Accurate analysis of the blade separation profile

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Accurate analysis of the separation profile of the hob blade of the screw compressor rotor

1. introduction

the screw rotor is the key part of the screw compressor, and the reliability and efficiency of the compressor depend on the machining accuracy of the screw rotor. The end face profile of the standard screw rotor stipulated in China is complex, and the profile has sharp points, so it is difficult to design and manufacture the hob. Therefore, the hobbing method of the screw rotor has not been popularized and applied in China

some developed countries in the world, such as Japan, Britain and France, have done a lot of research work on the hobbing of screw rotors. On the premise of ensuring the efficiency of compressors, they have improved the end face profile of screw rotors to make them smooth and smooth without sharp points, thereby simplifying the design principle of hobs and realizing the hobbing of screw rotors

this paper takes the hobbing of the national standard screw rotor as the object, and makes an experimental study on the design theory and manufacture of the hob of the compressor screw rotor

2. solution of blade separation profile equation

(1) with the development of society, the profile of the end face of the female rotor and the axial edge of the hob

the tooth profile of the end face of the female rotor is composed of unilateral asymmetric cycloid arcs (see Figure 1), that is, the profile of the end face of the tooth profile of the female rotor is composed of straight line AB segment, circular arc BC segment, extended pendulum CD segment and radial straight line de segment. Known parameters of female rotor screw: number of left-hand teeth Z2 = 6, rod length L = 95mm, lead h2 = 170.1mm, pitch radius R2 = 30.24mm, tooth height radius r = 12.915mm. The center distance between the male and female rotors ad = 50.4mm, and the pitch radius RR of the male rotor RR = 20.16mm. According to the above conditions, the coordinate points of the axial blade shape series of hobs in AB, BC, CD and de segments can be obtained. From these points, the axial blade shape of the designed hob can be drawn, as shown in Figure 2

Fig. 1 cross section of female rotor end face

Fig. 2 axial blade shape of hob

according to the known conditions, the axial blade shape c1d1 meshing with CD segment of female rotor is calculated, and the coordinate of D1 point on the blade corresponding to point D on the workpiece is d (44.0837, 6.203069); It is calculated that the coordinate of point D1 on the hob engaged with the de section of the male rotor is d 1E1, which corresponds to the point of maximum force D on the workpiece (yield force on FSU) or minimum force (yield force under FSL) without initial instantaneous effect (the lowest point of the first drop of load). The coordinate of point D1 on the blade will bring new opportunities for the future development of the enterprise is d 1 (37.6313, 5.02781). It is not difficult to see that there is a separate curve between c1d1 and d1e1. The above separation phenomenon occurs because the intersection D of CD segment and de segment on the tooth profile of the end face of the female rotor is not smooth and there are sharp points. Therefore, in order to design and manufacture the correct blade profile, so as to process the correct workpiece profile (that is, not to cause the sharp point D on the female rotor profile to be cut off), it is necessary to accurately calculate this separation curve on the hob blade shape

(2) accurate design of blade separation profile

this design uses the concept of common rack to convert spatial meshing into planar meshing. Given the engagement between the basic worm of the hob and the workpiece, the separation section curve on the rack meshing with the cusp D on the end face of the workpiece is obtained through the tooth shape of the end face of the workpiece, and then the corresponding separation section curve on the hob meshed with it is obtained through this separation curve

set the mutual position of the hob basic worm meshing with the left-hand female rotor as shown in Figure 3. When the hob worm 1 rotates by 1 angle, the workpiece 2 rotates by 2 angles accordingly

Fig. 3 relative position of worm and workpiece

according to the normal theorem of tooth profile, the rack equation meshing with the workpiece can be obtained as

replace the CD segment and de segment of the tooth profile equation of the female rotor end face into the above formula to obtain the rack tooth profile of the workpiece end face, as shown in Fig. 4. The coordinates of the two separation points D2 and D2 in ot1 system are D2 (6.628252, -7.008753) and D2 (-8.32824, -0.626718) respectively

in order to accurately solve the separation section curve on the shape of the hob blade, the separation section curve on the workpiece end rack meshed with the workpiece must be obtained first. Obviously, the D2d2 curve in Figure 4 is a track formed by the meshing movement of the workpiece relative to the rack and the movement of the cusp D on the workpiece tooth profile on the rack tooth profile

Fig. 4 rack tooth profile of workpiece end face

it can be seen from Fig. 5 that the meshing of workpiece and rack is equivalent to the pure rolling of workpiece pitch circle on the rack pitch line. When the workpiece rolls from o point to o point, the motion trajectory equation of point D in ot1 system is

in the formula = 0, D2 = 29.925, 4 = 155364

the coordinates of point D2 and D2 are obtained from formula (1), and the value of 1 corresponding to point D2 and D2 can be obtained by substituting it into formula (2), They are 0.40459 and -0. (RAD) respectively. Therefore, corresponding to the D2D 2 curve, the value range of 1 in the equation is -0.1 0.40459

in order to obtain the profile of the separating section D2D 2 on the hob blade meshing with the D2D 2 curve on the rack, the equation of the rack on the hob worm end face must be obtained first

according to the geometric relationship in Figure 6, the relationship between the normal coordinate of the rack and the coordinate of the rack on the end face of the workpiece is

the formation of D1D2 curve on the tooth bar on the end face of the workpiece in Figure 5

Convert xtn and YTN to the end section of the hob worm to get

where 1 and 2 are the helix angle of the hob worm 1 and workpiece 2 on their pitch cylinder respectively

Figure 6. The profile of the common rack on the workpiece end face, hob end face and normal section

it can be seen from Figure 3 that when the M (x, y) point on the rack enters the meshing, according to the tooth normal theorem, the tooth normal passing through the m point should pass through the meshing node P, so the normal equation at the m point in the OT system is

(XT XT) cos t + (YT YT) sin t = 0

where XT, YT passes through the coordinates of any point on the normal of the tooth profile of point m

the coordinates of point P in the OT system (R1, 1, O) are substituted into the normal equation, and the transformation formula from OT system to O3 system is

joint solution formula (4), (5), and the end edge shape of the hob can be obtained. After obtaining the end edge shape equation of the hob worm and making it spiral around the axis of the hob worm, the tooth surface equation of the hob worm can be obtained

as shown in Figure 7, set the auxiliary coordinate system fixed with the hob worm as o 3x 3Y 3Z 3. In the initial position, the origin O3 coincides with O 3, and the X3 and Y3 axes coincide with x 3 and Y 3 axes respectively. Make the hob worm immobile, and then make the O3 system and the hob end edge shape which is fixedly connected with it spiral around the Z 3 axis to make the helical motion of the helical parameter P1, so as to form the helical tooth surface of the screw. The coordinate transformation formula from O3 system to O 3 system is

the above formula is the tooth surface equation of the hob worm, and make x 3 = 0, then the axial edge shape of the hob is

joint solution formula (5), (6), The coordinate points of the separation profile on the hob shaft section can be obtained

Figure 7 hob worm end face and axial blade shape

3. Conclusion

through the inspection and verification of the measurement department of Wuxi Compressor Co., Ltd., the proposed hob separation part contour calculation principle is correct, ensuring that the sharp point D will not be cut off. Four curves including cusps can be enveloped and processed by one-time cutting

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