CN1648490A - Oval bevel gear wheel set - Google Patents

Abstract

The oval bevel gear pair consists of one pair of oval bevel gears with vertically crossed axes. Both the driving gear and the driven gear have oval great end pitch curves. The oval bevel gear pair has the advantages of both oval gear and bevel gear, may be used in transmitting inhomogeneous speed ratio motion between two crossed axes, and has compact structure, good dynamic balance performance, high bearing capacity and high transmission efficiency. The transmission motion is the combination of rotation and axial linear reciprocation, and may be used in the special field with simultaneous rotation and axial linear reciprocation.

Description

Oval bevel gear wheel set

Technical field

The present invention relates to a kind ofly be used to transmit two to intersect between centers non-at the uniform velocity than the gear mechanism of motion.

Background technique

Existingly be used for transmitting the motion of two between centers and the mechanism of power has: cylindrical gear pair, cone gear pair and noncircular gear pair.Wherein cylindrical gear pair be used for transmitting between two-parallel axis at the uniform velocity than motion; The cone gear pair be used for transmitting two intersect between centers at the uniform velocity than motion; Noncircular gear pair is used for transmitting non-at the uniform velocity than motion between two-parallel axis.Chinese patent CN1490541 discloses at the uniform velocity linear reciprocating motion mechanism of a kind of noncircular gear type, adopts the combination of noncircular gear pair and sine generator scotch yoke, realizes exporting at the uniform velocity linear reciprocating motion.Transmit two and intersect the non-of between centers at the uniform velocity than motion, prior art generally adopts combined mechanism or other combined mechanism of noncircular gear pair and cone gear pair, shortcomings such as mechanism's volume is big, relatively poor, the complex structure of dynamic balance but can cause, and efficient is low, and bearing capacity is more weak.

Summary of the invention

The objective of the invention is in order to overcome above-mentioned defective, provide a kind of and be used for transmitting two and intersect the non-of between centers and make it possess the advantage of oval gear and cone gear simultaneously, and compact structure, dynamic balance are good at the uniform velocity than the gear mechanism of motion, efficient is higher, and bearing capacity is good.。

Technological scheme of the present invention relates to a kind of oval bevel gear wheel set, is made up of the egg shape conical gear of a pair of intersect vertical axis, and wherein the large end face pitch curve of driving gear is avette, and its pitch circle equation is

${\mathrm{<figure-callout\; id="1"\; label="r"\; filenames="A20051002026100083.png"\; state="\{\{state\}\}">r</figure-callout>}}_1=a\&CenterDot;\frac{1-{\mathrm{<figure-callout\; id="2"\; label="e"\; filenames="A20051002026100083.png"\; state="\{\{state\}\}">e</figure-callout>}}^2}{1+e\&CenterDot;\mathrm{<figure-callout\; id="2"\; label="cos"\; filenames="A20051002026100083.png"\; state="\{\{state\}\}">cos</figure-callout>}2{\mathrm{\&phi;}}_1},$ A in the pitch circle equation is avette major semi axis, and e is an eccentricity, φ ₁Polar angle for driving gear.The large end face pitch curve of driven gear is avette, and the pitch circle equation is

${\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="A20051002026100083.png"\; state="\{\{state\}\}">r</figure-callout>}}_2=a\&CenterDot;\frac{1+2e\&CenterDot;\mathrm{<figure-callout\; id="2"\; label="cos"\; filenames="A20051002026100083.png"\; state="\{\{state\}\}">cos</figure-callout>}2{\mathrm{\&phi;}}_1+{\mathrm{<figure-callout\; id="2"\; label="e"\; filenames="A20051002026100083.png"\; state="\{\{state\}\}">e</figure-callout>}}^2}{1+e\&CenterDot;\mathrm{<figure-callout\; id="2"\; label="cos"\; filenames="A20051002026100083.png"\; state="\{\{state\}\}">cos</figure-callout>}2{\mathrm{\&phi;}}_1},$ A in the pitch circle equation is avette major semi axis, and e is an eccentricity, φ ₁Polar angle for driving gear.

