Simplified diagram of automatic mechanical transmission (AMT) with the gearshift assistant mechanism concept. 1: Inner combustion engine; 2: Main clutch; 3: Gear pair connect the engine output shaft and the secondary shaft; 4: Anticipated gear pair; 5: Synchronizer; 6: Present gear pair; 7: Primary shaft (output shaft); 8: Complementary gears; 9: Torque complementary motor; 10: Epicyclic mechanism; 11: Synchronizing clutch; 12: Secondary shaft. As shown in Figure 2, the kinematics of AMT with the gearshift assistant mechanism could be described by two angular velocities, e  and p  , as:

Simplified diagram of automatic mechanical transmission (AMT) with the gearshift assistant mechanism concept. 1: Inner combustion engine; 2: Main clutch; 3: Gear pair connect the engine output shaft and the secondary shaft; 4: Anticipated gear pair; 5: Synchronizer; 6: Present gear pair; 7: Primary shaft (output shaft); 8: Complementary gears; 9: Torque complementary motor; 10: Epicyclic mechanism; 11: Synchronizing clutch; 12: Secondary shaft. As shown in Figure 2, the kinematics of AMT with the gearshift assistant mechanism could be described by two angular velocities, e  and p  , as:

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Automatic mechanical transmission (AMT) with a gearshift assistant mechanism is a novel transmission architect concept aiming to improve the torque interruption and driveline jerk of AMT. During the shifting process, the shifting performance deteriorates as the varying road gradient and the friction coefficient worsen the coupling effect between th...

