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Design of shape memory alloy (SMA) coil springs for actuator applications
5 Design of shape memory alloy (SMA) coil springs for actuator applications T. ISHII, Sogo Spring Mfg Co. Ltd, Japan
Abstract: Titanium–nickel (TiNi) shape memory alloys (SMAs) are used in the form of coil springs in most products because the coil springs generate a large stroke and a high recovery force. Another advantage of using the SMA springs is that they can function as actuators as well as sensors. The SMA spring operates as a two-way actuator by the combination of a bias spring. This chapter introduces the design of the SMA spring and SMA actuator and the manufacturing process of SMA spring. Key words: spring, actuator, manufacturing process.
5.1
Introduction
Since the shape memory effect (SME) in the TiNi shape memory alloy (SMA) was discovered, many products have been developed that use the properties of SMAs (Table 5.1). SMAs are used in a variety of applications such as automobiles, electrical and home appliances, and housing. Most of these products use SMAs in the form of coil springs where they function as an actuator as well as a temperature sensor. The advantage of a coil spring shape is its large stroke compared with a wire as shown in Fig. 5.1, which compares the stroke of a straight wire and a coil of 30 mm free length. When the strain of 1.0% is given, the coil expands 60.3 mm while the stroke of the wire is only 0.3 mm. In this chapter, the design of SMA springs and actuator, and the manufacturing processes for SMA springs are discussed.
5.2
Design of shape memory alloy (SMA) springs
5.2.1 Difference from usual springs Conventional springs are designed to perform within the elastic region where Hooke’s law is obeyed. This allows easy design of the spring since the shear modulus and spring constant do not change within the elastic region. On the other hand, the relation between the deflection and load is not linear for the SMA spring since both shear modulus and spring constant change with strain. Moreover the characteristic changes greatly with small 63 © Woodhead Publishing Limited, 2011
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Shape memory and superelastic alloys Table 5.1 Application of the shape memory effect Application
Shape
Gearless transmission valve Automatic oil valve of Shinkansen Automatic desiccators Louver of air conditioner Coffee maker Rice cooker Camera Miniature robot Anti-scald valve Water purifier Thermostatic mixing valve Bathtub adapter for adding water Underfloor ventilating hole Easy-release screws by SMA washer Rock splitter
Coil Coil Coil Coil Coil Coil Wire Wire Coil Coil Coil Coil Coil Washer Rod
Wire diameter: 1.0 mm Outside coil diameter: 8.0 mm Wire turns: 30 turns Free length: 30 mm γ = 1.0%
30 30 Wire shape
Coil shape
30.3 90.3
5.1 Comparison of strokes of SMAs between wire shape and coil shape.
change in the alloy composition, shape memory treatment condition and operating condition such as temperature and strain. However, for the design of an SMA spring, the formulae of conventional springs are used by assuming the shear modulus is constant if the strain is small.
5.2.2 Selection of materials and shear modulus The materials used for the SMA spring can be classified according to the operation temperature (Table 5.2). The operation temperature of the SMA
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Design of SMA coil springs for actuator applications
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Table 5.2 Classification
Material
Use temperature (°C)
TiNi–Fe, Co, Cr
−20–40
TiNi TiNi–Cu
Thermal hysteresis (°C) 2–3
20–80 40–100
Application Actuators for low temperature (underfloor ventilating hole) Thermostatic mixing valve Actuators for high temperature (rice cooker / coffee maker)
2–3 10–15
10
TiNi–Fe
Load (N)
8
TiNi
6
4
2
TiNi–Cu
0 –20
0
20
40
60
80
100
Temperature (°C)
5.2 Load–temperature curves obtained by the fixed strain tests of the SMA springs.
spring is determined by its transformation temperature. The results of thermal cycling tests at the fixed strain for the SMA springs listed in Table 5.2 are compared in Fig. 5.2. It is clear that the recovery temperature increases by the addition of Cu but decreases by the addition of Fe. The shear modulus of the SMA spring exhibits a drastic change when the spring is cooled below the martensitic transformation temperature or heated above its reverse transformation temperature since the shear modulus of high temperature phase (parent phase) is substantially higher than that of the low temperature phase (martensite phase). For instance, the shear modulus of martensite phase is about 8000 MPa while that of the
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Shape memory and superelastic alloys
parent phase exceeds 20 000 MPa in Ti–Ni alloys. In TiNi–Cu alloys, the shear modulus of martensite phase is almost 0 MPa while that of the parent phase is about 16 000 MPa. It is generally acknowledged that the control of transformation temperature is difficult: only 0.1 at.% difference in composition results from a change of the transformation temperature of about 10 K. Thus the shear modulus of the SMA spring is also sensitive to the alloy composition.
