6-1 結論
本研究成功提出一整合混合動力功能之扭力分配差速器 （Hybrid Torque-vectoring Differential, H-TD）之機構，以下將重點條列出本研究之成果。
1. 本研究首先參考以馬達調控之扭力分配差速器並提出H-TD 之概念原型，
並且以機構拓樸、篩選之方式成功生成可行機構。
2. 本研究根據概念原型以及機構設計原則將H-TD 之機構實體化。
3. 本研究針對 H-TD 系統提出三種操作模式，並且提出模式切換之基本控 制策略，以供後續研究發展參考。
4. 為了解決機構本身之左右不對稱，並且同時達成扭力分配時角加速度變 化大小一致之設計要求，本研究以最佳化之基因演算法搭配整數限制得 到系統內所有桿件齒輪齒數的可行數值，並且提出馬達、煞車、離合器之 參數設定方法以供後續發展參考。
5. 本研究探討 H-TD 於一般四輪車輛上可能的系統配置，並且推導各種配 置的整車動力分配力學模型，以供後續模擬使用以及進一步發展之參考。
6. 本研究以數值模擬程式進行分析，證明本研究提出之 H-TD 所具備之扭 力分配功能可在車輛發生打滑時有效恢復車輛之驅動力、在車輛轉向時，
能藉由扭力向外側導引進一步提升車輛之轉向性能。另外，本系統所具備 之混合動力功能則能為車輛提供混合動力車輛具備的優勢，一為額外的 動力輸入，二為更多元的能量管理方式。另一方面，本研究亦對H-TD 之 前後軸配置差異作一簡單測試，同時以直線測試證明 H-TD 經最佳化參 數設計後，機構之左右不對稱性對於車輛之直線前進影響有限。最後本研 究整理H-TD 系統所需之馬達特性與要求，以供未來進一步發展參考。
6-2 未來展望
回顧本研究成果，並在此提出幾點可再深入探討的空間，以供後續研究之參考：
1. 針對 H-TD 之操作模式進行更加深入之分析，以達成最佳化控制系統模 式切換。
2. 針對扭力分配之功能，建立完整的馬達動力邏輯。例如進行完整實驗，討 論在各種車輛動態狀況（時速、主動力源扭力）下，應以多少的馬達扭力 調整扭力分配，才能達成最佳之效果。
3. 針對混合動力之功能，搭配主動力源（例：引擎）之詳細參數，建立更加 完整之動力及能量管理策略。
4. 本研究採用之三自由度車輛模型並未考慮車輛之側傾（roll）、俯仰（pitch）
之運動自由度，因此未來可以六自由度車輛模型，進行更加準確之車輛動 態模擬。
5. 量化更多車輛行駛情境，以進行更加完整的系統性能評估。
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附件 最佳化 1000 組結果
以下表格為 4-3-3 小節所述以 MATLAB 基因演算法函數運算所得之 1000 組 解，依照每組解之目標函數數值結果𝑓𝑣𝑎𝑙𝑢𝑒由小到大排列。
表格中✽：X 表示不符合 Hunting tooth ratio、O 表示符合 Hunting tooth ratio。
並且將符合Hunting tooth ratio 的解以灰底顯示。
7.428587307 17 17 51 23 50 44 27 0.0035 0.00355 0.00365 X
8.243527331 17 19 55 21 44 40 25 0.0035 0.00357 0.00357 X
9.192673962 17 20 57 22 45 41 26 0.0035 0.0035 0.0035 O
10.25053697 18 17 52 30 55 49 36 0.0035 0.0035 0.0035 X
11.0981368 24 17 58 17 59 54 22 0.0035 0.0035 0.0035 X
12.39630862 19 20 59 21 50 45 25 0.0035 0.0042 0.00426 X
13.19887945 25 17 59 30 38 32 36 0.0035 0.0035 0.0035 X
13.81912537 17 22 61 24 44 43 30 0.0035 0.00438 0.00408 X
14.497524 21 20 61 19 58 50 22 0.0035 0.00432 0.00462 X
14.96555708 18 21 60 28 54 43 29 0.0035 0.00396 0.00451 X
15.56686053 17 23 63 31 58 53 36 0.0035 0.0035 0.0035 O
15.98748109 20 22 64 23 43 37 26 0.0035 0.00441 0.00462 X
16.39114425 21 23 67 19 44 37 21 0.0035 0.00406 0.00441 O
16.96405988 20 24 68 26 37 33 30 0.0035 0.00368 0.00368 X
17.42651338 19 25 69 18 49 47 22 0.0035 0.00414 0.00402 O
17.69197046 21 24 69 23 40 36 27 0.0035 0.00368 0.00368 X
18.14982779 17 25 67 33 37 34 38 0.0035 0.00396 0.00385 X
18.50011463 24 22 68 22 38 37 29 0.0035 0.00418 0.0038 X
18.83749928 29 19 67 21 39 35 27 0.0035 0.00403 0.0039 X
19.33676527 25 22 69 18 35 40 28 0.0035 0.00476 0.00371 X
