Is It Safe To Apply 24V Across a 12V Motor

First we need to look at the uncertainties before we address possible solutions:

• Are there two motors in use or one - it could be either from your text.

• And, is the 40A for two motors in use or one?

• You say " ... motor was spun ..." - what does this mean? An unloaded motor is rated at 2.7A, at normal load it's 27A and max power = 68A.
  Where on that continuum is "was spun" ?

• You need to describe the nature of the load and your application. Whether it is possible to decrease input power to the motor to within battery specs and still meet your requirement is unknowable to us as you have not provided enough information.

• What is the mechanical arrangement?
  What attaches to the shaft(s)?
  Why do you need to run it at that power?
  Why can you not run it at lower power?
  Do you use a motor controller or just connect the battery to the motor directly?

• Please supply battery model and brand and very ideally a internet link.

• What else can you tell us that may help us to help you?

Mechanical:

Changing physical gear ratio inside the gearbox is a mechanical task outside the scope of this form. It is possibly possible, but more likely not to be. Doing this depends on the gearbox design. The manufacturer and/or user community will be able to comment on this.

If you are using or can use a belt or chain drive externally you may be able to change the ratio of pulleys or sprockets used to reduce speed and increase torque.

You MAY be able to move the motor back from where it is mounted so there is miore room and add an inline speed reducer - maybe 2:1.

Electrical:

You can PWM the motor(s) to limit battery current to 25A continuous this will reduce power to probably about 25/40 = 65% of that at 40A but maybe not. Motor efficiency rises usefully with decreasing current but it is not certain how it will run at 25A mean under your load.

Depending on facytors such as PWM frequency and duty cycle, motor imp[edance and more PWM may reduce peak moptor current to mean current or may still cause peaks greater than motor continuous maximum. So, if you use PWM yiou will ideally add capacitance to the PWM input = battery output that will supply the PWNM pulse currents while limiting mean and peak battery currents to no more than the continuous maximum rating.

Battery rated maximim continuous output is 25A.
Based on what you say the unseen by us data sheet says you can run it at 40A for 30 seconds followed by the rest period for 70A in the data sheet - ie at the 70A ratings. You MAY be able to run it for longer safely or with a lower rest period. Or not. If you provide a link to the battery data sheet and tell us the brand and model we may be able to tell you more. Maybe not, but without that it's a guess at best.

The voltage across a DC motor is made up of two components. A component from the resistance of the coils and a component from the inductive behaviour of the moving coils. When a motor is stalled it behaves like a resistive load.

Most motors if stalled while supplied by their rated voltage will draw considerably MORE than their rated power (and will overheat if a protection circuit doesn't kick in).

For a resistive load:

$$P=\frac{V^2}{R}$$ $$V^2 = PR$$ $$V=\sqrt{PR}$$

To get 500W into a 15 ohm resistive load would need about 80V. So that means that this motor is likely designed for a supply voltage of considerably more than 80V.

I would guess that this motor is designed to run at full power when fed with rectified mains and then there is some control circuitry to reduce power on lower power settings.