5.2.3 Design of helical springs The characteristic parameters for design of springs are shown in Fig. 5.3. The notations used in the calculation are listed in Table 5.3 and fundamental formulae used for the design of springs are listed as follows:
φd L
5.3 Characteristic parameters of design of a spring. Table 5.3 The sign to use for the calculation Symbol
Meaning
Unit
d D1 D2 D
Wire diameter Inside coil diameter Outside coil diameter Mean coil diameter D = (D1 + D2)/2 Total coils Active coils Free length Load Deflection Shear stress Shear strain Shear modulus Spring index Spring constant
mm mm mm mm
N n L P d t g G C k
– – mm N mm MPa % MPa – N/mm
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D2
P
R
D
P
D1
α
Design of SMA coil springs for actuator applications
67
d = 8PD3n / Gd4
5.1
g = dd / pnD2
5.2
t = 8PD / pd3
5.3
G=t/g
5.4
C=D/d
5.5
The load and the stroke at the high temperature are often demanded as a design condition of the SMA spring. An example of designing the compression spring when the following design conditions are given is shown below. Design conditions The deflection and the load at the high temperature: PH = 5 N at dH = 10 mm. Stroke: St = 5 mm (deflection at low temperature: dL = dH + St = 15 mm) The shear modulus: GH = 20 000 MPa at the high temperature. The shear modulus: GL = 8000 MPa at the low temperature. Shear strain at high temperature: gH = 0.6% Spring index: C = 8 Design procedure The shear stress at the high temperature becomes tH = 120 MPa from equation 5.4. Wire diameter d is calculated using equations 5.3 and 5.5. d2 = 8PC / ptH = (8 × 5 × 8) / (p × 120) d = 0.92 Hereafter, the wire diameter d is assumed to be ϕ1.0 mm. Then, mean coil diameter D becomes ϕ8.0 mm from equation 5.5. The number of coils n is obtained from equation 5.1: n = GHd4dH / 8PHD3 = (20 000 × 1.04 × 10) / (8 × 5 × 8.03) = 9.8 Finally we obtain the dimensions of the spring: 10 active coils with wire diameter of 1.0 mm and mean coil diameter of 8 mm. Shear strain gL at the low temperature is calculated from equation 5.2 using the dimensions of the spring: gL = ddL / pnD2 = (1.0 × 15) / (p × 10 × 8.02) = 0.0075
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Shape memory and superelastic alloys
Then, load PL at the low temperature is obtained from equation 5.1. PL = dLGLd4/8D3n = (15 × 8000 × 1.04) / (8 × 8.03 × 10) = 2.9 As for deflection dL at the low temperature, less than 0.8% of the total deflection is preferable. The free length L of the spring is an important parameter for considering applications. The solid length Hs of the spring becomes, for instance, 13 mm from the equation d[(n + 2) + 1] if we assume one turn at both end. Then free length L becomes 31.75 mm from the equation L = 1.25dL + Hs. The specification of the SMA spring to fill the abovementioned design conditions is summarized in Table 5.4.
5.2.4 Point of SMA spring design Shear strain gL at low temperature It is preferable to decide gL(= gmax) in the beginning with tmax in consideration of the fatigue life. It should be note that the SMA spring must be used within gmax. The recommended gmax of the SMA spring is as follows: gmax = 0.8% or less for TiNi spring and gmax = 2.0% or less for TiNi–Cu spring. Spring index C C = 6–10 is recommended. The change of C causes the change dimensions of the spring.
5.3
Design of shape memory alloy (SMA) actuators
Conventional SMA springs reveal the one-way shape memory effect. Therefore, in order to operate repeatedly, the bias stress is required. Figure 5.4 shows an example of two-way SMA actuator combined with a bias spring where an SMA spring and a bias spring are set so as to oppose each other (Ohkata and Suzuki, 1998). When the SMA spring is heated above Table 5.4 The specification of the SMA spring Wire diameter Mean coil diameter Total coils Active coils Free length dH = 10 mm dL = 15 mm gL (gmax)
1.0 mm 8.0 mm 12 10 31.8 mm PH = 5 N PL = 2.9 N 0.75%
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Design of SMA coil springs for actuator applications SMA spring
