagement in rotation.The size of its amount of interference is to determine the hobboing cutter heavy amount of cutting, the direction of Shaving Dressing amount and the big or small key parameter of profiling quantity, the heavy amount of cutting of hobboing cutter, the direction of Shaving Dressing amount and the size of profiling quantity are to guarantee that gear has good characteristic and the high strength of gear teeth and the important channel in working life accurately, test method determines that amount of interference accuracy is high, but need machining gears, set up test stand, be equipped with the testing apparatus of corresponding precision, the time, long expense was high.
Summary of the invention
The object of the invention is to provide a kind of two computational methods that contact gear turn amount of interference that do not need machining gears, the flank of tooth that short expense of time is low to be formed with transition curve by involute.
The computational methods of two contact gear turn amount of interference of the present invention, is characterized in that: its step of described computational methods is as follows:
A, set up model:
1), according to usage requirement, choose the parameter of coupling gear G and gear H:
Gear G: tooth number Z 1, modulus m1, pressure angle α 1, helixangleβ 1, tip diameter da1, root diameter di1, pitch diameter dj1;
Gear H: tooth number Z 2, modulus m2, pressure angle α 2, helixangleβ 2, tip diameter da2, root diameter di2, pitch diameter dj2;
The mounting center distance of gear G and gear H two gears is D 0;
2) according to above-mentioned selected gear parameter, optional on computer screen is some the fixed center point po2 of gear G, and its coordinate is xo2, yo2, sets up on computers the dynamic model of gear G and gear H turn engagement;
B, calculating:
A) given maximum step-length q maxwith step-length zdsd
B) calculate the dynamic coordinate xdd of the central point podd of gear H i, ydd i, calculating formula is:
q i = q i-1+ zdsd
Q i> q maxtime, forward c to and calculate rotation angle θ;
Q i< q maxtime, calculate:
xdd i = (xo2- D 0 * cos ((q ｉ/dj2) * 2 *0.017453293))
ydd i = (yo2- D 0 * sin ((q ｉ/dj2) *2* 0.017453293))
In formula: i=1,2,3,4....
q 0=0
Q istep-length variable
The central point of po2 gear G
The X of the central point po2 of xo2, yo2 gear G, Y coordinate
The extended phase plane of pod gear H
Xdd i, ydd ithe X of the extended phase plane podd of gear H, Y coordinate
Get back to b double counting q i, xdd i, ydd i;
C) calculate rotation angle θ, calculating formula is:
θ= (zdsd/ dj1) * 2
D) calculate revolution angle δ, calculating formula is:
δ= (zdsd/ dj2) * 2
E) by above dynamic calculation, while obtaining gear G and gear H engagement in rotation, the coordinate xdd of the extended phase plane podd of gear H i, ydd iwith calculate rotation angle θ and revolution angle δ, the interference spot that the involute of formative gear H part and gear G transition curve part are interfered mutually automatically on computer screen, directly measures width and the arc length of interference spot, has obtained the size of turn amount of interference.
Advantage of the present invention is the acquisition gear turn amount of interference of quicklook, computing time is short, accuracy is high, apply the size of the heavy amount of cutting, Shaving Dressing direction and profiling quantity of the definite hobcutter of this amount of interference, the accuracy of gear of processing is high thus, and flank of tooth fatigue strength has improved 30%, flexural strength has improved 15%; Two gears when engagement reducing noises 5～10 decibels, the wearing and tearing while having reduced by two gears engagements, the working life of having improved gear.
Accompanying drawing explanation
Fig. 1 is the schematic diagram of gear G and gear H engagement.
Fig. 2 is the track schematic diagram of gear G and gear H turn engagement.
In figure: 3, interference spot, L1, width, L2, arc length.
