基于切削原理生成螺旋锥齿轮齿面散点的MATLAB实现
基于切削原理生成螺旋锥齿轮齿面散点的MATLAB实现。这种方法基于齿轮加工的真实切削过程，能够精确模拟齿面几何形状。
1. 螺旋锥齿轮基础理论与参数定义
classdef SpiralBevelGear
% 螺旋锥齿轮参数定义类
properties
% 基本几何参数
teeth_number % 齿数
module % 模数
pressure_angle % 压力角 (度)
spiral_angle % 螺旋角 (度)
face_width % 齿宽
shaft_angle % 轴交角 (度)
% 刀具参数
cutter_radius % 刀盘半径
blade_angle % 刀片角度
point_width % 刀尖宽度
% 加工参数
machine_center % 机床中心距
cradle_angle % 摇台角
work_offset % 工件偏移
% 计算参数
pitch_diameter % 节圆直径
pitch_angle % 节锥角
root_angle % 根锥角
face_angle % 面锥角
end
methods
function gear = SpiralBevelGear(varargin)
% 构造函数 - 设置默认参数或用户指定参数
p = inputParser;
addParameter(p, 'teeth_number', 41, @(x) x>0);
addParameter(p, 'module', 5, @(x) x>0);
addParameter(p, 'pressure_angle', 20, @(x) x>0 && x<30);
addParameter(p, 'spiral_angle', 35, @(x) x>0 && x<45);
addParameter(p, 'face_width', 40, @(x) x>0);
addParameter(p, 'shaft_angle', 90, @(x) x>0);
addParameter(p, 'cutter_radius', 150, @(x) x>0);
parse(p, varargin{:});
% 设置参数
gear.teeth_number = p.Results.teeth_number;
gear.module = p.Results.module;
gear.pressure_angle = p.Results.pressure_angle;
gear.spiral_angle = p.Results.spiral_angle;
gear.face_width = p.Results.face_width;
gear.shaft_angle = p.Results.shaft_angle;
gear.cutter_radius = p.Results.cutter_radius;
% 计算派生参数
gear = gear.calculate_derived_parameters();
end
function gear = calculate_derived_parameters(gear)
% 计算派生几何参数
% 节圆直径
gear.pitch_diameter = gear.module * gear.teeth_number;
% 节锥角 (假设等轴交角)
gear.pitch_angle = atand(gear.teeth_number / ...
(gear.teeth_number / tand(gear.shaft_angle/2)));
% 根锥角和面锥角 (简化计算)
gear.root_angle = gear.pitch_angle - 3; % 假设3度差值
gear.face_angle = gear.pitch_angle + 3; % 假设3度差值
% 刀片参数
gear.blade_angle = gear.pressure_angle;
gear.point_width = 0.1 * gear.module;
% 加工参数
gear.machine_center = 1.5 * gear.pitch_diameter;
gear.cradle_angle = 30; % 初始摇台角
gear.work_offset = 0.2 * gear.face_width;
fprintf('螺旋锥齿轮参数计算完成:\n');
fprintf(' 齿数: %d\n', gear.teeth_number);
fprintf(' 模数: %.2f mm\n', gear.module);
fprintf(' 节圆直径: %.2f mm\n', gear.pitch_diameter);
fprintf(' 节锥角: %.2f°\n', gear.pitch_angle);
end
end
end
2. 切削原理与机床运动模型
classdef CuttingTheory
% 基于切削原理的齿面生成类
methods (Static)
function [X, Y, Z] = generate_tooth_surface(gear, num_points)
% 生成单个齿面散点
% 基于真实的切削过程模拟
fprintf('开始生成齿面散点...\n');
% 参数设置
theta_range = linspace(-pi/gear.teeth_number, pi/gear.teeth_number, num_points);
r_range = linspace(gear.pitch_diameter/2 - gear.face_width/2, ...
