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New Technology of Electrochemical Gear Shaping Based on Artificial Neural Network Control (CAD Center, Huazhong University of Science and Technology, Wuhan 430074, China) Yi Jianjun Hu Yujin (School of Mechanical Engineering, Dalian University of Technology, Dalian 116023, China) Zhou Jinjin Wang Dan Duobo is based on real-time control A new method for the modification of electrochemical gears; a mathematical model for the removal of electrochemical gears is established, and the artificial neural network method is used to obtain the processing power in the case of known shape and shape modification. law.
The processing example shows that the method is practical and feasible, and has great application and promotion value in actual production.
According to the law of removing the control of electrical parameters and motion parameters, the non-gas gHu of the tooth surface is analyzed by the above analysis. One of the methods for improving the gear load carrying capacity of the current density booklet by electroforming is to repair along the tooth profile (or tooth profile). Shape and tooth orientation. Gear shaping can compensate for manufacturing tolerances, mounting errors and elastic deformation, as well as improve the smoothness of the drive and reduce noise and vibration. This is essential for speeding up the gear drive and improving performance such as durability and reliability.
The gear shaping methods adopted by most gear manufacturers include manual shape modification, mechanical modification, and numerical control modification. Although the shaving can be used before the gear is not quenched, the distortion of the tooth surface can be caused by the bevel gear repairing drum, and the precision and surface quality of the shaved workpiece will decrease after the heat treatment. Although it is possible to perform caries after quenching, it is much more difficult to manufacture the grinding wheel than to machine the helical gear. Grinding teeth can shape the hardened gears, and the machining accuracy is also high. However, the machining cost is high and the productivity is low. It is impossible to modify the gears of special structures such as internal gears, multi-joints, large gears and bevel gears. Grinding teeth sometimes produce surface quality defects such as high temperature tempering, force deformation, and poor tooth surface stress. Therefore, the mechanical modification has the disadvantages of complicated tool manufacturing, expensive equipment, limited processing and hardness of the workpiece, and it is difficult to meet the needs of automobile gear shaping. The use of CNC trimming and EDM trimming also has high processing costs, low machining accuracy and limited size and hardness of gears. Therefore, automotive gear manufacturers in advanced countries are committed to developing some precision and productivity. Higher processing equipment, electrochemical gear shaping is a very valuable process.
The basic idea of ​​electrochemical gear shaping is to add a process to control the state of the current density distribution in the electric field based on the dissolution and removal of the anode gear. By controlling the current density distribution, the roots are removed to achieve the shape modification requirements. The shape modification can improve the tooth shape accuracy, reduce the tooth surface roughness, friction coefficient and meshing noise, and improve its anti-adhesive ability and service life. Electrochemical gear modification still belongs to the category of electrochemical machining, so the processing cost is low, the adaptability is strong, no complicated mechanical movement is required, and various automobile gears with complicated structure and high hardness of the tooth surface are easy to operate and easy to batch. Production is a practical, efficient and economical processing method. The prospect of the research is very optimistic. The maximum current amount corresponding to the truncated gap of the distribution density amplitude per unit time is truncated at the first sampling point in the effective processing area. The relationship between the gap and the effective processing area is as shown.
Indicates the input cumulative value of the neuron, W represents the weight of the neuron, 9 represents the threshold, S represents the output of the neuron; Equation (2) is the state equation, U represents the state of the neuron; /(U) is the transfer function, It is a bounded function that rises monotonically; in the nonlinear transformation, it is generally taken as 1+exp. The output layer has m neurons, that is, the output is an m-dimensional vector: Y=T. Let the input weight of the input layer and the intermediate layer w threshold. 9 then the relational expression satisfies the above formula/(w) satisfies equation (4).
The essence of the above two formulas is the mapping of the n-dimensional space of the B-P network. The essence of the learning process of the FB-P algorithm is to use the actual mapping pairs (X1, Y1), (X2, Y2), (Xp, Yp) as artificial neural networks. The learning instructor then uses the artificial neural to derive the mapping (XuY1'), (X2Y2'), (XP, Y/) and the actual mapping pair error, and constantly modify the connection weight and threshold to make the two as close as possible.
Since the B-P algorithm itself is a nonlinear optimization problem, there are problems such as slow convergence speed and local minimum point in the training process. We propose some improved methods.
=w(n) takes the step size as the variable plus amount term to accelerate convergence and prevent oscillation. Introduce a factor of r1 to quickly escape from the insensitive zone, add parameter tooth modulus, mm tooth width mm, average pressure angle axis, staggered corner angle (.) Active tooth 94. An example of applying neural network to solve the law of electric power. Taking an example of a hypoid wheel gear that was commissioned by an automobile gear factory in Shandong as an example, the neural network is used to solve the real-time control of electrochemical gear shaping. The law of electricity application. The gear parameters are shown in Table 1.
Table 1 processing gear parameters parameters surface angle root angle surface roughness Mm midpoint spiral backlash mm active tooth passive tooth parameters material surface hardness HRC core hardness HRC hardening layer spiral direction active tooth right passive tooth right to improve the effect of shaping, according to The characteristics of the gear shaping (the characteristic of the gear tooth shape modification is that there is less in the middle of the erosion at both ends). We set the relative movement speed v of the cathode slider and the tooth surface of the machining wheel in advance, and we have to do it multiple times.
According to the multi-layer neural network propagation theory (B-P network) described above.
