Methods for elimination of crosstalk and inertial effects in bicycle and
motorcycle steer torque estimation
Jason K. Moore and Mont Hubbard
University of California, Davis
November 13, 2013
Steering and Stability of Single-Track Vehicles
Wilson-Jones, R. A.; 1951
Predicted counter torque for entering a turn
Pointed out that torques were very light and difficult to measure
Experimental Study on the Stability and Control of Single-Track Vehicles
Kondo, M.; 1955
Probably first recorded measurement of steer torque. Steady turns, turns,
and figure 8's.
Man-Machine Dynamics in the Stabilization of Single-Track Vehicles
Eaton, D. J.; 1973
Motorcycle Handling
Weir, David H., Zellner, John W., and Teper, Gar; 1979
Quantification of Structural Loading During Off-road Cycling
de Lorenzo, D. S.; 1997
Potential first bicycle steer torque measurements
Larger torques about longitude compared to steer axis
Experimental investigation and simulation of motorcycle turning
performance
D. Bortoluzzi, A. Doria and R. Lot; 2000
6 DoF Force/Torque Sensor
Kageyama, et. al
Bicycle Torque Sensor Experiment
Kok Y. Cheng, David Bothman, and Karl J. Åström; 2003
Rider analysis using a fully instrumented motorcycle
Evertse, M. V. C; 2010
Uses bi-axial force transducers at each grip.
Inventory of bicycle motion for the design of a bicycle simulator
van den Ouden, J. H.; 2011
Measurement Design Types
Floating handlebars
Torque transducers along axis
Cantilever beams
Axial load cells perpendicular to axis
Fixed handlebars
Grip force transducers
6 DoF sensor below handle bars
Design Issues
Susceptible to loads other than steer torque: i.e. crosstalk
Calibration with only a single axial torque
Not sensitive enough
Calibration with only steer torque, not full loading
Inertial compensation if mass/inertia between riders hands and
transducer
Redo Cheng's Steer Torque Wrench Experiments
Torque Wrench Results
New design
Not sexy, but completely eliminates cross talk. Pure steer torque.
\(\pm17\) Nm range
Steer Dynamics
$$
\sum \bar{T}^{G/s} = {}^N\dot{\bar{H}}^{G/g_o} +
\bar{r}^{g_o/s} \times m_G\,{}^N\bar{a}^{g_o}
$$
Steer Dynamics
Angular Momentum
$$^N\bar{H}^{G/g_o} = I^{G/g_o} \cdot {}^N\bar{\omega}^G$$
Measured rear frame angular velocity
$$^N\bar{\omega}^B = w_{b1}\hat{b}_1 + w_{b2}\hat{b}_2 +
w_{b3}\hat{b}_3$$
Measured body fixed front frame angular velocity
$$
^N\bar{\omega}^G = (w_{b1}c_\delta + w_{b2}s_\delta)\hat{g}_1 +
(-w_{b1}s_\delta + w_{b2}c_\delta)\hat{g}_2 +
w_{h3}\hat{g}_3
$$
Measure linear acceleration of rear frame
$$^N\bar{a}^v = a_{v1}\hat{b}_1 + a_{v2}\hat{b}_2 + a_{v3}\hat{b}_3$$
Rider Applied Steer Torque
$$
\begin{align}
T_{\delta} =
& I_{G_{22}} \left[ \left( -w_{b1} s_\delta + w_{b2} c_\delta \right)
c_\delta + w_{b2} s_\delta \right] + I_{G_{33}} \dot{w}_{g3} + \nonumber \\
& I_{G_{31}} \left[ (-w_{g3} + w_{b3} ) w_{b1} s_\delta +
(-w_{b3} + w_{g3}) w_{b2} c_\delta +
s_\delta \dot{w}_{b2} + c_\delta \dot{w}_{b1} \right] + \nonumber \\
& \left[ I_{G_{11}} (w_{b1} c_\delta + w_{b2}s_\delta) +
I_{G_{31}} w_{g3} \right] \left[-w_{b1} s_\delta +
w_{b2} c_\delta \right] + \nonumber \\
& d m_G \left[ d (-w_{b1} s_\delta + w_{b2} c_\delta)
(w_{b1} c_\delta + w_{b2} s_\delta) + d \dot{w}_{g3} \right] - \nonumber \\
& d m_G \left[-d_{s1} w_{b2}^{2} + d_{s3} \dot{w}_{b2} -
(d_{s1} w_{b3} - d_{s3} w_{b1}) w_{b3} + a_{v1} \right] s_\delta + \nonumber \\
& d m_G \left[d_{s1} w_{b1} w_{b2} + d_{s1} \dot{w}_{b3} +
d_{s3} w_{b2} w_{b3} - d_{s3} \dot{w}_{b1} + a_{v2} \right]
c_\delta + \nonumber \\
& T_U + T_M
\end{align}
$$
Estimation of bearing friction
Estimation of bearing friction
VIDEO
Estimation of bearing friction
$$T_B = T_{Bc} + T_{Bv}$$
Coulomb
$$
T_{Bc} = t_B \operatorname{sgn}(\dot\delta) =
\begin{cases}
t_B & \textrm{if $\dot{\delta}>0$}\\
0 & \textrm{if $\dot{\delta}=0$}\\
-t_B & \textrm{if $\dot{\delta}<0$}
\end{cases}
$$
Viscous
$$T_{Bv} = c_B \dot{\delta}$$
EoM
$$
I_{HF} \ddot{\delta} + c_B \dot{\delta} + t_B
\operatorname{sgn}(\dot{\delta}) + 2 k l^2 \delta = 0
$$
Estimated values
$$c_B = 0.34 \pm 0.04 \textrm{N} \cdot \textrm{m} \cdot s^2$$
$$t_B = 0.15 \pm 0.05 \textrm{N} \cdot \textrm{m}$$
Estimation of handlebar inertia
$$I_{HF} = 0.1297+/-0.0005 \textrm{kg}\cdot \textrm{m}^2$$
Compensation
Torque Compensation
359 runs
Statistic
Median
Maximum
Coefficient of Determination
0.73
0.82
Maximum Error
2.45
6.59
RMS of the Errors
0.47
0.90
Conclusions
Elimination or compensation of the cross talk is essential for accurate
torque measurements.
With the standard sensors used for kinematics, the measurements needed
for inertial compensation is available.
Inertial compensation is important if there is significant inertia
about the steer axis above your sensor and/or your steer rotation
acceleration is high.
Steering column bearing friction can be estimated with Coulomb and
viscous friction.
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