66 lines
2.5 KiB
Python
66 lines
2.5 KiB
Python
# -*- coding: utf-8 -*-
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# ***************************************************************************
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# * *
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# * This program is free software: you can redistribute it and/or modify *
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# * it under the terms of the GNU General Public License as published by *
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# * the Free Software Foundation, either version 3 of the License, or *
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# * (at your option) any later version. *
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# * *
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# * This program is distributed in the hope that it will be useful, *
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# * but WITHOUT ANY WARRANTY; without even the implied warranty of *
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# * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the *
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# * GNU General Public License for more details. *
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# * *
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# * You should have received a copy of the GNU General Public License *
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# * along with this program. If not, see <http://www.gnu.org/licenses/>. *
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# * *
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# ***************************************************************************
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import numpy as np
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def compute_shifted_gears(m, alpha, t1, t2, x1, x2):
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"""Summary
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Args:
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m (float): common module of both gears [length]
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alpha (float): pressure-angle [rad]
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t1 (int): number of teeth of gear1
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t2 (int): number of teeth of gear2
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x1 (float): relative profile-shift of gear1
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x2 (float): relative profile-shift of gear2
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Returns:
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(float, float): distance between gears [length], pressure angle of the assembly [rad]
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"""
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def inv(x):
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return np.tan(x) - x
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inv_alpha_w = inv(alpha) + 2 * np.tan(alpha) * (x1 + x2) / (t1 + t2)
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def root_inv(x):
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return inv(x) - inv_alpha_w
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def d_root_inv(x):
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return 1.0 / np.cos(x) - 1
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alpha_w = find_root(alpha, root_inv, d_root_inv)
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dist = m * (t1 + t2) / 2 * np.cos(alpha) / np.cos(alpha_w)
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return dist, alpha_w
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def find_root(x0, f, df, epsilon=2e-10, max_iter=100):
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x_n = x0
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for i in range(max_iter):
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f_xn = f(x_n)
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if abs(f_xn) < epsilon:
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return x_n
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else:
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df_xn = df(x_n)
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if df_xn == 0:
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return None
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else:
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x_n = x_n - f_xn / df_xn / 2 # adding (/ 2) to avoid oscillation
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return None
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