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Theoretical analysis of planetary gear stepless speed regulation The linear motion analysis of the point on the circumference of the planetary gear indexing is as shown in the coordinate system: the radius of the conducting circle O1 and the rolling circle O2 are respectively R1 and R2. When the circle O2 is along the conducting circle O1 When the inner circumference is continuously purely rolling, the trajectory of the point B on the circumference of the circle O2 on the plane of the circle O1 is: x=(R1-R2)sin5-R2sin(WU)y=(R1-R2)cos5 R2cos(WU) (1) where: W is the rotation angle of the spheronization O2, and U is the spheronization O2 revolution angle.
They satisfy WR2=UR1, W=R1/R2U and let the transmission ratio i12=R1/R2, and substitute them into (1): x=(R1-R2)sinU R2sin(1-i12)Uy=(R1-R2) cosU R2cos(1-i12)U(2)(2) is an ordinary hypocycloid equation. Its shape depends on the spheronization and the rounding. Now take the circle radius R1=2R2 into the formula (2): x=0y=2R2cosU(3) The derivation of the equation of the pendulum (3): The trajectory of the point on the circumference of the circle O2 is the center of the O1 circle. A straight line in the y-axis direction. When 0[U[P], the length of the straight line can be obtained as 4R2 by using the solitary length formula. U is changed between 0 and 2P due to the rounding of the circle around the guide circle. Therefore, when the point on the circumference of the rolling circle reciprocates once through the center of the guide circle, the straight line length is 8R2.
We know that the meshing process between the planetary gear and the ring gear can be regarded as the pure rolling of the pitch circle (index circle) of the planetary gear on the pitch circle (index circle) of the inner ring gear. If the pitch circle (index circle) of the planetary gear is regarded as a circle, and the inner ring pitch circle (index circle) is regarded as a guide circle, the motion track at a point on the circumference of the planetary gear segment is a hypocycloid. When the diameter of the inner ring indexing circle is twice the diameter of the planetary gear indexing circle (Z1=2Z2), the trajectory at any point on the pitch circle (indexing circle) of the planetary gear becomes a straight line passing through the center of the ring gear, that is, Satisfy the formula (3). In order to take advantage of the linear motion of a point on the pitch circle (index circle) of the planetary gear and take out the linear motion, a cylindrical annular ferrule is designed and consolidated with the end face of the planetary gear. (The center line of the ferrule falls on the circumference of the planetary gear indexing.) Thus, in the process of the planetary gear meshing with the ring gear and making the planetary motion, the trajectory of the cylindrical ring ferrule is a straight line passing through the center of the ring gear.
The motion analysis of the cylindrical ring ferrule is fixed on the end face of the planetary gear, and its center line is located on the index circle of the planetary gear 1. Therefore, it can be regarded as the indexing circle of the planetary gear. The point is based on the above analysis: the motion analysis of the annular ferrule is the motion analysis of its center. Transform equation (2) into coordinate system X1OY1, and use equation (3) to obtain: x1=2RsinBcosUy1=2RcosBcosU(4)(4): Ming azimuth B is to determine the size and stroke motion of the annular ferrule The basic parameters of the orientation. When B=0b, the horizontal displacement of the annular ferrule is zero, only the linear displacement of the center of the inner ring gear in the vertical direction, the stroke is 4R2; when B=90b, the vertical displacement of the annular ferrule is zero. Only the linear displacement of the center of the ring gear in the horizontal direction, the stroke is 4R2; when 0b
July 28, 2024