Optimization design method of product general tolerance system

Abstract

A product manufacturing process starts from parts processing, then assembles parts into components, and forms the product finally. To obtain an expected product quality, the quality characteristics in the part level, component level, and product level must be controlled, and the deviations between their actual and target values are required to keep in specified tolerances. All these tolerances form a product tolerance system, and the quality characteristics of product levels contain the geometric and the non-geometric parameters, which are interrelated and form a complex system. General tolerance is the total amount the actual parameters are permitted to vary, which not only include the geometric parameters in machining, but also includes physical, chemical, electrical, and other parameters. What most concerns the product users is whether product quality characteristics meet their requirements, rather than a component quality characteristic or part quality characteristic, and the product quality characteristics are generally not only geometric quantities but also include many non-geometric quantities. The product tolerance system optimization design from part level to product level cannot be achieved, as it includes geometric and non-geometric quantities. In this paper, a product tolerance system model is developed on the basis of determining the quality characteristics of product levels, and the information of the product levels quality characteristics is excavated from data recorded in the product testing process using data mining methods through the support vector nonlinear regression relational model between parts quality characteristics deviations and product quality characteristics deviations. Then, the product manufacturing cost model is set up, which includes the machining dimensional tolerances and non-geometric tolerances, and the product tolerance system optimization model is developed by minimizing the product manufacturing costs as the objective function and the quality characteristics tolerances of product levels as constraint conditions. Finally, a micro-motor product is used as an example to optimize its tolerance system, and its manufacturing costs are decreased by 13.14 %. The results show that the developed method is effective and provides a new way for the product tolerance system optimization.

Appendix

The relationship model of the ith micro-motor product quality characteristic deviation and the parts quality characteristic deviations is as follows:

$$ \begin{array}{cc}\hfill {\lambda}_i\left(\boldsymbol{\delta} \right)=\boldsymbol{\delta} {\boldsymbol{A}}_i{\boldsymbol{\delta}}^T+{\boldsymbol{B}}_i{\boldsymbol{\delta}}^T+{\boldsymbol{C}}_i\hfill & \hfill i=1,2,3,4\hfill \end{array} $$

Where λ _i is the ith micro motor product quality characteristic deviation, λ ₁, λ ₂, λ ₃, λ ₄ is no-load current deviation, no-load speed deviation, load current deviation, load speed deviation of micro motor, respectively, δ is a deviation vector of micro-motor parts quality characteristic, δ = [δ ₁,δ ₂,…,δ ₁₄], A _i and B _i are the coefficient matrixes of the ith micro-motor product quality characteristic deviation, and C _i is a constant coefficient the ith micro-motor product quality characteristic deviation, which are expressed, respectively, as follows:

$$ {A}_1=\left[\begin{array}{cccccccccccccc}\hfill 64.289\hfill & \hfill 4.672\hfill & \hfill \hbox{--} 7.5485\hfill & \hfill 1.797\hfill & \hfill 2.233\hfill & \hfill 3.327\hfill & \hfill 2.3875\hfill & \hfill 4.9785\hfill & \hfill 1.38588\times {10}^{+2}\hfill & \hfill 3.2935\times {10}^{\hbox{--} 3}\hfill & \hfill 8.0855\hfill & \hfill \hbox{--} 1.3505\hfill & \hfill \hbox{--} 0.631\hfill & \hfill 6.590\hfill \\ {}\hfill 4.672\hfill & \hfill 20.345\hfill & \hfill 6.6085\hfill & \hfill \hbox{--} 0.7015\hfill & \hfill 1.376\hfill & \hfill 0.937\hfill & \hfill \hbox{--} 1.291\hfill & \hfill \hbox{--} 28.268\hfill & \hfill \hbox{--} 19.4645\hfill & \hfill \hbox{--} 2.6955\times {10}^{\hbox{--} 3}\hfill & \hfill \hbox{--} 15.552\hfill & \hfill \hbox{--} 0.7385\hfill & \hfill \hbox{--} 1.4895\hfill & \hfill \hbox{--} 4.064\times {10}^{\hbox{--} 1}\hfill \\ {}\hfill \hbox{--} 7.5485\hfill & \hfill 6.6085\hfill & \hfill \hbox{--} 1.048\hfill & \hfill 4.187\times {10}^{\hbox{--} 1}\hfill & \hfill \hbox{--} 1.801\times {10}^{\hbox{--} 1}\hfill & \hfill 1.5845\hfill & \hfill \hbox{--} 2.9065\times {10}^{\hbox{--} 1}\hfill & \hfill \hbox{--} 1.428\hfill & \hfill \hbox{--} 47.237\hfill & \hfill \hbox{--} 1.4855\times {10}^{\hbox{--} 5}\hfill & \hfill 2.159\hfill & \hfill 4.618\times {10}^{\hbox{--} 1}\hfill & \hfill \hbox{--} 1.035\hfill & \hfill \hbox{--} 2.593\times {10}^{\hbox{--} 1}\hfill \\ {}\hfill 1.797\hfill & \hfill \hbox{--} 0.7015\hfill & \hfill 4.187\times {10}^{\hbox{--} 1}\hfill & \hfill \hbox{--} 5.784\times {10}^{\hbox{--} 1}\hfill & \hfill 0.842\times {10}^{\hbox{--} 1}\hfill & \hfill 0.5725\times {10}^{\hbox{--} 1}\hfill & \hfill \hbox{--} 1.525\hfill & \hfill \hbox{--} 3.6075\hfill & \hfill \hbox{--} 12.255\hfill & \hfill 1.116\times {10}^{\hbox{--} 3}\hfill & \hfill \hbox{--} 0.500\hfill & \hfill \hbox{--} 4.109\times {10}^{\hbox{--} 1}\hfill & \hfill 1.3435\times {10}^{\hbox{--} 1}\hfill & \hfill \hbox{--} 1.3975\times {10}^{\hbox{--} 1}\hfill \\ {}\hfill 2.233\hfill & \hfill 1.376\hfill & \hfill \hbox{--} 1.801\times {10}^{\hbox{--} 1}\hfill & \hfill 0.842\times {10}^{\hbox{--} 1}\hfill & \hfill \hbox{--} 1.267\times {10}^{\hbox{--} 1}\hfill & \hfill 4.412\times {10}^{\hbox{--} 1}\hfill & \hfill \hbox{--} 1.701\hfill & \hfill \hbox{--} 1.736\times {10}^{\hbox{--} 1}\hfill & \hfill 2.502\hfill & \hfill 2.5365\times {10}^{\hbox{--} 4}\hfill & \hfill \hbox{--} 2.2955\hfill & \hfill 2.239\times {10}^{\hbox{--} 1}\hfill & \hfill 0.588\hfill & \hfill \hbox{--} 2.8235\times {10}^{\hbox{--} 1}\hfill \\ {}\hfill 3.327\hfill & \hfill 0.937\hfill & \hfill 1.5845\hfill & \hfill 0.5725\times {10}^{\hbox{--} 1}\hfill & \hfill 4.412\times {10}^{\hbox{--} 1}\hfill & \hfill 5.143\hfill & \hfill \hbox{--} 1.1465\times {10}^{\hbox{--} 1}\hfill & \hfill 3.706\hfill & \hfill 1.24528\times {10}^{+2}\hfill & \hfill \hbox{--} 1.0135\times {10}^{\hbox{--} 3}\hfill & \hfill \hbox{--} 4.6835\times {10}^{\hbox{--} 1}\hfill & \hfill \hbox{--} 3.7005\times {10}^{\hbox{--} 2}\hfill & \hfill 1.001\hfill & \hfill 2.498\hfill \\ {}\hfill 2.3875\hfill & \hfill \hbox{--} 1.291\hfill & \hfill \hbox{--} 2.9065\times {10}^{\hbox{--} 1}\hfill & \hfill \hbox{--} 1.525\hfill & \hfill \hbox{--} 1.701\hfill & \hfill \hbox{--} 1.1465\times {10}^{\hbox{--} 1}\hfill & \hfill \hbox{--} 9.461\hfill & \hfill \hbox{--} 0.551\times {10}^{\hbox{--} 1}\hfill & \hfill 61.599\hfill & \hfill \hbox{--} 8.270\times {10}^{\hbox{--} 3}\hfill & \hfill 7.5065\hfill & \hfill \hbox{--} 1.775\hfill & \hfill 2.7705\hfill & \hfill \hbox{--} 2.467\hfill \\ {}\hfill 4.9785\hfill & \hfill \hbox{--} 28.268\hfill & \hfill \hbox{--} 1.428\hfill & \hfill \hbox{--} 3.6075\hfill & \hfill \hbox{--} 1.736\times {10}^{\hbox{--} 1}\hfill & \hfill 3.706\hfill & \hfill \hbox{--} 0.551\times {10}^{\hbox{--} 1}\hfill & \hfill \hbox{--} 34.158\hfill & \hfill \hbox{--} 2.85731\times {10}^{+2}\hfill & \hfill 7.110\times {10}^{\hbox{--} 3}\hfill & \hfill 29.507\hfill & \hfill \hbox{--} 4.8205\times {10}^{\hbox{--} 1}\hfill & \hfill \hbox{--} 4.5445\times {10}^{\hbox{--} 2}\hfill & \hfill 4.9465\hfill \\ {}\hfill 1.38588\times {10}^{+2}\hfill & \hfill \hbox{--} 19.4645\hfill & \hfill \hbox{--} 47.237\hfill & \hfill \hbox{--} 12.255\hfill & \hfill 2.502\hfill & \hfill 1.24528\times {10}^{+2}\hfill & \hfill 61.599\hfill & \hfill \hbox{--} 2.85731\times {10}^{+2}\hfill & \hfill 522.775\hfill & \hfill \hbox{--} 1.411\times {10}^{\hbox{--} 1}\hfill & \hfill \hbox{--} 35.5325\hfill & \hfill \hbox{--} 12.128\hfill & \hfill 11.664\hfill & \hfill 7.3175\hfill \\ {}\hfill 3.2935\times {10}^{\hbox{--} 3}\hfill & \hfill \hbox{--} 2.6955\times {10}^{\hbox{--} 3}\hfill & \hfill \hbox{--} 1.4855\times {10}^{\hbox{--} 5}\hfill & \hfill 1.116\times {10}^{\hbox{--} 3}\hfill & \hfill 2.5365\times {10}^{\hbox{--} 4}\hfill & \hfill \hbox{--} 1.0135\times {10}^{\hbox{--} 3}\hfill & \hfill \hbox{--} 8.270\times {10}^{\hbox{--} 3}\hfill & \hfill 7.110\times {10}^{\hbox{--} 3}\hfill & \hfill \hbox{--} 1.411\times {10}^{\hbox{--} 1}\hfill & \hfill 1.182\times {10}^{\hbox{--} 5}\hfill & \hfill \hbox{--} 2.5205\times {10}^{\hbox{--} 3}\hfill & \hfill 2.546\times {10}^{\hbox{--} 3}\hfill & \hfill \hbox{--} 2.7145\times {10}^{\hbox{--} 3}\hfill & \hfill 4.421\times {10}^{\hbox{--} 5}\hfill \\ {}\hfill 8.0855\hfill & \hfill \hbox{--} 15.552\hfill & \hfill 2.159\hfill & \hfill \hbox{--} 0.500\hfill & \hfill \hbox{--} 2.2955\hfill & \hfill \hbox{--} 4.6835\times {10}^{\hbox{--} 1}\hfill & \hfill 7.5065\hfill & \hfill 29.507\hfill & \hfill \hbox{--} 35.5325\hfill & \hfill \hbox{--} 2.5205\times {10}^{\hbox{--} 3}\hfill & \hfill 5.966\hfill & \hfill 8.375\times {10}^{\hbox{--} 2}\hfill & \hfill 0.856\hfill & \hfill 1.118\hfill \\ {}\hfill \hbox{--} 1.3505\hfill & \hfill \hbox{--} 0.7385\hfill & \hfill 4.618\times {10}^{\hbox{--} 1}\hfill & \hfill \hbox{--} 4.109\times {10}^{\hbox{--} 1}\hfill & \hfill 2.239\times {10}^{\hbox{--} 1}\hfill & \hfill \hbox{--} 3.7005\times {10}^{\hbox{--} 2}\hfill & \hfill \hbox{--} 1.775\hfill & \hfill \hbox{--} 4.8205\times {10}^{\hbox{--} 1}\hfill & \hfill \hbox{--} 12.128\hfill & \hfill 2.546\times {10}^{\hbox{--} 3}\hfill & \hfill 8.375\times {10}^{\hbox{--} 2}\hfill & \hfill 2.753\times {10}^{\hbox{--} 1}\hfill & \hfill \hbox{--} 0.763\hfill & \hfill 3.863\times {10}^{\hbox{--} 1}\hfill \\ {}\hfill \hbox{--} 0.631\hfill & \hfill \hbox{--} 1.4895\hfill & \hfill \hbox{--} 1.035\hfill & \hfill 1.3435\times {10}^{\hbox{--} 1}\hfill & \hfill 0.588\hfill & \hfill 1.001\hfill & \hfill 2.7705\hfill & \hfill \hbox{--} 4.5445\times {10}^{\hbox{--} 2}\hfill & \hfill 11.664\hfill & \hfill \hbox{--} 2.7145\times {10}^{\hbox{--} 3}\hfill & \hfill 0.856\hfill & \hfill \hbox{--} 0.763\hfill & \hfill 8.507\times {10}^{\hbox{--} 1}\hfill & \hfill 4.4675\times {10}^{\hbox{--} 1}\hfill \\ {}\hfill 6.590\hfill & \hfill \hbox{--} 4.064\times {10}^{\hbox{--} 1}\hfill & \hfill \hbox{--} 2.593\times {10}^{\hbox{--} 1}\hfill & \hfill \hbox{--} 1.3975\times {10}^{\hbox{--} 1}\hfill & \hfill \hbox{--} 2.8235\times {10}^{\hbox{--} 1}\hfill & \hfill 2.498\hfill & \hfill \hbox{--} 2.467\hfill & \hfill 4.9465\hfill & \hfill 7.3175\hfill & \hfill 4.421\times {10}^{\hbox{--} 5}\hfill & \hfill 1.118\hfill & \hfill 3.863\times {10}^{\hbox{--} 1}\hfill & \hfill 4.4675\times {10}^{\hbox{--} 1}\hfill & \hfill 4.922\hfill \end{array}\right] $$