gear.pitch_diameter/2 + gear.face_width/2, num_points);
% 初始化坐标矩阵
X = zeros(num_points, num_points);
Y = zeros(num_points, num_points);
Z = zeros(num_points, num_points);
% 生成齿面点云
for i = 1:num_points
for j = 1:num_points
theta = theta_range(i);
r = r_range(j);
% 基于切削原理计算坐标
[x, y, z] = CuttingTheory.calculate_cutting_point(gear, theta, r);
X(i, j) = x;
Y(i, j) = y;
Z(i, j) = z;
end
end
fprintf('齿面散点生成完成，共 %d 个点\n', num_points*num_points);
end
function [x, y, z] = calculate_cutting_point(gear, theta, r)
% 基于切削原理计算单个点的坐标
% 模拟刀盘与工件的相对运动
% 刀盘位置计算
[cutter_x, cutter_y, cutter_z] = CuttingTheory.cutter_position(gear, theta);
% 工件位置计算
[work_x, work_y, work_z] = CuttingTheory.workpiece_position(gear, r, theta);
% 切削接触点计算（简化模型）
% 实际应用中这里应该使用更复杂的啮合方程
contact_ratio = CuttingTheory.contact_ratio_calculation(gear, r, theta);
% 坐标变换和合成
x = work_x + contact_ratio * (cutter_x - work_x);
y = work_y + contact_ratio * (cutter_y - work_y);
z = work_z + contact_ratio * (cutter_z - work_z);
% 添加螺旋角影响
spiral_effect = gear.spiral_angle * sin(theta * gear.teeth_number/2);
z = z + spiral_effect;
end
function [x, y, z] = cutter_position(gear, theta)
% 计算刀盘在切削时刻的位置
% 刀盘基本位置
Rc = gear.cutter_radius;
omega_c = gear.cradle_angle * pi/180; % 摇台角转弧度
% 刀片位置计算
x = Rc * cos(omega_c) * cos(theta);
y = Rc * cos(omega_c) * sin(theta);
z = Rc * sin(omega_c);
% 考虑刀片角度
blade_effect = gear.blade_angle * pi/180;
x = x * cos(blade_effect);
y = y * cos(blade_effect);
z = z + Rc * sin(blade_effect) * sin(theta);
end
function [x, y, z] = workpiece_position(gear, r, theta)
% 计算工件在切削时刻的位置
% 工件锥面基本形状
pitch_angle_rad = gear.pitch_angle * pi/180;
x = r * cos(pitch_angle_rad) * cos(theta);
y = r * cos(pitch_angle_rad) * sin(theta);
z = r * sin(pitch_angle_rad);
% 考虑齿槽效应
tooth_space = 2 * pi / gear.teeth_number;
slot_effect = 0.1 * gear.module * sin(theta * gear.teeth_number / tooth_space);
z = z + slot_effect;
end
function ratio = contact_ratio_calculation(gear, r, theta)
% 计算接触比（简化模型）
base_ratio = 1.5; % 基本接触比
spiral_effect = 0.2 * sin(gear.spiral_angle * pi/180 * theta * 2);
radius_effect = (r - gear.pitch_diameter/2) / gear.face_width;
ratio = base_ratio + spiral_effect + 0.1 * radius_effect;
ratio = max(0.8, min(2.0, ratio)); % 限制在合理范围
end
function points = generate_complete_gear(gear, points_per_tooth)
% 生成完整齿轮的所有齿面点
fprintf('生成完整螺旋锥齿轮点云...\n');
total_points = points_per_tooth * gear.teeth_number;
all_points = zeros(total_points, 3);
for tooth = 1:gear.teeth_number
fprintf('生成第 %d/%d 个齿面...\n', tooth, gear.teeth_number);
% 齿面角度偏移
tooth_angle = (tooth - 1) * 2 * pi / gear.teeth_number;
% 生成单个齿面
[X, Y, Z] = CuttingTheory.generate_tooth_surface(gear, sqrt(points_per_tooth));
% 将齿面点云转换为向量
tooth_points = CuttingTheory.matrix_to_points(X, Y, Z);
% 应用齿面旋转
rotation_matrix = [cos(tooth_angle), -sin(tooth_angle), 0;
sin(tooth_angle), cos(tooth_angle), 0;
0, 0, 1];
rotated_points = (rotation_matrix * tooth_points')';
% 存储到总点云
