Tom Bishop. P.E.
EASA Technical Support Specialist
It should not be assumed that because a motor can drive a running load, it also has the capability to accelerate the load up to rated speed. During starting, a motor must deliver the energy required to accelerate the load. To do this, the motor torque must exceed that needed to accelerate the load. The motor torque value in excess of the load torque requirement is termed the “torque available for acceleration,” as shown in Figure 1.
Though this explanation appears to be relatively simple and straightforward, there are some complex conditions. Namely, that the motor torque during starting is not constant, and unless the load is a pure inertia load (very rare), it does not have a constant speed-torque relationship. Therefore, the torque available for acceleration is the difference between the speed-torque curves for the motor and the load.
The acceleration time for the motor and load system can be determined from the following formula:
Acceleration time = (wk2 x rpm) / (308 x Tacc)
The inertia of the load is the wk2 factor in pound-feet squared, the rpm is the speed change of the load, and Tacc is the average accelerating torque of the motor in pound-feet.
The result is acceleration time in TM = seconds. In metric TA = units wk2 is inertia TL = in kilogram-meters squared and Tacc is average accelerating torque in Newton-meters.
The formula using metric units is: Acceleration time = (wk2 x rpm) / (9.55 x Tacc)
Calculating acceleration time
However, we need to refer back to the comment about torque available for acceleration not being constant. Calculating acceleration time would require determining the torque available at every point in the motor and load speed-torque curves. The practical method of accomplishing this is to break the curves into parts, or increments, and average the results.
Motor torque ratings are normally based on full rated voltage being available at the motor terminals. In many applications the voltage at the motor is less than rated, due to such conditions as voltage drop in the feeder circuit or reduced voltage starting. The result is a reduction in motor torque, varying approximately as the square of the ratio of applied voltage versus rated voltage.
The effects of saturation reduce the motor torque even more. For example, if the voltage at the motor were 80% of rated, the expected torque reduction would be (0.8/1.0)2 = 0.64, or 64%. Due to the reduced .ux however, the torque would probably be closer to 57% of rated.
Although the motor torque available has been reduced, the load torque remains unchanged. The result is a longer acceleration time. If the reduced motor torque is equal to that of the load, leaving none available for acceleration, the motor and load will not accelerate beyond that speed point. Further, if the motor torque is less than that of the load at initial startup, the rotor will not rotate. That is, it will remain in a locked-rotor condition. Figure 2 illustrates both of these conditions.
Effects of heat
A major limiting factor for the starting capability of a motor is heating of the stator and rotor. During acceleration, some of the electrical energy is used to drive the load, and the remainder is absorbed by the stator and rotor in the form of heat. The primary source of this heating is I2R losses in the stator and rotor, which are much greater during acceleration compared to normal operating conditions. The starting current of a motor is frequently between 6 and 8 times rated current. If we take the average value of this range, 7 times rated current, the ratio of I2R at starting compared to running would be 72 or 49, assuming the resistance remains unchanged. Since the heating also increases winding resistance, it would be reasonable to expect at least 50 times normal heating during starting conditions.
Fortunately, under normal starting conditions, the heating period is relatively short in duration. For example, NEMA MG1 Part 12.49 allows an acceleration time of up to 12 seconds for motors rated to 500 hp (375 kW) and rated 1 kV or less. During this period parts of the stator and rotor may reach temperatures in excess of their rated temperatures. Conservative motor designers assume that all of the heat generated during starting is absorbed in the components that produce the heating, e.g., the stator and the rotor. Therefore these components heat very rapidly, and to relatively high temperatures.
However, since the duration of acceleration time is very short, it does not normally have a negative impact on motor life. Upon attaining rated speed, the current and temperature drop to normal levels for the load conditions.
For motors larger than 500 hp (375 kW), or with loads with greater than normal inertia (see NEMA MG1 Table 12-7), the motor manufacturer should be consulted to determine the time limit for accelerating the load.