19.63362262 21 24 69 30 47 36 30 0.0035 0.0036 0.0042 X
20.07305695 21 25 71 24 30 27 28 0.0035 0.0044 0.00432 X
20.43874179 22 24 70 19 52 50 24 0.0035 0.00444 0.00426 X
20.81660601 25 22 69 25 55 42 26 0.0035 0.00374 0.0044 X 20.83482857 25 23 71 19 48 43 23 0.0035 0.00396 0.00402 O 20.83539266 17 26 69 29 43 44 37 0.0035 0.00441 0.00392 O 20.85563012 18 27 72 24 40 36 27 0.0035 0.00441 0.00448 X 20.88447131 28 19 66 28 42 39 37 0.0035 0.00418 0.00385 X 20.88975062 17 29 75 17 56 51 19 0.0035 0.0035 0.00365 O 20.89396019 22 24 70 31 46 35 31 0.0035 0.0036 0.0042 X 20.89675415 27 22 71 20 46 40 24 0.0035 0.00352 0.00363 X 20.89837008 30 20 70 17 53 48 22 0.0035 0.0035 0.0035 X 20.89837008 30 20 70 17 53 48 22 0.0035 0.0035 0.0035 X 20.90838892 30 18 66 28 42 34 33 0.0035 0.00402 0.0042 X 20.90838892 30 18 66 28 42 34 33 0.0035 0.00402 0.0042 X 20.90852626 30 20 70 18 47 42 23 0.0035 0.00357 0.00357 X 20.91907935 26 22 70 22 38 34 27 0.0035 0.00427 0.0042 X 20.92401887 30 19 68 21 41 42 31 0.0035 0.00438 0.00372 O 20.94971233 19 25 69 29 55 55 37 0.0035 0.00391 0.00357 O 20.95006513 17 27 71 37 37 25 31 0.0035 0.00364 0.00481 X 20.97735797 17 25 67 35 45 41 40 0.0035 0.00405 0.004 X 20.97898342 17 28 73 33 30 28 38 0.0035 0.00374 0.00357 X 21.01259354 20 26 72 27 41 38 32 0.0035 0.00385 0.00374 X 21.02042693 22 24 70 28 51 36 26 0.0035 0.00372 0.00474 X 21.04156531 24 23 70 25 44 38 29 0.0035 0.00402 0.00414 O 21.05425711 23 23 69 24 43 43 32 0.0035 0.0045 0.00402 X 21.07390977 22 25 72 24 36 31 27 0.0035 0.00406 0.0042 X 21.08500533 17 26 69 33 60 54 37 0.0035 0.00364 0.00372 X 21.08759648 28 21 70 19 41 37 24 0.0035 0.00427 0.0042 X 21.088712 18 28 74 25 45 42 29 0.0035 0.00355 0.0035 X 21.10789847 17 28 73 29 52 48 33 0.0035 0.0035 0.0035 X
附錄 車輛動態數值模擬程式
% for T_TM_change_AA = 60:0.5:110
%%
kmh2ms = 1000/60/60; % [km/h]->[m/s]
rpm2rs = 2*pi/60; % [rpm]->[r/s] slip_time_start_1L = 300; %左前輪開始打滑時間(s) slip_time_start_1R = 300; %右前輪開始打滑時間(s) slip_time_start_2L = 300; %左後輪開始打滑時間(s) slip_time_start_2R = 300; %右後輪開始打滑時間(s) slip_time_end_1L = 300; %左前輪結束打滑時間(s)
dot_precise = precise; %精度取到小數點後dot位，dot_precise位於p1_1_center_diff_open.m和 p2_Traction_case9.m
%% split road mu low_mu = 0.01;
high_mu = 0.85;
delta_l_c = 0; %front left wheel steering angle delta_r_c = 0; %front right wheel steering angle mu2L = high_mu; %設定左後輪地面摩擦力
cd('data'); %path into the folder car_spec;
cd ..
