The reason is that the first-order continuous conductivity of the original design function q(H1) cannot guarantee the smooth connection of the two-section curve at the intersection. Since q(H1) is monotonically increasing, there is only one minimum value, that is, the minimum value, and the initial point q(0) is the minimum value of this design interval. Thus, three conditions for a smooth curve of a pair of identical non-circular gear sections are obtained: monotonically increasing, first-order continuous ductility, and the original design function at the initial meshing point takes a minimum. A specific example of designing a smooth non-circular gear section curve is given below.
Design a pair of identical 3 non-circular gear pitch curves with a quadratic polynomial to make the original design function q(H1)=1 H21P2. Design according to the previous steps, calculate n=1.5736462, correspondingly, the original design function q (H1) is adjusted to: f(H1)=q(nH1)=1 1.2381812H21. The pitch curve of the resulting non-circular gear is as shown, which indicates that when the angular displacement H1=0b, that is, when the non-circular gear is at the starting meshing point The image shape of a pair of identical three non-circular gear smooth curve curves. It can be seen from the figure that the intersection of the adjacent two branch curves is smooth.
k is a dimensionless parameter that is an important parameter in determining the shape of a section curve. It can be used to design a series of similar non-circular gear section curves. It is advisable to refer to this series of section curves as a family of curve curves. k = bPa (k > 1), geometrically, this parameter can be used to measure the non-circularity of the non-circular gear section curve; from a kinematically speaking, it is the maximum speed ratio coefficient (ie the maximum value of the speed and The ratio of the minimum value. The closer the distance k is, the smaller the non-circularity of the non-circular gear is, the closer the maximum speed ratio coefficient is to 1, the smaller the range of the variable ratio transmission is realized; the farther the k distance 1 is, the non-circular gear is non-circular. The larger the roundness is, the larger the maximum speed ratio coefficient is, the larger the range of the variable ratio transmission is. When k is greater than a certain value, the curve of the non-circular gear section is smooth and a pair of identical three non-circular gear section curves begin to appear. The concave shape, and as the value of k continues to increase, the degree of the concave shape becomes larger and larger.
Conclusion Through the above analysis and discussion, the conclusions can be drawn as follows: (1) The design method of a pair of identical non-circular gear section curves is given. Five steps of initial section curve design are proposed, and the specific section curve function r1 is given. (H1) The initial pitch curve of a pair of identical 2, 3 and 4 non-circular gears is constructed. (2) Point out the necessary and sufficient conditions for guaranteeing the smoothness of the joint curve, even if the designed function has continuous first-order derivatives at the intersection of the adjacent two-section curve. (3) The range of values ​​of k which makes the non-circular gear section curve convex is analyzed. The three non-circular gear section curves are taken as an example. When 11.3269326, the section curve appears concave.
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