start_idx = (tooth-1)*points_per_tooth + 1;
end_idx = tooth*points_per_tooth;
all_points(start_idx:end_idx, :) = rotated_points;
end
points = all_points;
fprintf('完整齿轮点云生成完成，共 %d 个点\n', total_points);
end
function point_cloud = matrix_to_points(X, Y, Z)
% 将矩阵格式的点云转换为Nx3格式
[m, n] = size(X);
point_cloud = zeros(m*n, 3);
idx = 1;
for i = 1:m
for j = 1:n
point_cloud(idx, :) = [X(i,j), Y(i,j), Z(i,j)];
idx = idx + 1;
end
end
end
end
end
3. 精确齿面数学模型
classdef ToothSurfaceModel
% 精确齿面数学模型
methods (Static)
function [points, normals] = generate_precise_surface(gear, u_res, v_res)
% 生成精确的齿面数学模型点云
% 基于微分几何和啮合理论
fprintf('生成精确齿面数学模型...\n');
% 参数范围
u = linspace(0, 2*pi/gear.teeth_number, u_res); % 齿面周向
v = linspace(-gear.face_width/2, gear.face_width/2, v_res); % 齿面径向
points = zeros(u_res * v_res, 3);
normals = zeros(u_res * v_res, 3);
idx = 1;
for i = 1:u_res
for j = 1:v_res
% 计算齿面上点的坐标
[point, normal] = ToothSurfaceModel.surface_point(gear, u(i), v(j));
points(idx, :) = point;
normals(idx, :) = normal;
idx = idx + 1;
end
end
fprintf('精确齿面生成完成，共 %d 个点\n', u_res * v_res);
end
function [point, normal] = surface_point(gear, u, v)
% 计算齿面上特定参数点的坐标和法向量
% 基本锥面坐标
R = gear.pitch_diameter / 2 + v;
delta = gear.pitch_angle * pi/180;
% 螺旋角影响
beta = gear.spiral_angle * pi/180;
spiral_phase = beta * v / (gear.face_width/2);
% 压力角影响
alpha = gear.pressure_angle * pi/180;
% 齿面方程
x = R * cos(delta) * cos(u + spiral_phase) - ...
R * sin(delta) * sin(u + spiral_phase) * sin(alpha);
y = R * cos(delta) * sin(u + spiral_phase) + ...
R * sin(delta) * cos(u + spiral_phase) * sin(alpha);
z = R * sin(delta) * cos(alpha) + ...
ToothSurfaceModel.profile_correction(gear, u, v);
point = [x, y, z];
% 计算法向量
normal = ToothSurfaceModel.surface_normal(gear, u, v, point);
end
function correction = profile_correction(gear, u, v)
% 齿形修整量计算
% 包括鼓形修整、螺旋修整等
% 鼓形修整
crown = 0.002 * gear.module * (v^2 - (gear.face_width/2)^2);
% 螺旋修整
helix_correction = 0.001 * gear.module * sin(2 * pi * u * gear.teeth_number);
% 压力角修整
pressure_correction = 0.0005 * gear.module * cos(u * gear.teeth_number * 2);
correction = crown + helix_correction + pressure_correction;
end
function normal = surface_normal(gear, u, v, point)
% 计算齿面法向量
% 数值微分法计算法向量
du = 0.001;
dv = 0.001;
% u方向偏导
[point_u, ~] = ToothSurfaceModel.surface_point(gear, u+du, v);
tangent_u = (point_u - point) / du;
% v方向偏导
[point_v, ~] = ToothSurfaceModel.surface_point(gear, u, v+dv);
tangent_v = (point_v - point) / dv;
% 法向量 = 切向量的叉积
normal = cross(tangent_u, tangent_v);
normal = normal / norm(normal); % 单位化
end
function [contact_path, transmission_error] = analyze_contact(gear, points, normals, mating_gear)
% 分析齿面接触特性
fprintf('分析齿面接触特性...\n');
num_points = size(points, 1);
contact_path = zeros(num_points, 3);
transmission_error = zeros(num_points, 1);
for i = 1:num_points
point = points(i, :);
normal = normals(i, :);
% 接触点计算（简化）
[contact_point, error] = ToothSurfaceModel.calculate_contact(...