p0_Initial %to find initial tire slip n = 1;
% ====================================================== r_all=[r_pa r_pb r_pc r_pd]; %四輪座標矩陣
R_a_c = 1/2*c_d*rho_a*A_f*u_c^2; %空氣阻力 R_total_c = R_r_c + R_a_c; %總阻力
%% Normal Load of Each Tire
% fn1 = (m_car*g*l_b-l_h*(R_a_c+m_car*du))/l; %前軸總正向力
% fn2 = (m_car*g*l_a+l_h*(R_a_c+m_car*du))/l; %後軸總正向力
%
% F_n_1L_c = (fn1*l_d/2-l_b/l*m_car*dv*l_h)/l_d; %左前輪正向力
% F_n_1R_c = (fn1*l_d/2+l_b/l*m_car*dv*l_h)/l_d; %右前輪正向力
% F_n_2L_c = (fn2*l_d/2-l_a/l*m_car*dv*l_h)/l_d; %左後輪正向力
% F_n_2R_c = (fn2*l_d/2+l_a/l*m_car*dv*l_h)/l_d; %右後輪正向力
%% Build Tire Slip vs Traction Table for each tire
%後輪
srn_r=1; %只是一個計數器(for 後輪) for slipratio_r=0:0.01:1
List_itc_2L_c(srn_r)=XMagicFormula(F_n_2L_c,slipratio_r);
List_itc_2R_c(srn_r)=XMagicFormula(F_n_2R_c,slipratio_r);
List_i_s_r(srn_r)=slipratio_r;
srn_r=srn_r+1;
List_itc_1L_c(srn_f)=XMagicFormula(F_n_1L_c,slipratio_f);
List_itc_1R_c(srn_f)=XMagicFormula(F_n_1R_c,slipratio_f);
List_i_s_f(srn_f)=slipratio_f;
srn_f=srn_f+1;
end
%% Interpolate Resistance(Traction) to Find Tire Slip Ratio 只用前半部的滑差-縱向力曲線 switch Drive_type
case 1 %FWD
i_s_2L_c = interp1(List_itc_2L_c(1:12),List_i_s_r(1:12),0); %左後輪滑差 i_s_2R_c = interp1(List_itc_2R_c(1:12),List_i_s_r(1:12),0); %右後輪滑差
i_s_1L_c = interp1(List_itc_1L_c(1:12),List_i_s_f(1:12),R_total_c/2); %左前輪滑差
case 2 %RWD
i_s_2L_c = interp1(List_itc_2L_c(1:12),List_i_s_r(1:12),R_total_c/2); %左後輪滑差 i_s_2R_c = interp1(List_itc_2R_c(1:12),List_i_s_r(1:12),R_total_c/2); %右後輪滑差 i_s_1L_c = interp1(List_itc_1L_c(1:12),List_i_s_f(1:12),0); %左前輪滑差 i_s_1R_c = interp1(List_itc_1R_c(1:12),List_i_s_f(1:12),0); %右前輪滑差
case 3 %4WD
i_s_2L_c = interp1(List_itc_2L_c(1:12),List_i_s_r(1:12),R_total_c/4); %左後輪滑差 i_s_2R_c = interp1(List_itc_2R_c(1:12),List_i_s_r(1:12),R_total_c/4); %右後輪滑差 i_s_1L_c = interp1(List_itc_1L_c(1:12),List_i_s_f(1:12),R_total_c/4); %左前輪滑差 i_s_1R_c = interp1(List_itc_1R_c(1:12),List_i_s_f(1:12),R_total_c/4); %右前輪滑差 end
