222 lines
6.8 KiB
Python
222 lines
6.8 KiB
Python
# 计算直线塔不平衡张力
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# 新版输电线路大手册 P328
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import math
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# h_i 悬点高差
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# l_i 悬点档距
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# _alpha 导线膨胀系数 1/°C
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# _elastic 弹性系数 N/mm2
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# _t_e 架线时考虑初伸长的降温，取正值。单位°C
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# lambda_i 计算不平衡张力时导线比载 N/(m.mm)
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# sigma_i 计算不平衡张力时最低点水平应力 单位N/mm2
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# t_i 计算不平衡张力时导线温度 单位°C
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# _lambda_m 导线架线时时导线比载 N/(m.mm)
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# _sigma_m 导线架线时时最低点水平应力 单位N/mm2
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# _t_m 导线架线时时导线温度 单位°C
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def delta_li(
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h_i: float,
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l_i: float,
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lambda_i: float,
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_alpha: float,
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_elastic: float,
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_t_e: float,
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t_i: float,
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sigma_i: float,
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_lambda_m: float,
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_t_m: float,
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_sigma_m: float,
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) -> float:
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beta_i = math.atan(h_i / l_i) # 高差角
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_delta_li = (
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l_i
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/ ((math.cos(beta_i) ** 2) * (1 + (lambda_i * l_i / sigma_i) ** 2 / 8))
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* (
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(l_i * math.cos(beta_i)) ** 2
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/ 24
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* ((_lambda_m / _sigma_m) ** 2 - (lambda_i / sigma_i) ** 2)
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+ ((sigma_i - _sigma_m) / _elastic / math.cos(beta_i))
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+ _alpha * (t_i + _t_e - _t_m)
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)
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)
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return _delta_li
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# area 导线截面 单位mm2
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# sigma_i 第i档内水平应力 单位N/mm2
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# b_i 悬垂串沿线路方向水平偏移距离，沿大号方向为正，反之为负。 单位m
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# length_i 第i基直线塔串长 单位m
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# g_i 第i基直线塔串重 单位N
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# h_i 悬垂串处千中垂位置时，,第 i 基对第 i-1 杆塔上导线悬挂点间的高差大号比小号杆塔悬挂点高者h本身为正值，反之为负值。
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# lambda_i 第i档导线比载 N/(m.mm)
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# h_i1 悬垂串处千中垂位置时，第 i+1 基对第 i 杆塔上导线悬挂点间的高差大号比小号杆塔悬挂点高者h本身为正值，反之为负值。
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# lambda_i1
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def fun_sigma_i1(
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area: float,
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sigma_i: float,
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b_i: float,
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length_i: float,
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g_i: float,
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h_i: float,
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l_i: float,
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lambda_i: float,
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h_i1: float,
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l_i1: float,
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lambda_i1: float,
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):
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beta_i = math.atan(h_i / l_i)
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beta_i1 = math.atan(h_i1 / l_i1)
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_sigma_i1 = (
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(
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g_i / 2 / area
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+ lambda_i * l_i / 2 / math.cos(beta_i)
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+ lambda_i1 * l_i1 / 2 / math.cos(beta_i1)
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+ sigma_i * h_i / l_i
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)
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+ sigma_i / b_i * math.sqrt(length_i ** 2 - b_i ** 2)
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) / (math.sqrt(length_i ** 2 - b_i ** 2) / b_i + h_i1 / l_i1)
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return _sigma_i1
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# 求解循环。
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def cal_loop():
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loop_end = 100000 # 最大循环次数
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# 架线时的状态
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# 取外过无风
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string_length = 9.2 # 串长 单位m
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string_g = 60 * 9.8 # 串重 单位N
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t_m = 15 # 导线架设时的气温。单位°C
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t_e = 20 # 架线时考虑初伸长的降温，取正值。单位°C
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alpha = 0.0000155 # 导线膨胀系数 1/°C
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elastic = 95900 # 弹性系数 N/mm2
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area = 154.48 # 导线面积 mm2
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lambda_m = 14.8129 / area # 导线比载 N/(m.mm)
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# 取400m代表档距下
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sigma_m = 28517 / area # 架线时，初伸长未释放前的最低点水平应力。单位N/mm2
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span_count = 3 # 几个档距
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# n个档距,n-1个直线塔
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h_array = [0, 0, 0]
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l_array = [400, 400, 400]
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t_array = [15, 15, 15]
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lambda_array = [lambda_m, lambda_m, lambda_m]
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loop_count = 1
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sigma_0 = sigma_m * 0.8
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while True:
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sigma_0 = sigma_0 + 0.001
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sigma_array = [sigma_0, 0, 0]
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b_i = 0
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delta_l_i_array = []
