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Measuring the forces and moments at each wheel during braking and cornering

  • Forces Fx Fy Fz
  • Moments Mx My Mz
  • Wheel speed and angle
  • Side slip angle
Instrumented passenger car on a test track with wheel force transducers on its wheels
A passenger car on a test track with LW65 wheel force transducers on its four wheels. Michigan Scientific photo.

In brief

A wheel force transducer replaces the wheel center and measures the longitudinal, lateral and vertical force at that wheel, the camber moment, the wheel torque and the steer torque, each as an independent signal, with the wheel angle, the wheel speed and the X and Z accelerations. The signals are digitized on the wheel, leave it through a slip ring or by telemetry, and the CT2 interface box resolves them into vehicle axes in real time. With one transducer per wheel, a brake test, a lane change or a sharp turn is read wheel by wheel.

6
independent load signals per wheel
15.5 to 700 kN
radial force capacity, LW series
0.17°
angular resolution of the wheel angle, slip ring versions

Six loads at the wheel

Longitudinal forces, along the vehicle, serve the analysis of acceleration, braking and fuel consumption. Lateral forces, across the vehicle, serve cornering, handling and stability. Vertical forces, from gravity and the ground, serve ride comfort, vibration and road contact. The three moments, roll, pitch and yaw, show how the suspension reacts to turns, accelerations and road conditions.

All these loads reach the vehicle through its wheels, on a part that rotates and steers. The transducer measures the six components at the wheel center, separately from one another, and the interface box expresses them in the axes of the vehicle with the wheel angle at every instant.

The six load components measured at the wheel center A wheel seen in three-quarter view, with the transducer ring at its center. Three forces: Fx along the vehicle, Fy along the axle, Fz vertical. Three moments: Mx about the longitudinal axis, My about the axle, which is the drive and brake torque, and Mz about the vertical axis. Fz Fx Fy Mx My Mz Six components at the wheel center, vehicle axes
The six components at the wheel center: the forces Fx, Fy, Fz and the moments Mx, My, Mz, expressed in vehicle axes by the interface box.

Instrumentation

TransducerLW series, four-arm strain gage bridges, one independent signal per component
Capacity, radial15.5 to 700 kN · 50 kN on the LW12.8-50 and 65 kN on the LW65 for passenger cars and SUVs
Non-linearity≤ 0.2 % FS on Fx, Fz and My (LW12.8-50) · cross-axis sensitivity after correction < 0.5 % FS
Also measuredwheel angle at 0.17° resolution, wheel speed, X and Z acceleration
Mountingbetween a hub adapter and a rim adapter made for the vehicle; the stator held by a restraint rod, or by the stator angle correction device on steered wheels
Signal transmissionslip ring with spinning amplifier, or telemetry; swappable on the same transducer
Interface boxCT2: coordinate transformation and crosstalk compensation in real time, analog, CAN and Ethernet outputs
Environmentweatherproof, temperature compensated, −40 to 125 °C; IP67 on the LW65

Procedure

  1. 01

    Fit the transducer in place of the wheel center

    The transducer mounts between a hub adapter and a rim adapter made for the vehicle.

    LW series wheel force transducers
  2. 02

    Hold the stator

    On a steered wheel, the stator angle correction device corrects the wheel angle in real time, so the loads are resolved with the right angle.

    Stator restraint and angle correction
  3. 03

    Resolve the loads in the interface box

    The CT2 box does the coordinate transformation and the crosstalk compensation in real time, with analog, CAN and Ethernet outputs.

  4. 04

    Add the side slip angle if needed

    The TrueSlip optical sensor, on a wheel or on the body, gives the side slip angle on CAN. It can be mounted within the wheel force transducer assembly.

    TrueSlip side slip sensor

Double lane change on a class 8 truck

The same setup records brake tests, lane changes, sharp turns and normal driving. In this acceptance test on a class 8 truck, the right front wheel carries an LW-2T-100K. The lateral force rises as the truck leaves its lane, reverses as it returns, and the chart notes an over-correction at the end of the manoeuvre; the vertical force is recorded alongside.

Chart of longitudinal, lateral and vertical wheel force over time during a double lane change on a class 8 truck
Right front wheel of a class 8 truck during a double lane change at 61 km/h (38 mph): longitudinal, lateral and vertical force. Michigan Scientific chart, forces in lb.

Use of the data

Wheel force data is used in work on tires, brakes, suspension, comfort, aerodynamics, powertrain and vehicle dynamics models, and to compare vehicles with one another. On electric vehicles it serves efficiency work, and it feeds the development of the safety and control functions and of autonomous driving.

Camouflaged sports car prototype on a circuit, with wheel force transducers on its wheels
A camouflaged prototype on a circuit, with wheel force transducers on its four wheels. Michigan Scientific photo.

Result

Three forces, three moments, wheel speed and angle at each wheel, in vehicle axes, recorded through the manoeuvre. Each behaviour of the vehicle, from braking to cornering, is read in the loads at the wheels that produce it.

Frequent questions

What does a wheel force transducer measure in a vehicle dynamics test?

The longitudinal, lateral and vertical force at the wheel, the camber moment, the wheel torque and the steer torque, each as an independent signal, with the wheel angle, the wheel speed and the X and Z acceleration.

How is the side slip angle measured during a handling test?

With the TrueSlip optical sensor mounted on a wheel or on the vehicle body. It can be mounted within the wheel force transducer assembly and outputs the angle on CAN.

Can wheel forces be measured on a wet track?

Yes. The transducers are weatherproof and temperature compensated, and the LW65 is rated IP67.

How do the signals get from a rotating wheel to the data recorder?

They are digitized on the wheel, leave it through a slip ring or a telemetry link, and reach the CT2 interface box, which does the coordinate transformation and the crosstalk compensation in real time, with analog, CAN and Ethernet outputs.

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