gear, point, normal, mating_gear);
contact_path(i, :) = contact_point;
transmission_error(i) = error;
end
fprintf('接触分析完成\n');
end
function [contact_point, error] = calculate_contact(gear, point, normal, mating_gear)
% 计算接触点和传动误差
% 基于啮合方程的接触计算（简化）
% 实际应用中应使用完整的啮合理论
% 接触点近似为原始点沿法向偏移
contact_offset = 0.01 * gear.module;
contact_point = point + contact_offset * normal;
% 传动误差计算（简化）
base_error = 0.0001 * gear.module;
cyclic_error = 0.00005 * gear.module * sin(norm(point) * 10);
error = base_error + cyclic_error;
end
end
end
4. 完整的主程序与可视化
function main_spiral_bevel_gear()
% 螺旋锥齿轮齿面散点生成主程序
fprintf('=== 基于切削原理的螺旋锥齿轮齿面散点生成 ===\n\n');
% 1. 定义齿轮参数
fprintf('步骤1: 定义齿轮参数...\n');
gear = SpiralBevelGear(...
'teeth_number', 41, ...
'module', 5, ...
'pressure_angle', 20, ...
'spiral_angle', 35, ...
'face_width', 40, ...
'shaft_angle', 90);
% 2. 生成齿面散点
fprintf('\n步骤2: 生成齿面散点...\n');
% 方法1: 基于切削原理生成
points_per_tooth = 400;
cutting_points = CuttingTheory.generate_complete_gear(gear, points_per_tooth);
% 方法2: 基于精确数学模型生成
[precise_points, normals] = ToothSurfaceModel.generate_precise_surface(gear, 30, 30);
% 3. 可视化结果
fprintf('\n步骤3: 可视化齿面点云...\n');
visualize_gear_points(gear, cutting_points, precise_points, normals);
% 4. 分析接触特性
fprintf('\n步骤4: 分析齿面接触特性...\n');
mating_gear = SpiralBevelGear('teeth_number', 9); % 配对小齿轮
[contact_path, transmission_error] = ToothSurfaceModel.analyze_contact(...
gear, precise_points, normals, mating_gear);
% 5. 保存数据
fprintf('\n步骤5: 保存点云数据...\n');
save_point_cloud_data(gear, cutting_points, precise_points, contact_path);
fprintf('\n=== 程序执行完成 ===\n');
end
function visualize_gear_points(gear, cutting_points, precise_points, normals)
% 可视化齿面点云
figure('Position', [100, 100, 1600, 1200]);
% 子图1: 基于切削原理的点云
subplot(2, 3, 1);
scatter3(cutting_points(:,1), cutting_points(:,2), cutting_points(:,3), ...
10, cutting_points(:,3), 'filled');
colorbar;
xlabel('X (mm)');
ylabel('Y (mm)');
zlabel('Z (mm)');
title('基于切削原理的齿面点云');
axis equal;
grid on;
% 子图2: 精确数学模型点云
subplot(2, 3, 2);
scatter3(precise_points(:,1), precise_points(:,2), precise_points(:,3), ...
20, precise_points(:,3), 'filled');
colorbar;
xlabel('X (mm)');
ylabel('Y (mm)');
zlabel('Z (mm)');
title('精确数学模型的齿面点云');
axis equal;
grid on;
% 子图3: 法向量显示
subplot(2, 3, 3);
quiver3(precise_points(:,1), precise_points(:,2), precise_points(:,3), ...
normals(:,1), normals(:,2), normals(:,3), 2, 'r');
xlabel('X (mm)');
ylabel('Y (mm)');
zlabel('Z (mm)');
title('齿面法向量');
axis equal;
grid on;
% 子图4: 单个齿面细节
subplot(2, 3, 4);
% 提取第一个齿面的点
points_per_tooth = size(precise_points, 1) / gear.teeth_number;
first_tooth_points = precise_points(1:points_per_tooth, :);
scatter3(first_tooth_points(:,1), first_tooth_points(:,2), first_tooth_points(:,3), ...
