I have seen many posts where a simple AM transmitter can be made with a crystal oscillator and modulation transformer. Can this idea somehow be modified to FM. I don't want people to misunderstand me. I don't mean a crystal locked FM transmitter - these are everywhere. I mean a crystal oscillator somehow able to modulate FM? Does every FM transmitter need a VCO or is there another way to do it?
Yes, there are crystal oscillator designs which can be "pulled" slightly off frequency by introduction of extra capacitance. For crystals in the HF range, this is typically only a few kilohertz, but when multiplied up to VHF it could be on the same order as the typical deviation of narrowband FM voice as used in the amateur and land mobile services.
One possible modulator would be a voltage variable capacitance diode like a varactor. Technically this would make a voltage controlled (or perhaps we should say voltage "influenced") crystal oscillator.
Note that frequencies and power levels where and at which you can legally transmit FM signals are limited.
Also, you will not achieve enough deviation by this method for a wideband FM receiver, such as typically used for consumer music broadcast.
Crystals are electro-mechanical resonators. When properly included into active circuitry as a frequency-dependent feedback with sharp resonance, the frequency is very defined. Since it is difficult to change mechanical properties of the resonator, the frequency is rather stable, which is the whole purpose of the design.
However, predominant crystal oscillator designs (so-called Pierce Oscillator) assume certain capacitive load, CL, about 5pF to 30pF, which is specified for each particular crystal. This "load" has certain effect on the frequency of oscillations. This is called "crystal pullability". This linked article explains, that typical pullability of a crystal is about +-120ppm over the typical range of loads, or about 8ppm per pF. The formula is:
where C0 is shunt capacitance of the crystal, and C1 is the equivalent motion capacitance.
If you consider a 100 MHz crystal (typical for FM broadcast band), 100 ppm would translate into 10 kHz of frequency deviation. The quality FM broadcasting needs about 100 kHz bandwidth, see the Wikipedia article,
In essence, the idea of FM modulation using crystal-based generators contradicts to the entire idea of stable frequency generation.