Design and working principle of the new shaped grinding wheel dressing device of the classification number TH112 1 Based on the separated involute approximation method, the gear parameters of a certain base circle are trimmed by a whole base cylinder, and the structure of the retaining base cylinder is simple. On the basis of convenient adjustment, it overcomes that a base cylinder can only trim gears with the same base circle. While maintaining the advantages of the separate generation of involute method, the method only needs to replace the base cylinder on the basis of the base cylinder method, adjust the height of the base circle center and the starting position of the diamond, so that the replacement base circle can be gradually formed. The open line approaches the theoretical involute and achieves the tolerance of the tooth profile.
According to the principle of the overall base circle approximation, this paper developed a dresser (referred to as a type dresser) with a steel belt and a rolling rule structure. The dresser has a large improvement in structure, so that the steel belt tension and rolling rule The magnitude of the stress change is greatly reduced, and the stability of the trimming precision is greatly improved.
The principle of action is shown in [2]. The integral involute approximation method designed in this paper uses an involute curve generated by an integral base circle to approximate the involute curve generated by the theoretical base circle. The optimization adjustment parameters are: the base circle radius Rbx is selected, the center height H and the base circle groove half angle 4.2. The optimal design of the overall base circle approximation method 2. The principle of the overall base circle method The method adopts the involute approaching grinding method. The trimming approximation has high precision. In order to properly improve the versatility of the dresser, a base circle can process a certain range of different gears, and there is a new breakthrough in the structure, and the two involute profiles of the grinding wheel can be trimmed at the same time, and the precision is stable. Good sex makes the finishing efficiency greatly improved.
See the gear center coordinate system xy involute curve AB theoretical base circle radius Rte. The substitute base circle radius selected by the dresser is Rhx, the involute A height height h generated in the coordinate system OIX'Y', and the diamond The shape and position of the substitute involute can be changed by the base circle half angle 4 in the OIX 'Y' coordinate system. It can be known from the involute property that the shape of the involute depends on the size of the base circle. The smaller the base circle, the more the involute curve becomes, and the more straight the line is. The position of the substitute involute is determined by the adjustment parameter h4, and when the parameters Ri, h4 (available with the elongation of the diamond pen AL=4Rw) are used to simplify the structural adjustment of the trimmer), when the optimum value is taken, the approaching involute can be made. The approximation accuracy of line AB satisfies the requirements of tooth profile accuracy and tooth thickness accuracy. In order to serialize the substitute base circle size, when the optimal selection of the adjustment is made, the radius of the substitute base circle is first discretized, that is, it is manufactured according to a certain regular size array, and is automatically selected by the computer for optimization design.
The grinding spur gear is formed by a disc-shaped grinding wheel, and the axial truncated contour of the grinding wheel is always the same as the end tooth profile, regardless of the diameter change of the grinding wheel. When the helical gear is sharpened, the contact line between the grinding wheel and the gear is a spatial curve, and the shape of the curve depends on the gear parameters and the diameter of the grinding wheel. The spatial contact line rotates around the grinding wheel axis to become a working surface of the grinding wheel. Therefore, the exact axial section of the grinding wheel is not equal to the normal tooth profile of the helical gear, but should be calculated.
When machining the helicoid with a disc-shaped grinding wheel, the relative coordinate system is as shown in the equation of the right-handed involute spiral surface. After the coordinate transformation, the contact point M is in the grinding wheel coordinate system equation: the axial truncation of a grinding wheel surface Equation: Transform to the coordinate of the dresser coordinate system O1X1Y1: It is also obtained by the contact conditional vector equation: (kXR): Let +u+0=TT be the parametric variable, then (6) can be simplified by (7) substitution (2) (3) Equation (4) can be used to find the section equation of the grinding wheel in the O1X1Y1 coordinate system. According to the involute gear precision measurement, the tooth profile error and the tooth thickness error are measured along the involute direction, and the tooth profile error is calculated as the theoretical involute A. 'P' on the P' point, then the error vector 2.3 is determined by the objective function. The gear accuracy standard has tolerance requirements for the tooth profile error and the tooth thickness error. In order to minimize the approximation error, the tooth profile error can be controlled at the same time. The tooth thickness error is minimized. Therefore, here is an optimization problem for a multi-objective function. In order to make each of the sub-objective functions all tend to their respective optimal values. Here, the unified target method of weighted combination method is adopted.
1 The correction weighting factor of the weighting factor reflecting the relative importance of the first sub-goal is used to adjust the influence of the difference in magnitude between the sub-goals. Here is the adjustment in the iterative process (one and AS (the roughly equal weighting factor in the processing of the overall base circle generation involute approach optimization problem, because the objective function is to minimize the tooth shape, tooth thickness error, by know: Approximating the shape of the involute, the position depends on the parameter Rbx, hAL. It is known by the involute property that the shape of the involute depends on the size of the base circle. When the approximating base circle is the same as the theoretical base circle, h=0, AL= 0, the two involute lines coincide, that is, the approximation error is zero. If the variables Rbxh and Al are taken as continuous variables, the computer optimization result must be Ri, x=Ri, h=0, AL=0, and To achieve the intended purpose, that is, the versatility of a base circle within a certain range, in order to solve this problem, the program adopts the base circle size I of the size of the (3) fixed size as a discrete variable, that is, pre-selected Sequence arrangement. http://ww., 2.5 Optimization method selection This optimization is a hybrid variable (that is, there are continuous variables and discrete variables). Because the objective function of the optimization problem is more complicated, it is difficult to find the derivative. Considering the penalty function method and the absence of gradients The method of combining the constrained optimization methods is an effective method. Based on the original optimization method, this paper expands its function, and the whole continuous is improved into a continuous + discrete general-purpose hybrid penalty function method.
