To establish a helical gear modeling method for the analysis of the gear model, the first step is to obtain some of the main parameters of the gear. The commonly used parameters of the helical gear are: the number of teeth z, the modulus mn, the pressure angle A, the helix angle B, the displacement coefficient xn, the direction of rotation and the tooth width B. These parameters can be assigned through the program interface using the commonly used controls of VB.
The gear involute profile is the key and difficult point of the model building. It is a complex curve. Here, curve fitting is performed by selecting a plurality of points on the curve. As shown, any point A on the involute is determined by the radial direction ri and the central angle Ui to the center of the gear, and Ui can be obtained by the formula (1): Ui =180Pz-2r2b-r2irb-arccosrbri 2tanA-A(1) where: z gear tooth number; rb gear base circle radius; A pressure angle on the index circle.
The geometric model of the gear end face is a tensile model in which the helical gear of a certain thickness is divided into several equal parts along the axial direction, and the tooth shape in each split surface is a standard involute tooth shape. The involute profile in the facet is all the fundamental faces when the stretch is stretched, including the tooth profile on the front and rear faces of the gear. Now taking the number of splits as n, the thickness of each aliquot is B/n, and the involute profile of each aliquot is larger than the involute profile of the previous aliquot, on the XOY coordinate plane. The inside is rotated by the $H angle centered on the origin. $H can be calculated by referring to equation (3). When the gear is rotated right, $H is negative, otherwise it is positive. The helical gear can be regarded as a spiral, and its pitch p can be calculated by the formula (2), which is: p=AbsPzmnsinB(2)$H=2PpBn(3) where: Abs takes the absolute value operator; z helical gear tooth number; mn Helical gear normal modulus; B helical gear indexing circle spiral angle; B gear width.
After determining the rotation angle $H, the involute profile of the back n faces can be successively determined based on the first bisector involute (the face is the front end face of the gear). It is now set to any point A on the involute of the first bisector, the polar coordinates on the XOY plane are (ri, Hi1), and the Cartesian coordinates are (xi1, yi1), which can be obtained from equations (4) and (5). . Corresponding point Ak on the involute of the corresponding kth bisector, the polar coordinates in the XOY plane are (ri, Hi1 $H(k-1)), and the rectangular coordinates (xik, yik) can be obtained by the equation (6), 7) Find. Xi1=ricosHi1(4)yi1=risinHi1(5)xi1=ricos(Hi1 $H(k-1))(6)yi1=risin(Hi1 $H(k-1))(7) for each split plane Schematic diagram of the relationship between involute profiles. These involute profiles form the lofting base.
The program implementation of the helical gear modeling is based on the above-mentioned lofting principle and modeling method, and the program is programmed with Visual Basic 6.0 to realize the three-dimensional modeling of the helical gear. The key to the program is to calculate the coordinate positions of the basic stretch faces, ie the points of the involute profile, and plot them in SolidEdge.
The first step: obtain the main parameters of the helical gear, and calculate the coordinates of the involute profile of the first bisector. Through the program parameterization interface, the relevant parameters of the gear are obtained after input or calculation. With these parameters, the program will calculate the coordinates of the points on the involute profile of the first bisector. It is important to note that the fundamental modulus of the helical gear is converted to the end modulus. In the program, the involute line segment is calculated by 15 nodes, and the arc of the tooth top circle is calculated by three nodes, which ensures the accuracy of the shape of the involute profile.
Step 2: With the coordinates of these points, create the first sketch plane in SolidEdge. Using the coordinate positions of these points, after generating the involute on one side of the profile in the sketch plane, use the mirror copy command to generate the other involute. At the root circle and the tip circle, the respective end points of the two side curves are connected by a straight line and a 3-node curve, respectively. In this way, the first loft stretch fundamental is formed.
Step 3: Generate a second stretched base and a subsequent stretched base. According to the coordinates of the points on the side of the first stretched basic surface profile, the relationship between the corresponding points on the stretched surface is used, and the transformation between the corresponding polar coordinates and the rectangular coordinates is performed to obtain the second stretch basic The involute profile on the face corresponds to the coordinates of the point, creating a second stretched fundamental, which is generated in exactly the same way as the first stretched fundamental. Circulating sequentially, to generate n-1 such tensile fundamental planes, these involute profiles form the set of lofting basic faces. At this point, all the stretching fundamentals have been formed, and the next step is to call the loft stretching command to generate the helical gear tooth shape, and then generate a three-dimensional model 1 of the helical gear through the circumferential array.
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