The establishment method of the oval bevel gear wheel set pitch cone that technological scheme of the present invention is related is: in oval gear, the Pitch radius of establishing driving gear is r ₁, the centre distance of gear pair is A, the Pitch radius of driven gear is r ₂=A-r ₁, the corner of driving gear is φ ₁The same with the cone gear generate, with oval gear generate egg shape conical gear in the space.Two concurrent aceses be discussed be 90 ° situation, under rectangular coordinate system, to each specific φ ₁Value is got x=r ₁, y=r ₂, by initial point (0,0), and point (0, r ₂), point (r ₁, r ₂) formation triangle Δ ₁, by initial point (0,0), point (r ₁, 0), point (r ₁, r ₂) formation triangle Δ ₂Work as φ ₁When 0 ° turns to 360 °, each φ ₁All corresponding one group of triangle Δ ₁, Δ ₂, and guarantee point (r ₁, r ₂) on same plane, connect each φ ₁The triangle Δ that value is corresponding ₁, Δ ₂, triangle Δ like this ₁, Δ ₂Just constituted the cone of two sealings.Respectively with these two cones as the driving gear of oval bevel gear wheel set, the pitch cone of driven gear.So just set up the pitch cone of oval bevel gear wheel set.

The present invention is by obtaining egg shape conical gear with the oval gear pair at space development, make it possess the advantage of oval gear and cone gear simultaneously: can transmit two and intersect the non-of between centers at the uniform velocity than motion, compact structure, dynamic balance are good, bearing capacity is good, transmission efficiency is higher, its motion for rotate and Shaft to the compound transmission of linear reciprocating motion, can be used for having simultaneously rotation and Shaft special occasions to linear reciprocating motion.

The oval bevel gear wheel set that technological scheme of the present invention is related, velocity ratio and oval gear parafacies are same, and its equation is $i_{12}=\frac{1+2e\&CenterDot;\mathrm{<figure-callout\; id="2"\; label="cos"\; filenames="A20051002026100083.png"\; state="\{\{state\}\}">cos</figure-callout>}2{\mathrm{\&phi;}}_1+{\mathrm{<figure-callout\; id="2"\; label="e"\; filenames="A20051002026100083.png"\; state="\{\{state\}\}">e</figure-callout>}}^2}{1-{\mathrm{<figure-callout\; id="2"\; label="e"\; filenames="A20051002026100083.png"\; state="\{\{state\}\}">e</figure-callout>}}^2}\&CenterDot;$

The driven gear corner of the oval bevel gear wheel set that technological scheme of the present invention is related is φ ₂, its calculation expression is ${\mathrm{\&phi;}}_2=\arctan [\frac{1-\mathrm{<figure-callout\; id="1"\; label="e"\; filenames="A20051002026100083.png"\; state="\{\{state\}\}">e</figure-callout>}}{1+e}\&CenterDot;\tan {\mathrm{\&phi;}}_1]\&CenterDot;$

The related oval bevel gear wheel set of technological scheme of the present invention has following four characteristics:

1. the supporting axle of oval bevel gear wheel set has and moves axially (displacement, speed and acceleration)

1) oval bevel gear wheel set driving shaft and driven shaft move axially displacement:

If the initial polar angle φ of driving gear ₁=0, then working as polar angle is φ ₁The time driving shaft move axially displacement s ₁, its representation is $\mathrm{\&Delta;}{s}_1=a\&CenterDot;\frac{1-{\mathrm{<figure-callout\; id="2"\; label="e"\; filenames="A20051002026100083.png"\; state="\{\{state\}\}">e</figure-callout>}}^2}{1+e\&CenterDot;\mathrm{<figure-callout\; id="2"\; label="cos"\; filenames="A20051002026100083.png"\; state="\{\{state\}\}">cos</figure-callout>}2{\mathrm{\&phi;}}_1}-a(1-e)---\left(1\right)$

The axial displacement of driven shaft is $\mathrm{\&Delta;}{s}_2=a(1-e)-a\&CenterDot;\frac{1-{\mathrm{<figure-callout\; id="2"\; label="e"\; filenames="A20051002026100083.png"\; state="\{\{state\}\}">e</figure-callout>}}^2}{1+e\&CenterDot;\mathrm{<figure-callout\; id="2"\; label="cos"\; filenames="A20051002026100083.png"\; state="\{\{state\}\}">cos</figure-callout>}2{\mathrm{\&Phi;}}_1}---\left(2\right)$

By (1) and (2) as can be known: driving shaft and driven shaft moving displacement equal and opposite in direction, direction is opposite.The speed that moves axially of oval bevel gear wheel set driving shaft and driven shaft.