2. Determination of the base circle size array When the modulus is constant, as the number of teeth z is large, the radius of the base circle is smaller, and the involute line is more straight. When the approximating base circle is larger than the theoretical base circle, the approximation error is larger. The optimization design shows that when the same approximation accuracy is reached, when the number of gear teeth is small, the difference between the approximating base circle and the theoretical base circle is allowed to be large. The optimization calculation also shows that when the number of gear teeth is constant, the larger the modulus, the larger the approach error. From the above optimization calculation analysis: the number of base circle size numbers can be taken as a variable ratio.
Among them, the proportional coefficient K is related to the modulus of the modulus.
The above optimization calculation and analysis show that the common ratio coefficient of the base circle size array takes a small value when the large modulus is small, and the larger value when the small modulus has a large number of teeth.
When the value of K is too small, the number of base cylinders is large, and the value of K reaches the set approximation accuracy. Therefore, the principle of K value is as large as possible under the condition of ensuring a given approximation accuracy, so that the number of base cylinders is reduced.
Analysis of the calculation result of the optimal adjustment parameter of 92710202.7 Table 1 Gear adjustment parameter list Gear parameter selection Adjustment parameter Accuracy parameter number Base circle radius rb The optimal substitute base circle radius calculated by the above mixed variable penalty optimization method, dresser height adjustment parameter H And the amount of elongation of the diamond starting position is shown in Table 1. For different modulus and different number of teeth, the optimal calculation of the tooth profile error ratio is â–³/// //. It can be seen from the figure that the error calculation ratio obtained by the method is less than 0.35. From the above calculation and analysis, the substitute base circle size is discretized by a certain number of steps, and the calculated tooth shape error is obtained. The base circle is independent of the modulus and the number of teeth.
Moreover, the serialization of the replacement base circle size is ensured, which is advantageous for the structural analysis of the versatility of the three-expansion dresser when the helical gear is ground by the integral base circle involute method, and the approximation precision is high, and the precision and stability are good. The integral involute approximation method is convenient to adjust, simple in structure and convenient to manufacture, that is, the involute line generated by the appropriate base circle is used to rationalize the involute line generated by the base circle, and the computer can optimize the adjustment parameters to achieve a certain base circle. The range of gears allows the base cylinder to be serialized.
The reasonable structural parameters of the dresser vary with the diameter of the base circle, because when the diameter of the base circle changes, the symmetrical square angle of the left and right rolling feet and the horizontal plane also changes, and the position of the steel belt support wheel O3 must be changed, and the pressing wheel is pressed in the rolling. The action point on the ruler is not the cutting point of the rolling ruler and the base circle, but deviates from the distance color. In order to make the offset a: not too large, the center position of the rotation arm arm shaft must be changed, and the change of the two center positions can be made. By uniformly distributing the mounting holes on the same circle on the turntable i, the angle between the holes and the radius of the hole and the center are determined by structural optimization calculation.
By adjusting the center position of the wire support wheel and the center position of the rolling arm, the dressing range can be expanded to accommodate different numbers of teeth of a certain range of ~100 mm), and the dressing of the involute forming grinding wheel of different modulus.
The processing method of the mechanism structure is: the value of the length S of the rolling rule, and the segmentation processing method.
(2) The adjustment of the force parameter Pn is performed by adjusting the screw.
4 Forming gear grinding experiment To verify the accuracy of the newly developed wheel dresser and trimming helical gear, the author performed on the M8612A spline grinding machine. The gear parameters are M=surface carburizing and quenching, hardened layer depth (0.9 ~1.1)mm grinding wheel speed 3000rpm, grinding feed rate (longitudinal) V/w=(10 trimming feed rate Fa=0.20.5mm/grinding wheel 1 The number of times of n=35 grinding wheel is adjusted by the automatic indexing plate grinding machine equipped with the grinding machine: no coolant has passed a large number of tests and proved that it can be ground by 3 to 6 adjustments only by means of the involute inspection instrument. Gears with 6~7 tooth profile accuracy.
5 Summary In this paper, after comprehensive analysis of various curve approximation methods and trimmers in the hard tooth surface grinding process studied at home and abroad, we recommend a one-piece generation with good precision and stability, and easy manufacturing and adjustment. Involute curve approximation method, and the size of the alternative base circle is also serialized. In this paper, the optimization calculation of the helical gear with a certain modulus and tooth ~100) shows that the size of the substitute base circle is regular. Compared with the discretization of the series, the approximate error ratio of the tooth profile and the tooth thickness is less than 0.5. And has nothing to do with the modulus and the number of teeth.
The dresser with serialized cylindrical dimensions is an accessory product for grinding hard tooth surfaces, and has practical utility value.
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