Thermally Self-Regulating System Setup

[jamestyler]

TL;DR

Goal : to build a high torque system that is capable to self-regulate thermal dissipation through frictional heat to heat up test samples

I would like to design a system that is capable of generating frictional heat through its servo motor to heat up an enclosed chamber to 500 'Celsius . The challenge is that external heating source such as heating element, heat chamber etc. shall not be included in the design setup. Assuming that the rotor works at a speed of 1000 rpm, what is the torque needed so that the resulting frictional heat could heat the chamber from 30'Celsius to 500'Celsius?

I tried to make some simple calculations by correlating the three formulae below but the value I got doesn't really make any sense:
1) Continuous power (kW) = (2*pi*RPM*Torque)/60000
2) Power = Energy / time
3) Energy (thermal) = mass * specific heat capacity * temperature change

Did I calculate it correctly or it is not so straight forward?

 

[Lnewqban]

Welcome, jamestyler!

You can convert all mechanical work into heat.
It is that heat the energy that later will try to escape from your enclosure into its surroundings.
How much of that you can keep inside is what will increase the internal temperature.

If the natural heat transfer is excessive, you will never reach your goal temperature.
If insulation is sufficient, you will need a control system that stops or slows your wheel down when your goal temperature is reached, in such a way that you only generate enough to compensate for the outwards transfer.

The amount of torque and the rpm's will depend on how quickly you want to make the internal temperature reach the goal.
You can do it with good insulation and a slow-weak wheel (slow generation and accumulation of mechanical energy and heat), or with a strong and fast wheel.

 

[Baluncore]

Energy conversion is the credit side of the problem, but you need to analyse the deficit side of the energy budget.

1. What is the thermal resistance in watts/°C of the chamber insulation. That will tell you how much power is being lost, or is required to hold the temperature stable. It also gives you the increasing rate of heat loss as heating progresses, and the maximum temperature possible.

2. What is the thermal capacity of the insulated chamber, measured in joules/°C. That determines how much energy is needed to heat the contents. Are there any material phase changes expected in the samples that will require an energy input, such as evaporating water?

 

[berkeman]

Welcome to the PF.

to heat up an enclosed chamber to 500 'Celsius . The challenge is that external heating source such as heating element, heat chamber etc. shall not be included in the design setup.

Why is that a design constraint? Sounds pretty strange to me at first glance.

Is this an artificial schoolwork assignment, or a practical design problem and you plan to build and test this?

 

[essenmein]

Welcome to the PF.

Why is that a design constraint? Sounds pretty strange to me at first glance.

Is this an artificial schoolwork assignment, or a practical design problem and you plan to build and test this?

Yeah, esp when you consider a heating element (electrical) is simply a device the converts electrical energy into thermal energy (heat). The mechanical system proposed, is conceptually identical, ie a device that converts mechanical energy into thermal energy, ie you could argue that this is still a heating element!

Heating things from 30C to 500C is not an uncommon requirement, and the most effective way we have to achieve this is with electrical heating or fire, I can't imagine a friction device being better than those, other wise we'd be using them industrially!

 

[Baluncore]

I can't imagine a friction device being better than those, other wise we'd be using them industrially!

Friction welding is used to join pipeline sections.

 

[essenmein]

Friction welding is used to join pipeline sections.

Friction welding is used all over the place, wirebonding for example is a type friction welding.

Although I'm not sure friction is the best way to heat a curing oven for example.