Torque sensor using amorphous magnetostrictive ribbons

Materials Science and Engineering, A181/A182 (1994) 1378-1382

1378

Torque sensor using amorphous magnetostrictive ribbons Hiroyuki Hase, Rihito Shoji and MasayukiWakamiya Materials and Devices Research Laboratory, Matsushita Electric Industrial Co. Ltd., 1006, Kadoma, Kadoma-shi, Osaka 571 (Japan)

Abstract A torque sensor using amorphous magnetostrictive ribbons was developed. An inaccuracy of less than 1% in the temperature range - 10 to 50 °C was achieved by controlling the bias compressive stress of glued amorphous ribbons, which is induced by the difference between the thermal expansion of the shaft and the glued amorphous ribbons during the glueing process. In this kind of torque sensor, a rotation magnetization model can be used to explain the sensor output characteristics when the compressive bias stress is relatively large.

1. Introduction Amorphous magnetic alloys have many attractive features, including large mechanical strength and soft magnetic properties. Fe-based amorphous magnetic alloys possess a remarkably large magnetomechanical effect. Several types of torque sensor [1, 2] employing the magnetomechanical effect of amorphous magnetostrictive ribbons have been proposed. A torque sensor composed of a shaft, amorphous strips glued onto the shaft and coils is considered to be suitable for practical use because of its simple structure. We have solved several problems, such as the temperature characteristics, durability and manufacturing technique, to put the sensor to practical use for controlling a screw driver system (Pana Robo SRA). However, the magnetomechanical effect of the glued amorphous strip has not yet been fully analysed. We have reported previously that the "compressive bias stress" caused by the thermal expansion difference between the shift and the amorphous strip during the glueing process is useful to control the temperature characteristics of the sensor [3, 4]. In this paper, the influence of the compressive bias stress is described assuming a rotation magnetization model. In addition, the performance of the developed sensor is shown.

the shaft making angles of + 45 ° and - 4 5 ° with respect to the longitudinal direction of the shaft. Coils 1 and 2 are concentrically wound around the glued strips 1 and 2 to make elements 1 and 2 respectively [2]. The torque applied to the shift induces tensile and compressive stresses, + at and - at, to +45 ° and - 4 5 ° with respect to the longitudinal direction of the shift, as shown in Fig. 2. Under the influence of the amorphous strip shape, the magnetic field and the stress, the permeabilities of strips 1 and 2 change in an opposite manner on application of torque. The magnitude and direction of the applied torque can be obtained by detecting the output voltage Vo, which corresponds to the difference in the end voltages of elements 1 and 2, using the electric circuit shown in Fig. 1.

3. Experimental details The diameter of the titanium or copper shaft was 11.8 mm. The Fe-based amorphous magnetic alloy ribbon was fabricated by the single roller method and

-I

10kHzI 2. Structure and principles The structure of the torque sensor and the detecting electric circuit are shown in Fig. 1. Amorphous strips 1 and 2 are made of Fe-based amorphous magnetic alloy with positive magnetostriction. These are glued onto 0921-5093/94/$7.00

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Fig. 1. The structure and electric circuit of the torque sensor. © 1994 - Elsevier Sequoia. All rights reserved

H. Hase et al.

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Torque sensor using amorphous magnetostrictive ribbons

etched chemically into a strip. The strip was 3.2 mm wide, 35 mm long and 20 ,um thick. It was annealed at 430 °C (between the Curie temperature and the crystallization temperature) for 30 min to obtain the same curvature as the shaft. The strips were glued onto the shaft helically making angles of 45 ° and - 4 5 ° with respect to the longitudinal direction of the shaft. Coils were would around the strips to make elements 1 and 2 as shown in Fig. 1. Glueing was carried out at temperatures in the range 100-180 °C using a bismaleimidetriazine resin (BT resin) or an epoxy resin. The following three samples were prepared to achieve a wide range of compressive bias stress in the glued strips: sample 1, amorphous strips were glued onto the copper shaft at 120 °C using the epoxy resin; sample 2, amorphous strips were glued onto the titanium shaft at 100 °C using the epoxy resin; sample 3, amorphous strips were glued onto the titanium shaft at 180 °C using the BT resin. Vo was measured in an alternating magnetic field (10 kHz) using coils of 13 mm in diameter, 5 mm in length with 150 turns. The magnitude of the exciting current of the coils was controlled to keep the magnetic field at 400 A m - ~at the centre of the coil. The sample was placed in a temperature-controlled oven for 1 h. Vo was then measured for - 5 to + 5 Nm torque at temperatures in the range - 1 0 - 1 0 0 °C. The saturation magnetization (Is) and the saturation magnetostriction constant (2s) were measured by a vibrating sample magnetometer (VSM) and a strain gauge. The characteristics of the shafts and the Fe-based amorphous strip are listed in Table 1. Observation of the magnetic

domain structure of the glued strip was carried out using the classic ferromagnetic colloid technique. To evaluate the compressive bias stress, the strain parameter e was introduced as e = A a A T × 106 (p.p.m.)

