SOR
151 lines
5.6 KiB
Python
151 lines
5.6 KiB
Python
import math
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from decimal import Decimal, ROUND_HALF_EVEN
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"""
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Young's Modulus Calculator (Optical Lever & Successive Difference Method)
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杨氏模量计算器 (光杠杆 & 逐差法)
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不确定度传递公式:
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1. 杨氏模量公式:
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E = (32 * m * g * L * D) / (π * d^2 * b * Δn_avg)
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其中 Δn_avg 是 4 个砝码对应的平均刻度位移（由 8 个刻度值通过逐差法求得）。
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2. 相对不确定度传递公式:
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u_r(E) = u_E / E = sqrt( (u_L/L)^2 + (u_D/D)^2 + (2 * u_d/d)^2 + (u_b/b)^2 + (u_Δn/Δn_avg)^2 )
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3. 合成不确定度:
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u_E = E * u_r(E)
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其中各物理量 X 的不确定度 u_X = sqrt( u_A,X^2 + u_B,X^2 )
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u_A,X = s_X / sqrt(n)
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u_B,X = Δ_inst / sqrt(3)
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"""
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from utils import (
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scientific_round,
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calculate_stats,
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input_data_group
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)
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def main():
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# --- 1. 常量设置 ---
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M_WEIGHT = Decimal("0.350") # 单个砝码质量 350g = 0.350kg
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G = Decimal("9.80") # 重力加速度
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PI = Decimal(str(math.pi))
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print("========================================")
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print(" 杨氏模量计算 (光杠杆 & 逐差法) ")
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print("========================================")
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print(f"单个砝码质量 m = {M_WEIGHT} kg")
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print(f"重力加速度 g = {G} m/s^2")
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# --- 2. 几何长度输入 (各6次测量) ---
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# L: 钢丝长度, D: 镜面到刻度尺距离, d: 钢丝直径, b: 光杠杆臂长
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L_vals = input_data_group("钢丝长度 L", 6, "mm")
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D_vals = input_data_group("镜面到尺距离 D", 6, "mm")
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d_vals = input_data_group("钢丝直径 d", 6, "mm")
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b_vals = input_data_group("光杠杆臂长 b", 6, "mm")
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print("\n--- 输入仪器误差 Δ_inst ---")
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delta_L = Decimal(input("L 的仪器误差 (mm, 默认 1.0): ").strip() or "1.0")
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delta_D = Decimal(input("D 的仪器误差 (mm, 默认 1.0): ").strip() or "1.0")
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delta_d = Decimal(input("d 的仪器误差 (mm, 默认 0.005): ").strip() or "0.005")
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delta_b = Decimal(input("b 的仪器误差 (mm, 默认 0.02): ").strip() or "0.02")
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L_mean, L_u = calculate_stats(L_vals, delta_L)[:2]
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D_mean, D_u = calculate_stats(D_vals, delta_D)[:2]
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d_mean, d_u = calculate_stats(d_vals, delta_d)[:2]
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b_mean, b_u = calculate_stats(b_vals, delta_b)[:2]
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# --- 3. 刻度值输入 (0-7个砝码, 加重+减重) ---
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print("\n--- 输入刻度尺读数 n (单位: mm) ---")
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n_up = []
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n_down = []
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for i in range(8):
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while True:
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try:
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line = input(f"砝码数量 {i} (加重, 减重): ").replace(',', ' ').split()
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if len(line) != 2:
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print("请输入两个数值（空格或逗号隔开）")
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continue
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n_up.append(Decimal(line[0]))
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n_down.append(Decimal(line[1]))
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break
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except Exception:
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print("输入无效！")
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delta_n_inst = Decimal(input("刻度尺仪器误差 (mm, 默认 0.5): ").strip() or "0.5")
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# 计算平均读数 n_i
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n_means = [(u + d) / 2 for u, d in zip(n_up, n_down)]
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print("\n--- 中间量 (加重与减重的平均值 n_i) ---")
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for i, val in enumerate(n_means):
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print(f"n_{i} = {val} mm")
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# 逐差法计算 Δn (隔 4 项相减)
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# Δn_j = n_{j+4} - n_j, j = 0,1,2,3
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dn_list = []
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print("\n--- 逐差计算过程 ---")
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for j in range(4):
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diff = n_means[j+4] - n_means[j]
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dn_list.append(diff)
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print(f"Δn_{j} = n_{j+4} - n_{j} = {diff} mm")
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# Δn 的平均值及不确定度
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dn_mean = sum(dn_list) / Decimal("4")
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# A类: 针对这 4 个差值
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variance_dn = sum((x - dn_mean)**2 for x in dn_list) / Decimal("3")
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s_dn = Decimal(str(math.sqrt(float(variance_dn))))
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u_a_dn = s_dn / Decimal(str(math.sqrt(4)))
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# B类: 刻度尺误差
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# 因为 n_i = (n_up + n_down)/2, Δn = n_high - n_low
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# 传播得 u_B(Δn) = Δ_inst / sqrt(3)
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u_b_dn = delta_n_inst / Decimal(str(math.sqrt(3)))
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dn_u = Decimal(str(math.sqrt(float(u_a_dn**2 + u_b_dn**2))))
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# --- 4. 杨氏模量计算 ---
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# 全部转为标准单位 (m)
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L_m = L_mean / 1000
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D_m = D_mean / 1000
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d_m = d_mean / 1000
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b_m = b_mean / 1000
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dn_m = dn_mean / 1000
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# E = (32 * m * g * L * D) / (pi * d^2 * b * Δn)
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# 这里的 Δn 对应 4 个砝码的位移
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numerator = Decimal("32") * M_WEIGHT * G * L_m * D_m
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denominator = PI * (d_m**2) * b_m * dn_m
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E_val = numerator / denominator
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# --- 5. 不确定度传播 ---
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# rel_u = sqrt( (uL/L)^2 + (uD/D)^2 + (2*ud/d)^2 + (ub/b)^2 + (udn/dn)^2 )
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rel_u_sq = (L_u/L_mean)**2 + (D_u/D_mean)**2 + (Decimal("2")*d_u/d_mean)**2 + (b_u/b_mean)**2 + (dn_u/dn_mean)**2
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rel_u = Decimal(str(math.sqrt(float(rel_u_sq))))
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E_u = E_val * rel_u
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# --- 6. 修约与输出 ---
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# 通常用 10^11 Pa 表示
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E_11 = E_val / Decimal("1e11")
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E_u_11 = E_u / Decimal("1e11")
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E_final, u_final = scientific_round(E_11, E_u_11)
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print("\n" + "="*40)
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print(" 计算结果")
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print("="*40)
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print(f"L = {L_mean:.2f} ± {L_u:.2f} mm")
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print(f"D = {D_mean:.2f} ± {D_u:.2f} mm")
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print(f"d = {d_mean:.4f} ± {d_u:.4f} mm")
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print(f"b = {b_mean:.3f} ± {b_u:.3f} mm")
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print(f"Δn = {dn_mean:.3f} ± {dn_u:.3f} mm (4个砝码位移)")
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print("-" * 40)
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print(f"杨氏模量 E (原始): {E_val:.4e} Pa")
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print(f"相对不确定度 u_r: {rel_u*100:.2f}%")
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print("-" * 40)
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print(f"最终结果: E = {E_final} ± {u_final} × 10^11 Pa")
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print("="*40)
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if __name__ == "__main__":
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main()
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