69
Bias spring
Hot P
St Cool P
5.4 An example of a two-way SMA actuator combined with a bias spring and its actuation by temperature change.
the reverse transformation temperature, the axis moves to the right since the recovery force of the SMA spring overcomes the force exerted on the bias spring. The axis returns to original position when the SMA spring cooled below the martensitic transformation temperature. As a result, the SMA spring with a bias spring actuates by heating and cooling. The two-way motion generates a stroke of St. In general, the deflection and load of the SMA actuator can be estimated using the diagram as shown in Fig. 5.5. Figure 5.5 shows load–deflection curves of an SMA spring and bias spring. The slopes of load–deflection curves of the SMA spring and bias spring are spring constants and have opposite signs since they move in opposite directions. If there is an external force, the stroke is shortened to St′ for instance. Figure 5.5 also shows that a larger stroke can be obtained when the spring constant is small.
5.4
Manufacturing of shape memory alloy (SMA) springs
5.4.1 Coiling The SMA coil springs are fabricated using an automatic coil forming machine, which is the same machine that is used for a conventional coil spring. However, a larger forming pressure is required to form a required
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Shape memory and superelastic alloys 10 High temperature 8 Bias spring
Load (N)
6 A
A′ Low temperature
4 B′ 2
B
St′ St
0 0
5
10 15 Deflection (mm)
20
25
5.5 A load–deflection diagram for the SMA spring and bias spring in the two-way SMA actuator.
shape due to a larger spring-back effect of the SMA wires compared with conventional stainless wires or piano wires. Therefore a material and tool which can endure without burning are required. The coil diameter and the free length are changeable according to the adjustment of processing speed and improvement of slipping of the material.
5.4.2 Shape memory treatment (heat treatment) The SMA spring is heat treated after coiling in order to memorize the shape. The heat treatment condition is determined on the basis of productivity (cost) and durability. The spring is fastened on a jig so as to maintain the spring shape during heat treatment and heat treated at about 350–550 °C, followed by air cooling or water quenching. Heat treatment time is from several minutes to 60 minutes. The heat treatment condition is determined to obtain suitable properties such as transformation temperature, hysteresis and durability, which are also dependent on the alloy composition. It it is necessary to adjust the heat treatment condition for each lot of products when mass production, since the properties of each lot are always same even if the processing condition is same. Figure 5.6 shows the effect of heat treatment temperature on the transformation temperature and loads of an SMA spring (Ti–50.6 at.% Ni, g = 0.8%). It can be seen that the transformation temperatures (Af and As) decrease with increasing heat treatment temperature. The transformation
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Design of SMA coil springs for actuator applications
60.0
40.0
10
PH
8
Af
6
AS 4
Load (N)
Transformation temperature (°C)
80.0
71
PL 20.0
2
Ti–50.6 at.% Ni g = 0.8% 0.0
0 410
440
470
500
Heat treatment temperature (°C)
5.6 The effect of heat treatment temperature on the transformation temperature and loads of a SMA spring (Ti–50.6 at.% Ni, g = 0.8%).
temperature width (Af–As), i.e., the difference of Af and As, also decreases with increasing heat treatment temperature. The load at a low temperature PL decreases but the load at high temperature PH remains constant, resulting in the difference (PH–PL) increases with increasing heat treatment temperature. Figures 5.7 and 5.8 show the load–temperature curves for a Ti–50.6 at.% Ni spring heat treated at 470 °C for 60 minutes and 500 °C for 60 minutes, respectively. It is clearly seen that the hysteresis of transformation temperature increases with increasing heat treatment temperature: the spring heat treated at 470 °C exhibits an extremely small hysteresis of 2 °C. These results imply that the heat treatment at 470 °C is preferable to 500 °C since the small hysteresis leads to better durability and longer fatigue life. Figure 5.9 shows the effect of heat treatment temperature on the transformation temperatures and loads for the Ti–50.6 at.% Ni spring applied a strain of 1.0%. Similar dependences of heat treatment temperature were observed: the transformation temperatures, hysteresis and load at low temperature decrease with increasing heat treatment temperature. The load– temperature curve for the Ti–50.6 at.% Ni spring to which a strain of 1.0% was applied is shown in Fig. 5.10. When comparing Figs. 5.10 and 5.7, it should be noticed that the hysteresis of transformation temperature became larger by increasing the strain. The composition of the spring also affects the properties and heat treatment condition. Figures 5.11 and 5.12 show the effect of heat treatment temperature on the transformation temperatures and loads for a Ti–49.6 at.% Ni–Fe spring and a Ti–41.0 at.% Ni–Cu spring, respectively. For the
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Shape memory and superelastic alloys 10 HT 470 °C × 60 min
Ti–50.6 at.% Ni g = 0.8%
Load (N)
8
6
4
2
0 0
10
20
30
40
50
60
70
80
Temperature (°C)