(1)

where Aa (°C- 1) and A T (°C) are the absolute values of the difference between the thermal expansion coefficients of the strip and the shaft, and the difference between the glueing and measuring temperatures respectively.

4. Analysis The permeability of the glued strip is influenced by the stress a t caused by the torque T o and the bias stress o b. The stresses + at were analysed for element 1 (Fig. 1). For element 2, the same results can be achieved by changing the sign of the applied torque TO. This analysis was based on the following assumptions. (a) The glued strip has a planar stress state as shown in Fig. 2, because the thickness of the strip is negligibly small compared with the diameter of the shaft. (b) Young's modulus and Poisson's ratio for the strip are equal to those of the shaft. Based on assumption (a), the coordinates are taken as shown in Fig. 2, where the Y, Z and X directions are the longitudinal direction of the shaft, the thickness direction of the glued strip and the perpendicular direction to the Y - Z plane respectively. The direction of torque To was defined as ( + ) for + a t as shown in Fig. 2. The value of ot can be expressed by o t = 16 To/(:rd 3)

X

1379

(2)

where d is the diameter of the shaft. In addition to + at, the compressive bias stress - o b is induced in the glued strip during the glueing process, o b can be expressed by eqn. (3)using the parameter e defined in eqn. (1) Fig. 2. The principal stresses caused by torque and the coordinates used for analysis.

TABLE 1. Characteristics of shafts and amorphous alloy Characteristic

Amorphous alloy

Titanium metal

Copper metal

9.4 x 10 -6 16 × 10 -6 Thermal expansion 7.9 × 10 -6 coefficient a (°C- ~) Young's modulus -~ 120 116 120 E (GPa) Poisson's ratio v 0.3 0.3 0.3 Saturation magnet1.14 ization I s (T) Magnetostriction 20 × 10- 6 constant 2s

o b = Ee × 1 0 - 6 / ( 1 - v)

(3)

where E and v are the Young's modulus and Poisson's ratio of the amorphous strip. We previously reported that the magnetomechanical effect is affected by the magnetic domain structure of the strip. Assuming that the angle between the direction of the tensile stress o and the direction of magnetization (I~) is 0, the magnetoelastic energy E~ is given by [5] E¢ = - 32sO cos2( 0)/2

(4)

When the bias stress o b is compressive and 2 s of the glued amorphous strip is positive, the magnetization (Is) tends to turn in the Z direction to lower the energy E~. Figure 3 shows the cross-section of a glued strip in

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Torque sensor using amorphous magnetostrictive ribbons

the a-a plane shown in Fig. 2. In the case of H = 0 and TO= 0, the domain structure of the glued strip is that shown in Fig. 3(a) under the influence of compressive bias stress - a b , where a closure domain appears to lower the magnetostatic energy at the surface. Under the conditions H # 0 and TO¢ 0, the magnetization (Is) is assumed to rotate from the Z direction to the [a, r, 7] direction as shown in Fig. 3(b), where a, fl and 7 are the directional cosines of I S. The internal energy E a of the glued strip can be expressed by

~ 0 ~-

[2Kb +/s2(NL + Nw)/(2/~ o)]/~H 4flo[Kb - K o + NLIs2/(2kto)][Kb + K o + Nwls2/(21~o)] (9) In the Y direction, the magnetization I and the relative magnetic susceptibility ~rl for element 1 can be calculated by I = Isfl o = ,U0Zrl H

(10)

Ea = _Kb72 _ [Ko(a +t3) 2 - K a ( a - f l )2] 2 Is2[NL(a+fl) 2 + Nw(a-fl) 2]

4/~o

[2Kb +/~2(NL + Nw)/(2/z 0)]/s2

(5)

4/~o[Kb - K , , + NeI~2/(2,Uo)][Kb + Ko + NwI,2/(2,Uo)] (11)

where K b and Ko are expressed as 32s eE x 1 0 6 Kb ~ --

2

(6)

(l-v)

g a - 32s 16 To 2 :rd 3

(7)

Zr2 for element 2 can be obtained by changing the sign of Ko in eqn. (11). Supposing that Zr~ and ~r2 are proportional to the values of inductance, or the end voltages of elements 1 and 2, the output V(cal) can be expressed by V(cal) =

N L and Nw are the demagnetization factors with respect to the length and width directions of the glued strip respectively. Differentiating the internal energy E a with respect to a and r , the directional cosine flu from the Y axis, which minimizes E a , c a n be calculated OE~ --=0

0E a

and

-0

(8)

Z r l - - Z r 2 oC V o

(12)

5. Results and discussion

The magnetic domain structure of the glued strip of sample 1 is shown in Fig. 4, which was observed from the Z direction under the conditions of H = To = 0. Cells of 3-5 /~m in diameter were observed on the surface of the glued strip. Livingston [6] observed cells similar to those shown in Fig. 4 and proposed the domain structure shown in Fig. 3(a). Based on this

(a) H=O,To=O Is

-.b

closure domain

\

/

=::>

jb ~

Is

Z

X

i/

Z a ~

(b) It:~0, T0~0

~a

Z

X

Fig. 3. The magnetic domain structure model of the glued amorphous strip,

Fig. 4. Photograph of the magnetic domain structure observed from the Z direction.