%% 用滑差再推回tractive effort（脫褲子放屁）
F_tc_2L_c = interp1(List_i_s_r(1:12),List_itc_2L_c(1:12),i_s_2L_c); %左後輪驅動力(N) F_tc_2R_c = interp1(List_i_s_r(1:12),List_itc_2R_c(1:12),i_s_2R_c); %右後輪驅動力(N)
F_tc_1L_c = interp1(List_i_s_f(1:12),List_itc_1L_c(1:12),i_s_1L_c); %左前輪驅動力(N) F_tc_1R_c = interp1(List_i_s_f(1:12),List_itc_1R_c(1:12),i_s_1R_c); %右前輪驅動力(N)
%% Calculate total tractive force and torque
F_totaltc_c = F_tc_2L_c + F_tc_2R_c + F_tc_1L_c + F_tc_1R_c; %整車驅動力(N) F_totaltc_f_c = F_tc_1L_c + F_tc_1R_c; %前軸總驅動力(N)
F_totaltc_r_c = F_tc_2L_c + F_tc_2R_c; %後軸總驅動力(N) T_totaltc_c = F_totaltc_c*r_w; %整車總驅動力矩(Nm)
%% Calculate Wheel Speed (angular velocity of wheel) 由滑差.車速 推輪轉速 W_w2L_c = (u_c/r_w)/(1-i_s_2L_c); %左後輪轉速(rad/s)
W_w2R_c = (u_c/r_w)/(1-i_s_2R_c); %右後輪轉速(rad/s)
W_w1L_c = (u_c/r_w)/(1-i_s_1L_c); %左前輪轉速(rad/s) W_w1R_c = (u_c/r_w)/(1-i_s_1R_c); %右前輪轉速(rad/s)
%% Calculate Differential Input Speed 由輪轉速推出輸入轉速 switch Drive_type
速(rad/s)
%% Set input torque/ vectoring torque switch cyc_type
% if t>0.5
%% Wheel longitudinal moving speed
v_w2L_c = u_c - l_d/2*r_c; %左後輪縱向速度(m/s)
% fn1 = (m_car*g*l_b-l_h*(R_a_c+m_car*du))/l; %前軸總正向力
% fn2 = (m_car*g*l_a+l_h*(R_a_c+m_car*du))/l; %後軸總正向力
%
% F_n_1L_c = (fn1*l_d/2-l_b/l*m_car*dv*l_h)/l_d; %左前輪正向力
% F_n_1R_c = (fn1*l_d/2+l_b/l*m_car*dv*l_h)/l_d; %右前輪正向力
% F_n_2L_c = (fn2*l_d/2-l_a/l*m_car*dv*l_h)/l_d; %左後輪正向力
% F_n_2R_c = (fn2*l_d/2+l_a/l*m_car*dv*l_h)/l_d; %右後輪正向力
fn1 = (m_car*g*l_b-l_h*(R_a_c+m_car*(du-r_c*v_c)))/l; %前軸總正向力 fn2 = (m_car*g*l_a+l_h*(R_a_c+m_car*(du-r_c*v_c)))/l; %後軸總正向力
F_n_1L_c = (fn1*l_d/2-l_b/l*m_car*(dv+u_c*r_c)*l_h)/l_d; %左前輪正向力
alpha_fl=delta_l_c-atan( (l_a*r_c+v_c)/(u_c-l_d/2*r_c) ); %左前輪側滑角（rad）
alpha_fr=delta_r_c-atan( (l_a*r_c+v_c)/(u_c+l_d/2*r_c) ); %右前輪側滑角（rad）