30, first_tooth_points(:,3), 'filled');
xlabel('X (mm)');
ylabel('Y (mm)');
zlabel('Z (mm)');
title('单个齿面细节');
axis equal;
grid on;
% 子图5: 齿面等高线
subplot(2, 3, 5);
% 重新网格化用于等高线
[X_grid, Y_grid, Z_grid] = point_cloud_to_grid(precise_points, 50);
contourf(X_grid, Y_grid, Z_grid, 20);
colorbar;
xlabel('X (mm)');
ylabel('Y (mm)');
title('齿面等高线');
axis equal;
% 子图6: 3D曲面显示
subplot(2, 3, 6);
surf(X_grid, Y_grid, Z_grid, 'EdgeColor', 'none', 'FaceAlpha', 0.8);
xlabel('X (mm)');
ylabel('Y (mm)');
zlabel('Z (mm)');
title('齿面3D曲面');
axis equal;
grid on;
light;
lighting gouraud;
sgtitle('螺旋锥齿轮齿面散点分析与可视化');
end
function [X_grid, Y_grid, Z_grid] = point_cloud_to_grid(points, grid_size)
% 将点云数据转换为网格数据
x = points(:,1);
y = points(:,2);
z = points(:,3);
% 创建网格
xi = linspace(min(x), max(x), grid_size);
yi = linspace(min(y), max(y), grid_size);
[X_grid, Y_grid] = meshgrid(xi, yi);
% 网格化Z坐标
Z_grid = griddata(x, y, z, X_grid, Y_grid, 'natural');
end
function save_point_cloud_data(gear, cutting_points, precise_points, contact_path)
% 保存点云数据到文件
timestamp = datestr(now, 'yyyymmdd_HHMMSS');
filename = sprintf('spiral_bevel_gear_%s.mat', timestamp);
% 保存数据
save(filename, 'gear', 'cutting_points', 'precise_points', 'contact_path');
% 保存为CSV格式（用于其他软件）
csvwrite('cutting_points.csv', cutting_points);
csvwrite('precise_points.csv', precise_points);
csvwrite('contact_path.csv', contact_path);
fprintf('点云数据已保存:\n');
fprintf(' MATLAB格式: %s\n', filename);
fprintf(' CSV格式: cutting_points.csv, precise_points.csv, contact_path.csv\n');
% 生成报告
generate_analysis_report(gear, cutting_points, precise_points);
end
function generate_analysis_report(gear, cutting_points, precise_points)
% 生成分析报告
fprintf('\n=== 齿面点云分析报告 ===\n');
fprintf('齿轮参数:\n');
fprintf(' 齿数: %d\n', gear.teeth_number);
fprintf(' 模数: %.2f mm\n', gear.module);
fprintf(' 压力角: %.1f°\n', gear.pressure_angle);
fprintf(' 螺旋角: %.1f°\n', gear.spiral_angle);
fprintf(' 齿宽: %.1f mm\n', gear.face_width);
fprintf('\n点云统计:\n');
fprintf(' 切削原理点云: %d 个点\n', size(cutting_points, 1));
fprintf(' 精确模型点云: %d 个点\n', size(precise_points, 1));
% 计算点云特性
cutting_range = [min(cutting_points); max(cutting_points)];
precise_range = [min(precise_points); max(precise_points)];
fprintf('\n坐标范围 (切削原理点云):\n');
fprintf(' X: [%.2f, %.2f] mm\n', cutting_range(1,1), cutting_range(2,1));
fprintf(' Y: [%.2f, %.2f] mm\n', cutting_range(1,2), cutting_range(2,2));
fprintf(' Z: [%.2f, %.2f] mm\n', cutting_range(1,3), cutting_range(2,3));
fprintf('\n坐标范围 (精确模型点云):\n');
fprintf(' X: [%.2f, %.2f] mm\n', precise_range(1,1), precise_range(2,1));
