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在设计水平直元线犁体曲面时,确定其导曲线的形状和参数是重要的一环。导曲线座标值的精确度直接影响样板曲线的精确度。因此,有必要建立导曲线的方程式。本文就抛物线型导曲线的两种推导方法进行了评述,这两种方法都是用一组具体的导曲线参数值进行推导、计算的。 作者应用二次曲线的一般方程式x~2+axy+by~2+cx+dy+e=0推导了抛物线型导曲线的一般方程式。各系数a,b,c,d都以导曲线各参数l,h,ε,△ε的函数形式表示(假设曲线通过座标原点,因此e=0)。这样,给定任何一组参数值,就可方便地得出所需抛物线的方程式。实际计算表明,用此方程式求得的座标值具有很高的精确度。 本文还对传统上使用参考半径R求导曲线参数l及h的方法进行了评述。并建议用经验公式l=cb(cos△ε-sin ε)代替l=R(1-sin ε)及h=Rcosε。h值由所需犁体外形尺寸确定。
In the design of horizontal straight line plow surface, determine the shape and parameters of the guide curve is an important part. The accuracy of the guide curve coordinate value directly affects the accuracy of the sample curve. Therefore, it is necessary to establish the equation of the guide curve. In this paper, two derivations of parabolic guide curves are reviewed, both of which are derived and calculated using a set of specific guide curve parameter values. The general formula of the parabolic guide curve is deduced from the general equation of the quadratic curve x ~ 2 + axy + by ~ 2 + cx + dy + e = 0. The coefficients a, b, c, and d are all expressed as a function of the parameters l, h, ε, and Δε of the guide curve (assuming that the curve passes through the coordinate origin and therefore e = 0). In this way, given any set of parameter values, the equation for the desired parabola can be easily derived. The actual calculation shows that the coordinate value obtained by this equation has a high degree of accuracy. In this paper, we also review the traditional methods of using the reference radius R to derive the curve parameters l and h. And it is suggested to replace l = R (1-sin ε) and h = Rcosε with the empirical formula l = cb (cos △ ε-sin ε) The value of h is determined by the required plow body dimensions.