Embodiment
Embodiment 1
The computational methods of two contact gear turn amount of interference of the present invention, its calculation procedure is as follows:
A, set up model:
1), according to usage requirement, determine that the parameter of coupling gear G and gear H is:
A gear: tooth number Z 1=35, modulus m1=5.5, pressure angle α 1=20 °
Helixangleβ 1=15 ° 40 ' 29 ", tip diameter da1=206.2
Root diameter di1=176.392 millimeter, pitch diameter dj1=192.227 millimeter;
B gear: tooth number Z 2=35, modulus m2=5.5, pressure angle α 2=20 °
Helixangleβ 2=15 ° 40 ' 29 ", tip diameter da2=206.2,
Root diameter di2=176.392 millimeter, pitch diameter dj2=192.227 millimeter;
The mounting center of gear G and gear H two gears is apart from D 0=192.227 millimeters;
2) according to above-mentioned selected gear parameter, optional on computer screen is some the fixed center point po2 of gear G, and its coordinate is xo2=437.219, yo2=143.169, sets up on computers the dynamic model of gear G and gear H turn engagement;
B, calculating:
A) given maximum step-length q max=40 millimeters and step-length zdsd=30 millimeter
B) calculate the dynamic coordinate xdd of the central point podd of gear H i, ydd i, calculating formula is:
ｉ=1
q 1= q 0+30
q 1=30
Q 1< 40 calculates:
xdd 1= (437.219- 192.227 * cos ((30/192.227) * 2 *0.017453293)) ydd 1= (143.169- 192.227 * sin ((30/192.227) *2* 0.017453293))
Xdd 1=280.992 millimeters of ydd 1=143.169 millimeters
During i=2
q 2=30 +30=60
Q 2during > 40, forward c to and calculate rotation angle θ;
C) calculate rotation angle θ, calculating formula is;
θ= (zdsd/ dj1) * 2
=30/192.227* 2
=0.31213097(radian)
D) calculate revolution angle δ, calculating formula is:
δ= (zdsd/ dj2) * 2
=30/192.227* 2
=0.31213097(radian)
E) by above dynamic calculation, while obtaining gear G and gear H engagement in rotation, the coordinate xdd of the extended phase plane podd of gear H 1=280.992 millimeters, ydd 1=143.169 millimeters and calculating rotation angle θ=0.31213097(radian) and revolution angle δ=0.31213097(radian), the interference spot 3 that the involute of automatic formative gear H part and gear G transition curve part are interfered mutually on computer screen, directly measure width L1=1.3 millimeter and the arc length L2=2.5 millimeter of interference spot 3, obtained the size of turn amount of interference.
Embodiment 2
A, set up model:
1), according to usage requirement, determine the parameter of coupling gear G and gear H:
A gear: tooth number Z 1=33, modulus m1=5.5, pressure angle α 1=20 °
Helixangleβ 1=15 ° 40 ' 29 ", tip diameter da1=194.8
Root diameter di1=165.2 millimeter, pitch diameter dj1=180.322 millimeter;
B gear: tooth number Z 2=31, modulus m2=5.5, pressure angle α 2=20 °
Helixangleβ 2=15 ° 40 ' 29 ", tip diameter da2=183.4
Root diameter di2=153.8 millimeter, pitch diameter dj2=169.3 millimeter;
The mounting center of gear G and gear H two gears is apart from D 0=174.858 millimeters;
2) according to above-mentioned selected gear parameter, optional on computer screen is some the fixed center point po2 of gear G, and its coordinate is xo2=439.043, yo2=155.413, sets up on computers the dynamic model of gear G and gear H turn engagement;
B, calculating:
α) given maximum step-length q max=70 and step-length zdsd=30
B) calculate the dynamic coordinate xdd of the central point podd of gear H i, ydd i, calculating formula is:
ｉ=1
q 1=30
Q 1< 70 calculates:
xdd 1 = (439.043- 174.858 * cos ((30/169.3) * 2 *0.017453293))
ydd 1 = (155.413- 174.858 * sin ((30/169.3) *2* 0.017453293))
xdd 1=264.185 ydd 1= 155.394
i=2
q 2=( q 1 +zdsd)=30+30
q 2=60
Q 2during < 70, the xdd while calculating i=2 2, ydd 2;
xdd 2 = (439.043- 174.858 * cos ((60/169.3) * 2 *0.017453293))
ydd 2 = (155.413- 174.858 * sin ((60/169.3) *2* 0.017453293))
xdd 2=264.188 ydd 2=155.375
i=3
q 3=( q 2 +zdsd)=60+30
q 3=90
Q 3> 70 o'clock, forwards c to and calculates rotation angle θ;
C) calculate rotation angle θ, calculating formula is;
θ= (zdsd/ dj1) * 2
=30/180.322* 2
=0.332738102(radian)
D) calculate revolution angle δ, calculating formula is:
δ= (zdsd/ dj2) * 2
=30/169.393* 2
=0.3542059(radian)
E) by above dynamic calculation, while obtaining gear G and gear H engagement in rotation, gear H the coordinate xdd of extended phase plane podd 1=264.185 millimeters, ydd 1=155.394 millimeters, xdd 2=264.188 millimeters, ydd 2=155.375 millimeters and calculating rotation angle θ=0.332738102(radian) and revolution angle δ=0.3542059(radian), the interference spot 3 that the involute of automatic formative gear H part and gear G transition curve part are interfered mutually on computer screen, directly measure width L1=1.6 millimeter and the arc length L2=2.3 millimeter of interference spot 3, obtained the size of turn amount of interference.

