CN104462638A - Design method of high-order modified Pascal spiral curve non-circular gear pair - Google Patents
Design method of high-order modified Pascal spiral curve non-circular gear pair Download PDFInfo
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Abstract
The invention discloses a design method of a high-order modified Pascal spiral curve non-circular gear pair. The study on a Pascal spiral curve gear is only limited within the situation of the periodic transmission ratio symmetric change, and the application range of the Pascal spiral curve gear can be expanded through the deep study on a high-order modified spiral curve gear and a non-circular gear conjugated with the high-order modified spiral curve gear. The design method specifically comprises the following steps that firstly, a pitch curve equation of the high-order modified Pascal spiral curve non-circular gear pair is established, and a center distance is calculated through the numerical method; secondly, the concavity and convexity of a pitch curve are verified, the maximum modulus under the situation that undercutting is not carried out when a gear is machined through the gear shaping method is obtained, the pressure angle change range is calculated, the maximum pressure angle value is verified, and the contact ratio when the high-order modified Pascal spiral curve non-circular gear pair is meshed is calculated. According to the design method, a whole set of thorough design theoretical basis is provided for the high-order modified Pascal spiral curve non-circular gear pair in actual application, and the using and popularizing of a high-order modified Pascal spiral curve non-circular gear are promoted.
Description
Technical field
The present invention relates to a kind of non-circular gear pair designing method, be specifically related to a kind of method for designing of high-order denatured Pascal curve noncircular gear pair.
Background technology
Non-circular gear mechanism, cam mechanism and linkage assembly can both realize non-at the uniform velocity transmission, but non-circular gear has advantages such as transmission efficiency is high, stable movement, reliable operation, be widely used in a lot of fields.
In the research of the non-circular gear of Pascal curve type gear and conjugation thereof, Ren Tingzhi etc. give the equation of pitch curve and the computing method of centre distance, pitch curve length, basic radius of circle and pressure angle, and go out tooth profile equation by pitch curve equation inference, the approximate formula of high-order Pascal curve gear expression formula and the centre distance thereof of also having derived further, but these researchs are all only confined to the situation of ratio of gear periodic symmetry change, do not comprise the method for designing of the non-circular gear of all Pascal curve type gears and conjugation thereof.To the further investigation of the non-circular gear of high-order denatured snail linear gears and conjugation thereof, will the range of application of expansion Pascal curve non-circular gear.In actual applications, Pascal curve gear is applied on rice transplanter transplanting mechanism, is also applied in blade differential pump design.
Summary of the invention
The object of the invention is for the deficiencies in the prior art, a kind of method for designing of high-order denatured Pascal curve noncircular gear pair is proposed, for high-order denatured Pascal curve non-circular gear provides a whole set of perfect design theory basis in actual applications, all Pascal curve non-circular gear transmission mechanisms can be applied to, facilitate promoting the use of of high-order denatured Pascal curve non-circular gear.First this method for designing sets up the pitch curve equation of high-order denatured Pascal curve noncircular gear pair, and utilizes numerical calculations centre distance; Then verify pitch curve concavity and convexity, solve gear shaping method machining gears not root cut the maximum modulus in situation, calculating pressure angle variation range, verification maximum pressure angle value, calculates the registration during engagement of high-order denatured Pascal curve noncircular gear pair.
For solving the problems of the technologies described above, technical scheme of the present invention is:
Concrete steps of the present invention are as follows:
Step one, set up the mathematical model of driving wheel in high-order denatured Pascal curve noncircular gear pair.
The pitch curve of driving wheel is by the n of mechanical periodicity
1bar pitch curve line segment forms, and every bar pitch curve line segment comprises asymmetrical first denaturation curve section r
11with the second denaturation curve section r
12; The angular displacement of driving wheel
in first period of change, the radius vector of corresponding driving wheel is:
In formula, b is the generation circular diameter of single order Pascal curve non-circular gear, and l is length; m
11, m
12be respectively the first denaturation curve section r
11with the second denaturation curve section r
12sex change coefficient, and be positive number, and meet relational expression:
The numerical evaluation of step 2, high-order denatured Pascal curve noncircular gear pair centre distance a.Constructed fuction is as follows:
In formula, n
2for the exponent number of engaged wheel 2; Utilize the unimodal interval of advance and retreat method determination centre distance a, and utilize Fibonacci method to determine accurate centre distance.
