November 2004

Table of Contents

A Magnetostrictive
Torque Sensor

A new fabrication technique solves the problem of an external magnetic field’s adverse effects on a magnetostrictive torque sensor.


In 1842, the English physicist James Joule observed that a sample of nickel changed shape when placed in a magnetic field. This effect is called magnetostriction. The reciprocal effect, the change in the magnetization of a material when subjected to a mechanical stress, is known as the Villari effect. If a helical magnetic field is applied to a material, then a twisting in the material is observed. This is the Wiedemann effect. The inverse of this is the Matteucci effect, which refers to the creation of a magnetic field when a material is subjected to a torque. Magnetostrictive materials' ability to convert magnetic energy into mechanical energy and vice versa makes them suitable for building both actuation and sensing devices.

Accurate sensing and measurement of torque is one of the primary objectives in the automotive industry, and the Villari effect can be used to satisfy this requirement. The operating principle of a magnetostrictive torque sensor (U.S. Patent #5351555) is shown in Figure 1 in the form of a noncontact sensor for use with rotating shafts.

Figure 1. In the classical magnetostrictive torque sensor, a coating of magnetostrictive material is rigidly attached to the shaft and an easy axis of magnetization is created in the tangential direction by mechanical stresses. The coating is then magnetized by passing a pulsed current through the shaft (A). A newer design replaces the single circularly polarized coating with one divided into two oppositely polarized circumferential regions. The coating is magnetized by means of two identical permanent magnets brought close to the shaft while the shaft is rotating slowly (B).

A magnetostrictive material coating is rigidly attached to the shaft. An easy axis of magnetization is created in the tangential direction by mechanical stresses. The coating is then magnetized by passing a pulsed current through the shaft. Transducer operation is based on the reorientation of the circumferentially directed remanent magnetization in the coating.

The remanent magnetization, the amount of magnetization that remains in a material after an externally applied field has been removed, is initially oriented in the tangential direction, and the magnetic field created by the shaft is zero. When torque is applied to the shaft, the remanent magnetization reorients and becomes increasingly helical as the torque value increases. This reorientation produces a magnetic field, proportional to the torque, to be detected by a nearby magnetic-field sensing device. The output signal from this device is conditioned in associated electronic circuitry to provide a signal that can be used in a control unit. The drawback is that the generated magnetic fields are weak and the orientation of the magnetization in the coating can be affected by an external axial magnetic field-Earth's, for instance.

One way to overcome this problem is to replace the single circularly polarized coating with a coating divided into two oppositely polarized circumferential regions (U.S. Patent #5520059). The coating is magnetized using two identical permanent magnets brought close to the shaft while the shaft is rotating slowly.

The most important requirements for the sensor are:

  • Unambiguous indication of applied torque for the life of the shaft
  • Operation at temperatures between -40ºC and 150ºC
  • Immunity to EMI

Figure 2.
Material Saturation Magnetostriction
Ni -4 × 10–5
Ni 60% – Fe 40% 2.5 × 10–5
(Co ferrite)
1.1 × 10–4
(1.6 – 2.4) × 10–3
The suitability of a particular material for use in this type of application is determined by its saturation magnetostriction ls, defined as the fractional change in length as the magnetization increases from zero to its saturation value. Some practical materials for torque sensors are given in Figure 2. The coating's magnetic behavior under an applied torque can be modeled using an approach based on minimization of the sum of magnetoelastic and demagnetizing energies in the coating. For a coating with negligible residual radial strain, the dominant terms in the magnetic energy are:

equation (1)


1 and 2   =   direction cosines of magnetization along the X and Y coordinate axes (1 = cos, 2 = sin)
B1 and B2   =   magnetoelastic coefficients that express the coupling between the strains and the magnetization
ND   =   demagnetizing factor
exx   =   residual hoop strain
eyy   =   residual axial strain
exy   =   shear strain (proportional to applied torque)
Mr   =   remanence acquired by the coating after magnetization

By minimizing the energy (u/ = 0), the equilibrium orientation of the magnetization under different values of the applied torque can be obtained and the axial magnetic field created can be calculated.

Figure 3 shows the calculated value of B with torque for a nickel coating with a residual strain of 1200 µstrain, magnetized by pulsed current as in described in Figure 1A.

Figure 3. The B values are calculated for applied torque on a Ni coating having a built-in residual strain of 1200 µstrain.

The observation point is at the center of the magnetized section and at 0.35 mm from the coating surface. The parameters used in the calculation are D0 = 25.1 mm, Di = 24.1 mm and L = 28 mm.

Figure 4 shows the measured values of B and induced strain for the nickel coating, with torque cycling between -8 and 8 N·m (the units for magnetic field are arbitrary).

Figure 4. The induced strain and magnetic field generated with applied torque are measured.

It can be seen that both magnetic field and transferred strain (which is proportional to the applied torque) are highly linear under cycling torque loading.

In conclusion, by using a magnetostrictive material, torque values can be measured in a reliable, cost-effective manner. Magnetostriction is an inherent material property that will not degrade with time.

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