Division 4.4.6 Uncertainty calculation

United Kingdom

The total uncertainty U_T,loss of the torque loss shall be calculated based on the following parameters:

i..

Temperature effect
ii..

Parasitic loads
iii..

Uncertainty (incl. sensitivity tolerance, linearity, hysteresis and repeatability)

The total uncertainty of the torque loss (U_T,loss) is based on the uncertainties of the sensors at 95 % confidence level. The calculation shall be done for each applied sensor (e.g. three machine lay out: U_T,in, U_T,out,1, U_Tout,2) as the square root of the sum of squares (‘Gaussian law of error propagation’).

U_{T,loss} = \sqrt{U_{2}^{T,in} + \sum {(\frac{U_{T,out}}{i_{gear}})}^{2}}

U_{T,in ∕ out} = 2 \times \sqrt{U_{2}^{TKC} + U_{2}^{TK 0} + U_{2}^{cal} + U_{2}^{para}}

U_{TKC} = \frac{1}{\sqrt{3}} \times \frac{w_{tkc}}{K_{ref}} \times Δ K \times T_{c}

U_{TK 0} = \frac{1}{\sqrt{3}} \times \frac{w_{tk 0}}{K_{ref}} \times Δ K \times T_{n}

U_{cal} = 1 \times \frac{w_{cal}}{k_{cal}} \times T_{n}

U_{para} = \frac{1}{\sqrt{3}} \times w_{para} \times T_{n}

w_para = sens_para * i_para

where:

U_T,in/out

Uncertainty of input/output torque loss measurement separately for input and output torque; [Nm]

i_gear

Axle gear ratio [-]

U_TKC

Uncertainty by temperature influence on current torque signal; [Nm]

w_tkc

Temperature influence on current torque signal per K_ref, declared by sensor manufacturer; [%]

U_TK0

Uncertainty by temperature influence on zero torque signal (related to nominal torque) [Nm]

w_tk0

Temperature influence on zero torque signal per K_ref (related to nominal torque), declared by sensor manufacturer; [%]

K_ref

Reference temperature span for tkc and tk0, declared by sensor manufacturer; [°C]

ΔK

Absolute difference in sensor temperature measured at torque sensor between calibration and measurement; If the sensor temperature cannot be measured, a default value of ΔK = 15 K shall be used [°C]

T_c

Current/measured torque value at torque sensor; [Nm]

T_n

Nominal torque value of torque sensor; [Nm]

U_cal

Uncertainty by torque sensor calibration; [Nm]

w_cal

Relative calibration uncertainty (related to nominal torque); [%]

k_cal

calibration advancement factor (if declared by sensor manufacturer, otherwise = 1)

U_para

Uncertainty by parasitic loads; [Nm]

w_para

sens_para * i_para

Relative influence of forces and bending torques caused by misalignment

sens_para

Maximum influence of parasitic loads for specific torque sensor declared by sensor manufacturer [%]; if no specific value for parasitic loads is declared by the sensor manufacturer, the value shall be set to 1,0 %

i_para

Maximum influence of parasitic loads for specific torque sensor depending on test set-up as indicated in section 4.2.3 and 4.2.4 of this annex.