The pitch curve equation of step 3, calculating engaged wheel is as follows:
In formula, r
2for the angular displacement of engaged wheel
corresponding radius vector.
The concavity and convexity of step 4, differentiation driving wheel and engaged wheel.
The curvature radius calculation formula of driving wheel is as follows:
The curvature radius calculation formula of engaged wheel is as follows:
In formula, the ratio of gear of driving wheel and engaged wheel
the first order derivative of ratio of gear
the second derivative of ratio of gear
Driving wheel is corresponding
curvature radius calculation formula:
Engaged wheel is corresponding
curvature radius calculation formula:
First denaturation curve section r
11in, the radius vector of driving wheel asks single order, second derivative obtains:
Second denaturation curve section r
12in, the radius vector of driving wheel asks single order, second derivative obtains:
In formula (6), radius-of-curvature
molecule perseverance be just, order
formula (1), (8) and (9) are substituted into, must be
or
time, the radius-of-curvature of driving wheel pitch curve obtains extreme value k
11=(1+n
1 2m
11 2) b
2+ (2+n
1 2m
11 2) bl+l
2or k
12=(1+n
1 2m
11 2) b
2-(2+n
1 2m
11 2) bl+l
2.As (1+n
1 2m
11 2) b
2-(2+n
1 2m
11 2) bl+l
2during > 0, driving wheel first denaturation curve section r
11curvature ρ
1> 0, first denaturation curve section r
11without indent; Order
push away to obtain driving wheel first denaturation curve section r
11condition without indent is:
Namely
In like manner, formula (1), (10) and (11) are substituted into k
1, release driving wheel second denaturation curve section r
12condition without indent is:
So the pitch curve of driving wheel without the condition of indent is:
In formula (7), radius-of-curvature
molecule perseverance be just, order
formula (1), (8) and (9) are substituted into, must be
or
time, with the first denaturation curve section r of driving wheel
11the radius-of-curvature of the engaged wheel pitch curve be meshed obtains extreme value k
21=a ((1+n
1 2m
11 2) b
2+ (2+n
1 2m
11 2) bl-abn
1 2m
11 2+ l
2) or k
22=a ((1+n
1 2m
11 2) b
2+ abn
1 2m
11 2-(n
1 2m
11 2+ 2) bl+l
2).
As (1+n
1 2m
11 2) b
2+ b (2l+n
1 2m
11 2l-an
1 2m
11 2)+l
2during > 0, order
push away with the first denaturation curve section r of driving wheel
11the engaged wheel pitch curve be meshed without the condition of indent is:
(1+n
1 2m
11 2)ε
2+(2+n
1 2m
11 2)ε-γεn
1 2m
11 2+1>0 (15)
In like manner, formula (1), (10) and (11) are substituted into k
2, release the second denaturation curve section r with driving wheel
12the engaged wheel pitch curve be meshed without the condition of indent is:
(1+n
1 2m
12 2)ε
2+(2+n
1 2m
12 2)ε-γεn
1 2m
12 2+1>0 (16)
So engaged wheel pitch curve without the condition of indent is:
Step 5, solve gear shaping method machining gears not root cut the maximum modulus in situation, computing formula is as follows:
By the radius-of-curvature that formula (6) and (7) are tried to achieve, get minimum value ρ
min, substitute into formula (18), calculate gear not root cut the maximum modulus m in situation
max.Wherein, α
0for the normal pressure angle of pinion cutter,
for pinion cutter addendum coefficient.
Step 6, pressure angle variation range when solving the non-circular gear auxiliary driving of high-order denatured Pascal curve, and verify maximum pressure angle.
When the left side flank profil of driving wheel is active side, pressure angle α
12computing formula is as follows:
When the right side flank profil of driving wheel is active side, pressure angle α
12computing formula is as follows:
In formula (19) and (20), μ
1for the angle of pitch curve between tangent line positive dirction and radius vector.
Registration when step 7, the noncircular gear pair engagement of calculating high-order denatured Pascal curve, and verify minimum registration.Registration calculating formula:
In formula,
for the ad. of driving wheel,
for the ad. of engaged wheel; M is the modulus of driving wheel.