2) speed that moves axially of oval bevel gear wheel set driving shaft and driven shaft

If φ ₁=ω t, wherein ω is an input angular velocity, and t is the time, and it is v that driving shaft moves axially speed ₁, its representation is ${\mathrm{<figure-callout\; id="1"\; label="v"\; filenames="A20051002026100083.png"\; state="\{\{state\}\}">v</figure-callout>}}_1=2\mathrm{ae\&omega;}(1-e^2)\&CenterDot;\frac{\mathrm{<figure-callout\; id="2"\; label="sin"\; filenames="A20051002026100083.png"\; state="\{\{state\}\}">sin</figure-callout>}2{\mathrm{\&phi;}}_1}{{(1+e\&CenterDot;\mathrm{<figure-callout\; id="2"\; label="cos"\; filenames="A20051002026100083.png"\; state="\{\{state\}\}">cos</figure-callout>}2{\mathrm{\&phi;}}_1)}^2}---\left(3\right)$

The driven shaft axial velocity is ${\mathrm{<figure-callout\; id="2"\; label="v"\; filenames="A20051002026100083.png"\; state="\{\{state\}\}">v</figure-callout>}}_2=-2\mathrm{ae\&omega;}(1-e^2)\&CenterDot;\frac{\mathrm{<figure-callout\; id="2"\; label="sin"\; filenames="A20051002026100083.png"\; state="\{\{state\}\}">sin</figure-callout>}2{\mathrm{\&phi;}}_1}{{(1+e\&CenterDot;\mathrm{<figure-callout\; id="2"\; label="cos"\; filenames="A20051002026100083.png"\; state="\{\{state\}\}">cos</figure-callout>}2{\mathrm{\&phi;}}_1)}^2}----\left(4\right)$

By (3) and (4) as can be known: driving shaft and driven shaft move axially velocity magnitude and equate that direction is opposite.

3) oval bevel gear wheel set driving shaft and driven shaft moves axially acceleration

The driving shaft acceleration $a_1=4\mathrm{ae}{w}^2(1-e^2)\&CenterDot;\frac{\mathrm{<figure-callout\; id="2"\; label="cos"\; filenames="A20051002026100083.png"\; state="\{\{state\}\}">cos</figure-callout>}2{\mathrm{\&phi;}}_1\&CenterDot;(1+e\&CenterDot;\mathrm{<figure-callout\; id="2"\; label="cos"\; filenames="A20051002026100083.png"\; state="\{\{state\}\}">cos</figure-callout>}2{\mathrm{\&phi;}}_1)+2\mathrm{<figure-callout\; id="2"\; label="esi\; n"\; filenames="A20051002026100083.png"\; state="\{\{state\}\}">esi</figure-callout>}{n}^{}{}^{2}2{\mathrm{\&phi;}}_1}{{(1+e\&CenterDot;\mathrm{<figure-callout\; id="2"\; label="cos"\; filenames="A20051002026100083.png"\; state="\{\{state\}\}">cos</figure-callout>}2{\mathrm{\&phi;}}_1)}^3}---\left(5\right)$

The driven shaft acceleration $a_2=-4\mathrm{ae}{w}^2(1-e^2)\&CenterDot;\frac{\mathrm{<figure-callout\; id="2"\; label="cos"\; filenames="A20051002026100083.png"\; state="\{\{state\}\}">cos</figure-callout>}2{\mathrm{\&phi;}}_1\&CenterDot;(1+e\&CenterDot;\mathrm{<figure-callout\; id="2"\; label="cos"\; filenames="A20051002026100083.png"\; state="\{\{state\}\}">cos</figure-callout>}2{\mathrm{\&phi;}}_1)+2\mathrm{<figure-callout\; id="2"\; label="esi\; n"\; filenames="A20051002026100083.png"\; state="\{\{state\}\}">esi</figure-callout>}{n}^{}{}^{2}2{\mathrm{\&phi;}}_1}{{(1+e\&CenterDot;\mathrm{<figure-callout\; id="2"\; label="cos"\; filenames="A20051002026100083.png"\; state="\{\{state\}\}">cos</figure-callout>}2{\mathrm{\&phi;}}_1)}^3}---\left(6\right)$

By (5) and (6) as can be known: driving shaft and driven shaft move axially acceleration magnitude and equate that direction is opposite.

2. the line of contact of egg shape conical gear has swing (pivot angle variable quantity, pivot angle pace of change and pivot angle change acceleration)

1) oval bevel gear wheel set pivot angle variable quantity

If initial driving gear polar angle φ ₁=0, then working as polar angle is φ ₁The time pivot angle variable quantity be Δ θ, its representation is $\mathrm{\&Delta;\&theta;}=\arctan \left(\frac{1+e}{1-e}\right)-\arctan i_{12}---\left(7\right)$

By (7) as can be known: pivot angle variation delta θ is only relevant with eccentric ratio e.