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for i in range(span_count - 1):
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h_i = h_array[i]
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l_i = l_array[i]
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lambda_i = lambda_array[i]
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t_i = t_array[i]
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sigma_i = sigma_array[i]
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_delta_l_i = delta_li(
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h_i,
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l_i,
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lambda_i,
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alpha,
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elastic,
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t_e,
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t_i,
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sigma_i,
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lambda_m,
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t_m,
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sigma_m,
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)
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delta_l_i_array.append(_delta_l_i)
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b_i += _delta_l_i
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length_i = string_length
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g_i = string_g
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h_i1 = h_array[i + 1]
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l_i1 = l_array[i + 1]
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lambda_i1 = lambda_array[i + 1]
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sigma_i1 = fun_sigma_i1(
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area,
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sigma_i,
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b_i,
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length_i,
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g_i,
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h_i,
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l_i,
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lambda_i,
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h_i1,
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l_i1,
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lambda_i1,
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)
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sigma_array[i + 1] = sigma_i1
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# print("第{loop_count}轮求解。".format(loop_count=loop_count))
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# print(b_i)
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loop_count += 1
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if math.fabs(b_i) < 1e-5:
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print("迭代{loop_count}次找到解。".format(loop_count=loop_count))
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print("悬垂串偏移累加bi为{b_i}".format(b_i=b_i))
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for i in range(span_count):
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print("第{i}档导线应力为{tension}".format(i=i, tension=sigma_array[i]))
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for i in range(span_count - 1):
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print("第{i}串偏移值为{bias}".format(i=i, bias=delta_l_i_array[i]))
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verify(
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area,
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h_array,
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l_array,
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string_length,
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string_g,
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sigma_array,
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delta_l_i_array,
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lambda_array,
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)
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break
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if loop_count >= loop_end:
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print("!!!未找到解。")
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print(sigma_array)
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print(b_i)
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break
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# 检验等式。
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def verify(
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area: float,
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h_array: [float],
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l_array: [float],
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string_length: [float],
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string_g: [float],
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sigma_array: [float],
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delta_l_i_array: [float],
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lambda_array: [float],
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):
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# 用新版大手册p329页(5-61)最第一个公式校验
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for i in range(len(delta_l_i_array)):
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sigma_i = sigma_array[i]
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sigma_i1 = sigma_array[i + 1]
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left_equ = sigma_array[i + 1]
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_delta_l_i = delta_l_i_array[i]
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lambda_i = lambda_array[i]
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lambda_i1 = lambda_array[i + 1]
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h_i = h_array[i]
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h_i1 = h_array[i + 1]
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l_i = l_array[i]
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l_i1 = l_array[i + 1]
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beta_i = math.atan(h_i / l_i)
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beta_i1 = math.atan(h_i1 / l_i1)
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w_i = (
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lambda_i * l_i / 2 / math.cos(beta_i)
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+ sigma_i * h_i / l_i
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+ (lambda_i1 * l_i1 / 2 / math.cos(beta_i1) - sigma_i1 * h_i1 / l_i1)
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)
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right_equ = sigma_i + delta_l_i_array[i] / math.sqrt(
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string_length ** 2 - delta_l_i_array[i] ** 2
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) * (string_g / 2 / area + w_i)
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if math.fabs(right_equ - left_equ) > 1e-4:
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print("!!!等式不满足")
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return
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print("等式满足。")
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cal_loop()
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print("Finished.")
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