When stainless steel is heated to welding temperatures, it turns lots of pretty colors - gold, red, purple, blue - depending on the temperatures. These look nice, but if you want your stainless steel to look like stainless again, a polishing step is required.
Mechanical polishing using a surface conditioning pad works nicely to remove the color, but has disadvantages - any mechanical polishing will change the surface texture. If you've polished the steel to a different texture before welding, it can be difficult to get the original texture back. Additionally, mechanical polishing requires getting the polisher in what might now be a limited space.
The best way to clean stainless steel without these problems is by electropolishing. Electropolishing works by accelerating an oxidation reaction of an acidic electrolyte on a metal surface using electricity. For the details, you can read the electropolishing wikipedia entry. As a side benefit, cleaning your stainless steel using electropolishing helps it become properly passivated. This means the surface is covered in an iron-free chromium oxide layer. If the surface is not properly passivated, your stainless steel might not be so stainless.
There are some commercial tools out there for electropolishing stainless steel that look really great but are prohibitively expensive, even the cheapest costs nearly as much as the TIG welder I used to make these welds in the first place. Fortunately, it's not hard to do with a standard bench power supply and a little polishing wand that you can either DIY or use some fancy parts.
Step 1: Power Supply
Any power supply that puts out 30 V / 5 A should be fine. This one I bought on the internet for $70. It's pretty handy having the digital voltage and current display and current limit control.
Step 2: DIY Wand
One end of the power supply connects directly to the workpiece (the piece you're polishing), and the other connects to a wand that you do the polishing with. The wand is made from a metal electrode wrapped in a cloth to keep it from making direct contact with the workpiece. The cloth holds the electrolyte liquid and conducts electricity but prevents arcing.
Here I've made the electrode from a scrap piece of 12ga stainless steel cut into a rectangle. It's important to grind off any pointy corners or sharp edges because those will cause arcing a lot sooner. The electrode is connected to a banana plug to alligator clip cable. I used a high current clip in between the alligator clip and the electrode because it clips to the electrode a little bit more securely, but it's not totally necessary.
The electrode is wrapped in fiberglass tape from the auto parts section of a hardware store. This stuff is cheap and holds up ok. I wrap the electrode with the fiberglass tape and secure the fiberglass with electrical tape. I just use one layer of fiberglass, more than that it is difficult to get much current to flow.
To use this you soak the cloth in electrolyte and touch it to the workpiece with the power connected. The circuit is completed causing electricity to flow and the electropolishing reaction to occur on the workpiece surface.
Step 3: Less DIY Wand
This is a wand made from commercial parts designed for this purpose. It is considerably more expensive for this stuff than for the DIY wand, but it's worth it if you want reliability. The electrode is Walter part number 54B038 and a pack of sponges is Walter part number 54B028. One little plastic ring for holding the sponge to the electrode is included with a pack of sponges, or you can just use a rubber band.
This setup is a lot more resistant to arcing than the DIY wand - the sponge lasts a lot longer than the fiberglass before burning out. It conducts electricity better too, so you can polish faster.
Step 4: Polishing Setup
Here you can see my whole setup.
I built the wand using the red wire, since I think of it as the active thing and the workpiece as ground. However, you want the electrode at negative voltage with respect to the workpiece. Since the power supply only puts out positive voltage, I have swapped the connectors where they plug into the power supply. Don't forget, electrode negative!
The electrolyte I used is Walter Surfox-T. I tried a couple other things that worked okay but this cleaned the fastest. It contains strong phosphoric acid, 30 - 60%, with a pH less than 1 (according to the MSDS). Be careful with it! When working with this stuff I wear a respirator mask, safety glasses, heavy welding jacket to keep it off my clothes, and big rubber gloves. You don't need to use a lot of liquid, so just pour a little into a container you can dip the wand into.
To polish, you clip the ground clip to the work piece, turn on the power supply, dip the wand in the electrolyte, and touch it where you want to polish. I set the power supply to the maximum voltage (30 V) and then tweak the current control to control the reaction speed. Ideally the wand will conduct lots of current and the power supply will have to drop the voltage to reach the current setting you indicate. If you are at 30 V and < 1 A is conducted, it probably means you need a more conductive wand. I like to set the current control around 3 A but it's okay to let it run at 5 A. This process can also make your metal shinier, I like to keep the reaction under control to minimize that effect.
After you're done polishing the acid should be wiped up and then the surface washed with a neutralizer such as Walter Surfox-N. This stuff is much less nasty than the electrolyte, but it's a bit basic with a pH of 12.5 or so. If it's not neutralized the acid will continue to attack your metal, leaving it with a milky texture. After neutralization I like to shine it up with some stainless steel cleaner.
Step 5: Before
Here is a picture of some welded stainless steel before polishing. All of those colors came from the heat.
Step 6: After
Here you can see the piece after polishing. The weld and surrounding area looks like nice shiny stainless steel again.
I also included an after picture from an application of this technique on a sculpture of mine. These small welds hold a sculpture to its baseplate. The stainless steel plate was polished and sanded to a nice uniform matte texture before welding. The piece was electropolished after and the texture was recovered. It would've been impossible to get the polisher in there to clean that weld, and even if I could've it would've changed the texture.