The beneficial effect that the present invention has:
1, the present invention is that high-order denatured Pascal curve non-circular gear provides a whole set of perfect design theory basis in actual applications, all Pascal curve non-circular gear transmission mechanisms can be applied to, facilitate promoting the use of of high-order denatured Pascal curve non-circular gear.
2, the present invention can obtain periodically variable ratio of gear, and in each cycle, ratio of gear change is asymmetric, therefore can be applicable to the occasion that the change of special ratio of gear requires.
3, the present invention adopts the exact value of numerical solution computing center distance, and be easy to programming realization, solving precision is high, convenient and swift.
Accompanying drawing explanation
Fig. 1 is the pitch curve mesh schematic representation of single order Pascal curve noncircular gear pair;
Fig. 2 is the pitch curve mesh schematic representation of high-order denatured Pascal curve noncircular gear pair;
Fig. 3 is that in six blade differential pumps, the first impeller three rank sex change Pascal curve drives wheel set and the second impeller three rank sex change Pascal curve to drive the pitch curve mesh schematic representation of wheel set;
Fig. 4 is that in six blade differential pumps, the first impeller three rank sex change Pascal curve drives wheel set and the second impeller three rank sex change Pascal curve to drive the transmission ratio curve figure of wheel set;
Fig. 5 is that the leakage fluid dram aperture of six blade differential pumps becomes the schematic diagram starting greatly discharge opeing;
Fig. 6 is the schematic diagram that the leakage fluid dram aperture of six blade differential pumps starts to diminish;
Fig. 7 is the schematic diagram that the leakage fluid dram aperture of six blade differential pumps is about to close.
Embodiment
Below in conjunction with drawings and Examples, the invention will be further described.
The method for designing of high-order denatured Pascal curve noncircular gear pair, concrete steps are as follows:
Step one, as shown in Figure 1, set up the mathematical model of driving wheel 1 in high-order denatured Pascal curve gear pair.The pitch curve equation of single order Pascal curve non-circular gear is
wherein, for there is circular diameter in b, l is length,
for the angular displacement that radius vector r is corresponding.As shown in Figure 2, in high-order denatured Pascal curve gear pair, the pitch curve of driving wheel 1 is by the n of mechanical periodicity
1bar pitch curve line segment forms, and every bar pitch curve line segment comprises asymmetrical first denaturation curve section r
11with the second denaturation curve section r
12; The angular displacement of driving wheel 1
radius vector corresponding in first period of change is the (angular displacement of driving wheel 1
consistent at radius vector expression formula corresponding to all the other periods of change and first period of change):
In formula, m
11, m
12be respectively the first denaturation curve section r
11with the second denaturation curve section r
12sex change coefficient, and be positive number, and meet relational expression:
The numerical evaluation of step 2, high-order denatured Pascal curve gear pair centre distance a.Closure condition according to non-circular gear pitch curve obtains following relational expression:
In formula, n
2for the exponent number of engaged wheel 2, i is the ratio of gear of driving wheel and engaged wheel,
Constructed fuction is as follows:
Utilize the unimodal interval of advance and retreat method determination centre distance a, and utilize Fibonacci method to determine accurate centre distance.
The pitch curve equation of step 3, calculating engaged wheel 2 is as follows:
In formula, r
2for the angular displacement of engaged wheel
corresponding radius vector.
The concavity and convexity of step 4, differentiation driving wheel 1 and engaged wheel 2; Concavity and convexity affects the stationarity of the intensity of non-circular gear, the convenience of processing and transmission.