5.7 The load–temperature curve for a Ti–50.6 at.% Ni spring (g = 0.8%) heat treated at 470 °C for 60 minutes.
10 HT 500 °C × 60 min
Ti–50.6 at.% Ni 8
Load (N)
72
g = 0.8%
6
4
2
0 –10
0
10
20
30
40
50
60
70
Temperature (°C)
5.8 The load–temperature curve for a Ti–50.6 at.% Ni spring (g = 0.8%) heat treated at 500 °C for 60 minutes.
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Design of SMA coil springs for actuator applications 10 PH 60.0
40.0
8 Af 6
PL AS
Load (N)
Transformation temperature (°C)
80.0
73
4
20.0
2
Ti–50.6 at.% Ni g = 1.0% 0.0
0 410
440
470
500
Heat treatment temperature (°C)
5.9 The effect of heat treatment temperature on the transformation temperature and loads of a SMA spring (Ti–50.6 at.% Ni, g = 1.0%). 10
Load (N)
8
6
4
2
Ti–50.6 at.% Ni
HT 470 °C × 60 min g = 1.0%
0 0
10
20
30
40
50
60
70
80
Temperature (°C)
5.10 The load–temperature curve for a Ti–50.6 at.% Ni spring (g = 1.0%) heat treated at 470 °C for 60 minutes.
Ti–49.6 at.% Ni–Fe spring, the dependences of transformation temperatures and loads on the heat treatment temperature are similar to those of the binary Ti–Ni spring. However, the best heat treatment condition is different: the spring heat treated at 550 °C exhibited excellent properties with a very small hysteresis for the Ti–49.6 at.% Ni spring as shown in Fig. 5.13.
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Shape memory and superelastic alloys
Transformation temperature (°C)
80.0
10 Ti–49.6 at.% Ni–Fe g = 0.8%
60.0
PH
8
6 40.0 PL 20.0
4
Af
Load (N)
74
2
AS 0.0
0 460
490
520
550
Heat treatment temperature (°C)
5.11 The effect of heat treatment temperature on the transformation temperature and loads of an SMA spring (Ti–49.6 at.% Ni–Fe, g = 0.8%). 10 Af 8 60.0
AS 6
PH 40.0
4 20.0
Ti–41.0 at.% Ni–Cu g = 0.8%
Load (N)
Transformation temperature (°C)
80.0
2
PL 0.0
0 410
440
470
500
Heat treatment temperature (°C)
5.12 The effect of heat treatment temperature on the transformation temperature and loads of an SMA spring (Ti–41.0 at.% Ni–Cu, g = 0.8%).
On the other hand, the Ti–41.0 at.% Ni–Cu spring revealed different temperature dependence: the transformation temperatures increased with increasing heat treatment temperature and the load differences at low and high temperatures are very large. However, it is noted that the Ti–41.0 at.% Ni–Cu spring exhibited higher transformation temperatures even though the hysteresis is large as shown in Fig. 5.14.
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Design of SMA coil springs for actuator applications 10 Ti–49.6 at.% Ni–Fe g = 0.8%
8
Load (N)
HT 550 °C × 60 min
6
4
2
0 –40
–30 –20
–10
0
10
20
30
40
Temperature (°C)
5.13 The load–temperature curve for a Ti–49.6 at.% Ni–Fe spring (g = 0.8%) heat treated at 550 °C for 60 minutes.
10 Ti–41.0 at.% Ni–Cu g = 0.8%
8
Load (N)
HT 440 °C × 60 min
6
4
2
0 20
30
40
50 80 60 70 Temperature (°C)
90
100
5.14 The load–temperature curve for a Ti–41.0 at.% Ni–Cu spring (g = 0.8%) heat treated at 440 °C for 60 minutes.
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Shape memory and superelastic alloys
In conclusion, it should be mentioned that not only the heat treatment condition but also strain have a strong effect on to the properties of the SMA spring. Furthermore, the alloy composition is another important factor controlling the properties of the SMA spring.
5.5
Reference
Ohkata I and Suzuki Y, (1998), ‘The design of shape memory alloy actuators and their applications’, in: Otsuka K and Wayman C M, Shape Memory Materials, Cambridge, Cambridge University Press, 240–266.
