| Gear transmission is widely used in the fields of aerospace,automobile,robot,high-speed rail and other mechanical transmission device.The manufacturing precision of gear has an important influence on the transmission and contact performance.As an efficient and precise gear finishing abrasive process,internal gearing power honing is able to polish the gear surface and eliminate the gear surface deformation after heat treatment,and improve the geometric accuracy of lead direction and profile direction to the greatest extent.In order to improve the gear surface contact performance,noise and vibration,transmission accuracy and carrying capacity,and improve service life,almost all gears of high-speed and high-precision transmission gearboxes need to be modified.In the process of gear honing,a strict relationship,which is defined by electronic gearbox(EGB),between the honing wheel and the workpiece gear or the dressing tool is to be maintained,and the accuracy of gear machining is directly affected by the synchronization accuracy of EGB.Similar to the contour error definition of multi-axis linkage,the tooth surface contour error is defined as the normal deviation between the point on the actual tooth surface and the theoretical tooth surface.Studying the tooth surface contour error modeling and compensation method can effectively improve the gear machining accuracy.In order to improve the processing precision of the internal gearing power honing,this paper designs and develops the electronic gearbox and the modification electronic gearbox structure,and embeds it into the self-developed open CNC system based on the Ethernet bus.The modeling and compensation method of tooth surface contour error,the modification method of full tooth surface based on the multi axis linkage,the modeling and compensation method of electronic gearbox synchronization error are studied.The main research work of this paper is as follows:(1)The gear CNC system based on Ethernet bus is developed,and the function of internal gearing power honing electronic gearbox is embedded into the CNC system seamlessly.Combined with the timing of sensors,actuators and controllers in the CNC system,the delay mechanism of the Ethernet bus signal transmission in the servo drive system and its influence on the control performance are studied.The results show that the steady-state error of the servo control system is directly proportional to the position feedback delay and the target speed,and is not affected by the delay of the control instruction.An Ethernet bus delay compensation strategy based on position feedback and velocity feedback is proposed to estimate the actual position of the current cycle.The synchronous control of the electronic gearbox under the network numerical control system is studied.The generative control error model of electronic gearbox under the network induced delay is established,and the simulation and experimental results show that the proposed compensation method can effectively improve the control precision.(2)A strategy of online synchronization error estimation and control compensation for internal gearing power honing EGB is proposed.By representing the desired trajectory of EGB on the desired plane in the space coordinate system,the point closest to the actual position on the desired plane,namely the synchronization position,can be found,so that the synchronization error can be precisely estimated online.The axis components of the synchronization error are compensated proportionately to the control quantity of each axis,and the synchronization error can be reduced significantly.For the EGB whose synchronization signal is derived from the position feedback,the Taylor expansion of the feedback position is used to estimate the current actual position,thereby compensating the interpolation period lag error.Simulation and experiment are carried out on a self-developed CNC platform for internal gearing power honing.The results show that online estimation and control compensation can reduce the synchronization error to about 40%of the uncompensated.The following axis pre-compensation can basically eliminate the synchronization error of the interpolation trajectory.(3)A general modeling method for tooth surface contour error and an ACCC architecture were proposed.The modeling result shows that the tooth surface contour error is proportional to the tracking error of each axis.The ACCC is designed which comprises the cross coupling controller(CCC)and the fuzzy PID controllers whose universes of membership functions in fuzzy rules are optimized by particle swann optimization(PSO)to improve the adaptability and robustness to disturbance fluctuation and model uncertainty of the system.Simulation and experiment results on internal gearing power honing machine Fassler HMX-400 have shown that the proposed modeling method can estimate tooth profile error very well.Compared with the uncompensated and the CCC methods,the ACCC can effectively improve the tracking precision and gear machining accuracy.Moreover,the proposed modeling and control compensation method can be used in other gear machine tools,such as gear milling,shaping,hobbing,scudding,and grinding machine by changing the relationship of EGB.(4)The influence law of motion control error on tooth surface contour error are analyzed.On this basis,the movement of each axis is changed artificially by adding small periodic motion on axes A and B to actively control the shape of tooth surface,so as to realize the purpose of tooth surface topographic modification only by multi-axis linkage.Firstly,the tooth surface of the honing wheel and the workpiece gear is established by using homogeneous coordinate transformation and meshing principle.and the tooth surface contour error model of workpiece gear is established.Secondly,a topological modification method for full tooth surface of internal gearing power honing is proposed by setting the movement of A and B axes as two fourth order polynomial functions of axial feed of work gear.Diamond dressing gear used for honing wheel in dressing process is standard involute,and it is not necessary to design an especial diamond dressing gear for each different modified gear.Thirdly,the sensitivity matrix of polynomial coefficients is calculated by the normal deviation of the gear tooth surface,and the influence of the variation of polynomial coefficients on the tooth surface is studied.The honed tooth surface can be approximated to the given tooth surface by adjusting the polynomial coefficients through least squares estimation with the aim of minimization of the tooth surface errors based on sensitivity matrix.Finally,numerical examples are used to study the influences of control error on the machining accuracy of workpiece gear tooth surface.The effectiveness of the topological modification method is confirmed numerically using a helical gear on the internal gearing power honing machine.The results show that the method can effectively realize the modification of workpiece gear tooth surface.(5)An on-line estimation and compensation strategy for generalized synchronization error of modification electronic gearbox is proposed.First,the motion of the five axes of the modification electronic gearbox is considered in a five dimensional space.By finding the point closest to the actual position on the interpolation small line segment(namely synchronous position)and then estimating the point closest to the actual position on the continuous trajectory,the generalized synchronization error and its axis component can be accurately estimated.Secondly,the estimated axial component of the generalized synchronization error is proportionally compensated to the position control loop of each axis,and the stability of the proposed control system is analyzed.The simulation results show that the proposed method can accurately estimate the generalized synchronization error of the modification electronic gearbox,and the proposed control compensation method can reduce the generalized synchronization error several times.Experiments on the CNC of internal gearing power honing developed independently demonstrate the effectiveness of the proposed method. |
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