Modeling And Error Measurement Of Planar Double-Enveloping Hourglass Worm

Compared with the ordinary cylindrical worm drive,the planar double enveloping hourglass worm drive is widely used in all kinds of mechanical deceleration drive devices because of its large carrying capacity,high transmission efficiency,and multiple teeth showing double-line contact.However,because the tooth surface of planar enveloping hourglass worm is a complex spatial curved surface,the curvature and normal direction of each point on the tooth surface are different,leading to the detection of its error is more complex.At present,special gauges are used to detect worm's errors generally.According to the special structure and error measurement of hourglass worm,this paper mainly studies the measurement and analysis of various errors of hourglass worm on CNC gear measuring machine.Based on the mathematical model of the plane double enveloping hourglass worm,this paper uses CNC gear measuring center to measure the errors of hourglass worm,and analyses the influence of worm throat position offset on helix error.Firstly,based on the structural characteristics of the hourglass worm and the principle of machining and forming,the modeling coordinate system and the measurement coordinate system are unified,the mathematical model of worm is established by using the two methods,and MATLAB software is used to solve the tooth surface model of hourglass worm to provide a theoretical basis for error measurement.Secondly,based on the principle of plane quadratic envelope hourglass worm and the error measurement principle of CNC gear measurement center,the software of hourglass worm measuring system is developed with Microsoft Visual C ++ 6.0,and the measuring and evaluating equation of hourglass worm is determined.And the experiments are completed,the helix error,tooth profile error and pitch error are measured.Finally,considering the throat of the hourglass worm as the main error factor to measure and analyze and the up-and-down deviation is calculated.The theoretical error of the helix after offset is calculated and compared with the measured error after the offset,the error variation is obtained.The corresponding helical error correction method is obtained,and finally the hourglass worm's throat position is optimized.