The theorem of the body-by-open gear and the contour digital selection operation
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S1m0 is the involute of the base circle O1, and S1m1 is the involute of the base circle Oc1. According to the involute property, the centers of curvature of m0 and m1 are respectively at the n0 and n1 points on the pitch line PL. It is easy to prove that the angle between the tangent line n0m0 and g1S1 is D, the angle between the tangent line n1m1 and g1S1 is D1, and the normal angle between the end points m0 and m1 of the involute line m0m1 is D D1, and the Oc1n1 to O2 point is extended. NN2O2n1=A1=A0 D D1,Nn1O2Oc2=D, and make O2Oc2=2rb2, then take O2 and Oc2 as the center, rb2 as the radius and then make two tangent base circles, and their intersection with PL is n1 and n2, respectively. According to the principle of involute formation, a small involute m1m2 is formed, and the center of curvature of the end point m2 of the involute is the point n2 on the node line. The above method is repeated, and the connection of many micro-segments is formed above the pitch line. The convex tooth shape, and below the pitch line is a concave tooth shape symmetrical with the upper part of the pitch line. It is obvious that the smaller the D is, the shorter the length of the involute of the micro-segment, and the more the micro-incremental segments that make up the tooth shape.
The relationship between the micro-section involute rack tooth profile and the micro-section involute rack tooth profile parameters. Modern Manufacturing Engineering 2003 (6) In the micro-segment involute mimi 1, set mi, Si, mi 1 The radius of curvature of the points is Qmi, Qsi, and Qmi 1, respectively. According to the nature of the involute, the radius of curvature of the Si point is: Qsi=Qmi rbi 1D(1), Qsi=Qmi 1 rbi 1Di 1(2), (2), Equation (1): Qmi 1 = Qmi rbi 1 (D-Di 1) (3) The radius of curvature of the mk point can be deduced: Qk = Qm0 rb1 (D-D1) rb2 (D-D2 , rbk(D-Dk)=Qm0 2k-1i=0rbi(D-Di 1)(4), in equation (4), Qm0 is the radius of curvature of the m0 point; Qk is the involute of the kth microsegment The radius of curvature of the endpoint mk point; rbi 1 is the radius of the i-th base circle; D is the pressure angle increment; Di 1 is the central angle of the i-th base circle (as shown).
The radius of curvature of the point of the involute of the micro-segment and the pressure angle of the pressure angle relationship mk point are Ak=Ak-1 D Di 1, recursively: Ak=A0 kD 2k-1i=0Di 1(5), equation (5) Medium A0 is the initial pressure angle. In the middle, ninci is perpendicular to OiOci, the foot is nci, ni 1nci 1 is perpendicular to OiOci, and the foot is nci 1, then the properties of the right triangle and the triangle similarity can be used to find the relationship between the two adjacent curvature centers nini 1 The distance is: nini 1=rbi 1(sinD-sinDi 1)cos(Ai D)(6) where Di 1 is: Di 1=arccos[2cos(Ai D)-cosAi]-(Ai D)(7) From the equations (3) and (7), the Cartesian coordinate equation of the involute rack tooth profile can be established, and the Cartesian coordinate equation of the involute gear tooth profile is established according to the meshing relationship between the rack and the gear. slightly.
The parameters affecting the involute profile curve of the micro-segment and the parameters affecting the involute profile of the micro-segment are: initial pressure angle A0, initial pressure angle increment D, maximum pressure angle Amax, initial base circle radius rb1, and radius. Change the law.
The initial pressure angle A0 is known from the formula (5). The pressure angle of the mkth meshing point with the meshing relative curvature of 0 is: Ak=A0 kD 2ki=1Di. When the Amax value is defined and other conditions are the same, the larger the A0, the k value. The smaller, that is, the number of micro-incremental segments on the tooth profile is reduced, and the number of meshing points with zero relative curvature is less. In general, according to the actual calculation experience, it is better to take Ab 4b8b.
The smaller the pressure angle increment D and the maximum pressure angle Amax, the smaller the pressure angle increment D is. When other conditions are constant, the number of meshing points with the relative curvature of the micro-segment tooth profile is zero. As can be seen from equation (7), the pressure angle increment Dk at the kth point increases as D increases. When A0 and Amax are determined, the value of k decreases, and the number of meshing points with a relative curvature of zero decreases. The value of k which decreases with increasing D is given.