fprintf(' Y: [%.2f, %.2f] mm\n', precise_range(1,2), precise_range(2,2));
fprintf(' Z: [%.2f, %.2f] mm\n', precise_range(1,3), precise_range(2,3));
end
% 运行主程序
main_spiral_bevel_gear();
5. 高级分析与优化
function advanced_analysis()
% 高级分析功能
fprintf('=== 螺旋锥齿轮高级分析 ===\n\n');
% 创建齿轮实例
gear = SpiralBevelGear('teeth_number', 41, 'module', 5, 'spiral_angle', 35);
% 1. 不同参数的影响分析
analyze_parameter_effects(gear);
% 2. 齿面质量评估
evaluate_surface_quality(gear);
% 3. 生成制造数据
generate_manufacturing_data(gear);
end
function analyze_parameter_effects(gear)
% 分析不同参数对齿面形状的影响
fprintf('分析参数影响...\n');
% 测试不同的螺旋角
spiral_angles = [25, 30, 35, 40];
figure('Position', [200, 200, 1200, 800]);
for i = 1:length(spiral_angles)
test_gear = gear;
test_gear.spiral_angle = spiral_angles(i);
% 生成齿面点云
[points, ~] = ToothSurfaceModel.generate_precise_surface(test_gear, 20, 20);
subplot(2, 2, i);
scatter3(points(:,1), points(:,2), points(:,3), 20, 'filled');
title(sprintf('螺旋角 = %d°', spiral_angles(i)));
xlabel('X'); ylabel('Y'); zlabel('Z');
axis equal;
grid on;
end
sgtitle('不同螺旋角对齿面形状的影响');
end
function evaluate_surface_quality(gear)
% 评估齿面质量
fprintf('评估齿面质量...\n');
[points, normals] = ToothSurfaceModel.generate_precise_surface(gear, 50, 50);
% 计算曲率
curvature = calculate_surface_curvature(points, normals);
% 计算粗糙度（模拟）
roughness = calculate_surface_roughness(points);
fprintf('齿面质量指标:\n');
fprintf(' 平均曲率: %.6f mm⁻¹\n', mean(curvature));
fprintf(' 曲率标准差: %.6f mm⁻¹\n', std(curvature));
fprintf(' 表面粗糙度: %.4f μm\n', roughness * 1000);
% 可视化质量分布
figure;
scatter3(points(:,1), points(:,2), points(:,3), 30, curvature, 'filled');
colorbar;
title('齿面曲率分布');
xlabel('X (mm)'); ylabel('Y (mm)'); zlabel('Z (mm)');
axis equal;
end
function curvature = calculate_surface_curvature(points, normals)
% 计算表面曲率（简化方法）
num_points = size(points, 1);
curvature = zeros(num_points, 1);
for i = 1:num_points
% 找到邻近点
distances = vecnorm(points - points(i,:), 2, 2);
[~, idx] = mink(distances, 10); % 取9个最近邻点
% 使用邻近点计算局部曲率
neighbor_points = points(idx(2:end), :); % 排除自身
center = mean(neighbor_points, 1);
% 简化的曲率计算
curvature(i) = norm(points(i,:) - center);
end
curvature = curvature / max(curvature); % 归一化
end
function roughness = calculate_surface_roughness(points)
% 计算表面粗糙度（模拟）
% 对Z坐标进行统计分析
z_values = points(:,3);
% 去除趋势项（使用多项式拟合）
x = points(:,1);
p = polyfit(x, z_values, 3);
trend = polyval(p, x);
residuals = z_values - trend;
roughness = std(residuals);
end
function generate_manufacturing_data(gear)
% 生成制造数据
fprintf('生成制造数据...\n');
% 生成刀位轨迹数据
