ASHRAE Journal - July 2010 - 100

Wire-to-Shaft Eff iciency
By James B. (Burt) Rishel, P.E., Fellow/Life Member ASHRAE

Variable Speed Electric Motors

T

 he  efficiency  of  a  variable  speed  drive  and  motor  is  known as the “wire-to-shaft efficiency.” It is the energy  imparted to the shaft of the driven member (fan, pump,  or compressor) divided by the energy supplied to the switchgear  for the motor. Figure 1 describes this efficiency. Wire to Shaft Efficiency = bhp at driven shaft × 0.746 × 100 %  (1)   kW input to VFD

Incoming Power

Since most such motors are operated by variable frequency  drives, why not just multiply the efficiency of the drive by that  of the constant speed motor? Variable frequency drives have  improved greatly, but some distortion still occurs of the sine  wave to the motor at reduced speeds. Therefore, it is not possible  to simply multiply the two efficiencies. Also, the efficiency of  the variable speed motor is quite different than the efficiency  of a constant speed motor. For example, the rolling friction and  windage losses are less for the variable speed motor. Wire-toshaft efficiency is one efficiency for the drive and motor. Why is this efficiency so important? It is impossible to compute accurately the energy consumption of a variable speed device without it. To simplify this discussion, the following pertains  to centrifugal pumps only. When a study is made to determine  the value of a variable speed, centrifugal pump compared to a  constant speed pump, it cannot be done unless a wire-to-shaft  efficiency curve is available to determine the energy consumption of the drive/motor combination at various pump speeds. The energy required by the centrifugal pump is easy to compute at various speeds. It uses a system head curve (Figure 2).  This figure is for a 1,000 gpm (63 L/s) pump with a design total  dynamic head of 100 ft (299 kPa). It shows the problem that  complicates  the  development  of  the  wire-to-shaft  efficiency  curve,  namely,  the  presence  of  constant  head  in  the  system  head curve. This figure includes 20 ft (60 kPa) of head that is  the differential pressure maintained on a chilled water distribution loop regardless of the speed of the pump. Therefore, the  operation of this pump is not truly a variable torque process.  Centrifugal  pumps  are  usually  considered  variable  torque  machines where the torque required to turn the pump varies as  the square of the speed. Equation 2 describes this:      S12  (2) T1 = T2  2       S2    where, T is the torque and S is the pump speed.
100	 ASHRAE	Journal	

Variable Frequency Drive Wire-to-Shaft Efficiency

Electric Motor

Figure 1: Wire-to-shaft efficiency.

The curve of Figure 2 can be used to produce Table 1 and  the curve of Figure 3 (the brake horsepower required by the  pump at various percentages of full speed). The pump speeds  and efficiencies are determined at various system loads through  the use of the affinity laws for pumps. Equation 3 describes the  formula for the calculation of pump brake horsepower at various  percentages of system load on the pump.       Pump Brake Horsepower, bhp =   System Flow (gpm) × System Head (ft) 3,960 × Pump Efficiency (as a fraction) (3)

Table 1 can be developed as the flow on the pump varies from  10% to 100% of the design flow. Columns A and B of Table 1  are the data for the curve in Figure 2, while Columns C and E  are the data for the curve in Figure 3. We now are at a stopping point until we secure a reasonable  wire-to-shaft efficiency curve or data. This is demonstrated by  Equation 4:
ashrae.org	 	 July	 2010
ASHRAE Journal - July 2010

Table of Contents for the Digital Edition of ASHRAE Journal - July 2010