$$ {B}_1=\left[\begin{array}{cccccccccccccc}\hfill -1.736\times {10}^{-1}\hfill & \hfill 2.115\times {10}^{-1}\hfill & \hfill 1.285\times {10}^{-2}\hfill & \hfill 4.675\times {10}^{-2}\hfill & \hfill 8.918\times {10}^{-2}\hfill & \hfill 2.303\times {10}^{-2}\hfill & \hfill -8.356\times {10}^{-2}\hfill & \hfill -1.644\hfill & \hfill 7.882\hfill & \hfill 1.827\times {10}^{-4}\hfill & \hfill -2.699\times {10}^{-1}\hfill & \hfill 1.618\times {10}^{-2}\hfill & \hfill 9.917\times {10}^{-2}\hfill & \hfill -2.581\times {10}^{-1}\hfill \end{array}\right] $$

$$ {C}_1=-3.232\times 1{0}^{-3} $$

$$ {A}_2=\left[\begin{array}{cccccccccccccc}\hfill 502818.250\hfill & \hfill \hbox{--} 20151.283\hfill & \hfill \hbox{--} 5595.072\hfill & \hfill 20087.796\hfill & \hfill \hbox{--} 16194.432\hfill & \hfill \hbox{--} 87780.524\hfill & \hfill 51416.741\hfill & \hfill \hbox{--} 99097.25\hfill & \hfill 1287429.1085\hfill & \hfill 148.847\hfill & \hfill 90876.785\hfill & \hfill 10887.606\hfill & \hfill \hbox{--} 16609.421\hfill & \hfill \hbox{--} 176442.081\hfill \\ {}\hfill \hbox{--} 20151.283\hfill & \hfill \hbox{--} 71743.263\hfill & \hfill \hbox{--} 7145.018\hfill & \hfill 16656.8645\hfill & \hfill 34041.8905\hfill & \hfill 33730.4715\hfill & \hfill 9732.154\hfill & \hfill 132448.85\hfill & \hfill \hbox{--} 1084116.628\hfill & \hfill 46.896\hfill & \hfill \hbox{--} 1163.472\hfill & \hfill \hbox{--} 7308.962\hfill & \hfill 12809.61\hfill & \hfill 8835.491\hfill \\ {}\hfill \hbox{--} 5595.072\hfill & \hfill \hbox{--} 7145.018\hfill & \hfill 12148.430\hfill & \hfill 1355.068\hfill & \hfill \hbox{--} 234.2105\hfill & \hfill \hbox{--} 21010.5365\hfill & \hfill \hbox{--} 8544.882\hfill & \hfill 30608.294\hfill & \hfill 165764.315\hfill & \hfill 23.6625\hfill & \hfill \hbox{--} 1085.5715\hfill & \hfill 6651.1175\hfill & \hfill 797.8515\hfill & \hfill 8761.058\hfill \\ {}\hfill 20087.796\hfill & \hfill 16656.8645\hfill & \hfill 1355.068\hfill & \hfill 2329.140\hfill & \hfill \hbox{--} 2222.364\hfill & \hfill 5352.408\hfill & \hfill \hbox{--} 726.509\hfill & \hfill 1753.475\hfill & \hfill \hbox{--} 167772.6015\hfill & \hfill 6.454\hfill & \hfill \hbox{--} 1058.3055\hfill & \hfill \hbox{--} 2002.7285\hfill & \hfill \hbox{--} 1449.5735\hfill & \hfill \hbox{--} 2905.9425\hfill \\ {}\hfill \hbox{--} 16194.432\hfill & \hfill 34041.8905\hfill & \hfill \hbox{--} 234.2105\hfill & \hfill \hbox{--} 2222.364\hfill & \hfill \hbox{--} 9836.114\hfill & \hfill 15636.0745\hfill & \hfill 5289.8395\hfill & \hfill 20603.8225\hfill & \hfill \hbox{--} 297967.104\hfill & \hfill 15.9245\hfill & \hfill \hbox{--} 1887.473\hfill & \hfill 1653.6375\hfill & \hfill \hbox{--} 4331.6825\hfill & \hfill \hbox{--} 1879.728\hfill \\ {}\hfill \hbox{--} 87780.524\hfill & \hfill 33730.4715\hfill & \hfill \hbox{--} 21010.5365\hfill & \hfill 5352.408\hfill & \hfill 15636.0745\hfill & \hfill 15763.408\hfill & \hfill 11907.225\hfill & \hfill 69457.8025\hfill & \hfill \hbox{--} 287758.8325\hfill & \hfill \hbox{--} 41.118\hfill & \hfill \hbox{--} 17481.6955\hfill & \hfill \hbox{--} 4329.4855\hfill & \hfill \hbox{--} 14028.05\hfill & \hfill \hbox{--} 6698.049\hfill \\ {}\hfill 51416.741\hfill & \hfill 9732.154\hfill & \hfill \hbox{--} 8544.882\hfill & \hfill \hbox{--} 726.509\hfill & \hfill 5289.8395\hfill & \hfill 11907.225\hfill & \hfill 22434.156\hfill & \hfill \hbox{--} 156366.9515\hfill & \hfill \hbox{--} 653262.4115\hfill & \hfill \hbox{--} 19.8555\hfill & \hfill 12887.8305\hfill & \hfill \hbox{--} 14497.945\hfill & \hfill 10494.9975\hfill & \hfill 95969.3255\hfill \\ {}\hfill \hbox{--} 99097.25\hfill & \hfill 132448.85\hfill & \hfill 30608.294\hfill & \hfill 1753.475\hfill & \hfill 20603.8225\hfill & \hfill 69457.8025\hfill & \hfill \hbox{--} 156366.9515\hfill & \hfill 262629.222\hfill & \hfill 2295082.8365\hfill & \hfill \hbox{--} 123.009\hfill & \hfill \hbox{--} 28125.931\hfill & \hfill 9043.175\hfill & \hfill 13980.7715\hfill & \hfill \hbox{--} 31818.992\hfill \\ {}\hfill 1287429.1085\hfill & \hfill \hbox{--} 1084116.628\hfill & \hfill 165764.315\hfill & \hfill \hbox{--} 167772.6015\hfill & \hfill \hbox{--} 297967.104\hfill & \hfill \hbox{--} 287758.8325\hfill & \hfill \hbox{--} 653262.4115\hfill & \hfill 2295082.8365\hfill & \hfill 17442391.976\hfill & \hfill \hbox{--} 419.2875\hfill & \hfill 463650.7585\hfill & \hfill 6038.254\hfill & \hfill \hbox{--} 449179.441\hfill & \hfill 101594.996\hfill \\ {}\hfill 148.847\hfill & \hfill 46.896\hfill & \hfill 23.6625\hfill & \hfill 6.454\hfill & \hfill 15.9245\hfill & \hfill \hbox{--} 41.118\hfill & \hfill \hbox{--} 19.8555\hfill & \hfill \hbox{--} 123.009\hfill & \hfill \hbox{--} 419.2875\hfill & \hfill 5.106\times {10}^{\hbox{--} 2}\hfill & \hfill \hbox{--} 39.254\hfill & \hfill \hbox{--} 1.079\hfill & \hfill 6.6875\hfill & \hfill \hbox{--} 3.6755\hfill \\ {}\hfill 90876.785\hfill & \hfill \hbox{--} 1163.472\hfill & \hfill \hbox{--} 1085.5715\hfill & \hfill \hbox{--} 1058.3055\hfill & \hfill \hbox{--} 1887.473\hfill & \hfill \hbox{--} 17481.6955\hfill & \hfill 12887.8305\hfill & \hfill \hbox{--} 28125.931\hfill & \hfill 463650.7585\hfill & \hfill \hbox{--} 39.254\hfill & \hfill \hbox{--} 2318.485\hfill & \hfill\ 6223.5585\hfill & \hfill \hbox{--} 23247.373\hfill & \hfill 15345.7175\hfill \\ {}\hfill 10887.606\hfill & \hfill \hbox{--} 7308.962\hfill & \hfill 6651.1175\hfill & \hfill \hbox{--} 2002.7285\hfill & \hfill 1653.6375\hfill & \hfill \hbox{--} 4329.4855\hfill & \hfill \hbox{--} 14497.945\hfill & \hfill 9043.175\hfill & \hfill 6038.254\hfill & \hfill \hbox{--} 1.079\hfill & \hfill\ 6223.5585\hfill & \hfill \hbox{--} 180.558\hfill & \hfill 85.402\hfill & \hfill \hbox{--} 7778.7705\hfill \\ {}\hfill \hbox{--} 16609.421\hfill & \hfill 12809.61\hfill & \hfill 797.8515\hfill & \hfill \hbox{--} 1449.5735\hfill & \hfill \hbox{--} 4331.6825\hfill & \hfill \hbox{--} 14028.05\hfill & \hfill 10494.9975\hfill & \hfill 13980.7715\hfill & \hfill \hbox{--} 449179.441\hfill & \hfill 6.6875\hfill & \hfill \hbox{--} 23247.373\hfill & \hfill 85.402\hfill & \hfill \hbox{--} 690.307\hfill & \hfill 7349.064\hfill \\ {}\hfill \hbox{--} 176442.081\hfill & \hfill 8835.491\hfill & \hfill 8761.058\hfill & \hfill \hbox{--} 2905.9425\hfill & \hfill \hbox{--} 1879.728\hfill & \hfill \hbox{--} 6698.049\hfill & \hfill 95969.3255\hfill & \hfill \hbox{--} 31818.992\hfill & \hfill 101594.996\hfill & \hfill \hbox{--} 3.6755\hfill & \hfill 15345.7175\hfill & \hfill \hbox{--} 7778.7705\hfill & \hfill 7349.064\hfill & \hfill \hbox{--} 16519.761\hfill \end{array}\right] $$