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... a synchronizing clutch will be engaged to synchronize the preshift gear and the transmission output shaft. The synchronizing clutch is a substitute for the synchronizers and the clutch of AMT in the shifting process (as shown in Figure 1). Yet, the structure of the gearshift assistant mechanism inevitably leads to mutual coupling between the motor torque and the clutch friction torque. ...
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... shown in Figure 1, the gearshift assistant mechanism consists of an electric motor, an epicyclic mechanism, and a synchronizing clutch. The motor directly transmits power to the output shaft through a pair of gears, namely the complementary gear. ...
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... As shown in Figure 10, when Thres = 0.001, the calculation finishes at 99 iterations, and the minimum value obtained by the simulation results is about 80.3; when Thres is reduced to 0.0001, the calculation finishes at 377 iterations, and the result is about 57.02. If Thres is set to 0, the simulation will continue, but after 1022 iterations, the result is about 56.79, and the simulation has not finished yet. ...
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... it can be inferred that if the Thres selected is too large, the simulation result is likely to fall into the local minimum; if Thres is selected too small, as the number of iterations continues to increase (taking the standard shown in Figure 4 as more than 300 iterations), the convergence rate of the function value does not change significantly. As shown in Figures 11 and 12, after changing the weight coefficients scl w and m w , the cost function value ( ) V x changes accordingly. In the current model, increasing m w will increase the value of the function because the two variables e scl and e m are calculated in scalar form, and the latter is numerically larger than the former. ...
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... the current model, increasing m w will increase the value of the function because the two variables e scl and e m are calculated in scalar form, and the latter is numerically larger than the former. The minimum values obtained by convergence in Figures 11 and 12 have increased in different degrees compared to that in Figure 10, and so does the number of iterations. In order to explore the effect of different initial points on the simulation results, seven random initial points were defined into the 7 × 6 matrix B: ...
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... the current model, increasing m w will increase the value of the function because the two variables e scl and e m are calculated in scalar form, and the latter is numerically larger than the former. The minimum values obtained by convergence in Figures 11 and 12 have increased in different degrees compared to that in Figure 10, and so does the number of iterations. In order to explore the effect of different initial points on the simulation results, seven random initial points were defined into the 7 × 6 matrix B: ...
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... meaning of matrix B is consistent with the meaning of matrix A in Formula (13). As shown in Figure 13, the simulation was aborted at 349 iterations and the function value converged to about 60.58. Compared with Figure 10, after 99 iterations, the function value of each initial point in Figure 13 is about 89, and the iteration is not terminated; the function value of each initial point in Figure 10 converges to 80.3 and satisfies Thres = 0.001. ...
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... shown in Figure 13, the simulation was aborted at 349 iterations and the function value converged to about 60.58. Compared with Figure 10, after 99 iterations, the function value of each initial point in Figure 13 is about 89, and the iteration is not terminated; the function value of each initial point in Figure 10 converges to 80.3 and satisfies Thres = 0.001. When the function value of each initial point in Figure 13 meets Thres = 0.001, the convergence result is close to the minimum value of 57.02, which is the minimum function value in Figure 10 when its initial points iterated to meet Thres = 0.0001. ...
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... shown in Figure 13, the simulation was aborted at 349 iterations and the function value converged to about 60.58. Compared with Figure 10, after 99 iterations, the function value of each initial point in Figure 13 is about 89, and the iteration is not terminated; the function value of each initial point in Figure 10 converges to 80.3 and satisfies Thres = 0.001. When the function value of each initial point in Figure 13 meets Thres = 0.001, the convergence result is close to the minimum value of 57.02, which is the minimum function value in Figure 10 when its initial points iterated to meet Thres = 0.0001. ...
Context 10
... shown in Figure 13, the simulation was aborted at 349 iterations and the function value converged to about 60.58. Compared with Figure 10, after 99 iterations, the function value of each initial point in Figure 13 is about 89, and the iteration is not terminated; the function value of each initial point in Figure 10 converges to 80.3 and satisfies Thres = 0.001. When the function value of each initial point in Figure 13 meets Thres = 0.001, the convergence result is close to the minimum value of 57.02, which is the minimum function value in Figure 10 when its initial points iterated to meet Thres = 0.0001. ...
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... with Figure 10, after 99 iterations, the function value of each initial point in Figure 13 is about 89, and the iteration is not terminated; the function value of each initial point in Figure 10 converges to 80.3 and satisfies Thres = 0.001. When the function value of each initial point in Figure 13 meets Thres = 0.001, the convergence result is close to the minimum value of 57.02, which is the minimum function value in Figure 10 when its initial points iterated to meet Thres = 0.0001. It can be deduced from this that the selection of the initial value points will affect the number of iterations and the accuracy of the result; when the function value change has a greater impact on the system output performance, the value of Thres should be reduced to obtain a more accurate result. ...
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... with Figure 10, after 99 iterations, the function value of each initial point in Figure 13 is about 89, and the iteration is not terminated; the function value of each initial point in Figure 10 converges to 80.3 and satisfies Thres = 0.001. When the function value of each initial point in Figure 13 meets Thres = 0.001, the convergence result is close to the minimum value of 57.02, which is the minimum function value in Figure 10 when its initial points iterated to meet Thres = 0.0001. It can be deduced from this that the selection of the initial value points will affect the number of iterations and the accuracy of the result; when the function value change has a greater impact on the system output performance, the value of Thres should be reduced to obtain a more accurate result. ...
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... reduce the amount of calculation, Thres can be directly set as 0.0001 in this case. As shown in Figure 14, when Thres is unchanged and the weight coefficient scl w is reduced to 0.5, the target tracking ability will be decreased, and as it decreases below 0.5, the target tracking ability will also decrease, but the trend is flat. In the case of applying the same weight coefficients to the initial points taken from matrix B, although more iterations are required to meet the same Thres condition, the results obtain a lower function value and better target tracking ability. ...
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... the case of applying the same weight coefficients to the initial points taken from matrix B, although more iterations are required to meet the same Thres condition, the results obtain a lower function value and better target tracking ability. As shown in Figure 15, the relationship between the target tracking ability of the output shaft angular acceleration p   and Thres is similar to that of scl   , but when Thres = 0.001, the fluctuation is large, which will deteriorate the riding comfort of the vehicle. Combining with Figure 14, when Thres = 0.0001, the algorithm can get better target tracking ability of two outputs through 377 iterations at the same time. ...
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... shown in Figure 15, the relationship between the target tracking ability of the output shaft angular acceleration p   and Thres is similar to that of scl   , but when Thres = 0.001, the fluctuation is large, which will deteriorate the riding comfort of the vehicle. Combining with Figure 14, when Thres = 0.0001, the algorithm can get better target tracking ability of two outputs through 377 iterations at the same time. As shown in Figure 15, when the other conditions remain unchanged, increasing the weight coefficient of the error norm of output p   up to 0.5 will significantly improve the target tracking ability. ...
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... with Figure 14, when Thres = 0.0001, the algorithm can get better target tracking ability of two outputs through 377 iterations at the same time. As shown in Figure 15, when the other conditions remain unchanged, increasing the weight coefficient of the error norm of output p   up to 0.5 will significantly improve the target tracking ability. However, when the weight coefficient is greater than 0.5, the performance will not be significantly improved. ...
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... when the weight coefficient is greater than 0.5, the performance will not be significantly improved. By changing the initial points, the value of the cost function obtained from matrix B is lower, and the improvement of the target tracking ability can be more obvious than in Figure 15. ...
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... surging toque interferes with the synchronization of the clutch pads. As shown in Figure 15, higher weighting parameters or lower termination thresholds are essential for preventing the output torque from overshooting. Hence, the weighting parameters are selected as =0.5 =0.5 scl m w w , ...
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... Figures 16-18 show the shifting performance of AMT with the gearshift assistant mechanism in different road grades. It is shown that with the perturbing parameters and the interferences well estimated, the upshift of the proposed transmission can still be successful, and the torque filling effect is also acceptable. ...

Citations

... The orientation of a rigid body in a coordinate system can be characterized based on the three Euler angles, which can also be used to translate a point's coordinates from one reference frame to another and to explain the relationship between two reference frames [32][33][34][35]. The Euler angles, which show how a body rotates around the axes of a coordinate system, are represented by the symbols for the roll, pitch, and yaw angles. ...
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... However, when manual transmission shifts, the power is interrupted, it is difficult to shift, and the driving performance of the vehicle depends on the driving level. At the same time, complex shift operations are easy to cause driver fatigue and affect road safety [3]. Therefore, automatic transmission technology has become an important research direction, and the rapid development of electronic technology and its wide application in vehicles also provide a good opportunity for the development of automatic transmission [4]. ...
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