Abstract
With increasing demands for high-speed and high-precision machining technology, CBN shape grinding is an effective means in the field of precision machining for screw rotors. Aiming at the high precision machining of screw rotors, a mathematical model for the axial profiles of the CBN wheel for machining screw rotors is developed based on theory of gear engagement. Small electroplated CBN wheel is firstly used to grinding screw rotors. Taking the backlash of screw rotors and the coating thickness of CBN layer into consideration, the modification of the base body of the wheel shape is introduced into the design of CBN wheel. For reducing the tooth profile errors of screw rotors induced by mounting errors and wears of CBN wheel, a mathematical model of the error analyses is established and the influence curves of the profile errors affected by mounting errors and radius error of grinding wheel are proposed. The electroplated CBN wheels for the screw rotors are made to verify the validity and effectiveness of the presented method and the machining experiments were performed. Results of this study reveals that the method proposed in this paper can be used as the precision grinding of screw rotors.
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Abbreviations
- p :
-
screw parameter of the screw rotor
- H :
-
lead length of the screw rotor
- Σ :
-
mounting angle of the axes of grinding wheel and the rotors
- A u :
-
distance between axes of the rotors and grinding wheel
- φ :
-
rotated angle if one point in the rotors being contact point
- δ :
-
modified value of the theoretical axial section of wheel
- δ b :
-
the backlash of two screw rotors
- δ c :
-
the coating thickness of CBN layer
- δ c1 :
-
the average of grit size
- δ c2 :
-
CBN basement thickness
- x1, y1, z1:
-
components at the rotor profile in system σ 1
- x, y, z :
-
components at the rotor profile in system σ
- x u , y u , z u :
-
components at the grinding wheel surface
- n x , n y , n z :
-
omponents of the normal vector of axis x, y, z
- \( \overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\rightharpoonup}$}} {n} \) :
-
normal vector at the screw rotor
- n u , n u , n u :
-
components of the normal vector of axis x u , y u , z u
- \( \overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\rightharpoonup}$}} {n} _u \) :
-
normal vector at the grinding wheel surface
- \( \overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\rightharpoonup}$}} {\omega } _u \) :
-
angular velocity vector of rotation of the grinding wheel
- Ω u :
-
module of angular velocity \( \overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\rightharpoonup}$}} {\omega } _u \)
- \( \overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\rightharpoonup}$}} {\omega } _1 \) :
-
angular velocity of rotation of the screw rotor
- Ω 1 :
-
module of angular velocity \( \overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\rightharpoonup}$}} {\omega } _1 \)
- \( \overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\rightharpoonup}$}} {\nu } _1 \) :
-
velocity of the contact point at the rotor surface
- \( \overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\rightharpoonup}$}} {\nu } _1^0 \) :
-
initial velocity of the contact point at the rotor surface
- \( \overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\rightharpoonup}$}} {\nu } _u \) :
-
velocity of the contact point at the grinding wheel surface
- \( \overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\rightharpoonup}$}} {\nu } _u^0 \) :
-
initial velocity of the contact point at the wheel surface
- R u :
-
theoretical radius of the grinding wheel
- Z u :
-
theoretical axis position of the grinding wheel
- R′ u :
-
modified radius of the grinding wheel profiles
- Z′ u :
-
modified axis position of the grinding wheel profiles
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Wei, J., Zhang, Q., Xu, Z. et al. Study on precision grinding of screw rotors using CBN wheel. Int. J. Precis. Eng. Manuf. 11, 651–658 (2010). https://doi.org/10.1007/s12541-010-0076-2
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DOI: https://doi.org/10.1007/s12541-010-0076-2