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The Elliptical gear-crank slider mechanism 1 is a simplified diagram of an elliptical gear-crank slider mechanism and its initial position.
The center of rotation of the active elliptical gear 1 is a focus O of the elliptical gear, and the long axis deviation of the active elliptical gear is D (the angle between the long axis of the active elliptical gear and the center line AO ​​of the two elliptical gears), the offset of the slider For H. The transmission of the elliptical gear and the crank slider ABC reaches the requirement that the working stroke of the slider is uniform (or near-smooth-moving and returning to the stroke quickly).
1.1 Mathematical model of angular displacement and angular velocity of driven elliptical gears Firstly, a mathematical model is established with angular displacement and angular velocity of the driven elliptical gear. See the relevant parameters of the elliptical gear-crank slider mechanism. The initial position of the elliptical gear meshing, for example, O and A, respectively, is an in-phase focus of the elliptical gears 1 and 2, which is the center of rotation of the elliptical gear. The meshing point P is at the line of the OA at any time. Therefore, when the two gears mesh at any position, the transmission is smooth, which is the greatest advantage of the elliptical gear to achieve non-uniform speed transmission. When the driving wheel 1 rotates counterclockwise at a constant speed, the driven wheel 2 rotates clockwise. Let the driving wheel 1 turn over the angle U1, and the driven wheel 2 turn over the angle U2. At this time, the two elliptical instantaneous lines are in contact at B1 and B2 (coincidence-.
1 elliptical gear - crank slider mechanism related parameters symbol meaning a / mm elliptical gear long half shaft b / mm elliptical gear short half shaft c / mm elliptical gear half focal moment, c2 = a2-b2k eccentricity, k = b / Ar1/mm axis O to the meshing point P distance r2 / mm axis A to the meshing point P distance U1/rad drive wheel 1 angular displacement U2 / rad driven wheel 2 angular displacement U1/ (rad / s - active Wheel 1 angular velocity (for uniform velocity counterclockwise - U2 / (rad / s - angular velocity of driven wheel 2 D / (b - active elliptical gear long axis and AO cable angle l1/mm crank AB length l2 / mm link BC Length j1/(b-the angle between the crank AB and the x-axis j2/(b-the angle between the link BC and the x-axis B/(b- crank AB initial position r1=b2/(a ccosU1-U1I[0, 2P-(1-r2=b2/(a ccosU2-U2I[-2P,0-(2-) is obtained by the transmission characteristics of the elliptical gear: r1=2a-r2 (3- is cosU2=(a ccosU1-b2(2a2 2accosU1 -b2-c-ac (4- by equation (1-(4) can calculate the relationship between the driven wheel angular displacement U2 and the driving wheel angular displacement U1.
U2=U1r1r2(5-
1.2 The mathematical model of the crank slider speed equation establishes that the crank and the driven elliptical gear are fixed, so the angular velocity of the crank is the same as that of the driven elliptical gear, that is, j1=U2.
From the trainable equation: xB=l1cosj1yB=l1sinj1(6-
Offset crank slider mechanism (6-j1=B-U2(7-xC=xB l2cosj2yC=yB l2sinj2=H(8- by equation (8- get: sinj2=(yC-yB-l2(9- :j2=arctan(sinj2/1-sinj2-(0
3 analysis of the influence of several important parameters on the motion characteristics of the mechanism 1.k=0.8, 2.k=0.9, 3.k=15 eccentricity k affects the slider speed 3.1 eccentricity k when H=0, D=0b, When l1=120mm, l2=300mm, n=300r/min, change k to get the k-to-slider speed influence curve shown. As can be seen from Figure 5, the slider speed change increases as k decreases.
When H=0, D=210b, l1=120mm, l2=300mm, n=300r/min, change k to obtain the influence of the eccentricity k on the near-uniform interval and the influence curve of the k-stroke ratio coefficient Z. . It can be seen that when the value of k is appropriately reduced, the speed of the push is reduced and tends to be gentle. It can be seen that the change of k can adjust the size of the near uniform interval. It can be seen that when the ellipse eccentricity k is around 0.87, the stroke speed ratio coefficient Z reaches the maximum value, and the snapback characteristic is most obvious.
3.2 Slider offset amount H When k=0.9, D=0b, l1=120mm, l2=300mm, n=300r/min, the influence curve of the offset amount H shown on the slider's reverse speed ratio coefficient Z is obtained. As can be seen from the figure, Z decreases slowly with the increase of H. When D=210b, the influence curve of the H-to-slider stroke speed ratio coefficient Z is shown. It can be seen from the figure that Z increases with H and reaches a maximum value near H=40 mm.
3.3 elliptical gear long axis declination D
The long axis declination D of the active elliptical gear has a great influence on the motion characteristics of the slider. The choice of D determines whether the slider can achieve the uniform working speed of the slider in the required interval (or near uniform speed - and has the quick return characteristic). When l1=120mm, l2=300mm, k=0.9, H=0, n=300r/min, the influence curve of D on the slider speed shown by 0 and the D-to-slider speed ratio coefficient shown in 1 are obtained. Z influence curve.
4 Case analysis 2 is the speed curve of the deformed elliptical gear-crank slider combination mechanism obtained in the literature [2]. The combined mechanism satisfies the mechanism motion requirement of uniform velocity (or near uniform velocity - and rapid return characteristics) within a certain interval. .
According to the prepared elliptical gear-crank slider auxiliary analysis software, a set of parameters is selected: a=100mm, k=0.89, l1=120mm, l2=300mm, H=10mm, D=210b, n=300r/min. The resulting slider speed curve is shown as 3. It can be seen that the mechanism can also meet the requirements of the mechanism motion in a certain interval (or near constant speed - and has the quick return characteristic, the slider push, the maximum speed ratio of the return stroke can reach 4.87.
5 Conclusion a- The parameters affecting the snapback characteristics of the elliptical gear-crank slider mechanism are: eccentricity k, offset H and active elliptical gear long axis declination D, where D has the most significant effect.
B- Through parameter optimization, the elliptical gear-crank slider mechanism can achieve similar functions to the degenerated ellipse-crank slider, satisfying the uniformity of the working stroke (or near-smooth-motion, and the return stroke is fast returning motion characteristics).
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