MATLAB三次样条插值拟合齿轮传动比与节圆直径关系曲线

基于MATLAB的三次样条插值拟合齿轮传动比与节圆直径关系

本示例程序演示如何使用MATLAB对齿轮传动比与节圆直径关系进行三次样条插值拟合，并绘制相关曲线图。

% 给定四条线的坐标数据（对数坐标）
U1_points_log = [log10([5, 40, 300, 650, 10000]); log10([25, 50, 100, 125, 333])];
U2_points_log = [log10([4, 8, 80, 700, 9000]); log10([17.5, 22.5, 50, 100, 225])];
U4_points_log = [log10([3, 70, 700, 6000, 10000]); log10([12.5, 37.5, 75, 150, 175])];
U10_points_log = [log10([8, 70, 600, 2000, 9000]); log10([12.5, 25, 50, 75, 125])];

% 将对数坐标转换为线性坐标
U1_points = 10 .^ U1_points_log;
U2_points = 10 .^ U2_points_log;
U4_points = 10 .^ U4_points_log;
U10_points = 10 .^ U10_points_log;

% 绘制原始数据的曲线图
figure;
hold on;
plot(U1_points(1, :), U1_points(2, :), '-ro');
plot(U2_points(1, :), U2_points(2, :), '-go');
plot(U4_points(1, :), U4_points(2, :), '-bo');
plot(U10_points(1, :), U10_points(2, :), '-mo');
set(gca, 'XScale', 'log');
set(gca, 'YScale', 'log');
legend('U1', 'U2', 'U4', 'U10');
xlabel('传动比');
ylabel('节圆直径');
title('原始数据的曲线图');
grid on;
hold off;

% 使用三次样条插值函数进行拟合
u_interp = logspace(log10(min(U1_points(1, :))), log10(max(U1_points(1, :))), 100); % 在传动比范围内生成均匀采样点

% U1曲线拟合
U1_interp = spline(U1_points(1, :), U1_points(2, :), u_interp);

% U2曲线拟合
U2_interp = spline(U2_points(1, :), U2_points(2, :), u_interp);

% U4曲线拟合
U4_interp = spline(U4_points(1, :), U4_points(2, :), u_interp);

% U10曲线拟合
U10_interp = spline(U10_points(1, :), U10_points(2, :), u_interp);

% 绘制拟合后的曲线
figure;
hold on;
plot(U1_points(1, :), U1_points(2, :), 'ro');
plot(U2_points(1, :), U2_points(2, :), 'go');
plot(U4_points(1, :), U4_points(2, :), 'bo');
plot(U10_points(1, :), U10_points(2, :), 'mo');
plot(u_interp, U1_interp, '-r');
plot(u_interp, U2_interp, '-g');
plot(u_interp, U4_interp, '-b');
plot(u_interp, U10_interp, '-m');
set(gca, 'XScale', 'log');
set(gca, 'YScale', 'log');
legend('U1', 'U2', 'U4', 'U10');
xlabel('传动比');
ylabel('节圆直径');
title('拟合后的曲线图');
grid on;
hold off;

% 根据给定的扭矩在对应的传动比 u 曲线上获得四个齿轮节圆直径值
T_given = 50; % 给定的传动扭矩
u_given = [1, 2, 4, 10]; % 给定的传动比
d1_given = interp1(U1_interp, u_interp, u_given);
d2_given = interp1(U2_interp, u_interp, u_given);
d4_given = interp1(U4_interp, u_interp, u_given);
d10_given = interp1(U10_interp, u_interp, u_given);

% 绘制传动比与节圆直径的二维曲线图
figure;
hold on;
plot(u_interp, U1_interp, '-r');
plot(u_interp, U2_interp, '-g');
plot(u_interp, U4_interp, '-b');
plot(u_interp, U10_interp, '-m');
plot(u_given, d1_given, 'ro');
plot(u_given, d2_given, 'go');
plot(u_given, d4_given, 'bo');
plot(u_given, d10_given, 'mo');
set(gca, 'XScale', 'log');
set(gca, 'YScale', 'log');
legend('U1', 'U2', 'U4', 'U10', '给定扭矩下的齿轮节圆直径');
xlabel('传动比');
ylabel('节圆直径');
title('传动比与节圆直径的关系');
grid on;
hold off;

这段MATLAB代码首先定义了四组齿轮传动比和节圆直径的对应关系，然后使用spline函数进行三次样条插值拟合，最后绘制了拟合曲线图以及给定扭矩下传动比与节圆直径的关系图。