Linkage model and interpolation analysis of helical non-circular gear hobbing
- PDF / 2,256,533 Bytes
- 13 Pages / 595.276 x 790.866 pts Page_size
- 69 Downloads / 150 Views
(2020) 42:582
TECHNICAL PAPER
Linkage model and interpolation analysis of helical non‑circular gear hobbing Jiang Han1 · Dazhu Li1 · Xiaoqing Tian1 · Lian Xia1 Received: 8 July 2020 / Accepted: 1 October 2020 © The Brazilian Society of Mechanical Sciences and Engineering 2020
Abstract The design flexibility and transmission stability of the non-circular gears can be improved using the helical tooth scheme. Herein, a linkage model was derived for hobbing the helical non-circular gears based on the influence of the axial feed motion of the hob on the motion of the projecting rack on the gear-blank end face. This axial feed motion produces additional motion effects on the rotary axis of the gear-blank and the moving axis of the hob. Further, the accuracy of the linkage model was verified by kinematic simulations. The global convergence characteristics of the transcendental equation used for obtaining the polar angle of the pitch curve were ascertained to derive the interpolation calculation process for the linkage model-based electronic gearbox. The cause of cumulative error during the multi-turn hobbing process of the gear blank was analyzed. The error accumulation was effectively controlled by optimizing the interpolation algorithm. The hobbing experiments and meshing transmission test were conducted using the self-developed non-circular gear hobbing system to verify the effectiveness of the linkage model and interpolation algorithm. Graphic abstract
Keywords Helical non-circular gear · Hobbing · Linkage model · Interpolation error List of symbols ωc The angular velocity of the gear-blank axis ωb The angular velocity of the hob axis vx The linear velocity of the hob axis in x-axis vz The linear velocity of the hob axis in z-axis vy The linear velocity of the virtual rack in y-axis Technical Editor: Marcelo Areias Trindade. * Dazhu Li [email protected] 1
CIMS Institute, Hefei University of Technology, Hefei 230009, People’s Republic of China
A and B The points on pitch curve of non-circular gear vB The velocity of point B θ The rotation angle of gear blank φ The polar angle of pitch curve μ The angle between the polar radius and the tangent δ The angle between vB and vy r The polar radius of pitch curve β The helical angle of non-circular gear ∆ωc The additional angle of gear blank M-M The section parallel to the end face of the gear blank
13
Vol.:(0123456789)
582
Page 2 of 13
Journal of the Brazilian Society of Mechanical Sciences and Engineering
N–N The section parallel to the end face of the gear blank Q1 The point located on the centerline of the equivalent rack in the M–M section Q2 The point located on the centerline of the equivalent rack in the N–N section P1 and P2 The points located on the pitch plane of the equivalent helical rack Q3 The point located on the segment P1P2 and the section N–N ∆z The distance between sections M-M and N–N vy* The moving speed of the projection rack in the y-axis direction T The number of hob threads mn The normal modulus of non-circ
Data Loading...