$$ {B}_2=\left[\begin{array}{cccccccccccccc}\hfill \hbox{--} 604.728\hfill & \hfill 157.689\hfill & \hfill \hbox{--} 3135.938\hfill & \hfill 805.940\hfill & \hfill 1573.904\hfill & \hfill 4611.032\hfill & \hfill \hbox{--} 6739.0512\hfill & \hfill 7309.487\hfill & \hfill 47076.363\hfill & \hfill \hbox{--} 6.178\hfill & \hfill \hbox{--} 1422.510\hfill & \hfill \hbox{--} 298.267\hfill & \hfill 245.413\hfill & \hfill \hbox{--} 1166.468\hfill \end{array}\right] $$

$$ {C}_2=145.894 $$

$$ {A}_3=\left[\begin{array}{cccccccccccccc}\hfill 37.598\hfill & \hfill 13.684\hfill & \hfill \hbox{--} 6.243\hfill & \hfill 3.9135\hfill & \hfill \hbox{--} 5.560\hfill & \hfill 2.9495\hfill & \hfill 3.8065\hfill & \hfill 5.3445\hfill & \hfill 294.154\hfill & \hfill 5.255\times {10}^{\hbox{--} 3}\hfill & \hfill 1.23\hfill & \hfill 1.878\hfill & \hfill \hbox{--} 3.824\hfill & \hfill \hbox{--} 3.625\hfill \\ {}\hfill 13.684\hfill & \hfill 18.781\hfill & \hfill 5.8325\hfill & \hfill 0.534\hfill & \hfill 1.2535\hfill & \hfill 2.9335\hfill & \hfill 0.961\hfill & \hfill \hbox{--} 14.388\hfill & \hfill \hbox{--} 90.5185\hfill & \hfill \hbox{--} 2.030\times {10}^{\hbox{--} 3}\hfill & \hfill \hbox{--} 15.0965\hfill & \hfill \hbox{--} 4.735\times {10}^{\hbox{--} 1}\hfill & \hfill 1.2545\hfill & \hfill \hbox{--} 7.150\hfill \\ {}\hfill \hbox{--} 6.243\hfill & \hfill 5.8325\hfill & \hfill 5.345\times {10}^{\hbox{--} 1}\hfill & \hfill 3.137\times {10}^{\hbox{--} 1}\hfill & \hfill \hbox{--} 6.16\times {10}^{\hbox{--} 2}\hfill & \hfill \hbox{--} 1.631\times {10}^{\hbox{--} 1}\hfill & \hfill \hbox{--} 1.4195\hfill & \hfill \hbox{--} 2.289\hfill & \hfill \hbox{--} 9.556\hfill & \hfill 1.709\times {10}^{\hbox{--} 3}\hfill & \hfill 1.256\hfill & \hfill 6.255\times {10}^{\hbox{--} 1}\hfill & \hfill \hbox{--} 3.745\times {10}^{\hbox{--} 1}\hfill & \hfill \hbox{--} 5.505\times {10}^{\hbox{--} 1}\hfill \\ {}\hfill 3.9135\hfill & \hfill 0.534\hfill & \hfill 3.137\times {10}^{\hbox{--} 1}\hfill & \hfill \hbox{--} 4.161\times {10}^{\hbox{--} 1}\hfill & \hfill \hbox{--} 3.1345\times {10}^{\hbox{--} 1}\hfill & \hfill \hbox{--} 4.129\times {10}^{\hbox{--} 1}\hfill & \hfill \hbox{--} 1.037\hfill & \hfill \hbox{--} 4.3275\hfill & \hfill \hbox{--} 8.5865\hfill & \hfill 1.058\times {10}^{\hbox{--} 3}\hfill & \hfill \hbox{--} 7.85\times {10}^{\hbox{--} 1}\hfill & \hfill \hbox{--} 4.9075\times {10}^{\hbox{--} 1}\hfill & \hfill 2.132\times {10}^{\hbox{--} 2}\hfill & \hfill \hbox{--} 1.2255\hfill \\ {}\hfill \hbox{--} 5.560\hfill & \hfill 1.2535\hfill & \hfill \hbox{--} 6.16\times {10}^{\hbox{--} 2}\hfill & \hfill \hbox{--} 3.1345\times {10}^{\hbox{--} 1}\hfill & \hfill 5.799\times {10}^{\hbox{--} 1}\hfill & \hfill 8.48\times {10}^{\hbox{--} 1}\hfill & \hfill \hbox{--} 1.787\hfill & \hfill 1.3295\hfill & \hfill \hbox{--} 6.177\hfill & \hfill 1.447\times {10}^{\hbox{--} 3}\hfill & \hfill \hbox{--} 2.452\hfill & \hfill 2.527\times {10}^{\hbox{--} 1}\hfill & \hfill 4.6785\times {10}^{\hbox{--} 1}\hfill & \hfill \hbox{--} 5.37\times {10}^{\hbox{--} 1}\hfill \\ {}\hfill 2.9495\hfill & \hfill 2.9335\hfill & \hfill \hbox{--} 1.631\times {10}^{\hbox{--} 1}\hfill & \hfill \hbox{--} 4.129\times {10}^{\hbox{--} 1}\hfill & \hfill 8.48\times {10}^{\hbox{--} 1}\hfill & \hfill 6.742\hfill & \hfill 2.346\hfill & \hfill 11.745\hfill & \hfill 113.267\hfill & \hfill \hbox{--} 5.74\times {10}^{\hbox{--} 3}\hfill & \hfill \hbox{--} 9.16\times {10}^{\hbox{--} 1}\hfill & \hfill \hbox{--} 6.38\times {10}^{\hbox{--} 1}\hfill & \hfill \hbox{--} 5.015\times {10}^{\hbox{--} 1}\hfill & \hfill 8.385\times {10}^{\hbox{--} 1}\hfill \\ {}\hfill 3.8065\hfill & \hfill 0.961\hfill & \hfill \hbox{--} 1.4195\hfill & \hfill \hbox{--} 1.037\hfill & \hfill \hbox{--} 1.787\hfill & \hfill 2.346\hfill & \hfill \hbox{--} 8.851\hfill & \hfill 3.326\hfill & \hfill 40.1535\hfill & \hfill \hbox{--} 1.1455\times {10}^{\hbox{--} 2}\hfill & \hfill 8.419\hfill & \hfill \hbox{--} 1.8695\hfill & \hfill 3.922\hfill & \hfill 5.406\hfill \\ {}\hfill 5.3445\hfill & \hfill \hbox{--} 14.388\hfill & \hfill \hbox{--} 2.289\hfill & \hfill \hbox{--} 4.3275\hfill & \hfill 1.3295\hfill & \hfill 11.745\hfill & \hfill 3.326\hfill & \hfill \hbox{--} 20.428\hfill & \hfill \hbox{--} 393.924\hfill & \hfill 2.5355\times {10}^{\hbox{--} 3}\hfill & \hfill 18.271\hfill & \hfill \hbox{--} 2.4715\hfill & \hfill \hbox{--} 4.0215\times {10}^{\hbox{--} 1}\hfill & \hfill 6.7075\hfill \\ {}\hfill 294.154\hfill & \hfill \hbox{--} 90.5185\hfill & \hfill \hbox{--} 9.556\hfill & \hfill \hbox{--} 8.5865\hfill & \hfill \hbox{--} 6.177\hfill & \hfill 113.267\hfill & \hfill 40.1535\hfill & \hfill \hbox{--} 393.924\hfill & \hfill 2056.512\hfill & \hfill \hbox{--} 1.9435\times {10}^{\hbox{--} 1}\hfill & \hfill \hbox{--} 35.1735\hfill & \hfill \hbox{--} 32.9625\hfill & \hfill 4.0235\hfill & \hfill 88.452\hfill \\ {}\hfill 5.255\times {10}^{\hbox{--} 3}\hfill & \hfill \hbox{--} 2.030\times {10}^{\hbox{--} 3}\hfill & \hfill 1.709\times {10}^{\hbox{--} 3}\hfill & \hfill 1.058\times {10}^{\hbox{--} 3}\hfill & \hfill 1.447\times {10}^{\hbox{--} 3}\hfill & \hfill \hbox{--} 5.74\times {10}^{\hbox{--} 3}\hfill & \hfill \hbox{--} 1.1455\times {10}^{\hbox{--} 2}\hfill & \hfill 2.5355\times {10}^{\hbox{--} 3}\hfill & \hfill \hbox{--} 1.9435\times {10}^{\hbox{--} 1}\hfill & \hfill 1.475\times {10}^{\hbox{--} 5}\hfill & \hfill \hbox{--} 1.3475\times {10}^{\hbox{--} 3}\hfill & \hfill 2.966\times {10}^{\hbox{--} 3}\hfill & \hfill \hbox{--} 2.3865\times {10}^{\hbox{--} 3}\hfill & \hfill 9.145\times {10}^{\hbox{--} 3}\hfill \\ {}\hfill 1.23\hfill & \hfill \hbox{--} 15.0965\hfill & \hfill 1.256\hfill & \hfill \hbox{--} 7.85\times {10}^{\hbox{--} 1}\hfill & \hfill \hbox{--} 2.452\hfill & \hfill \hbox{--} 9.16\times {10}^{\hbox{--} 1}\hfill & \hfill 8.419\hfill & \hfill 18.271\hfill & \hfill \hbox{--} 35.1735\hfill & \hfill \hbox{--} 1.3475\times {10}^{\hbox{--} 3}\hfill & \hfill 9.218\hfill & \hfill 1.05\hfill & \hfill \hbox{--} 1.8185\times {10}^{\hbox{--} 1}\hfill & \hfill 2.1105\hfill \\ {}\hfill 1.878\hfill & \hfill \hbox{--} 4.735\times {10}^{\hbox{--} 1}\hfill & \hfill 6.255\times {10}^{\hbox{--} 1}\hfill & \hfill \hbox{--} 4.9075\times {10}^{\hbox{--} 1}\hfill & \hfill 2.527\times {10}^{\hbox{--} 1}\hfill & \hfill \hbox{--} 6.38\times {10}^{\hbox{--} 1}\hfill & \hfill \hbox{--} 1.8695\hfill & \hfill \hbox{--} 2.4715\hfill & \hfill \hbox{--} 32.9625\hfill & \hfill 2.966\times {10}^{\hbox{--} 3}\hfill & \hfill 1.05\hfill & \hfill 4.871\times {10}^{\hbox{--} 1}\hfill & \hfill \hbox{--} 7.095\times {10}^{\hbox{--} 1}\hfill & \hfill \hbox{--} 2.7745\times {10}^{\hbox{--} 1}\hfill \\ {}\hfill \hbox{--} 3.824\hfill & \hfill 1.2545\hfill & \hfill \hbox{--} 3.745\times {10}^{\hbox{--} 1}\hfill & \hfill 2.132\times {10}^{\hbox{--} 2}\hfill & \hfill 4.6785\times {10}^{\hbox{--} 1}\hfill & \hfill \hbox{--} 5.015\times {10}^{\hbox{--} 1}\hfill & \hfill 3.922\hfill & \hfill \hbox{--} 4.0215\times {10}^{\hbox{--} 1}\hfill & \hfill 4.0235\hfill & \hfill \hbox{--} 2.3865\times {10}^{\hbox{--} 3}\hfill & \hfill \hbox{--} 1.8185\times {10}^{\hbox{--} 1}\hfill & \hfill \hbox{--} 7.095\times {10}^{\hbox{--} 1}\hfill & \hfill 1.392\hfill & \hfill 4.6885\times {10}^{\hbox{--} 1}\hfill \\ {}\hfill \hbox{--} 3.625\hfill & \hfill \hbox{--} 7.150\hfill & \hfill \hbox{--} 5.505\times {10}^{\hbox{--} 1}\hfill & \hfill \hbox{--} 1.2255\hfill & \hfill \hbox{--} 5.37\times {10}^{\hbox{--} 1}\hfill & \hfill 8.385\times {10}^{\hbox{--} 1}\hfill & \hfill 5.406\hfill & \hfill 6.7075\hfill & \hfill 88.452\hfill & \hfill 9.145\times {10}^{\hbox{--} 3}\hfill & \hfill 2.1105\hfill & \hfill \hbox{--} 2.7745\times {10}^{\hbox{--} 1}\hfill & \hfill 4.6885\times {10}^{\hbox{--} 1}\hfill & \hfill 9.519\times {10}^{\hbox{--} 1}\hfill \end{array}\right] $$

