General Solution Model of Non-numerical Machining Special Rotary Milling Cutter

1 Introduction

Special rotary milling cutter is an essential tool for machining free-form surfaces such as aerospace parts and metal molds. It can be used with CNC machine tools or machining centers to achieve high-quality, high-efficiency machining. With the development of numerical control processing technology and the increasingly complex processing objects, the application range and consumption of special rotary surface tools are continuously increasing. At present, special rotary surface tools mainly use multi-axis linkage CNC grinding machine processing, because the equipment is expensive (importing a CNC grinding machine requires about more than one million US dollars), so the manufacturing cost is higher. If you can use the existing common tool grinders to achieve non-numerical machining of special rotary tools, you can greatly reduce the manufacturing costs of such tools. This paper presents a universal design model based on non-numerical machining programs and suitable for large-volume machining of different types of special rotary milling cutters, and discusses the realization methods of axial and radial relative feed motions. The author has successfully manufactured ball-end spiral milling cutters using non-numerical machining solutions. This article is the popularization and application of the results of the previous work. 2 General Mathematical Model of Edge Curve The working profile of the special revolving milling cutter is a revolving surface. The spiral cutting edge curve on the revolving surface (see Fig. 1) is defined as the inclined line that forms a fixed angle with the warp on the revolving surface. The equation can be expressed as r={x,y,z}={f(u)cosv,f(u)sinv,g(u)} (1)

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Figure 1 Spiral edge curve on a revolving plane

In the formula, u and v are parameter variables; f(u) is the radius of gyration of the surface, f(u)≥0; v is the angle between the positive direction of the x-axis and f(u). In order to find the slope line on the revolving plane, the first basic amount must be solved first. From equation (1), we can get ru={f'(u)cosv,f'(u)sinv,g'(u)} rv={-f(u)sinv,f (u)cosv,0}
Therefore, E=ru2=f'2+g'2 F=ru·rv=0 G=f'2 It is noted that the tangent vector at any point on the oblique driving line is dr, and the warp tangent vector passing this point is dr. Considering that for the meridian dv=0, there is therefore dr=rudu|rvdv dr=rudu Since the inclined lead and the meridian form a certain angle j, the angle between dr and dr is the fixed value j, and the included angle is calculated as cos2j=(dr ·dr )2= Edu2 |dr||dr| Edu2 + Gdv2 After finishing, get Esin2jdu2=Gcos2jdv2 to get positive root dv=tanj(E/G)1⁄2du=tanj[(f'2+g'2)1⁄2/f ]du (2)
After integration, v = tanj ∫ u (f'2+g'2)1⁄2 du + C u0 f (3) Where C is to be given according to the initial conditions of the specific problem, with the cutting edge curve between different turning surfaces. The continuous condition is the initial condition. Substituting Eq. (3) into Eq. (1), a general mathematical model of a blade curve with only one parameter and a fixed angle j with the meridian can be obtained. 3 The realization of the relative feed movement When the special rotary milling cutter is processed by non-NC, the machined milling cutter only performs the constant speed rotary motion. The forming of the spiral groove on the tool is performed by the grinding wheel at the same time as the constant speed rotation. To exercise to achieve. In addition, since the radius of the different rounding circles on the revolving surface is different, and the grinding wheel is usually designed according to the maximum rounding radius, it is necessary to grind grooves with different radii through the radial feed movement of the grinding wheel. Therefore, in the non-numerical machining of special rotary milling cutters, the relative feed motion refers to the combined movement of the grinding wheel with respect to the axial movement and radial movement of the milling cutter. Axial feed motion This article uses the face cam mechanism to realize the non-numerical axial feed motion of the special rotary milling cutter. The cam mechanism can produce the trajectory of a given function. The displacement function of the cam mechanism designed in this paper is based on the edge curve equation on the surface of revolution. Set the rotational angular speed of the cutter to be processed as w=dv/dt (v is the angle parameter in the edge curve formula (1)), and the rotary angular velocity of the cam during uniform rotation is w'. Let a'w '=w(a'> 0), then the general formula of cam displacement function can be obtained through the tool edge curve formula (3), the method is to satisfy the formula of the edge curve equation under the initial conditions v = v (u Inverse function u = u (v), and its substitution into the rotary surface edge curve formula (1) in the axial component z = g (u) = g [u (v)], can be obtained The displacement function of the cam. Because the design of the cutting edge curve of the cutting tool is smooth and continuous at the connection of two rotating surfaces, the cam displacement function derived from this is also smooth and continuous at the junction of the two turning surfaces. Radial feed motion Special rotary milling cutters Non-numerically machined radial feed motion is achieved by means of a master mechanism on a tool grinding machine. The radial feed rate changes with the radius of the swivel surface, ie the cutter radius is from R At 0, the feed rate is r→0 from the core thickness, so that only the revolving surface will appear without overcutting, and the remaining revolving surface will be easily compensated by the grinding wheel. Suppose the feed radius at the f(u) point on the surface of revolution is s, then the formula for solving the radial feed can be obtained according to the model curve equation s = r Rf(u) R-0. =r-(r/R)f(u)=r-(r/R)(x2+y2)1⁄2 (4) Simply substituting the coordinates at any point on the surface of revolution into (4), we can find this The radial feed of the point. Because each rotating surface is smoothly connected and the cutting edge curve is smooth and continuous at the connection of the two rotating surfaces, the curve of the mold curve is smooth and continuous at the intersection of the two surfaces. 4 Examples of Solving The table below presents examples of the solution of the cutting edge curves and relative kinematics equations of two special rotary milling cutters (ball nose circular cutters and angled circular cone cutters). The meaning of the parameters in the table is shown in Figure 2 and Figure 3. q in the table is the angle value of the cam displacement curve between different turning surfaces.
Table Solving example Ball head circular arc milling cutter with corner round conical milling cutter Ball head Partial arc Rotary surface angle Circle surface Conical surface

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Figure 2 Ball end circular cutter

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Fig. 3 Tapered circular cone cutter

5 Conclusions The design method of spiral groove and grinding wheel for special rotary milling cutters has been discussed in many literatures. This article describes the special rotary milling cutter manufacturing method using non-CNC machining program, the process is simple, low cost, especially suitable for mass production of special rotary milling cutter, has a good market prospects. However, this method is not suitable for experimental tool development or single-piece production.

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