The machining center, which should at least be a three-coordinate linkage system, is unquestionable. We make the following provisions: 1. The problem is solved and solved on the horizontal three-coordinate 1 2 system, the definition of the 1 3 coordinate 1 4 system: the horizontal movement direction of the x-axis table; the y-axis bed box The vertical movement direction of the column; the z-axis column moves forward and backward, that is, the tool length compensation direction; M machine zero point; My surface tool radius compensation plane.

1. 2 We set the mathematical equation of the finished workpiece in the machine system coordinate system as y = ax 2 + bx + c(1) ( a, b, c is a constant). For the discussion of the problem, let us set a > 0 (A < 0 can adjust the upper and lower clamping direction of the machining surface) can be expressed in the system coordinate system.

2 simplification of the problem

Set the vertex of the parabolic cylinder to the workpiece zero of the workpiece, and use the workpiece zero W as the origin to translate the equipment system coordinate system to obtain the workpiece zero coordinate system. Then the equation (1) is simplified in the workpiece zero coordinate system: The length of the parabolic cylinder is L, the thickness of the cutter is H, and the cutter has 70% thickness. The parabolic cylinder is machined in accordance with the direction of the path provided by the projection of the parabolic cylinder on the XWY plane. Each time the tool adds a feed rate of 0 7H in the Z direction, along the above rail, we will complete a machining cycle, and the entire machining process requires L/0 7H machining cycles. Therefore, the problem of processing the parabolic cylinder Y = aX2 can be simply understood as the processing of the parabolic line in the XWY plane: Y = aX2.

3 milling cutter radius selection

In order to avoid excessive machining of the part of the curve near the point where the tool is in contact with the curve during machining, the radius of the tool should be less than or equal to the minimum of the radius of curvature at each point on the curve. It is known by mathematical theory that the parabola has the largest curvature at its apex, that is, the parabola has the smallest radius of curvature at its apex, and the maximum value of the tool radius is the radius of curvature of the parabola at its apex. Let the tool radius R be equal to the radius of curvature P of the parabola at its apex, ie: R = P, at which time the machining efficiency and the machining accuracy of the machined curve are the highest.

Therefore, we get the radius of the milling cutter R = 1 / 2a. It can be seen from this formula that the smaller a is, the larger the R is, but the actual situation is that R is not infinitely large. Therefore, at this time, it is necessary to appropriately reduce the size of the tool radius on the premise of maximizing the machining efficiency and machining accuracy according to the limitation of the tool carrying capacity of the device itself.

4 Determination of the center track of the milling cutter

If the equipment system does not provide the compensation function of the milling cutter radius, how can we determine the trajectory of the tool center? Set the tool center coordinate at any point N (X, Y) on the parabola of the milling cutter to be: 0(m, n), Then the tangent slope of the curve at point N (X, Y) is Y = 2aX. The line connecting the tool center 0 ( m, n) to the machining point N (X, Y) on the curve is perpendicular to the curve at point N (X, The tangent at Y) is shown as follows: n - Y m - X = 1 2aX(8) The distance from the tool center 0 ( m, n) to the point N (X, Y) is equal to the radius of the tool 1 / 2a , ie: ( n - Y 2) + ( m- X 2) = 1 4a

(Finish)

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