Design of a Cheap Thermal Switch ENGR 0135 Due: 10/9/15 Professor Qing-Ming Wang Madison Milligan, Josh Haupt, Caroline Collopy
ABSTRACT The purpose of this design project is to come up with a way to develop a cheaper version of a currently used thermal switch. This is to be done by reducing the temperature needed to cause enough stress in the central aluminum strip, which will make it snap and connect with either the steel plate to its left or the plate to its right. To be able to reduce the temperature however, the cross sectional area of each strip must be modified. So, we came up with a formula which incorporates the dimensions of the cross sectional area of the aluminum strip and the temperature change in order to develop a relationship between all variables in question, and to find a potential solution. We did this by using the connection between the deformation in each strip and between the forces acting in the strips; then by solving the system of equations, we found one formula. Included in this paper is an introduction to the problem, the steps taken to find the final formula, and an explanation as to how we used it to back up our final design solution. INTRODUCTION A thermal switch has been designed for incorporation into a low cost product. The switch consists of three metal strips clamped rigidly together in an assembly of insulating pieces. Currently, the aluminum strip snaps to the side at a temperature increase of about 180 F. We are asked to vary the dimensions of the central aluminum strip so the circuit will close at a temperature increase of only 105 F instead. We intend to solve this by deriving a formula that incorporates all variables in question. We hypothesize that if the temperature of closure is to be lowered, the cross sectional area will need to be lowered as well because the two are directly proportional.
ANALYSIS & DESIGN All calculations and logic used to develop a formula relating change in temperature to the crosssectional area of the aluminum strip are shown in Figure 1. Figure 1: Initial calculations for a formula
We verified this formula by plugging in the original dimensions and ensuring that the result was in fact 180 F. Using this formula, we re-arranged the variables to make it easier to find possible solutions for the width and thickness that would allow the temperature change to be 105 F. Those calculations are shown in figure 2. Figure 2: Manipulation of formula to find potential new Dimensions for aluminum strip ta also cannot be 0. Since the ultimate goal is to make a cheaper thermal switch, the cross sectional area also needs to be minimized. After trying out a few options, we realized that
regardless of the dimensions chosen, the cross sectional area will be reduced significantly from the original area of 0.0156 in² because of the drop in the desired change in temperature. A few suggestions are as followed: Option 1 ta = 0.054 in wa = 1.51e-6 in Cross-sectional area = 8.17e-8 in 2 Option 2 ta = 0.040 in wa = 1.21e-5 in Cross-sectional area = 8.83e-8 in 2 Option 3 ta = 0.030 in wa = 3.30e-5 in Cross-sectional area = 9.90e-7 in 2 As ta decreases, the cross sectional area increases, so the ideal pair to pick would be the first. It allows for the temperature change as well as minimizes cross sectional area. (All original copies of the calculations are attached) DISCUSSION As the strips are attached at both ends, the total deformation of the aluminum strip (before failure) must be zero. When the temperature is raised on the switch, the stress induced on the aluminum will be compressive and the rigid supports will push the strip axially. With this in mind, we were able to use the following equations in the derivation of our formula: 1 δ!"!"# = δ! + δ! 2 αδtl + σl E = 0 We also used Euler s formula for the buckling of columns, along with the formula for the minimum second moment of inertia of the cross-section (3 and 4 respectively). 3 P!" = 4πEI L! 4 I = w!t!! 12 Using these fundamental formulas and our understanding of thermal expansion and statically indeterminate members, we derived our formula for determining the thickness and width of the aluminum strip.
CONCLUSION In conclusion, after relating the deformation of the switch s Aluminum and Steel components to give us ΔT as a function of the Aluminum strip s dimensions, we found that ta decreases, the cross sectional area increases. In order for the product to remain inexpensive, we decided on the experimental dimensions that allowed the smallest cross-sectional area while still resulted in only ΔT=105 F required for operation. Those dimensions were: t! = 0.054 inches w! =1.51e-6 inches Our design was successful in the sense that it does decrease the change in temperature needed for the switch to activate to only 105 F while adhering to given restraints. However, in order to do this, we had to set width to a virtually non-existent size. This raises concerns in durability or manufacturing practicality for the product. To improve the design, we might suggest that the thickness and length may be allowed to vary. The lengths of all three strips must remain equal to each other, however lengthening them overall would also give more flexibility and options in way to decrease required changed in temperature while upholding cost efficiency.