According to infinitesimal geometry knowledge, the curvature radius calculation formula of driving wheel is as follows:
The curvature radius calculation formula of engaged wheel is as follows:
In formula, the first order derivative of ratio of gear
the second derivative of ratio of gear
Driving wheel 1 is corresponding
curvature radius calculation formula:
Engaged wheel 2 is corresponding
curvature radius calculation formula:
First denaturation curve section r
11in, the radius vector of driving wheel asks single order, second derivative obtains:
Second denaturation curve section r
12in, the radius vector of driving wheel asks single order, second derivative obtains:
If radius-of-curvature
be positive, then the pitch curve of driving wheel is in angular displacement
place is evagination; Otherwise pitch curve is in angular displacement
place is indent.In formula (8), radius-of-curvature
molecule perseverance be just, as long as ensure radius-of-curvature
denominator
just can ensure what driving wheel 1 was evagination.Formula (1), (10) and (11) are substituted into k
1, can be
or
time, driving wheel pitch curve radius-of-curvature obtains extreme value, and its value is k
11=(1+n
1 2m
11 2) b
2+ (2+n
1 2m
11 2) bl+l
2or k
12=(1+n
1 2m
11 2) b
2-(2+n
1 2m
11 2) bl+l
2.Therefore, as (1+n
1 2m
11 2) b
2-(2+n
1 2m
11 2) bl+l
2during > 0, driving wheel first denaturation curve section r
11curvature ρ
1> 0, first denaturation curve section r
11without indent; Order
push away to obtain driving wheel first denaturation curve section r
11condition without indent is:
Namely
In like manner, formula (1), (12) and (13) are substituted into k
1, release driving wheel second denaturation curve section r
12condition without indent is:
So the pitch curve of driving wheel without the condition of indent is:
If radius-of-curvature
be positive, then the pitch curve of engaged wheel is in angular displacement
place is evagination; Otherwise pitch curve is in angular displacement
place is indent.In formula (9), radius-of-curvature
molecule perseverance be just, as long as ensure denominator
the pitch curve just can protecting engaged wheel is evagination.Formula (1), (10) and (11) are substituted into k
2, can be
or
time, the radius-of-curvature of the engaged wheel pitch curve be meshed with the first denaturation curve section r11 of driving wheel obtains extreme value k
21=a ((1+n
1 2m
11 2) b
2+ (2+n
1 2m
11 2) bl-abn
1 2m
11 2+ l
2) or k
22=a ((1+n
1 2m
11 2) b
2+ abn
1 2m
11 2-(n
1 2m
11 2+ 2) bl+l
2).
Therefore, as (1+n
1 2m
11 2) b
2+ b (2l+n
1 2m
11 2l-an
1 2m
11 2)+l
2during > 0, order
push away with the first denaturation curve section r of driving wheel
11the engaged wheel pitch curve be meshed without the condition of indent is:
(1+n
1 2m
11 2)ε
2+(2+n
1 2m
11 2)ε-γεn
1 2m
11 2+1>0 (17)
In like manner, formula (1), (12) and (13) are substituted into k
2, release the second denaturation curve section r with driving wheel
12the engaged wheel pitch curve be meshed without the condition of indent is:
(1+n
1 2m
12 2)ε
2+(2+n
1 2m
12 2)ε-γεn
1 2m
12 2+1>0 (18)
So engaged wheel pitch curve without the condition of indent is:
Step 5, solve gear shaping method machining gears not root cut the maximum modulus in situation, computing formula is as follows:
By the radius-of-curvature that formula (8) and (9) are tried to achieve, get minimum value ρ
min, substitute into formula (20), calculate gear not root cut the maximum modulus m in situation
max.Wherein, α
0for the normal pressure angle of pinion cutter,
for pinion cutter addendum coefficient.
Step 6, pressure angle variation range when solving the non-circular gear auxiliary driving of high-order denatured Pascal curve, and verify maximum pressure angle.
When the left side flank profil of driving wheel 1 is active side, pressure angle α
12computing formula is as follows:
When the right side flank profil of driving wheel 1 is active side, pressure angle α
12computing formula is as follows:
In formula (21) and (22), μ
1for the angle of pitch curve between tangent line positive dirction and radius vector.Pressure angle α when obtaining driving wheel 1 transmission by formula (21), (22)
12maximal value, require α
12maximal value be no more than 65 °.
Registration when step 7, the noncircular gear pair engagement of calculating high-order denatured Pascal curve, and verify minimum registration.Registration during non-circular gear engagement is effective length of action and the ratio of rolling circle tooth pitch, registration ε
αfor:
In formula,
for the ad. of driving wheel,
for the ad. of engaged wheel; M is the modulus of driving wheel.
The method for designing of this high-order denatured Pascal curve noncircular gear pair, for high-order denatured Pascal curve non-circular gear provides a whole set of perfect design theory basis in actual applications, facilitates promoting the use of of high-order denatured Pascal curve non-circular gear.Below just for three rank sex change Pascal curve non-circular gear driving mechanisms of six blade differential pumps, illustrate and design high-order denatured Pascal curve non-circular gear according to engineering requirements.
