Table 5 Transmission ratio and partial derivative in the acceleration gear 6.
From: Performance analysis and optimization design of variant CR-CR 9-speed automatic transmission
Transmission ratio\({i_6}\) | \(\frac{{{n_i}}}{{{n_o}}}=\frac{{({K_1}+1)({K_4}+1)}}{{1+{K_1}+{K_4}+{K_1}{K_3}+{K_1}{K_4}}}\) |
|---|---|
\(ln{i_6}\) | \(\ln [({K_1}+1)({K_4}+1)] - \ln (1+{K_1}+{K_4}+{K_1}{K_3}+{K_1}{K_4})\) |
Partial derivative | Â |
\(\frac{{\partial \ln {i_6}}}{{\partial {K_1}}}\) | \(\frac{{{K_4}+1}}{{({K_1}+1)({K_4}+1)}} - \frac{{{K_3}+{K_4}+1}}{{1+{K_1}+{K_4}+{K_1}{K_3}+{K_1}{K_4}}}\) |
\(\frac{{\partial \ln {i_6}}}{{\partial {K_2}}}\) | 0 |
\(\frac{{\partial \ln {i_6}}}{{\partial {K_3}}}\) | \(- \frac{{{K_3}}}{{1+{K_1}+{K_4}+{K_1}{K_3}+{K_1}{K_4}}}\) |
\(\frac{{\partial \ln {i_6}}}{{\partial {K_4}}}\) | \(\frac{{{K_1}+1}}{{({K_1}+1)({K_4}+1)}} - \frac{{{K_1}+1}}{{1+{K_1}+{K_4}+{K_1}{K_3}+{K_1}{K_4}}}\) |