© Woodhead Publishing Limited, 2011
Abstract: Titanium–nickel (TiNi) shape memory alloys (SMAs) are used in the form of coil springs in most products because the coil springs generate a large stroke and a high recovery force. Another advantage of using the SMA springs is that they can function as actuators as well as sensors. The SMA spring operates as a two-way actuator by the combination of a bias spring. This chapter introduces the design of the SMA spring and SMA actuator and the manufacturing process of SMA spring. Key words: spring, actuator, manufacturing process.
5.1
Introduction
Since the shape memory effect (SME) in the TiNi shape memory alloy (SMA) was discovered, many products have been developed that use the properties of SMAs (Table 5.1). SMAs are used in a variety of applications such as automobiles, electrical and home appliances, and housing. Most of these products use SMAs in the form of coil springs where they function as an actuator as well as a temperature sensor. The advantage of a coil spring shape is its large stroke compared with a wire as shown in Fig. 5.1, which compares the stroke of a straight wire and a coil of 30 mm free length. When the strain of 1.0% is given, the coil expands 60.3 mm while the stroke of the wire is only 0.3 mm. In this chapter, the design of SMA springs and actuator, and the manufacturing processes for SMA springs are discussed.
5.2
Design of shape memory alloy (SMA) springs
5.2.1 Difference from usual springs Conventional springs are designed to perform within the elastic region where Hooke’s law is obeyed. This allows easy design of the spring since the shear modulus and spring constant do not change within the elastic region. On the other hand, the relation between the deflection and load is not linear for the SMA spring since both shear modulus and spring constant change with strain. Moreover the characteristic changes greatly with small 63 © Woodhead Publishing Limited, 2011
64
Shape memory and superelastic alloys Table 5.1 Application of the shape memory effect Application
Shape
Gearless transmission valve Automatic oil valve of Shinkansen Automatic desiccators Louver of air conditioner Coffee maker Rice cooker Camera Miniature robot Anti-scald valve Water purifier Thermostatic mixing valve Bathtub adapter for adding water Underfloor ventilating hole Easy-release screws by SMA washer Rock splitter
Coil Coil Coil Coil Coil Coil Wire Wire Coil Coil Coil Coil Coil Washer Rod
Wire diameter: 1.0 mm Outside coil diameter: 8.0 mm Wire turns: 30 turns Free length: 30 mm γ = 1.0%
30 30 Wire shape
Coil shape
30.3 90.3
5.1 Comparison of strokes of SMAs between wire shape and coil shape.
change in the alloy composition, shape memory treatment condition and operating condition such as temperature and strain. However, for the design of an SMA spring, the formulae of conventional springs are used by assuming the shear modulus is constant if the strain is small.
5.2.2 Selection of materials and shear modulus The materials used for the SMA spring can be classified according to the operation temperature (Table 5.2). The operation temperature of the SMA
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Design of SMA coil springs for actuator applications
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Table 5.2 Classification
Material
Use temperature (°C)
TiNi–Fe, Co, Cr
−20–40
TiNi TiNi–Cu
Thermal hysteresis (°C) 2–3
20–80 40–100
Application Actuators for low temperature (underfloor ventilating hole) Thermostatic mixing valve Actuators for high temperature (rice cooker / coffee maker)
2–3 10–15
10
TiNi–Fe
Load (N)
8
TiNi
6
4
2
TiNi–Cu
0 –20
0
20
40
60
80
100
Temperature (°C)
5.2 Load–temperature curves obtained by the fixed strain tests of the SMA springs.
spring is determined by its transformation temperature. The results of thermal cycling tests at the fixed strain for the SMA springs listed in Table 5.2 are compared in Fig. 5.2. It is clear that the recovery temperature increases by the addition of Cu but decreases by the addition of Fe. The shear modulus of the SMA spring exhibits a drastic change when the spring is cooled below the martensitic transformation temperature or heated above its reverse transformation temperature since the shear modulus of high temperature phase (parent phase) is substantially higher than that of the low temperature phase (martensite phase). For instance, the shear modulus of martensite phase is about 8000 MPa while that of the
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Shape memory and superelastic alloys
parent phase exceeds 20 000 MPa in Ti–Ni alloys. In TiNi–Cu alloys, the shear modulus of martensite phase is almost 0 MPa while that of the parent phase is about 16 000 MPa. It is generally acknowledged that the control of transformation temperature is difficult: only 0.1 at.% difference in composition results from a change of the transformation temperature of about 10 K. Thus the shear modulus of the SMA spring is also sensitive to the alloy composition.