Six blade differential pumps needed to complete three same movement rules within 2 π cycles, therefore can by three rank Pascal curve gear drive, for obtaining better performance, according to six blade differential pump structure and the characteristics of motion, need when adjacent two panels blade openings is little (as best shown in figures 5 and 7) to make the absolute motion speedup of the differential motion of adjacent two blades and every sheet blade, be conducive to opening chamber and reducing liquid resistance; As shown in Figure 6, time adjacent two panels blade openings is maximum, the differential of adjacent two blades is maximum, needs to make the absolute motion of every sheet blade slack-off, improves flow.On high-order basis, introduce sex change coefficient, this designing requirement can be realized, therefore adopt three rank sex change Pascal curve non-circular gears to drive.As shown in Figure 3, first impeller three rank sex change Pascal curve active drive wheel 3 is identical with the pitch curve parameter that the second impeller three rank sex change Pascal curve active drive takes turns 5, and phase 90 ° is installed, the driven driving wheel of the first impeller three rank sex change Pascal curve 4 is identical with the pitch curve parameter of the driven driving wheel of the second impeller three rank sex change Pascal curve 6.
In the design parameter of the first impeller three rank sex change Pascal curve active drive wheel 3, first impeller three rank sex change Pascal curve driven driving wheel 4, second impeller three rank sex change Pascal curve active drive wheel 5 and the driven driving wheel 6 of the second impeller three rank sex change Pascal curve, there is circular diameter b=2mm, length l=24mm; First denaturation curve section r of the first impeller three rank sex change Pascal curve active drive wheel 3 and the second impeller three rank sex change Pascal curve active drive wheel 5
11sex change Coefficient m
11=0.95.
1, the first impeller three rank sex change Pascal curve active drive wheel 3 and the second impeller three rank sex change Pascal curve active drive wheel 5 exist
first period of change in corresponding radius vector be:
2, the pitch curve of the driven driving wheel of the first impeller three rank sex change Pascal curve 4 and the driven driving wheel 6 of the second impeller three rank sex change Pascal curve can be obtained according to formula (5).The ratio of gear i of the first impeller three rank sex change Pascal curve active drive wheel 3 and the driven driving wheel 4 of the first impeller three rank sex change Pascal curve
34, the second impeller three rank sex change Pascal curve active drive wheel 5 and ratio of gear i of the driven driving wheel 6 of the second impeller three rank sex change Pascal curve
56curve as shown in Figure 4.
3, the first impeller three rank sex change Pascal curve drives wheel set and the second impeller three rank sex change Pascal curve to drive the centre distance initial value of wheel set to be a
0=40mm, adopts numerical evaluation mode, and by the unimodal interval of advance and retreat method determination centre distance a, recycling Fibonacci method calculates accurate centre distance a=48.1657mm.
4, the actual practicality determining non-circular gear whether easy to process, therefore requires that pitch curve is convex.Judge formula (16) and (19) according to concavity and convexity, can show that the pitch curve of the first impeller three rank sex change Pascal curve active drive wheel 3, first impeller three rank sex change Pascal curve driven driving wheel 4, second impeller three rank sex change Pascal curve active drive wheel 5 and the driven driving wheel of the second impeller three rank sex change Pascal curve 6 is all convex.
5, maximum pressure angle calculates:
Get α
0=20 °, pressure angle when the first impeller three rank sex change Pascal curve active drive wheel 3 engages with the driven driving wheel 4 of the first impeller three rank sex change Pascal curve is calculated respectively by formula (21), (22), and the pressure angle of the second impeller three rank sex change Pascal curve active drive wheel 5 when engaging with the driven driving wheel 6 of the second impeller three rank sex change Pascal curve, thus the maximum pressure angle of trying to achieve when the first impeller three rank sex change Pascal curve drives wheel set and the second impeller three rank sex change Pascal curve to drive wheel set to engage is 33.46 °.
6, root does not cut maximum modulus calculating:
Get
obtain the m of the first impeller three rank sex change Pascal curve active drive wheel 3, first impeller three rank sex change Pascal curve driven driving wheel 4, second impeller three rank sex change Pascal curve active drive wheel 5 and the driven driving wheel 6 of the second impeller three rank sex change Pascal curve
max=1.72mm.
