Bimetal strips or thermostat metals comprise two (or more) layers of dissimilar metals bonded together. When subjected to a change in temperature, the strip will bend by virtue of the difference in thermal coefficients of expansion of the metals. Basically, therefore, thermostat metals are simple transducers, converting thermal energy into mechanical energy. Bimetal strips, also known as thermo-metals, may be used for the following functions: Temperature indication: e.g., in thermometers employing a bimetal strip sensor Temperature control: e.g., in thermostats Control of functions with temperature change: e.g., in automatic chokes on automobile engines Compensation for length or force with changes in temperature: e.g., in lever mechanisms Control devices: e.g., circuit breakers, which are heated by the load circuit and which trip if the current reaches overload values. The first four functions are direct transducer reactions, where temperature change (heat) is converted into mechanical movement. The fifth function is an indirect application involving two separate stages of conversion: electric current into heat, and then heat into mechanical movement.
STRAIGHT-STRIP DEFLECTION In the case of a narrow straight strip of bimetal (ill. 15-1), the strip will bend to an arc of a circle, the radius of curvature of which is dependent on the difference in coefficients of expansion of the two metals, their thicknesses and elastic moduli, and the change in temperature. If you ignore the difference in elastic moduli (which is usually quite small with thermo-metals), you can use the working formula R = [(t1 + t2)^3] / [6d T1 t2] where R is the radius of curvature t2 and t2 are the thicknesses of the two metals in millimeters d is the difference in coefficients of expansion of the two T is the temperature change in degrees Celsius The significance of this formula is that curvature is greatest when the two metal thicknesses are the same. Thus, for maximum mechanical movement, if you were making your own bimetal strip, you would bond two strips of the same thickness together from metals with the largest difference in coefficients of expansion. ill. 15-1: A bimetal strip bends along a circular arc with a rise or fall in temperature from the straight condition. In practice, ready-made thermometals (bimetal strips) would normally be used, where the curvature can be determined from the simple formula R= t / 2KT where t is the total thickness of the thermo-metal, and K is a constant that is different for each thermometal. The quantity 2K, known as the flexivity, is the change in curvature per unit temperature change per unit thickness. For proprietary thermometals the value of K is usually of the order of 7.3 x 10^-5 but may be higher or lower with special types. If possible get the maker or supplier to specify the actual K value for the thermometal you are using. If not, use the value 3 x 10^-6. FREE-END MOVEMENT The usual requirement in designing a bimetal transducer is determining not the radius of curvature but the deflection produced at one end of the strip when the other end is clamped; you must also determine the force produced if this deflection is restrained. Deflection can be calculated from the formula deflection (D) = KTL^2/t The actual mechanical force developed can be calculated from the formula force (ounces) = 4ETwt^2/L where L = the effective length of the strip in inches E = effective elastic modulus of strip in lb/in^2 w = width of strip in inches t = thickness of strip in inches Typically the modules of elasticity of thermometal will be of the order of 2.4 x 10^-5 lb/in^2. Use this value of calculating force, unless you have a specific value for the thermometal chosen. If we assume typical values for K and E, the force formula can be simplified to F(ounces) = 550 (Twt^2 / L) where w, t, and L are in inches T is temperature difference in degrees Fahrenheit Note that in determining deflection or force developed by a bimetal strip, the width of the strip does not affect the result. In other words, the width used can be whatever is convenient. When it comes to determining the force developed, however, the width of the strip must also be taken into account. Project 1. Design a high-temperature warning system or thermostat using a sample piece of thermo-metal available. The warning signal is to come on at a temperature of 90 deg. F. Normal ambient temperature is 70 deg. F. The basic design is shown in ill. 15-2, where deflection of the thermo-metal (bimetal strip) completes the lamp circuit when the temperature rises by 90° — 70 deg or 20 deg F. Thus T in the deflection formula is 20. ill. 15-2. A temperature-warning system using a bimetal strip. We assume that only a piece of thermometal is