Division 3.3.9 Measurement uncertainty

United Kingdom

The part of the calculated total uncertainty U_T,loss exceeding 5 % of T_loss or 1 Nm (ΔU_T,loss ), whichever value of ΔU_T,loss is smaller, shall be added to T_loss for the reported torque loss T_loss,rep . If U_T,loss is smaller than 5 % of T_loss or 1 Nm, then T_loss,rep = T_loss .

T_loss,rep = T_loss + MAX (0, ΔU_T,loss )

ΔU_T,loss = MIN ((U_T,loss – 5 % * T_loss ), (U_T,loss – 1 Nm))

For each measurement set, the total uncertainty U_T,loss of the torque loss shall be calculated based on the following parameters:

(1)
Temperature effect
(2)
Parasitic loads
(3)
Calibration error (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 as the square root of the sum of squares (‘Gaussian law of error propagation’).

$U_{T,loss} = \sqrt{{U_{T,in}}^{2} + {(\frac{U_{T,out}}{i_{gear}})}^{2}}$
$U_{T,in ∕ out} = 2 \times \sqrt{u_{2}^{TKC} + u_{2}^{TK 0} + u_{2}^{cal} + u_{2}^{para}}$
$u_{TKC} = \frac{1}{\sqrt{3}} \times \frac{w_{tkc}}{K_{ref}} \times Δ K \times T_{c}$
$u_{TK 0} = \frac{1}{\sqrt{3}} \times \frac{w_{tk 0}}{K_{ref}} \times Δ K \times T_{n}$
$u_{Cal} = 1 \times \frac{W_{cal}}{k_{cal}} \times T_{n}$
$u_{para} = \frac{1}{\sqrt{3}} \times w_{para} \times T_{n}$
w_para = sens_para * i_para

where:

T_loss

Measured torque loss (uncorrected) [Nm]

T_loss,rep

Reported torque loss (after uncertainty correction) [Nm]

U_T,loss

Total expanded uncertainty of torque loss measurement at 95 % confidence level [Nm]

u_T,in/out

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

i_gear

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 u_TKC and u_TK0, w_tk0 and w_tkc, declared by sensor manufacturer [K]

ΔK

Difference in sensor temperature between calibration and measurement [K]. If the sensor temperature cannot be measured, a default value of ΔK = 15 K shall be used.

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 setup (A/B/C, as defined below).

A) 10 % in case of bearings isolating the parasitic forces in front of and behind the sensor and a flexible coupling (or cardan shaft) installed functionally next to the sensor (downstream or upstream); furthermore, these bearings can be integrated in a driving/braking machine (e.g. electric machine) and/or in the transmission as long as the forces in the machine and/or transmission are isolated from the sensor. See figure 3.

B) 50 % in case of bearings isolating the parasitic forces in front of and behind the sensor and no flexible coupling installed functionally next to the sensor; furthermore, these bearings can be integrated in a driving/braking machine (e.g. electric machine) and/or in the transmission as long as the forces in the machine and/or transmission are isolated from the sensor. See figure 4.

C) 100 % for other setups