2) oval bevel gear wheel set pivot angle pace of change

The pivot angle pace of change ${\mathrm{\&omega;}}_2=\frac{4\mathrm{e\&omega;}}{1-{\mathrm{<figure-callout\; id="2"\; label="e"\; filenames="A20051002026100083.png"\; state="\{\{state\}\}">e</figure-callout>}}^2}\&CenterDot;\frac{\mathrm{<figure-callout\; id="2"\; label="sin"\; filenames="A20051002026100083.png"\; state="\{\{state\}\}">sin</figure-callout>}2{\mathrm{\&phi;}}_1}{1+i_{12}^2}---\left(8\right)$

By (8) as can be known: pivot angle pace of change ω ₂Only relevant with eccentric ratio e.

3) the oval bevel gear wheel set pivot angle changes acceleration

Pivot angle changes acceleration $\mathrm{\&xi;}=\frac{8e{\mathrm{\&omega;}}^2}{1-{\mathrm{<figure-callout\; id="2"\; label="e"\; filenames="A20051002026100083.png"\; state="\{\{state\}\}">e</figure-callout>}}^2}\&CenterDot;(\frac{\mathrm{<figure-callout\; id="2"\; label="cos"\; filenames="A20051002026100083.png"\; state="\{\{state\}\}">cos</figure-callout>}2{\mathrm{\&phi;}}_1}{1+i_{12}^2}+\frac{4e{i}_{12}\mathrm{si}{\mathrm{<figure-callout\; id="2"\; label="n"\; filenames="A20051002026100083.png"\; state="\{\{state\}\}">n</figure-callout>}}^{2}2{\mathrm{\&phi;}}_1}{(1-e^2)\&CenterDot;{(1+i_{12}^2)}^2})---\left(9\right)$

By (9) as can be known: it is only relevant with eccentric ratio e that pivot angle changes acceleration ξ.

3. the velocity ratio i of oval bevel gear wheel set ₁₂Satisfy $\frac{1-\mathrm{<figure-callout\; id="1"\; label="e"\; filenames="A20051002026100083.png"\; state="\{\{state\}\}">e</figure-callout>}}{1+e}\&le;i_{12}\&le;\frac{1+e}{1-e}\&CenterDot;$

The motion of oval bevel gear wheel set for rotation He Shaft to linear reciprocating motion compound.

Description of drawings

Fig. 1 is the drive mechanism schematic representation of oval bevel gear wheel set.

Fig. 2 is 0 ° of a driving gear, 180 ° of sectional views.

Fig. 3 is 45 ° of driving gears, 225 ° of sectional views.

Fig. 4 is 90 ° of driving gears, 270 ° of sectional views.

Fig. 5 is a driving gear large end face schematic representation.

Fig. 6 is the transmission ratio curve of oval bevel gear wheel set.A=10 wherein, the transmission ratio curve of oval bevel gear wheel set when L1 is e=0.2, the transmission ratio curve of oval bevel gear wheel set when L2 is e=0.5.

Fig. 7 is the displacement diagram of oval bevel gear wheel set driving shaft.A=10 wherein, the displacement diagram of oval bevel gear wheel set driving shaft when L3 is e=0.2, the displacement diagram of oval bevel gear wheel set driving shaft when L4 is e=0.5.

Fig. 8 is an oval bevel gear wheel set driving shaft travelling speed curve.A=10 wherein, input angular velocity ω=1, the travelling speed curve of oval bevel gear wheel set driving shaft when L5 is e=0.2, the displacement diagram that the oval bevel gear wheel set driving shaft moved when L6 was e=0.5.

Fig. 9 is an oval bevel gear wheel set driving shaft translational acceleration curve.A=10 wherein, input angular velocity ω=1, the translational acceleration curve of oval bevel gear wheel set driving shaft when L7 is e=0.2, the translational acceleration curve of oval bevel gear wheel set driving shaft when L8 is e=0.5.

Figure 10 is an oval bevel gear wheel set pivot angle variable quantity curve.A=10 wherein, input angular velocity ω=1, oval bevel gear wheel set pivot angle variable quantity curve when L9 is e=0.2, oval bevel gear wheel set pivot angle variable quantity curve when L10 is e=0.5.

