Useful electric motor formulas.

Mechanical Formulas.

Torque in lb.ft. =

HP x 5250 rpm

HP =

Torque x rpm 5250

rpm =

120 x Frequency No. of Poles

To Find	Alternating Current
	Single-Phase	Three-Phase
Amperes when horsepower is known	HP x 746 E x Eff x pf	HP x 746 1.73 x E x Eff x pf
Amperes when kilowatts are known	Kw x 1000 E x pf	Kw x 1000 1.73 x E x pf
Amperes when kva are known	Kva x 1000 E	Kva x 1000 1.73 x E
Kilowatts	I x E x pf 1000	1.73 x I x E x pf 1000
Kva	I x E 1000	1.73 x I x E 1000
Horsepower = (Output)	I x E x Eff x pf 746	1.73 x I x E x Eff x pff 746

Symbols

Basic Horsepower Calculations

Horsepower is work done per unit of time. One HP equals 33,000 ft-lb of work per minute. When work is done by a source of torque (T) to produce (M) rotations about an axis, the work done is:

radius x 2 x rpm x lb. or 2 TM

When rotation is at the rate N rpm, the HP delivered is:

HP = radius x 2 x rpm x lb. 33,000 = TN 5,250

For vertical or hoisting motion:

HP =

W x S 33,000 x E

Where:

For fans and blowers:

HP = Volume (cfm) x Head (inches of water) 6356 x Mechanical Efficiency of Fan

Or

HP = Volume (cfm) x Pressure (lb. Per sq. ft.) 3300 x Mechanical Efficiency of Fan

Or

HP = Volume (cfm) x Pressure (lb. Per sq. in.) 229 x Mechanical Efficiency of Fan

For purpose of estimating, the eff. of a fan or blower may be assumed to be 0.65.

Equivalent Inertia      motor formulas

In mechanical systems, all rotating parts do not usually operate at the same speed. Thus, we need to determine the "equivalent inertia" of each moving part at a particular speed of the prime mover.

The total equivalent WK² for a system is the sum of the WK² of each part, referenced to prime mover speed.

The equation says:

WK2EQ = WK2part Npart Nprime mover 2

This equation becomes a common denominator on which other calculations can be based. For variable-speed devices, inertia should be calculated first at low speed.

Let's look at a simple system which has a prime mover (PM), a reducer and a load.

The formula states that the system WK² equivalent is equal to the sum of WK²_parts at the prime mover's RPM, or in this case:

WK2EQ = WK2pm + WK2Red. Red. RPM PM RPM 2 + WK2Load Load RPM PM RPM 2

Note: reducer RPM = Load RPM

WK2EQ = WK2pm + WK2Red. 1 3 2 + WK2Load 1 3 2

The WK² equivalent is equal to the WK² of the prime mover, plus the WK² of the load. This is equal to the WK² of the prime mover, plus the WK² of the reducer times (1/3)², plus the WK² of the load times (1/3)².

This relationship of the reducer to the driven load is expressed by the formula given earlier:

WK2EQ = WK2part Npart Nprime mover 2

In other words, when a part is rotating at a speed (N) different from the prime mover, the WK²_EQ is equal to the WK² of the part's speed ratio squared.

In the example, the result can be obtained as follows:

The WK² equivalent is equal to:

WK2EQ = 100 lb.ft.2 + 900 lb.ft.2 1 3 2 + 27,000 lb.ft.2 1 3 2

Finally:

The total WK² equivalent is that WK² seen by the prime mover at its speed.