$$ {B}_3=\left[\begin{array}{cccccccccccccc}\hfill 1.953\hfill & \hfill 7.581\times {10}^{\hbox{--} 1}\hfill & \hfill \hbox{--} 1.826\times {10}^{\hbox{--} 1}\hfill & \hfill 5.014\times {10}^{\hbox{--} 2}\hfill & \hfill 9.105\times {10}^{\hbox{--} 2}\hfill & \hfill 3.023\times {10}^{\hbox{--} 1}\hfill & \hfill \hbox{--} 2.569\times {10}^{\hbox{--} 1}\hfill & \hfill \hbox{--} 3.557\times {10}^{\hbox{--} 1}\hfill & \hfill 5.179\hfill & \hfill \hbox{--} 5.293\times {10}^{\hbox{--} 4}\hfill & \hfill \hbox{--} 5.378\times {10}^{\hbox{--} 1}\hfill & \hfill \hbox{--} 1.189\times {10}^{\hbox{--} 1}\hfill & \hfill \hbox{--} 4.127\times {10}^{\hbox{--} 2}\hfill & \hfill 4.451\times {10}^{\hbox{--} 2}\hfill \end{array}\right] $$

$$ {C}_3=1.076\times 1{0}^{-2} $$

$$ {A}_4=\left[\begin{array}{cccccccccccccc}\hfill 562915.067\hfill & \hfill \hbox{--} 11613.4265\hfill & \hfill \hbox{--} 21732.251\hfill & \hfill 7608.936\hfill & \hfill \hbox{--} 512.4925\hfill & \hfill \hbox{--} 81219.3115\hfill & \hfill 6755.868\hfill & \hfill 11817.952\hfill & \hfill 655651.586\hfill & \hfill 33.0975\hfill & \hfill 35927.7355\hfill & \hfill \hbox{--} 15690.206\hfill & \hfill \hbox{--} 3892.2285\hfill & \hfill \hbox{--} 89648.5235\hfill \\ {}\hfill \hbox{--} 11613.4265\hfill & \hfill 49654.853\hfill & \hfill \hbox{--} 2510.9\hfill & \hfill \hbox{--} 111.4835\hfill & \hfill 26703.272\hfill & \hfill 30092.329\hfill & \hfill 30415.476\hfill & \hfill \hbox{--} 54204.636\hfill & \hfill \hbox{--} 1275499.0035\hfill & \hfill 32.143\hfill & \hfill \hbox{--} 18236.2355\hfill & \hfill 8124.808\hfill & \hfill \hbox{--} 11471.752\hfill & \hfill \hbox{--} 16067.8645\hfill \\ {}\hfill \hbox{--} 21732.251\hfill & \hfill \hbox{--} 2510.9\hfill & \hfill 2621.817\hfill & \hfill \hbox{--} 574.8265\hfill & \hfill 817.808\hfill & \hfill \hbox{--} 9222.022\hfill & \hfill \hbox{--} 24138.4135\hfill & \hfill 14731.291\hfill & \hfill 41165.555\hfill & \hfill 34.237\hfill & \hfill \hbox{--} 4721.664\hfill & \hfill 3541.6685\hfill & \hfill \hbox{--} 4570.6805\hfill & \hfill \hbox{--} 3920.5825\hfill \\ {}\hfill 7608.936\hfill & \hfill \hbox{--} 111.4835\hfill & \hfill \hbox{--} 574.8265\hfill & \hfill \hbox{--} 757.458\hfill & \hfill \hbox{--} 2915.0075\hfill & \hfill 5505.8725\hfill & \hfill \hbox{--} 11112.5385\hfill & \hfill \hbox{--} 12592.9205\hfill & \hfill \hbox{--} 118297.9805\hfill & \hfill 14.160\hfill & \hfill 2630.6275\hfill & \hfill \hbox{--} 1428.6955\hfill & \hfill \hbox{--} 2403.876\hfill & \hfill \hbox{--} 4178.5915\hfill \\ {}\hfill \hbox{--} 512.4925\hfill & \hfill 26703.272\hfill & \hfill 817.808\hfill & \hfill \hbox{--} 2915.0075\hfill & \hfill \hbox{--} 6671.182\hfill & \hfill 7880.6495\hfill & \hfill \hbox{--} 651.333\hfill & \hfill \hbox{--} 2134.673\hfill & \hfill \hbox{--} 100763.0325\hfill & \hfill 23.377\hfill & \hfill \hbox{--} 4197.819\hfill & \hfill 1600.3525\hfill & \hfill 1322.962\hfill & \hfill 484.6075\hfill \\ {}\hfill \hbox{--} 81219.3115\hfill & \hfill 30092.329\hfill & \hfill \hbox{--} 9222.022\hfill & \hfill 5505.8725\hfill & \hfill 7880.6495\hfill & \hfill 17453.410\hfill & \hfill 1760.526\hfill & \hfill 37386.11\hfill & \hfill \hbox{--} 261131.537\hfill & \hfill \hbox{--} 17.777\hfill & \hfill \hbox{--} 21383.0715\hfill & \hfill 229.55\hfill & \hfill \hbox{--} 15797.764\hfill & \hfill \hbox{--} 5796.569\hfill \\ {}\hfill 6755.868\hfill & \hfill 30415.476\hfill & \hfill \hbox{--} 24138.4135\hfill & \hfill \hbox{--} 11112.5385\hfill & \hfill \hbox{--} 651.333\hfill & \hfill 1760.526\hfill & \hfill \hbox{--} 21456.195\hfill & \hfill \hbox{--} 63703.1415\hfill & \hfill \hbox{--} 