available; its specific properties being unknown. We therefore adopt a typical value for K of 7.3 x 10^-5. We can find the thickness of the strip (t) by actual measurement. Suppose it's 0.025 in. This now leaves only L and D as unknown values. We can either allocate a value for length L and calculate the resulting deflection, or we can calculate the value of L required to produce a given deflection. The latter is the best design practice, so let us set D = 0.1 in. Rewriting the deflection formula as a solution for L, we get L = sqr-rt [Dt/KT] Substituting values gives L = sqr-rt [0.1x0.025/ 7.3 x 10^-5 x 20] L = 1.3 in It now only remains to check that the strip deflects the right way with increasing temperature: that is, towards the contact, not away from it. The only way to do this is to try it and see. If it deflects the wrong way, simply turn the strip over. Note that this circuit is a high-temperature warning, switching on at 90 deg. F. It will remain switched off at any lower temperature. Check its actual switch-on temperature against a thermometer and a flow of hot air directed against it (from a hairdryer, for exam- pie). The actual contact position may need adjustment up or down, because the K value for the strip may not be the typical value used for the calculation. Note: this example is also the basis for the design of a thermostat. In this case the mechanical movement (deflection) of the bimetal strip is separated from the electrical circuit and is used to close a pair of contacts at a predetermined temperature. To make the thermostat adjustable for temperature setting, you can make either the free length of the bimetal strip or the deflection distance variable. The latter is the easiest to achieve, a simple way being to mount the fixed end of the bimetal strip on a friction pivot to make the displacement gap adjustable. Project 2. Using the same thermometal, design a circuit to switch on at 20 deg. F. above an ambient temperature of 700 F. and also if the temperature drops to 15° F. below ambient. ill. 15-3: Another temperature-warning system, giving an indication for temperatures outside a prescribed range. The circuit is basically the same, except that a second contact is added, as shown in ill. 15-3. For simplicity, let’s make the top contact the high-temperature contact with the same strip deflection and strip length as before. It now only remains to calculate the deflection of the strip downwards (D2) for a temperature drop of 15 deg. F. below ambient. This will determine the position of the low-temperature contact. Using the same formula, we get D = 7.3 x 10^-5 x 1014 = 0.074 in. Project 3. Design a bimetal-strip system to operate a latch when the temperature rises by 10 deg. F. The force required to operate the latch is 2 oz. Thermo-metal material available is 0.025 in thick. No other properties are known. This is a purely mechanical system with the free end of the bimetal strip resting against the latch at normal temperature (ill. 15-4). The known rates are T = 10 deg. F t = 0.025 in This leaves the length of strip (L) and the width of strip (w) to be used as unknowns. The force formula is F(ounces) = 550 [Twt^2 / L] ill. 15-4: A bimetal strip can be used to open a latch. When the force F is sufficient, the strip moves the latch. This happens at a temperature determined by the mechanical resistance of the latch, and the length and configuration of the bimetal strip. Inserting the known values, we have F = 2 = 550 x [10 x w x 0.025 x 0.025 / L] = 3.4375 x w/L or w/L = 2 / 3.4375 = 0.58 In other words, we can use any combination of strip length and width where the length L is 1/0.58 = 1.724 x w. Let’s choose 0.5 in as a convenient width to cut the strip. Then L= 1.72x0.5 = 0.86 in. As a check, recalculate the force with these values: F = 550 x [10 x 0.5 x 0.025 x 0.025]/ 0.86 = 1.999 oz. We should also check that the bimetal strip is not overstressed with this load applied. A formula for the safe maximum load (maximum force) is max. force (ounces) = 40,000 x wt^2/L Check against the project calculation: max. force = 40,000 x [0.5 x 0.025 x 0.025 / 0.86] = 14.5 oz. Our design load is well below this. COILED BIMETAL STRIP Bimetal-strip transducers can also be used in the form of coils, when the deflection will be in the form of angular rotation. Such coils will thus develop a torque with a change in temperature, the value of which can be calculated from the formula torque (oz in) = 4700 Twt^2 where T is the temperature difference in degrees Fahrenheit w is the width of the strip in inches t is the thickness of the strip in inches This is an approximate formula, based on typical values for K and E for thermometals. PREV: Thermocouples |
Updated: Friday, January 23, 2009 2:38 PST