5.2.3 Design of helical springs The characteristic parameters for design of springs are shown in Fig. 5.3. The notations used in the calculation are listed in Table 5.3 and fundamental formulae used for the design of springs are listed as follows:
φd L
5.3 Characteristic parameters of design of a spring. Table 5.3 The sign to use for the calculation Symbol
Meaning
Unit
d D1 D2 D
Wire diameter Inside coil diameter Outside coil diameter Mean coil diameter D = (D1 + D2)/2 Total coils Active coils Free length Load Deflection Shear stress Shear strain Shear modulus Spring index Spring constant
mm mm mm mm
N n L P d t g G C k
– – mm N mm MPa % MPa – N/mm
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D2
P
R
D
P
D1
α
Design of SMA coil springs for actuator applications
67
d = 8PD3n / Gd4
5.1
g = dd / pnD2
5.2
t = 8PD / pd3
5.3
G=t/g
5.4
C=D/d
5.5
The load and the stroke at the high temperature are often demanded as a design condition of the SMA spring. An example of designing the compression spring when the following design conditions are given is shown below. Design conditions The deflection and the load at the high temperature: PH = 5 N at dH = 10 mm. Stroke: St = 5 mm (deflection at low temperature: dL = dH + St = 15 mm) The shear modulus: GH = 20 000 MPa at the high temperature. The shear modulus: GL = 8000 MPa at the low temperature. Shear strain at high temperature: gH = 0.6% Spring index: C = 8 Design procedure The shear stress at the high temperature becomes tH = 120 MPa from equation 5.4. Wire diameter d is calculated using equations 5.3 and 5.5. d2 = 8PC / ptH = (8 × 5 × 8) / (p × 120) d = 0.92 Hereafter, the wire diameter d is assumed to be ϕ1.0 mm. Then, mean coil diameter D becomes ϕ8.0 mm from equation 5.5. The number of coils n is obtained from equation 5.1: n = GHd4dH / 8PHD3 = (20 000 × 1.04 × 10) / (8 × 5 × 8.03) = 9.8 Finally we obtain the dimensions of the spring: 10 active coils with wire diameter of 1.0 mm and mean coil diameter of 8 mm. Shear strain gL at the low temperature is calculated from equation 5.2 using the dimensions of the spring: gL = ddL / pnD2 = (1.0 × 15) / (p × 10 × 8.02) = 0.0075
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Shape memory and superelastic alloys
Then, load PL at the low temperature is obtained from equation 5.1. PL = dLGLd4/8D3n = (15 × 8000 × 1.04) / (8 × 8.03 × 10) = 2.9 As for deflection dL at the low temperature, less than 0.8% of the total deflection is preferable. The free length L of the spring is an important parameter for considering applications. The solid length Hs of the spring becomes, for instance, 13 mm from the equation d[(n + 2) + 1] if we assume one turn at both end. Then free length L becomes 31.75 mm from the equation L = 1.25dL + Hs. The specification of the SMA spring to fill the abovementioned design conditions is summarized in Table 5.4.
5.2.4 Point of SMA spring design Shear strain gL at low temperature It is preferable to decide gL(= gmax) in the beginning with tmax in consideration of the fatigue life. It should be note that the SMA spring must be used within gmax. The recommended gmax of the SMA spring is as follows: gmax = 0.8% or less for TiNi spring and gmax = 2.0% or less for TiNi–Cu spring. Spring index C C = 6–10 is recommended. The change of C causes the change dimensions of the spring.
5.3
Design of shape memory alloy (SMA) actuators
Conventional SMA springs reveal the one-way shape memory effect. Therefore, in order to operate repeatedly, the bias stress is required. Figure 5.4 shows an example of two-way SMA actuator combined with a bias spring where an SMA spring and a bias spring are set so as to oppose each other (Ohkata and Suzuki, 1998). When the SMA spring is heated above Table 5.4 The specification of the SMA spring Wire diameter Mean coil diameter Total coils Active coils Free length dH = 10 mm dL = 15 mm gL (gmax)
1.0 mm 8.0 mm 12 10 31.8 mm PH = 5 N PL = 2.9 N 0.75%
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Design of SMA coil springs for actuator applications SMA spring
69
Bias spring
Hot P
St Cool P
5.4 An example of a two-way SMA actuator combined with a bias spring and its actuation by temperature change.
the reverse transformation temperature, the axis moves to the right since the recovery force of the SMA spring overcomes the force exerted on the bias spring. The axis returns to original position when the SMA spring cooled below the martensitic transformation temperature. As a result, the SMA spring with a bias spring actuates by heating and cooling. The two-way motion generates a stroke of St. In general, the deflection and load of the SMA actuator can be estimated using the diagram as shown in Fig. 5.5. Figure 5.5 shows load–deflection curves of an SMA spring and bias spring. The slopes of load–deflection curves of the SMA spring and bias spring are spring constants and have opposite signs since they move in opposite directions. If there is an external force, the stroke is shortened to St′ for instance. Figure 5.5 also shows that a larger stroke can be obtained when the spring constant is small.
