The internal gear transmission mechanism is compact and has been widely used in the industry. Due to the small relative sliding between the conjugate tooth surfaces of the internal gear, the induced radius of curvature is large, the root thickness is increased, the lubrication condition is improved, and the contact strength, bending strength and seizure resistance of the gear are improved; The meshing gear is high and the transmission ratio is large. However, due to the structural limitation of the internal gear, generally only the gear shaping is used, the gear precision and the surface quality are low, and the shaping of the gear can not be completed, so that the internal potential of the internal gear is difficult to play. The application of the electrochemical gear shaping technology to the internal gear can accurately correct the internal gears of various types (straight teeth, helical teeth), and the electrochemical machining has an anode leveling effect, which improves the tooth surface quality. .
In electrochemical machining, the metal erosion rate mainly depends on the current density. Accurately calculating and controlling the tooth surface current density distribution is the key to accurately control the actual shape modification and shape modification. Numerical methods are used to simulate various gear parameters and process parameters. The lower tooth surface current density distribution can provide a reliable theoretical basis for the determination of cathode structure parameters and optimal process parameters for internal parameters of different parameters.
1 The basic equation of the electric field shows the positional relationship between the cylindrical cathode and the internal gear. In the electrochemical gear modification, the current density distribution along the tooth height in the tooth surface has a great influence on the trimming result. When the effect of polarization on the current density distribution is not considered, the anode surface current density distribution is determined by the electric field distribution in the solution. When the electrolyte is uniformly filled between the cathode and the anode, the potential distribution h(x, y, z) in the solution can be calculated based on the same cross-sectional shape of the gear and the cathode along the axial direction, and the electric field distribution in the electrochemical gear shaping can be calculated. Simplify solving for planar problems. Since the inner gear and the cathode have a circular domain characteristic, a differential calculation in the form of polar coordinates can be employed. The expansion of the two-dimensional Laplace equation in polar coordinates is that the current density at any point in the solution is the current density at any point on the tooth surface = the current density i is the scalar, which is perpendicular to the anode surface.
2 Boundary conditions are determined because the center of the gear shape is symmetrical, so half of the base section is taken as the field of numerical calculation (the curved boundary of the calculated field of the sector of the circular ring field is ABCDEFGA. Where AB is the root circle and BCD is the tooth Profile, DE is the tip circle, FG is the cathode; BCD points are the intersection of the tooth profile and the root circle, the index circle, and the addendum circle, O is the tooth base point; AG is the tooth root symmetry line, EF is the tooth The symmetry line at the top. The surface potential of the gear (anode) in processing is the same as the positive potential of the DC power supply, set to U, and the cathode potential is always zero. The boundary condition of the calculated field can be expressed according to the geometric principle of the gear, corresponding to each point on the tooth profile. The polar angle 0r can be expressed by the pole diameter r of the point. For a standard involute gear, the pressure angle at the index circle is D = 20° 0.344907 rad), and the polar angle at the index circle is 0g = n / 2z, the polar angle 0b at the base circle can be determined by the following equation: the polar angle between the pole angle 0r and the pole diameter r has the following relationship: the potential of the inner gear surface and the cathode surface and the root and the tooth top symmetry line satisfy the boundary condition.
3 tooth surface current density calculation formula (4) is the basic formula for calculating the tooth surface current density. According to the difference calculation, the potential distribution between the teeth can be used to find the tangent of a point on the tooth surface along the pole diameter and the arc grid. The denser the current density of the direction, the more accurate the calculation result; U is the ratio of the radius of the arc-shaped grid line, U=1+00 4 The numerical simulation result of the tooth surface current density distribution is the cathode and the tip spacing The effect of the surface current density distribution. z = 40, gear modulus md = 6mm, potential difference between cathode and anode U = 10V, cathode to tip circle spacing s are 1020304050mm, using 15% NaN3 aqueous solution, conductivity in 40C solution is 0L0152 (mm -U-1). The abscissa is the distance from the top of the tooth, the top of the tooth is rounded, the abscissa is X=0; the indexing circle is X=mod; the root is round, X=225md. The ordinate is the current density i(mA'mm-2 ). It can be seen that the current density at the top of the tooth is large, and the further away from the tip, the smaller the current density, and the current density to the root is almost equal to zero. Near the crest, the current density value decreases rapidly with increasing distance from the crest, and then slows down. The other parameters are unchanged, the cathode and the tip circle are spaced apart, and the current density is generally high. When the distance between the cathode and the tip of the tooth is large, the current density is generally low.
3 is the distribution of tooth surface current density at z 10, 20, 30V. The composition, concentration, and operating temperature of the solution are the same. The potential difference between the cathode and the anode increases, and the current density at each point on the tooth surface increases proportionally; at the same time, the difference in current density between the tip of the tooth and the starting point of the trimming increases rapidly.
Component, line (vector summation counts the point is40; Cg sputum tank is divided. 0. Numerical simulation results also show that when the distance between the cathode and the tip is greater than 20mm, and the number of teeth is greater than 40, the modulus is greater than 2mm, the number of teeth And the modulus has little effect on the tooth surface current density distribution and can be ignored.
5 Conclusion The current density value near the tooth tip on the tooth surface is the largest. The farther from the tooth tip, the smaller the current density value, the current density at the root is negligible compared with the tooth tip. This is decisive for ensuring the original tooth shape of the non-shaping area while completing the shaping process.
The numerical simulation results show that the influence of various gear structure parameters and process parameters on the distribution law of tooth surface current density is different. The spacing between the cathode and the gear has a great influence on the current distribution law of the tooth surface. The current density of the tooth surface is generally large when the spacing is small; the spacing is too large, and the current density distribution of the tooth surface tends to be uniform, which is unfavorable for the shaping process. The larger the potential difference between the cathode and the anode, the more generally the tooth surface current density increases. The change of solution concentration and processing temperature will lead to the change of solution conductivity, and the tooth surface current density will increase proportionally with the increase of conductivity. When the distance between the cathode and the tip is greater than 20 mm, the number of gear teeth and the modulus have little effect on the tooth surface current density, which can be ignored. The numerical simulation results have a clear guiding role in the determination of process parameters.
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