The meshing process of gear transmission is the relative sliding between gear teeth, butThe common law of the meshing point of the two tooth profiles isThe intersection point of the line and the two-wheel connecting line remains unchanged, and this point is called the gear transmission point.The projection of the gear transmission node on the gear plane is called the toothThe motion trajectory of the wheel node and gear node is called the pitch circle, and the pitch circles of two gears areThe circle is tangent to the gear transmission node, and the speeds of the two wheel nodes are equal.Therefore, the meshing transmission of two gears can be regarded as pure rolling of two wheel pitch circles.The rack can be seen as a gear with infinite radius, and the gear and rack meshDuring transmission, the pitch circle of the rack becomes the pitch line, so the contact between the gear and the rackMeshing transmission can be regarded as pure rolling between the pitch circle of the gear and the pitch line of the rack.Point D in Figure 1 is the node of gear and rack transmission, which is not discussed in this article.On the motion of the meshing point of gear transmission, only the nodes of gear transmission are discussedThe movement.
Common motion component connections areHinge connection and sliding connection. Hinge connection (rotational pair) between two components,The hinge point has the same speed and acceleration, while the two componentsSmooth contact (sliding pair), the velocity and acceleration of the contact point are not equalSimilarly, the relative velocity of the contact points must be along the common tangent of the contact pointsThe direction of the line. However, gear meshing transmission or rack meshing transmission onlyThe acceleration is different from the same speed of the node.
geometric method for calculating the angular velocity and angular acceleration of gears and racksSpeed.
The rack AB drives the gear to roll on the horizontal rack purely, that is, the teethBoth wheel and rack AB are in planar motion. D is a gear andThe node on the rack is marked as D1, and the node on the gear is marked as D2.The point is marked as D2, and the speeds of the two points are equal, that is, vD1＝ ｖＤ２．
1) In the plane gear transmissionmedium (including rack and pinion transmission), regardless of whether the gear or rack is fixedWhether it is rotating or making planar motion, the acceleration of each node isThe projections in the tangential direction are equal. In fact, for mutually effective meshes,Or an object is in pure rolling on the surface of another object.This conclusion is valid.With the vigorous development of the Internet, teachers and students can easilyTo obtain more abundant teaching reference materials, but due to the Internet platformThe breadth of information sources, coupled with the lack of strict review mechanisms,This is more harmful to students than no information.Moreover, it is recommended that teachers and students choose relevant examples and exercisesWhen solving a problem, be cautious to avoid getting wrong conclusions.