5.4
Manufacturing of shape memory alloy (SMA) springs
5.4.1 Coiling The SMA coil springs are fabricated using an automatic coil forming machine, which is the same machine that is used for a conventional coil spring. However, a larger forming pressure is required to form a required
© Woodhead Publishing Limited, 2011
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Shape memory and superelastic alloys 10 High temperature 8 Bias spring
Load (N)
6 A
A′ Low temperature
4 B′ 2
B
St′ St
0 0
5
10 15 Deflection (mm)
20
25
5.5 A load–deflection diagram for the SMA spring and bias spring in the two-way SMA actuator.
shape due to a larger spring-back effect of the SMA wires compared with conventional stainless wires or piano wires. Therefore a material and tool which can endure without burning are required. The coil diameter and the free length are changeable according to the adjustment of processing speed and improvement of slipping of the material.
5.4.2 Shape memory treatment (heat treatment) The SMA spring is heat treated after coiling in order to memorize the shape. The heat treatment condition is determined on the basis of productivity (cost) and durability. The spring is fastened on a jig so as to maintain the spring shape during heat treatment and heat treated at about 350–550 °C, followed by air cooling or water quenching. Heat treatment time is from several minutes to 60 minutes. The heat treatment condition is determined to obtain suitable properties such as transformation temperature, hysteresis and durability, which are also dependent on the alloy composition. It it is necessary to adjust the heat treatment condition for each lot of products when mass production, since the properties of each lot are always same even if the processing condition is same. Figure 5.6 shows the effect of heat treatment temperature on the transformation temperature and loads of an SMA spring (Ti–50.6 at.% Ni, g = 0.8%). It can be seen that the transformation temperatures (Af and As) decrease with increasing heat treatment temperature. The transformation
© Woodhead Publishing Limited, 2011
Design of SMA coil springs for actuator applications
60.0
40.0
10
PH
8
Af
6
AS 4
Load (N)
Transformation temperature (°C)
80.0
71
PL 20.0
2
Ti–50.6 at.% Ni g = 0.8% 0.0
0 410
440
470
500
Heat treatment temperature (°C)
5.6 The effect of heat treatment temperature on the transformation temperature and loads of a SMA spring (Ti–50.6 at.% Ni, g = 0.8%).
temperature width (Af–As), i.e., the difference of Af and As, also decreases with increasing heat treatment temperature. The load at a low temperature PL decreases but the load at high temperature PH remains constant, resulting in the difference (PH–PL) increases with increasing heat treatment temperature. Figures 5.7 and 5.8 show the load–temperature curves for a Ti–50.6 at.% Ni spring heat treated at 470 °C for 60 minutes and 500 °C for 60 minutes, respectively. It is clearly seen that the hysteresis of transformation temperature increases with increasing heat treatment temperature: the spring heat treated at 470 °C exhibits an extremely small hysteresis of 2 °C. These results imply that the heat treatment at 470 °C is preferable to 500 °C since the small hysteresis leads to better durability and longer fatigue life. Figure 5.9 shows the effect of heat treatment temperature on the transformation temperatures and loads for the Ti–50.6 at.% Ni spring applied a strain of 1.0%. Similar dependences of heat treatment temperature were observed: the transformation temperatures, hysteresis and load at low temperature decrease with increasing heat treatment temperature. The load– temperature curve for the Ti–50.6 at.% Ni spring to which a strain of 1.0% was applied is shown in Fig. 5.10. When comparing Figs. 5.10 and 5.7, it should be noticed that the hysteresis of transformation temperature became larger by increasing the strain. The composition of the spring also affects the properties and heat treatment condition. Figures 5.11 and 5.12 show the effect of heat treatment temperature on the transformation temperatures and loads for a Ti–49.6 at.% Ni–Fe spring and a Ti–41.0 at.% Ni–Cu spring, respectively. For the
© Woodhead Publishing Limited, 2011
Shape memory and superelastic alloys 10 HT 470 °C × 60 min
Ti–50.6 at.% Ni g = 0.8%
Load (N)
8
6
4
2
0 0
10
20
30
40
50
60
70
80
Temperature (°C)
