The parameter equation of the involute of the spur gear depends on the size of the base circle. The smaller the radius of the base circle, the more the involute curve bends. Let the base circle radius of the spur gear be rb, the straight line BK be the occurrence line, the starting point of the K point be the A point (ie, the initial position of the involute), and set the Z coordinate of the point A to Z0. Then the position of the K point can be Expressed as: x = rksinH = rbsinH / cosAk (1) (involute in the range of the first and fourth quadrants, respectively -) y = rkcosH = rbcosH / cosAk (2) where: rk involute at any point K The radial direction, rk=rb/cosAk; the radius of the rb base circle; the pressure angle of the K point on the Ak involute tooth profile.
When the initial position of the involute point A is determined, by programming, in the numerical control machine coordinate system, the angle in the XOY coordinate plane can be considered.
In the figure, L=Pd/tgB, and d=mtZ tooth=mnZ tooth/cosB type: L lead of the involute spiral; d index circle diameter of the involute cylindrical gear; end face of the mt helical gear Modulus; the normal modulus of the mn helical gear; the number of teeth of the Z tooth helical gear; the angle between the tangent of the spiral of the cylindrical gear on the cylindrical surface of the B helical gear and the axis Z direction, ie the spiral angle. The angle between the tangent of the spiral of the Bb-based circular cylindrical surface and the direction of the axis Z.
The parameter equation of the involute spur gear is involute. The difference between the spur gear and the helical gear is the same. The involute spur gear has only one modulus, ie m=mt=mn, and the involute There are two modules of the spur gear, namely mt and mn; the tooth line of the involute spur gear is a straight line, that is, a special case when the helix angle of the tooth line is B=0b.
Parametric equation of spur gear In view of the above analysis, the parametric equation of spur gear can be obtained directly from the parametric equation of helical gear: x=rbsin(Hc-invAk)/cosAk(7)y=rbcos(Hc -invAk)/cosAk(8)z=z0 PmZ tooth invAk/360bsinB(10) Discussion: In equation (10), sinB is on the denominator. When B=0b, sinB=0, obviously Z=], which can be considered mathematically meaningless, but in engineering practice, since the Z value is exactly the size of the spur gear in the tooth width direction, this just explains The tooth width of the gear can be arbitrarily determined by the producer according to the purpose of use (in the program) without affecting the involute profile. This gives the machine a lot of flexibility.
Conclusion From the above parameter equations established around the principle of involute cylindrical gear formation, it can be seen that the parameters of the gradual opening of the cylindrical gear can be described in the corresponding equations in the form of variable parameters, which means The geometry of the open cylindrical gear can be accurately described and changed by changing the parameters in the parametric equation. In fact, this is the purpose of parametric geometry modeling. With this method, it is very easy and efficient to use a computer for variable parameter design and computer aided manufacturing. This inevitably creates excellent conditions for efficient and high-quality design and manufacture of involute cylindrical gears.
Squeezing Granulator,Granulation Equipment,Plastic Granulator
Mixing Equipment Co., Ltd. , http://www.plastic-granulator-equipment.com