# Thermal Switch Design Project fast

• naevitar77
In summary, the conversation discusses a problem involving three vertical metal strips (steel, aluminum, and steel) between two horizontal rigid bodies. The dimensions and materials of the strips are given, along with the necessary equations and formulas. The goal is to modify the dimensions of the aluminum strip in order for the switch to activate with a 100 degF temperature increase. The conversation also addresses a minor mistake in the calculations, where Pcr should be negative instead of positive.
naevitar77

## Homework Statement

There are three vertical metal strips (Steel, Aluminum, Steel) between two horizontal rigid bodies

alphaa = 12.5 E-6 /degF -- coefficient of thermal expansion
alphas = 6.6 E-6 /degF
Ea = 10 E6 psi -- Young's Modulus
Es = 30 E6 psi

The original dimensions of the switch are
ta = .0625 in -- thickness of aluminum
wa = .25 in -- width of aluminum
ts = .0625 in
ws = .125 in
L = 4 in -- length of all metals

With these dimensions, the switch will activate with a 180 degF temperature increase

By only changing the dimensions of the aluminum strip, I have to modify the switch to activate with 100 degF temperature increase

## Homework Equations

δ = P*L/(E*A) + alpha*ΔT*L

Pcr = 4*pi^2*Ea*Ia / L^2 -- critical axial compressive load for the aluminum to buckle
Ia = wa*ta^3/12 -- minimum second moment of inertia

## The Attempt at a Solution

I tried setting the deformation of the aluminum equal to that of the steel

δa = δs
Pa*L/(Ea*Aa) + alphaa*ΔT*L = Ps*L/(Es*As) + alphas*ΔT*L

from a free body diagram, I got Ps = -.5*Pa

Pa*L/(Ea*Aa) + alphaa*ΔT*L = -Pa*L/(2*Es*As) + alphas*ΔT*L
Pa*(1/(Ea*Aa) + 1/(2*Es*As)) = ΔT*(alphas - alphaa)

solving for Pa and simplifying using (1/a + 1/b)^-1 = ab/(a+b)

Pa = ΔT*(alphas - alphaa)*(2*Ea*Aa*Es*As / (Ea*Aa + 2*Es*As))

substituting Pcr = Pa

pi^2*Ea*wa*ta^3/(3*L^2) = ΔT*(alphas - alphaa)*(2*Ea*Aa*Es*As / (Ea*Aa + 2*Es*As))

now solving this for the temperature..

ΔT = pi^2*ta^2/(3*L^2) * (Ea*Aa + 2*Es*As)/(2*Es*As(alphas - alphaa))

when I plug in the variables for the 180 degF switch from above, I am getting
ΔT = -181.5 degF and I do not see anything wrong in my algebra; my units still come out to be degF.

Can someone tell me what I am doing wrong? Am I approaching this the right way?

Last edited:
naevitar77: Excellent work, so far, except for one minor mistake. Pcr should be, Pcr = -4*Ea*Ia*(pi/L)^2. You erroneously omitted the negative sign here. Try it again.

By the way, numbers less than 1 should always have a zero before the decimal point. E.g., 0.25, not .25. See the international standard for writing units (ISO 31-0).

nvn said:
naevitar77: Excellent work, so far, except for one minor mistake. Pcr should be, Pcr = -4*Ea*Ia*(pi/L)^2. You erroneously omitted the negative sign here. Try it again.

The handout my professor passed out on this project defines Pcr without a negative sign. Why is it suppose to be negative?

Pcr is negative because it is compressive force. Your professor listed the magnitude.

That makes sense. Thank you so much nvn. You're a life saver!

## 1. What is a thermal switch used for?

A thermal switch is a type of temperature-dependent switch that is designed to control the flow of electricity based on changes in temperature. It is commonly used in electronic devices to prevent overheating and to regulate temperature.

## 2. How does a thermal switch work?

A thermal switch typically consists of a bimetallic strip, which is made of two different metals with different rates of thermal expansion. As the temperature changes, the metals expand or contract at different rates, causing the strip to bend and make or break an electrical connection.

## 3. What are the key factors to consider when designing a thermal switch?

The key factors to consider when designing a thermal switch include the temperature range it will operate in, the required temperature sensitivity, the desired switching speed, and the level of current or voltage it needs to handle.

## 4. What are the advantages of using a thermal switch in electronic devices?

Some of the advantages of using a thermal switch include its simplicity, reliability, and low cost. It also helps to prevent overheating and damage to electronic components, making it an essential safety feature in many devices.

## 5. What are some common applications of thermal switches?

Thermal switches are commonly used in a variety of electronic devices such as computers, refrigerators, air conditioners, and heaters. They are also used in industrial equipment, automotive systems, and medical devices.

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