Claims (1)

1. computational methods for two contact gear turn amount of interference, is characterized in that: its step of described computational methods is as follows:
A, set up model:
1), according to usage requirement, choose the parameter of coupling gear G and gear H:
Gear G: tooth number Z 1, modulus m1, pressure angle α 1, helixangleβ 1, tip diameter da1, root diameter di1, pitch diameter dj1;
Gear H: tooth number Z 2, modulus m2, pressure angle α 2, helixangleβ 2, tip diameter da2, root diameter di2, pitch diameter dj2;
The mounting center distance of gear G and gear H two gears is D 0;
2) according to above-mentioned selected gear parameter, optional on computer screen is some the fixed center point po2 of gear G, and its coordinate is xo2, yo2, sets up on computers the dynamic model of gear G and gear H turn engagement;
B, calculating:
A) given maximum step-length q maxwith step-length zdsd
B) calculate the dynamic coordinate xdd of the central point podd of gear H i, ydd i, calculating formula is:
q i = q i-1+ zdsd
Q i> q maxtime, forward c to and calculate rotation angle θ;
Q i< q maxtime, calculate
xdd i = (xo2- D 0 * cos ((q ｉ/dj2) * 2 *0.017453293))
ydd i = (yo2- D 0 * sin ((q ｉ/dj2) *2* 0.017453293))
In formula: i=1,2,3,4....
q 0=0
Q istep-length variable
The central point of po2 gear G
The X of the central point po2 of xo2, yo2 gear G, Y coordinate
The extended phase plane of podd gear H
Xdd i, ydd ithe X of the extended phase plane podd of gear H, Y coordinate
Get back to b double counting q i, xdd i, ydd i; ;
C) calculate rotation angle θ, calculating formula is:
θ= (zdsd/ dj1) * 2
D) calculate revolution angle δ, calculating formula is:
δ= (zdsd/ dj2) * 2
E) by above dynamic calculation, while obtaining gear G and gear H engagement in rotation, the coordinate xdd of the extended phase plane podd of one group of gear H i, ydd iwith calculating rotation angle θ and revolution angle δ, the interference spot (3) that the involute of automatic formative gear H part and gear G transition curve part are interfered mutually on computer screen, directly measure width L1 and the arc length L2 of interference spot, obtained the size of turn amount of interference.
CN201210183345.6A 2012-06-06 2012-06-06 Computing method of rotary interference amount of double contact gears Active CN102691773B (en)

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CN103883705A (en) * 2014-04-10 2014-06-25 王榕生 Non-equivalent-modulus gear pair and scanning and numerical control machining template thereof
CN106198217A (en) * 2016-06-29 2016-12-07 内蒙古第机械集团有限公司 A kind of method for designing of gear stress-life testing process
CN108875288A (en) * 2018-09-10 2018-11-23 重庆市綦江源泉机电（集团）有限公司 A kind of design method and gearbox of the point line gear applied to automotive transmission

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