7, minimum registration calculates:
Get m=1.5,
Can obtain, minimum registration when the first impeller three rank sex change Pascal curve drives wheel set and the second impeller three rank sex change Pascal curve to drive wheel set to engage
Claims (1)
1. the method for designing of high-order denatured Pascal curve noncircular gear pair, is characterized in that: the concrete steps of this method for designing are as follows:
Step one, set up the mathematical model of driving wheel in high-order denatured Pascal curve noncircular gear pair;
The pitch curve of driving wheel is by the n of mechanical periodicity
1bar pitch curve line segment forms, and every bar pitch curve line segment comprises asymmetrical first denaturation curve section r
11with the second denaturation curve section r
12; The angular displacement of driving wheel
in first period of change, the radius vector of corresponding driving wheel is:
In formula, b is the generation circular diameter of single order Pascal curve non-circular gear, and l is length; m
11, m
12be respectively the first denaturation curve section r
11with the second denaturation curve section r
12sex change coefficient, and be positive number, and meet relational expression:
The numerical evaluation of step 2, high-order denatured Pascal curve noncircular gear pair centre distance a; Constructed fuction is as follows:
In formula, n
2for the exponent number of engaged wheel 2; Utilize the unimodal interval of advance and retreat method determination centre distance a, and utilize Fibonacci method to determine accurate centre distance;
The pitch curve equation of step 3, calculating engaged wheel is as follows:
In formula, r
2for the angular displacement of engaged wheel
corresponding radius vector;
The concavity and convexity of step 4, differentiation driving wheel and engaged wheel;
The curvature radius calculation formula of driving wheel is as follows:
The curvature radius calculation formula of engaged wheel is as follows:
In formula, the ratio of gear of driving wheel and engaged wheel
the first order derivative of ratio of gear
the second derivative of ratio of gear
Driving wheel is corresponding
curvature radius calculation formula:
Engaged wheel is corresponding
curvature radius calculation formula:
First denaturation curve section r
11in, the radius vector of driving wheel asks single order, second derivative obtains:
Second denaturation curve section r
12in, the radius vector of driving wheel asks single order, second derivative obtains:
In formula (6), radius-of-curvature
molecule perseverance be just, order
formula (1), (8) and (9) are substituted into, must be
or
time, the radius-of-curvature of driving wheel pitch curve obtains extreme value k
11=(1+n
1 2m
11 2) b
2+ (2+n
1 2m
11 2) bl+l
2or k
12=(1+n
1 2m
11 2) b
2-(2+n
1 2m
11 2) bl+l
2; As (1+n
1 2m
11 2) b
2-(2+n
1 2m
11 2) bl+l
2during > 0, driving wheel first denaturation curve section r
11curvature ρ
1> 0, first denaturation curve section r
11without indent; Order
push away to obtain driving wheel first denaturation curve section r
11condition without indent is:
[(1-(n
1 2m
11 2+1)ε)](1-ε)>0 (12)
Namely
In like manner, formula (1), (10) and (11) are substituted into k
1, release driving wheel second denaturation curve section r
12condition without indent is:
So the pitch curve of driving wheel without the condition of indent is:
In formula (7), radius-of-curvature
molecule perseverance be just, order
formula (1), (8) and (9) are substituted into, must be
or
time, with the first denaturation curve section r of driving wheel
11the radius-of-curvature of the engaged wheel pitch curve be meshed obtains extreme value k
21=a ((1+n
1 2m
11 2) b
2+ (2+n
1 2m
11 2) bl-abn
1 2m
11 2+ l
2) or k
22=a ((1+n
1 2m
11 2) b
2+ abn
1 2m
11 2-(n
1 2m
11 2+ 2) bl+l
2);
As (1+n
1 2m
11 2) b
2+ b (2l+n
1 2m
11 2l-an
1 2m
11 2)+l
2during > 0, order
push away with the first denaturation curve section r of driving wheel
11the engaged wheel pitch curve be meshed without the condition of indent is:
(1+n
1 2m
11 2)ε
2+(2+n
1 2m
11 2)ε-γεn
1 2m
11 2+1>0 (15)