alpha_rl=atan( (l_b*r_c-v_c)/(u_c-l_d/2*r_c) ); %左後輪側滑角（rad）
alpha_rr=atan( (l_b*r_c-v_c)/(u_c+l_d/2*r_c) ); %右後輪側滑角（rad）
end
%% Road Friction 地面摩擦係數設定 打滑時slip ratio 為traction倒推
% if x_c > 1.5 && x_c < 1.6
% mu1L = high_mu;
% end
if t == slip_time_start_1L %左前輪 mu1L = low_mu;
elseif t == slip_time_end_1L mu1L = high_mu;
end
if t == slip_time_start_1R %右前輪 mu1R = low_mu;
elseif t == slip_time_end_1R
mu1R = high_mu;
end
if t == slip_time_start_2L %左後輪 mu2L = low_mu;
elseif t == slip_time_end_2L mu2L = high_mu;
end
if t == slip_time_start_2R %右後輪 mu2R = low_mu;
F_tc1L_c = F_n_1L_c*mu1L*ratio_tc_1L/sqrt(ratio_tc_1L*ratio_tc_1L+ratio_y_1L*ratio_y_1L);
F_y1L = F_n_1L_c*mu1L*ratio_y_1L/sqrt(ratio_tc_1L*ratio_tc_1L+ratio_y_1L*ratio_y_1L);
slip_w1L = 1; %結尾不加分號，為了讓打滑時command window可以顯示
F_tc1R_c = F_n_1R_c*mu1R*ratio_tc_1R/sqrt(ratio_tc_1R*ratio_tc_1R+ratio_y_1R*ratio_y_1R);
F_y1R = F_n_1R_c*mu1R*ratio_y_1R/sqrt(ratio_tc_1R*ratio_tc_1R+ratio_y_1R*ratio_y_1R);
slip_w1R = 2;
F_tc2L_c = F_n_2L_c*mu2L*ratio_tc_2L/sqrt(ratio_tc_2L*ratio_tc_2L+ratio_y_2L*ratio_y_2L);
F_y2L = F_n_2L_c*mu2L*ratio_y_2L/sqrt(ratio_tc_2L*ratio_tc_2L+ratio_y_2L*ratio_y_2L);
slip_w2L = 3;
F_tc2R_c = F_n_2R_c*mu2R*ratio_tc_2R/sqrt(ratio_tc_2R*ratio_tc_2R+ratio_y_2R*ratio_y_2R);
F_y2R = F_n_2R_c*mu2R*ratio_y_2R/sqrt(ratio_tc_2R*ratio_tc_2R+ratio_y_2R*ratio_y_2R);
slip_w2R = 4;
% c_r = 0.0136+0.4*1e-7*(u_c*3.6)^2; %滾動阻力係數
%% Calculate the total/ individual tractive effort and torque
F_totaltc_c = F_tc2L_c + F_tc2R_c + F_tc1L_c + F_tc1R_c; %整車驅動力(N) F_totaltc_f_c = F_tc1L_c + F_tc1R_c; %前軸總驅動力(N)
F_totaltc_r_c = F_tc2L_c + F_tc2R_c; %後軸總驅動力(N) T_tc1L_c = F_tc1L_c*r_w; %左前輪驅動力矩(Nm)
dW_w1L_c = roundn(sol_c(2),dot_precise); %左前輪角加速度(rad/s^2)
p2_HTVD_FWD_RWD_Hybrid_mode
T_in_r_c = roundn(sol_c(12),dot_precise); %後軸差速器輸入扭力(Nm)