DC motor efficiency which formula to use?
\$ V_f I_f\$ is a pure loss, it is needed for the excitation. If the excitation winding would be made of superconductor, then you could fill the current only once and close the windings contacts. The other solution is to use permanent magnets instead.
Then you have a copper loss \$I_a^2 R_a\$ and a iron loss in the rotor \$P_{fe}=k_{fe}\Omega\$, as the rotor field is AC, but let's say that you can omit this for simpler calculation.
Post the formulas you did before, so we can take a look and discuss.

EDIT:
You could rewrite the efficiency formula from loss. \$P_{in}=P_{EM} + P_{loss} = P_{EM}+ P_{Cu}+P_{Fe}\$, where \$P_{EM}\$ is the electromagnetic energy and it is converted into a mechanical energy, so let's make a new formula:
$$\eta=\dfrac{P_{mech}}{P_{mech}+P_{loss}}=\dfrac{P_{mech}}{P_{mech}+V_fI_f+I_a^2R_a}$$
The formula is omits the iron losses. At least you won't get over 100% efficiency, additionally you need a resistance of the armature \$R_a\$