Every periodic signal can be described as sum of "basis" functions. These basis functions are the sin and cosines at frequencies of integer multiples of a fundamental freqeuency. This fundamental freqeuency is a consequence of the periodicity of the signal. So if a signal is periodic with time $T$, then the fundamental frqeuency is $F_o = \frac{1}{T}$ Hz. That's the basic Fourier series theorem for periodic signals.
It is the waveform of the signal which will define which of these sines and cosines are present.
Consider the figure below:
It is not straightforward to look at the periodic signal above and tell that it will be comprised of so many frequencies. But it is, that's just a consequence that periodic signals are made of a sum of weighted sinusoids at integer multiples of a fundamental frequency.
Just as you require basis vectors in a vector space to define "any signal" in the vector space, the contributions of these basis vectors can vary depending on the vector being defined.Similarly periodic signals live in a vector space whose basis vectors are these sinusoids (that are defined by the periodicity) of the signal and hence there are contributions (big or small) from all these frequencies to define the periodic signal.
So your observations regarding the frquencies appearing in the spectrum are justified. Infact from the fundamental freuency of the motor (150Hz) we even know how fast the motor is rotating :)