The velocity v(x) of the tooth surface, the machining gap S, and the processing time t are decisive factors that determine the distribution of the applied current /(x). E(x) and v(x) are the input layers of the neural network, and the electric current distribution is used as the output layer of the neural network, and a hidden layer is hidden in the middle, which constitutes an artificial neural network as shown. Training data is obtained for the 20 sets of test data (limited to length, data not listed) that satisfy the condition, thereby adjusting the connection weight and threshold between neurons, so that the mapping is successful.
BP network processing model 75, under the condition of a momentum factor of 0.5, the sample is trained 4.5X 105 times, the network reaches global convergence, record the connection weights and thresholds when the network converges, and use the artificial neural network's own prediction function to process The amount of modification E(x) can be used to inversely determine the applied current Kx) required for processing. Through the obtained electric current 8:1), the hyperbolic large gear is aligned for electrochemical modification processing, and the actual modification amount H(x) and the required modification amount E(x) are processed after processing for 12 minutes as required. The error and comparison result are shown in Table 2.
Table 2 Comparison of neural network approximation error Position of tooth surface No. Applied current value Amp Actual erosion amount Calculation of modification amount Mm Error value Mm Tooth surface position No. Application current value Amp Actual erosion amount m Calculation of correction amount Mm Error value Mm position of the tooth surface No. of the current value Amp The actual amount of the erosion is calculated. The amount of the Mm error value Mm Note: The measurement point is taken at a distance of about 1. 4 mm in the direction of the tooth direction of a tooth. The value is close to the actual calculated value, which indicates that it is feasible to apply the artificial neural network to reverse the electric current application law when it is known to modify the shape.
The relationship between the position coordinates of the tooth points and the corresponding shape correction amount The eight-speed 1 rate is determined according to the above-mentioned law mainly to improve the repair of the bookmark2. It is worth noting that we have previously processed the relative motion of the cathode slider to produce production efficiency because When trimming a tooth, when the total time of the trimming process is given, the amount of erosion at a certain point on the tooth mainly depends on the magnitude of the machining current and the length of time facing the slider in the cutoff gap. (ie effective processing time) The former is controlled by the control system through a controllable power supply, while the latter is directly related to the relative movement rate of the slider.
The latter is directly related to the relative rate of movement of the slider when the rate at which the slider is at a point relative to the flank is greater. When the rate of the slider relative to a point on the tooth surface is larger, the shorter the time facing the point in the intercept gap (ie, the shorter the effective machining time), the smaller the amount of machining erosion, and vice versa. The greater the amount of erosion. The above-mentioned motion law is consistent with the requirement of the tooth tooth modification (there are few intermediate ends). Another purpose of doing this is to simplify the control structure. When the motion law of the slider relative to the tooth surface is given, since the relative motion trajectory of the slider and the shaping surface of the hypoid gear are parallel to each other, the gear parameters are determined, at a given wheel. When the tooth and the slider are in a certain position, it is easy to calculate the moving speed of the slider and the rotational speed of the gear. In the specific control, the two angular displacement sensors can respectively measure the angular displacement of the screw and the gear rotation, and according to a predetermined algorithm, it can be converted into the position of the corresponding slider and the tooth surface on the tooth surface; according to the data The control system can accurately control the rotation speed of the stepping motor, so that the slider keeps sliding on the tooth surface of the machining wheel, thereby achieving the purpose of shape modification processing. Of course, if the shape of the tooth is not as regular as this example, then in the processing model of the neural network, the speed of the stepper motor will be used as the output layer, and the network model will become the B-P network with multiple inputs and multiple outputs. The control principle is the same as this type, which also forms a conformal requirement with the profile of the tooth profile, so that the tooth profile is trimmed while the tooth profile is being modified. It is the shaping curve of the tooth and the measurement result of the meshing area before and after the modification (measurement method is 5). It can be clearly seen from this that both the amount of modification and the shape of the shape have achieved the desired effect. We also measured the surface roughness of the profile before and after the modification. It was found that the surface roughness Ra of the workpiece after trimming was 1.6. It was doubled before the modification. These and the requirements and theoretical analysis of the gear manufacturer The amount of modification is basically the same.
5 Conclusion Electrochemical gear modification is a valuable modification process, which is practical, efficient, economical, etc. It has unique features for gear shaping for hard tooth surface, high strength, high toughness, large size and special structure. The advantages are worth promoting in practical applications.
The mathematical model of the removal rule of the gear teeth is established, and it is pointed out that the actual shape can be obtained by controlling the law of power application.
In the actual modification, the shape of the shape modification and the curve of the shape adjustment should be determined in advance, that is, the shape of the shape required to be deformed along the tooth direction E(x).
In order to realize the real-time control of the electrochemical gear shaping process, it is necessary to control the law of the electric current distribution of the cathode slider along the tooth surface of the tooth surface/(x) and the inverse of E(x) to obtain /(x). Since it is very difficult to pass the classical numerical solution, and there is the discrete non-analytic E(x) and the uncertainty of the processing parameters in the process of shaping, we propose a real-time electrochemical gear shaping based on artificial neural network. The control method of the machining current.
The control mechanism of artificial neural network is analyzed, the mathematical model of artificial neural network is established, and some improvement measures of B-P network are proposed.
The test data of the processing conditions were applied to learn and train the B-P network, and the network mapping was successful. Based on this, according to the requirements of shape modification and shape modification, the real-time controlled electrochemical modification of the electric control law can be obtained. The feasibility of the modification process was proved by the coloring test and the obtained tooth profile and tooth profile curve.