In like manner, formula (1), (10) and (11) are substituted into k
2, release the second denaturation curve section r with driving wheel
12the engaged wheel pitch curve be meshed without the condition of indent is:
(1+n
1 2m
12 2)ε
2+(2+n
1 2m
12 2)ε-γεn
1 2m
12 2+1>0 (16)
So engaged wheel pitch curve without the condition of indent is:
Step 5, solve gear shaping method machining gears not root cut the maximum modulus in situation, computing formula is as follows:
By the radius-of-curvature that formula (6) and (7) are tried to achieve, get minimum value ρ
min, substitute into formula (18), calculate gear not root cut the maximum modulus m in situation
max; Wherein, α
0for the normal pressure angle of pinion cutter,
for pinion cutter addendum coefficient;
Step 6, pressure angle variation range when solving the non-circular gear auxiliary driving of high-order denatured Pascal curve, and verify maximum pressure angle;
When the left side flank profil of driving wheel is active side, pressure angle α
12computing formula is as follows:
When the right side flank profil of driving wheel is active side, pressure angle α
12computing formula is as follows:
In formula (19) and (20), μ
1for the angle of pitch curve between tangent line positive dirction and radius vector;
Registration when step 7, the noncircular gear pair engagement of calculating high-order denatured Pascal curve, and verify minimum registration; Registration calculating formula:
In formula,
For the ad. of driving wheel,
for the ad. of engaged wheel; M is the modulus of driving wheel.
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CN106184448A (en) * | 2016-09-29 | 2016-12-07 | 浙江工业职业技术学院 | A kind of mechanism that leaps on one leg driven based on Pascal curve non-circular gear |
CN106379433A (en) * | 2016-09-29 | 2017-02-08 | 浙江工业职业技术学院 | Single-leg jump mechanism based on eccentric non-circular gear drive |
CN106838158A (en) * | 2017-03-28 | 2017-06-13 | 浙江理工大学 | Off-centre operation-Fourier's not rounded-not rounded three-wheel toothed belt transmission method for designing |
CN106870661A (en) * | 2017-03-28 | 2017-06-20 | 浙江理工大学 | Circle-ellipse-not rounded three-wheel toothed belt transmission method for designing |
CN108916318A (en) * | 2018-07-18 | 2018-11-30 | 武汉理工大学 | A kind of design method and its mechanical driving device of the change center away from non-circular gear pair |
CN109058424A (en) * | 2018-09-29 | 2018-12-21 | 金华职业技术学院 | Asymmetric transmission ratio high-order non-circular gear pair designing method |
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Cited By (9)
Publication number | Priority date | Publication date | Assignee | Title |
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CN106184448A (en) * | 2016-09-29 | 2016-12-07 | 浙江工业职业技术学院 | A kind of mechanism that leaps on one leg driven based on Pascal curve non-circular gear |
CN106379433A (en) * | 2016-09-29 | 2017-02-08 | 浙江工业职业技术学院 | Single-leg jump mechanism based on eccentric non-circular gear drive |
CN106184448B (en) * | 2016-09-29 | 2018-05-11 | 浙江工业职业技术学院 | A kind of mechanism that leaps on one leg based on the driving of Pascal curve non-circular gear |
CN106838158A (en) * | 2017-03-28 | 2017-06-13 | 浙江理工大学 | Off-centre operation-Fourier's not rounded-not rounded three-wheel toothed belt transmission method for designing |
CN106870661A (en) * | 2017-03-28 | 2017-06-20 | 浙江理工大学 | Circle-ellipse-not rounded three-wheel toothed belt transmission method for designing |
CN106838158B (en) * | 2017-03-28 | 2018-11-06 | 浙江理工大学 | Not rounded-not rounded three-wheel toothed belt transmission design method of off-centre operation-Fourier |
CN108916318A (en) * | 2018-07-18 | 2018-11-30 | 武汉理工大学 | A kind of design method and its mechanical driving device of the change center away from non-circular gear pair |
CN109058424A (en) * | 2018-09-29 | 2018-12-21 | 金华职业技术学院 | Asymmetric transmission ratio high-order non-circular gear pair designing method |
CN109058424B (en) * | 2018-09-29 | 2020-04-21 | 金华职业技术学院 | Design method of asymmetric transmission ratio high-order non-circular gear pair |
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