TRA轴定义及MATLAB计算代码分享
The TRA is defined as an axis around which rotation occurs when a torque is exerted on a free rigid body about an arbitrary direction. Since the system is unconstrained, the TRA is determined by the inertial properties of the powertrain and the direction of the torque. TRA vector is defined as follows：
图1 TRA轴定义
以下是MATLAB代码,供大家验证：
前置前驱代码：
Jxx=6.65; Jyy=4.07; Jzz=5.52;
Jxy=-0.171; Jzx=-0.249; Jyz=1.13;
M=[Jxx,-Jxz,-Jzx;-Jxy,Jyy,-Jyz;-Jzx,-Jyz,Jzz];
N=inv(M);
p=sqrt(N(1,2)^2+N(2,2)^2+N(3,2)^2);
A=N(1,2)/p;
B=N(2,2)/p;
C=N(3,2)/p;
cos_value=[A,B,C]
angle_value=[acosd(A),acosd(B),acosd(C)]
计算结果：
>> TRA_FF
cos_value =
-0.1178 0.9718 0.2043
angle_value =
96.7623 13.6365 78.2143
前置后驱：
Jxx=4.76; Jyy=11.97; Jzz=10.47;
Jxy=-0.23; Jzx=1.13; Jyz=0.63;
M=[Jxx,-Jxz,-Jzx;-Jxy,Jyy,-Jyz;-Jzx,-Jyz,Jzz];
N=inv(M);
p=sqrt(N(1,1)^2+N(2,1)^2+N(3,1)^2);
A=N(1,1)/p;
B=N(2,1)/p;
C=N(3,1)/p;
cos_value=[A,B,C]
angle_value=[acosd(A),acosd(B),acosd(C)]
计算结果：
TRA_FR
cos_value =
0.9942 -0.0135 0.1065
angle_value =
6.1622 90.7735 83.8869
以上代码参考郭荣、章桐《汽车动力总成悬置》一书。
该代码成立的条件是惯量参数是在质心坐标系下的情况，如果是整车坐标系，由于动力总成在整车中的摆放有仰角和偏角，需要获取实际的曲轴向量，建议用Excel小软件。
图2 TRA计算软件
图3 TRA与悬置硬点关系图