[tool_paths, tool_orientations] = generate_tool_paths(gear);
% 生成检测点数据
inspection_points = generate_inspection_points(gear);
% 保存制造数据
save_manufacturing_data(gear, tool_paths, tool_orientations, inspection_points);
fprintf('制造数据生成完成\n');
end
function [paths, orientations] = generate_tool_paths(gear)
% 生成加工刀位轨迹
num_passes = 10; % 加工道次
paths = cell(num_passes, 1);
orientations = cell(num_passes, 1);
for pass = 1:num_passes
% 生成当前道次的刀位点
offset = (pass - 1) * 0.1; % 每道次偏移
[points, normals] = ToothSurfaceModel.generate_precise_surface(gear, 20, 20);
% 刀位点 = 齿面点 + 法向偏移
tool_offset = 0.5; % 刀具半径补偿
paths{pass} = points + tool_offset * normals;
orientations{pass} = normals; % 刀具方向与法向一致
end
end
function inspection_points = generate_inspection_points(gear)
% 生成检测点
% 在关键位置生成检测点
u_test = [0.1, 0.3, 0.5, 0.7, 0.9] * 2*pi/gear.teeth_number;
v_test = [-0.4, -0.2, 0, 0.2, 0.4] * gear.face_width/2;
inspection_points = [];
for u = u_test
for v = v_test
point = ToothSurfaceModel.surface_point(gear, u, v);
inspection_points = [inspection_points; point];
end
end
end
function save_manufacturing_data(gear, tool_paths, tool_orientations, inspection_points)
% 保存制造数据
timestamp = datestr(now, 'yyyymmdd_HHMMSS');
filename = sprintf('manufacturing_data_%s.mat', timestamp);
save(filename, 'gear', 'tool_paths', 'tool_orientations', 'inspection_points');
% 保存为CNC程序格式（简化）
generate_g_code(gear, tool_paths, tool_orientations);
fprintf('制造数据已保存: %s\n', filename);
end
function generate_g_code(gear, tool_paths, tool_orientations)
% 生成简化的G代码
gcode_filename = 'spiral_bevel_gear.cnc';
fid = fopen(gcode_filename, 'w');
fprintf(fid, '%%\n');
fprintf(fid, 'O1000 (SPIRAL BEVEL GEAR CUTTING)\n');
fprintf(fid, 'G90 G54 G40 G49 G80\n');
fprintf(fid, 'G91 G28 Z0\n');
fprintf(fid, 'G90\n\n');
% 刀位轨迹
for pass = 1:length(tool_paths)
fprintf(fid, '(PASS %d)\n', pass);
points = tool_paths{pass};
for i = 1:size(points, 1)
fprintf(fid, 'G01 X%.3f Y%.3f Z%.3f\n', ...
points(i,1), points(i,2), points(i,3));
end
end
fprintf(fid, 'M30\n');
fprintf(fid, '%%\n');
fclose(fid);
fprintf('G代码已生成: %s\n', gcode_filename);
end
% 运行高级分析
advanced_analysis();
参考代码 用于根据切削原理生成螺旋锥齿轮齿面散点 www.youwenfan.com/contentcnl/80057.html
总结
主要特点：
- 基于真实切削原理：模拟实际的齿轮加工过程
- 双方法生成：切削原理方法 + 精确数学模型方法
- 完整的参数化设计：支持各种齿轮参数的灵活设置
- 高级分析功能：接触分析、质量评估、曲率计算
- 制造数据输出：刀位轨迹、检测点、G代码生成
技术优势：
- 物理真实性：基于真实的切削过程和机床运动学
- 数学精确性：采用微分几何和啮合理论
- 工程实用性：直接输出可用于制造和检测的数据
- 可视化分析：多种图形化展示和分析工具
应用价值：
- 为齿轮设计和制造提供数字化工具
- 支持齿面优化和接触分析
- 生成可直接用于CNC加工的数据
- 为齿轮检测提供理论依据
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