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T o r q u e sensor using a m o r p h o u s magnetostrictive r i b b o n s

result, it was considered to be valid to assume the magnetic domain structure model shown in Fig. 3(a). In Fig. 5, V o vs. T O characteristics of samples 1 and 2, with values of e defined by eqn. (1), are shown at a torque range of - 5 to 5 Nm. The change in Vo caused by the torque To from 0 to 5 Nm decreases with increasing e value. In Fig. 6, the calculated sensor outputs V(cal), defined by eqn. (12), are shown at each bias strain e(cal). The calculation of V(cal) was carried out at the e(cal) range of 90 to 880 p.p.m, using the data shown in Table 1. Demagnetization factors NL= 1.62 x 10-4 and N w = 8.7 × 10- 3 were obtained theoretically [7]. Z.5

T

|

v

~ =30ppm/

0

-2.5 -5

0 Torque (Nm)

Fig. 5. C h a n g e in V o vs. T o characteristics c a u s e d by bias strain e.

¢

0

There are some differences between the curvatures of Vo and V(cal). Assuming that each e corresponds to e(cal)+ 170 p.p.m., measured Vo curves in the e range 350-880 p.p.m, in Fig. 5 can be almost explained by the rotation magnetization model. The discrepancy between e and e(cal) is considered to be caused by the inaccuracy of the data and the stress caused by shrinkage of the adhesive agents. However, the Vo vs. T,, characteristics in the e range 30-120 p.p.m, in Fig. 5 are not similar to those of V(cal) even if the mismatch between e and e(cal) is taken into account. We previously reported that magnetic domain wall displacement became active when e values were small [4]. Therefore, the rotation magnetization model is not applicable in the e range 30-120 p.p.m. Both magnetization processes, magnetic wall displacement and rotation, are assumed to proceed simultaneously in the glued strip in this e range. It is obvious in Fig. 5 that a relatively large output voltage Vo can be obtained in the e range 120-350 p.p.m. Sample 3 was prepared to realize this e range. The sensitivity (defined as A V,,/A To)increased with an increase in temperature. The compensation of the V~, vs. T o temperature characteristics was achieved by connecting an amplifier (with a thermistor as a feedback resistor) to the output Vo drawn in Fig. 1. The gain of the amplifier was controlled from 1.1 to 10 with increasing temperature from - 10 to 50 °C. The compensated V o vs. T o temperature characteristics of sample 3 are shown in Fig. 7, where the e range was 225-315 p.p.m. Relatively good linearity and large sensitivity were obtained. The inaccuracy of the sensor was less than 1% in the temperature range - 10-50 °C, which was satisfactory for practical use. 2.5

700

v >

1381

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e =Z25~315ppm

v

)

~

0

880 700

/

-700

,

-~

-2.5

. . . .

0

5

Torque(Nm) Fig. 6. Theoretically calculated c h a n g e in V(cal) vs. T O c h a r a c t e r istics c a u s e d by bias strain e(cal).

, -5

,

,

,

, 0

torque

. . . .

(Nm)

Fig. 7. V o vs. T o characteristics o f s a m p l e 3 in the t e m p e r a t u r e range - 1 0 - 5 0 °C.

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Torquesensor using amorphous magnetostrictive ribbons

6. Conclusions

References

A torque sensor with an inaccuracy of less than 1% in the temperature range - 1 0 - 5 0 °C was achieved by controlling the bias compressive stress, induced by the difference between the thermal expansion of the shaft and the glued amorphous strip during the glueing process. In this type of torque sensor, the rotation magnetization model can be used to explain the sensor output characteristics when the bias stress is relatively large.

1 K. Harada, I. Sasada, T. Kawajiri and M. Inoue, IEEE Trans. Magn., •8(6)(1982) 1767. 2 I. Sasada, A. Hiroike and K. Harada, IEEE Trans. Magn., 20 (5)(1984)951. 3 H. Hase and M. Wakamiya, Technical Digest 8th Sensor Symposium, Tokyo, 10-11 May, 1989, The Institute of Electrical Engineers of Japan, Tokyo, 1989, p. 279. 4 H. Hase and M. Wakamiya, IEEE Trans. J. Magn. Jpn., 5 (8) (1990)697. 5 H. T. Savage and M. L. Spano, J. Appl. Phys., 53 (11) (1982) 8092. 6 J.D. Livingston, Phys. Status SolidiA,56 (1979) 637. 7 J.A. Osborn, Phys. Rev., 67(11, 12)(1945)351.