I agree with Atheus, there are quite a lot of linear regulators that are just as cheap but have better specifications compared to LM317, and have the same pinout. Just the adjustment resistors may have different values.
Speaking of those, I'm not 100% sure but I think the 220 ohm resistors may be a bit too high value in that circuit, the circuit would probably more happy with 100 or 120 ohm resistors there.
In the
datasheet , you can find there at page 5 "Minimum load current to maintain regulation" with 3.5mA typical value, max 10mA ... so with these linear regulators you should aim to make them consume always at least 10mA to be sure the output is always regulated.
Note that the led also uses some power, but due to the 1k resistor in series, it's only going to use about 1-2mA.
Some of the current will be used by that feedback, and that's where lower resistor like 100-120 ohm helps but for extra safety you can also simply connect a resistor between output voltage and ground of each regulator which would dissipate around 10mA as heat ... you have the formula V = I x R so for let's say minimum 4v output and 10mA , you'd place a R = V / R = 4/0.010 = 400 ohm across the output and ground (make it 470 ohm for a standard value). Considering the led will also use 1-2mA and the feedback resistors will also take some current, a larger resistor will probably be Ok to use... something like 1000 ohm would be just fine.
You'd have to be careful to use a properly rated resistor, to make sure it would handle the dissipated power.. you have the formula P = I^2 x R .. so for 10mA and 1000 ohm resistor, the power dissipated would be 0.01 x 0.01 x 1000 = 0.1 watts, so you should use at least a 0.25w or 0.5w resistor.
Also note that you have there 1.5kohm resistor in series with a potentiometer with a 2kohm value. That would make the minimum resistance value possible in your circuit to be 1.5 kohm and the maximum 3.5 kohm.
The output voltage is set with the formula V out = Vref x ( 1 + R2/R1) where Vref for LM317 and LM337 is 1.25v , R1 is that 220 ohm (which I recommend to lower to 100-120 ohm) and R2 is the other resistor (or resistor+potentiometer in series)
So your circuit will have the minimum voltage Vmin = 1.25 x ( 1 + 1500/220) = 1.25x7.8 = 9.75v and the maximum would be Vmax = 1.25x(1+3500 / 220) = 1.25*16.9 = 21v
If you want larger adjustment range, you should use lower minimum resistor. For example, I'd recommend r1 = 100 ohm and maybe a 220 ohm resistor in series with a 1k potentiometer (easier to find)
this will give you a V min = 1.25 x (1 + 220 / 100) = 1.25 x (1+2.2) = 4v and Vmax = 1.25 x (1 + 1220/100) = 1.25 x (1+12.2) = 16.5v ... so your output range would be 4v .. 16.5v
If you want more than maximum 16.5v, you'd use either a larger potentiometer or a bigger resistor in series with the potentiometer (but that will set the minimum configurable voltage higher)
You also used 1n4004 diodes in that circuit. They're good choice, but they may be harder to find compared to 1n4007 for example. The difference between 1n4001 to 1n4007 is just the maximum voltage the diodes can handle... 1n4001 is rated for maximum 50v , 1n4004 is rated for maximum 400v and 1n4007 is rated for maximum 1000v (and slightly lower reverse voltages, 35v for the smallest 1n4001).
Your circuit works with up to around 25v DC so even 1n4001 could be used in your circuit, but the diodes in this series are so cheap and easy to manufacture you're most likely going to find 1n4007 in bigger stocks and at the same price (or lower price) compared to the other models in the series.
Here's a
datasheet for the 1n400x series diodes.
Most linear regulators aren't very picky about how much capacitance is the output, so you don't have to use exactly 22 uF which may be harder to find , or may be more convenient other values. For example, you may want to use 10uF , same as you use in other parts of the circuit because it may be cheaper to buy 5-10 capacitors of same value instead of 2-3 pieces of two different capacitance values.
Or, you may find 100uF or 220-470uF capacitors easier than you find 22uF capacitors... just be careful to buy capacitors with voltage rating higher than the maximum voltage you'd want your power supply to output.
SOME linear regulators require capacitors at the output with some particular specifications, like having a minimum ESR value between some range, like 0.1 ohm to 1 ohm. In such cases, datasheets suggest using tantalum capacitors or electrolytic capacitors (because ceramic capacitors typically have ESR values below 0.1 ohm and small capacitance electrolytic capacitors can have ESR values above 1 ohm so since most tantalum capacitors have ESR values within a narrow range of let's say 0.1ohm to 0.6 ohm they're safe and easy to recommend in a datasheet). One such linear regulator is LM1117 (or any with 1117 in the name).
But the thing is some designs for such linear regulators were invented 10-15 years ago, when there wasn't such a wide selection of electrolytic capacitors and the chemical formulas used to produce the substance in electrolytic capacitors weren't as modern as today. Today you can actually buy electrolytic capacitors that would fit those requirements (for example use a 100uF 25v capacitor with ESR value below 1 ohm, which was very hard to find when those datasheets were written years ago).