Figure 11 is an oval bevel gear wheel set pivot angle pace of change curve.A=10 wherein, input angular velocity ω=1, oval bevel gear wheel set pivot angle pace of change curve when L11 is e=0.2, oval bevel gear wheel set pivot angle pace of change curve when L12 is e=0.5.

Figure 12 changes acceleration diagram for the oval bevel gear wheel set pivot angle.A=10 wherein, input angular velocity ω=1, the oval bevel gear wheel set pivot angle changed acceleration diagram when L13 was e=0.2, and the oval bevel gear wheel set pivot angle changed acceleration diagram when L14 was e=0.5.

Embodiment

As follows below in conjunction with accompanying drawing to the kinematics characteristic brief analysis of egg shape conical gear:

As shown in Figure 6: 1. oval bevel gear wheel set has identical velocity ratio with the oval gear pair; 2. eccentric ratio e is big more, the velocity ratio i of oval bevel gear wheel set ₁₂Excursion just big more.Eccentric ratio e is big more, and transmission ratio curve changes just sharp-pointed more.

As shown in Figure 7: eccentric ratio e is big more, and the excursion of the displacement s of oval bevel gear wheel set driving shaft is just big more.Eccentric ratio e is big more, and the driving shaft displacement diagram changes just sharp-pointed more.

As shown in Figure 8: eccentric ratio e is big more, and the excursion of the movement speed v of oval bevel gear wheel set driving shaft is just big more.Eccentric ratio e is big more, and the driving shaft velocity curve changes just sharp-pointed more.

As shown in Figure 9: eccentric ratio e is big more, and the excursion of the translational acceleration a of oval bevel gear wheel set driving shaft is just big more.Eccentric ratio e is big more, and the driving shaft acceleration diagram changes just sharp-pointed more.

As shown in Figure 10: eccentric ratio e is big more, and the excursion of oval bevel gear wheel set pivot angle variation delta θ is just big more.Eccentric ratio e is big more, and the curvilinear motion of pivot angle variable quantity is just sharp-pointed more.

As shown in Figure 11: eccentric ratio e is big more, oval bevel gear wheel set pivot angle pace of change ω ₁Excursion just big more.Eccentric ratio e is big more, and the curvilinear motion of pivot angle pace of change is just sharp-pointed more.

As shown in Figure 12: eccentric ratio e is big more, and the excursion of oval bevel gear wheel set pivot angle variation acceleration ξ just more greatly.Eccentric ratio e is big more, and pivot angle changes acceleration diagram and changes just sharp-pointed more.

Provide an embodiment of egg shape conical gear below

The structural drawing of present embodiment as shown in Figure 1, oval bevel gear wheel set is made of active egg shape conical gear 1 and driven egg shape conical gear 2.Both large end face pitch curve coordinate length units are millimeter, can determine that its mounting distance is 78.6 millimeters.The avette major semi axis of driving gear large end face is 53, and eccentricity is 0.2, and the number of teeth is 54, and pressure angle is 20 °, the facewidth is 15, and the avette major semi axis of driven gear large end face is 53, and eccentricity is 0.2, and the number of teeth is 54, pressure angle is 20 °, and the facewidth is 15, and the modulus of driving gear driven gear is 2.Maximum radius place on the driving gear 1 is a tooth top, and the least radius place is a teeth groove, and the maximum radius place on the driven gear 2 is a tooth top, and the least radius place is a teeth groove, so that accurately mesh at driving gear maximum radius place and driven gear least radius place when mounted.

Claims (2)

1 one kinds of oval bevel gear wheel sets is characterized in that: the egg shape conical gear by a pair of intersect vertical axis is formed, and wherein the large end face pitch curve of driving gear is avette, and the pitch circle equation is $r_1=a\&CenterDot;\frac{1-e^2}{1+e\&CenterDot;\cos {2\mathrm{\&phi;}}_1},$ A is avette major semi axis in the pitch circle equation, and e is an eccentricity, φ ₁Polar angle for driving gear; The large end face pitch curve of driven gear is avette, and the pitch circle equation is $r_2=a\&CenterDot;\frac{1+2e\&CenterDot;\cos 2{\mathrm{\&phi;}}_1+e^2}{1+e\&CenterDot;\cos 2{\mathrm{\&phi;}}_1},$ A is avette major semi axis in the pitch circle equation, and e is an eccentricity, φ ₁Polar angle for driving gear.

2 oval bevel gear wheel sets as claimed in claim 1 is characterized in that: the least radius of the maximum radius of driving gear and driven gear engagement when main driven gear is installed.

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