5.7 The load–temperature curve for a Ti–50.6 at.% Ni spring (g = 0.8%) heat treated at 470 °C for 60 minutes.
10 HT 500 °C × 60 min
Ti–50.6 at.% Ni 8
Load (N)
72
g = 0.8%
6
4
2
0 –10
0
10
20
30
40
50
60
70
Temperature (°C)
5.8 The load–temperature curve for a Ti–50.6 at.% Ni spring (g = 0.8%) heat treated at 500 °C for 60 minutes.
© Woodhead Publishing Limited, 2011
Design of SMA coil springs for actuator applications 10 PH 60.0
40.0
8 Af 6
PL AS
Load (N)
Transformation temperature (°C)
80.0
73
4
20.0
2
Ti–50.6 at.% Ni g = 1.0% 0.0
0 410
440
470
500
Heat treatment temperature (°C)
5.9 The effect of heat treatment temperature on the transformation temperature and loads of a SMA spring (Ti–50.6 at.% Ni, g = 1.0%). 10
Load (N)
8
6
4
2
Ti–50.6 at.% Ni
HT 470 °C × 60 min g = 1.0%
0 0
10
20
30
40
50
60
70
80
Temperature (°C)
5.10 The load–temperature curve for a Ti–50.6 at.% Ni spring (g = 1.0%) heat treated at 470 °C for 60 minutes.
Ti–49.6 at.% Ni–Fe spring, the dependences of transformation temperatures and loads on the heat treatment temperature are similar to those of the binary Ti–Ni spring. However, the best heat treatment condition is different: the spring heat treated at 550 °C exhibited excellent properties with a very small hysteresis for the Ti–49.6 at.% Ni spring as shown in Fig. 5.13.
© Woodhead Publishing Limited, 2011
Shape memory and superelastic alloys
Transformation temperature (°C)
80.0
10 Ti–49.6 at.% Ni–Fe g = 0.8%
60.0
PH
8
6 40.0 PL 20.0
4
Af
Load (N)
74
2
AS 0.0
0 460
490
520
550
Heat treatment temperature (°C)
5.11 The effect of heat treatment temperature on the transformation temperature and loads of an SMA spring (Ti–49.6 at.% Ni–Fe, g = 0.8%). 10 Af 8 60.0
AS 6
PH 40.0
4 20.0
Ti–41.0 at.% Ni–Cu g = 0.8%
Load (N)
Transformation temperature (°C)
80.0
2
PL 0.0
0 410
440
470
500
Heat treatment temperature (°C)
5.12 The effect of heat treatment temperature on the transformation temperature and loads of an SMA spring (Ti–41.0 at.% Ni–Cu, g = 0.8%).
On the other hand, the Ti–41.0 at.% Ni–Cu spring revealed different temperature dependence: the transformation temperatures increased with increasing heat treatment temperature and the load differences at low and high temperatures are very large. However, it is noted that the Ti–41.0 at.% Ni–Cu spring exhibited higher transformation temperatures even though the hysteresis is large as shown in Fig. 5.14.
© Woodhead Publishing Limited, 2011
Design of SMA coil springs for actuator applications 10 Ti–49.6 at.% Ni–Fe g = 0.8%
8
Load (N)
HT 550 °C × 60 min
6
4
2
0 –40
–30 –20
–10
0
10
20
30
40
Temperature (°C)
5.13 The load–temperature curve for a Ti–49.6 at.% Ni–Fe spring (g = 0.8%) heat treated at 550 °C for 60 minutes.
10 Ti–41.0 at.% Ni–Cu g = 0.8%
8
Load (N)
HT 440 °C × 60 min
6
4
2
0 20
30
40
50 80 60 70 Temperature (°C)
90
100
5.14 The load–temperature curve for a Ti–41.0 at.% Ni–Cu spring (g = 0.8%) heat treated at 440 °C for 60 minutes.
© Woodhead Publishing Limited, 2011
75
76
Shape memory and superelastic alloys
In conclusion, it should be mentioned that not only the heat treatment condition but also strain have a strong effect on to the properties of the SMA spring. Furthermore, the alloy composition is another important factor controlling the properties of the SMA spring.
5.5
Reference
Ohkata I and Suzuki Y, (1998), ‘The design of shape memory alloy actuators and their applications’, in: Otsuka K and Wayman C M, Shape Memory Materials, Cambridge, Cambridge University Press, 240–266.
© Woodhead Publishing Limited, 2011