Research on the gear pair in the design of plane mechanism structure
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Research on the gear high pair in the design of plane mechanism structure Lin Benyi C Jiangmen Gasoline Engine Co., Ltd., Jiangmen 529020, Guangdong, the type, number and relative position of the mobile pair, and applied the Kutzbach discriminant to demonstrate the gear high pair, overcoming the The chaotic condition of the gear high pair as the envelope pair or the instantaneous line pair.
In mechanical design, how to correctly and reasonably select the type of mechanism and the size of the component, improve the machine running speed, and solve the imbalance and vibration problems caused by inertia, improve the efficiency of the designed machine, save energy, this is the design work One of the top issues that must be considered. According to the principle of mechanical composition, any mechanism can be seen as consisting of a frame, a moving part and a kinematic chain with zero degrees of freedom. The relative motion of the components in the mechanism depends only on the type, number and relative position of all the motion pairs in the mechanism, regardless of its shape, section size, number of parts of the component, and the specific structure.
1 Kuzbach discriminant application in the calculation of planar mechanism plane mechanism is widely used in a variety of machines, such as the familiar main mechanism of the 170F diesel engine is also a planar mechanism, see. According to the working condition, the cylinder block is a fixed member, that is, the frame, the piston is the original moving member, and the A constitutes the moving pair, which moves along the axis direction of the cylinder block; the piston and the connecting rod, the connecting rod and the crank, the crank and the frame respectively constitute a rotation. vice. Since the number of the original moving parts of the mechanism must be equal to the degree of freedom of the mechanism, the degree of freedom after each of the original moving parts and the frame is low. 1. According to the Kutzbach discriminant formula for calculating the degree of freedom of the planar mechanism: 2 degrees of freedom of the piece The number of sports vices is high.
The degree of freedom of this main body is: this is consistent with the actual movement.
Another example is the valve cam mechanism of a diesel engine, as shown. According to the working conditions, the cam, the rod and the follower rod are movable members, that is, the number of movable members = 3; the cam and the frame, the rod and the frame constitute a rotary pair, and the driven rod and the frame constitute a moving pair, that is, the low number =3; the cam and the rod, the rod and the driven rod form a high pair, that is, the high sub-number PH = 2; the roller rotates around its own axis, does not affect the movement of the mechanism, and is a local degree of freedom. It can be seen that the degree of freedom of this mechanism is also: (the local degree of freedom of the roller has been removed). This is also in line with the actual situation. However, in the illustrated connecting rod, gear, and rack, the connecting rod-gear six-bar mechanism, If the two gear pairs are treated as envelope pairs, the degree of freedom of the mechanism is still calculated according to the Kutzbach discriminant. The degree of freedom of the mechanism is: this does not correspond to the actual situation. Because the mutual envelope between the two gear members and the gear and rack members limits the free rotation of the two gears about their center of rotation, they cannot simply be regarded as cylindrical rollers with local degrees of freedom, resulting in F=3. In fact, due to the gear-to-gear six-bar mechanism, the relative motion of the two gear members with the high pair can be seen as a pure roll along the relative motion of the two pitch circles, ie, the circular gear mechanism, through the node. There can be relative scrolling between two instantaneous elements, but they cannot move relative to the common normal direction along the common tangent of the two elements of the instantaneous line. It can be seen that the constraint condition of the instantaneous line pair should be calculated according to the single degree of freedom motion pair with two constraints, that is, A=2. Thus, the degree of freedom of the gear-spin six-bar mechanism should be: this and the actual motion situation. Consistent.
The above facts show that when calculating the degree of freedom in the gear mechanism, the gear is generally connected to the frame by the slewing pair at its center. At this time, due to the existence of the flank clearance, only one flank of the gear transmission is in contact with each other, using Kutzbach. The discriminant F is realistic according to the degree; if the center of a gear is suspended, as shown, it is not directly connected to the frame, then the contact of the two gears is not the side contact of a tooth profile, but the gear The two sides of the tooth profile are in contact with the side of the other gear, that is, the composition of the "double high pair in the case of the suspension center distance, the Kuzbach distinction should be calculated by two high-levels, which can be in line with the actual movement of the mechanism. Happening.
2 Gear high pair discussion In the gear mechanism, the gear high pair is both the envelope line and the instantaneous line pair. This unified relationship is the criterion for determining the position of the gear pair in Kuzbach. It can be further explored. .
The gear transmission mechanism shown has a mutual envelope pair. The degree of freedom of this mechanism is: the calculation result is in accordance with the actual situation. However, according to the concept of the instantaneous line, the degree of freedom of this mechanism is calculated as = then the high number PH = 0, which is: does not meet the actual situation.
The transform rack method is now used to obtain the forms shown in (a) and (b).
If the member on the mechanism and the rotary pair at both ends are removed separately, a secondary body composed of two members can be obtained. As shown in (c) and contrast, the rolling and sliding high pair cannot be defined as the two-component motion pair. The relative sliding along the line and the relative rolling of the point around the point, so that the motion trajectory of point A changes from the original aa arc to an indeterminate trajectory. It can be seen that the original mechanism removes the rod and the hinge and loses a real constraint.
However, in contrast to (d) and (b), since the purely rolling high pair shown in (d) can exactly define the distance between the neutral points of the two component motion pairs, the trajectory of the points is unchanged, and is still a circular arc. It can be seen that the original mechanism removes the rod and the hinge and loses a virtual constraint.
3 Conclusion When there is a rod and hinge constraint between the two centers of the gears that determine the shape and position relationship of the two elements of the instantaneous line, the gear pair should be treated according to the mutual envelope; when there are no rods or hinges in the two When the constraint, or the two stored rods and the hinged virtual constraint have been removed, the gear pair should be treated in accordance with the instantaneous line.
For the above gear transmission, it can be verified that if there is a real constraint between the two centers of the two gears, according to the calculation of the mutual envelope, the degree of freedom of the mechanism is: if the virtual constraints of 2 are removed, the calculation is based on the instantaneous line. The degree of freedom of the mechanism is: for the six-bar mechanism of the above-mentioned connecting rod and gear, it can be verified that if there is a real constraint between C, D and C, (to join the connecting rod CD and the slider as two real constraints), press the mutual envelope. Line calculation, the degree of freedom of the mechanism is: If the virtual constraint has been removed, the degree of freedom of the mechanism is calculated according to the instantaneous line of the line: the rule of determining the application of the gear pair in Kuzbach It overcomes the chaos and contradiction of the gear high pair as the mutual envelope pair or the instantaneous line pair processing. It is inspired by the theoretical exploration of the plane mechanism structure analysis and provides parameters for the gear mechanism design.
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