Stator and rotor limits
Motor starting capabilities are thermally limited by either the stator or the rotor. If the stator is the limiting factor, the motor is termed to be “stator-limited”; and if the rotor is the limiting factor, the motor is termed to be “rotor-limited.” In general, smaller motors, such as in NEMA frames, tend to be stator-limited; and larger motors, well above NEMA frame size, tend to be rotor-limited.
The limits of load inertia for motors rated from 1 to 500 hp (0.75 to 375 kW) are given in NEMA MG1 Table 12-7 and for motors rated 100 to 15,000 hp (75 to 11000 kW) in Table 20-1. The overlap in power ratings is due to different speed ratings, with higher speeds (for the same hp rating) appearing in Table 12-7 and lower speed ratings in Table 20-1. According to the NEMA standards, there are three conditions that apply to the maximum inertia ratings given in these tables. The .rst is that the applied voltage and frequency are at rated values. Thus, if voltage is reduced at starting, the inertia limits given in the tables may not apply.
Torque variables
The second condition is that the load torque is equal to or less than a torque that varies as the square of the speed and attains 100% full-load torque at rated speed. Further, the motor must develop a torque that exceeds these values by at least 10%, up to the speed at which breakdown torque occurs. Essentially this means that the motor should be able to accelerate a load with a variable or constant torque speed-torque characteristic.
The third condition is the number of starts allowed. There are three subsets of conditions that apply. The .rst is that the motor is allowed “two starts in succession, coasting to rest between starts, with the motor initially at ambient temperature.” The second is that the motor is allowed “one start with the motor initially at a temperature not exceeding its rated load operating temperature.” A potential dif.culty with adhering to this condition is determining the rated load operating temperature. That would require temperature sensing in the windings, such as from resistance temperature detectors (RTDs). Without such devices, the operating temperature will not be known.
The third subset of the third condition applies to additional starts and states: “If additional starts are required, it is recommended that none be made until all conditions affecting operation have been thoroughly investigated and the apparatus has been examined for evidence of excessive heating. It should be recognized that the number of starts should be kept to a minimum since the life of the motor is affected by the number of starts.”
Among the dif.culties in dealing with this last requirement are determining that “all” conditions affecting operation have been “thoroughly” investigated. Further, examining the motor for evidence of excessive heating would necessitate an internal inspection. While these constraints are not very practical, they are the standard that applies.
Contact motor manufacturer
Although it does not fulfill the necessary requirements to be considered an alternative, at the very least the motor should be allowed to cool to room temperature (ambient) prior to restarting. A better alternative, which may not always be practical, is to contact the manufacturer for restarting and additional start requirements for the specific motor and load application.
The disadvantages of exceeding the limits of motor starting capability can range from overheating of components to failure to accelerate the load, and on to failure of the motor itself.
Overheating of components during starting often has a long term cumulative effect that reduces the life of the component such as the stator or rotor. The consequences of failure to start the load are obvious; the motor is unsuitable and unusable for the application.
Failure of motor components may be due to a number of stresses associated with acceleration. In the rotor, the bars and end rings that make up the rotor cage are subject to high and cyclic (alternating) magnetic forces. Heating of the rotor cage results in axial expansion of the bars and radial expansion of the end rings, creating stress in various sections of the bars and end rings.
Current tends to “crowd” the tops of the bars during starting, causing bending stresses as the top of the bars try to expand more than the bottoms. This is depicted in Figure 3. As speed increases during acceleration, centrifugal forces add mechanical “hoop” stresses to the thermal and other stresses already mentioned.
Mechanical and electrical forces
The mechanical and electrical forces also affect the stator windings.
The excessive starting current leads to rapid heating of the windings, and consequently, rapid thermal expansion resulting in physical stress. The torque forces associated with starting are many times normal, leading to winding movement and possible motion between adjacent conductors, or conductors and frame or core, which can result in a short circuit or ground fault.
Each acceleration period is a fatigue cycle and the cumulative effect results in a .nite life for the motor based on the number of starts. However, there are no standards or guides for the minimum number of starts for a motor. Returning to our opening statement, use caution with motor applications since it should not be assumed that because a motor can drive a running load, it also has the capability to accelerate that load up to rated speed.
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