371355.901\hfill & \hfill \hbox{--} 43.6675\hfill & \hfill 10772.2525\hfill & \hfill \hbox{--} 10627.4895\hfill & \hfill 5853.974\hfill & \hfill 36418.8785\hfill \\ {}\hfill 11817.952\hfill & \hfill \hbox{--} 54204.636\hfill & \hfill 14731.291\hfill & \hfill \hbox{--} 12592.9205\hfill & \hfill \hbox{--} 2134.673\hfill & \hfill 37386.11\hfill & \hfill \hbox{--} 63703.1415\hfill & \hfill \hbox{--} 59882.273\hfill & \hfill \hbox{--} 433397.1905\hfill & \hfill \hbox{--} 88.0305\hfill & \hfill 82498.027\hfill & \hfill \hbox{--} 8064.017\hfill & \hfill 19469.425\hfill & \hfill 8441.8125\hfill \\ {}\hfill 655651.586\hfill & \hfill \hbox{--} 1275499.0035\hfill & \hfill 41165.555\hfill & \hfill \hbox{--} 118297.9805\hfill & \hfill \hbox{--} 100763.0325\hfill & \hfill \hbox{--} 261131.537\hfill & \hfill \hbox{--} 371355.901\hfill & \hfill \hbox{--} 433397.1905\hfill & \hfill 2200263.876\hfill & \hfill \hbox{--} 889.929\hfill & \hfill \hbox{--} 125739.5045\hfill & \hfill \hbox{--} 64279.3595\hfill & \hfill \hbox{--} 641350.246\hfill & \hfill 4.07226067\hfill \\ {}\hfill 33.0975\hfill & \hfill 32.143\hfill & \hfill 34.237\hfill & \hfill 14.160\hfill & \hfill 23.377\hfill & \hfill \hbox{--} 17.777\hfill & \hfill \hbox{--} 43.6675\hfill & \hfill \hbox{--} 88.0305\hfill & \hfill \hbox{--} 889.929\hfill & \hfill 7.8321\times {10}^{\hbox{--} 2}\hfill & \hfill \hbox{--} 14.6995\hfill & \hfill 2.5875\hfill & \hfill 6.6665\hfill & \hfill 5.5725\hfill \\ {}\hfill 35927.7355\hfill & \hfill \hbox{--} 18236.2355\hfill & \hfill \hbox{--} 4721.664\hfill & \hfill 2630.6275\hfill & \hfill \hbox{--} 4197.819\hfill & \hfill \hbox{--} 21383.0715\hfill & \hfill 10772.2525\hfill & \hfill 82498.027\hfill & \hfill \hbox{--} 125739.5045\hfill & \hfill \hbox{--} 14.6995\hfill & \hfill 33393.312\hfill & \hfill 9892.5025\hfill & \hfill \hbox{--} 29659.5555\hfill & \hfill 18072.105\hfill \\ {}\hfill \hbox{--} 15690.206\hfill & \hfill 8124.808\hfill & \hfill 3541.6685\hfill & \hfill \hbox{--} 1428.6955\hfill & \hfill 1600.3525\hfill & \hfill 229.55\hfill & \hfill \hbox{--} 10627.4895\hfill & \hfill \hbox{--} 8064.017\hfill & \hfill \hbox{--} 64279.3595\hfill & \hfill 2.5875\hfill & \hfill 9892.5025\hfill & \hfill 1642.126\hfill & \hfill \hbox{--} 2665.88\hfill & \hfill \hbox{--} 5452.498\hfill \\ {}\hfill \hbox{--} 3892.2285\hfill & \hfill \hbox{--} 11471.752\hfill & \hfill \hbox{--} 4570.6805\hfill & \hfill \hbox{--} 2403.876\hfill & \hfill 1322.962\hfill & \hfill \hbox{--} 15797.764\hfill & \hfill 5853.974\hfill & \hfill 19469.425\hfill & \hfill \hbox{--} 641350.246\hfill & \hfill 6.6665\hfill & \hfill \hbox{--} 29659.5555\hfill & \hfill \hbox{--} 2665.88\hfill & \hfill 5866.807\hfill & \hfill 6664.1415\hfill \\ {}\hfill \hbox{--} 89648.5235\hfill & \hfill \hbox{--} 16067.8645\hfill & \hfill \hbox{--} 3920.5825\hfill & \hfill \hbox{--} 4178.5915\hfill & \hfill 484.6075\hfill & \hfill \hbox{--} 5796.569\hfill & \hfill 36418.8785\hfill & \hfill 8441.8125\hfill & \hfill 4.07226067\hfill & \hfill 5.5725\hfill & \hfill 18072.105\hfill & \hfill \hbox{--} 5452.498\hfill & \hfill 6664.1415\hfill & \hfill 27391.078\hfill \end{array}\right] $$

$$ {B}_4=\left[\begin{array}{cccccccccccccc}\hfill 352.939\hfill & \hfill \hbox{--} 811.724\hfill & \hfill 169.933\hfill & \hfill 1234.601\hfill & \hfill 159.700\hfill & \hfill 4810.620\hfill & \hfill \hbox{--} 2248.793\hfill & \hfill \hbox{--} 022.814\hfill & \hfill 55872.962\hfill & \hfill \hbox{--} 5.825\hfill & \hfill \hbox{--} 1765.801\hfill & \hfill \hbox{--} 223.986\hfill & \hfill 626.993\hfill & \hfill \hbox{--} 2335.851\hfill \end{array}\right] $$

$$ {C}_4=115.970 $$