Electric motor Derive inline engines in six steps

Related Vendors

FAULHABER Drive Systems

Wuxi InfiMotion Technology Co., Ltd.

To save on construction costs, it is worthwhile to derive inline engines with unchanged cross-sectional dimensions. Our author demonstrates this using the example of discrete large DC motors with commutating and compensating windings.

Dipl. Eng. Harald Reich, St. Georgen

In the field of calculation and design of electric motors, the axial extension of the active part (stator laminated core, rotor including windings) is rightfully considered the simplest method to create further motors derived from a successful motor design. This saves on drawing effort, manufacturing tools, and molding devices, if – apart from the winding data – the dimensions remain unchanged in the radial direction.

Therefore, this method is applied to motors ranging from smaller ones through industrial motors to large asynchronous motors (power plant pumps, railway drives, etc.). The situation is somewhat different for large DC motors, which, in addition to the armature winding and the pole-exciting field winding, also have a commutating pole and a compensating winding, and which are used, for example, as mine hoist motors, rolling mill drives, ship motors and generators, or test stand motors.

Since these usually involve low quantities (>=1, < 10), they are individually designed and calculated using the motor calculation or motor simulation programs commonly available at their manufacturing companies, because due to the usually customer-specific design, there are no catalog or already built and measured series motors. In practice, this means that – with the exception of a number of identical rolling mill motors – almost each of these large DC motors represents a unique piece, requiring its own stamping and bending tools, its own drawings, its own straightening molds, and much more during construction.

These DC motors can range from motors with a large yoke outer diameter and many poles with a short axial laminated core length to motors with a long axial laminated core length and a small yoke outer diameter with a low number of poles. The following will show that from a set of already built DC motors, series motors can indeed be created by axially extending the active part, which initially only exist through calculation/simulation, but then offer a good preview of DC motors that are simpler and cheaper to build. Imagine taking an existing reference motor with its windings and extending or compressing it, while the windings remain unchanged except for the axial length change.

Prerequisites for derivation

Here, only the energy-converting active part of the motor is considered, namely the armature laminated core with winding, stator yoke with field winding, commutating pole, and compensating winding. Components such as the commutator, bearings, cooling methods, motor housing, etc., are not considered, as they depend on the active length of the construction, special bearing conditions, permissible noise development, and the losses to be dissipated. The commutator design is based on the segment voltage, the armature winding – which is supposed to remain unchanged here –, and the overload capability of the motor with ü = M_peak [Nm]/M_rated [Nm] and the maximum burst speed [rpm].

Step 1: Start with a set of already built and calculated DC motors, which can vary arbitrarily in number of poles, yoke outer diameter, rotor diameter, and axial length, but all with commutating and compensating windings in the stator. Let's assume here that there are nine different DC motors.

Step 2: Starting from the laminated core length of the built reference motor l_reference [m], set four more package lengths. For example, determine the technically possible maximum and minimum package lengths l_min [m] and l_max [m], as well as two intermediate sizes, e.g., l_inter1[m] = (l_min+l_reference)/2 and l_inter2 [m] = (l_reference+l_max)/2. This provides five support points over a buildable length range from l_min [m] to l_max [m]. Enough to, as will be further shown, lay out a curve, and also enough to identify and eliminate any outliers.

Step 3: Now, enter these four new theoretical construction lengths into the motor calculation program, whose existence is assumed here because large, heavy, and accordingly expensive DC motors cannot be built "just like that" on a trial basis. Instead, they must be calculated theoretically with such accuracy that the final product must meet customer specifications taking into account technical VDE tolerances without fail.

The four new motors, existing only as drafts, are individually calculated with the new assumed package lengths in such a way that the nominal data U_rated [V] and n_rated [rpm] are varied until the same winding data and copper cross-sections are obtained as those present in the real reference motor. From this, the corresponding nominal torques M_rated [Nm], the nominal currents I_rated [A], and the overload values ü [-] (see above) resulting from the usual design rules are then calculated for the four new package lengths.

Step 4: This provides a total of five support points including the real reference motor, allowing for the plotting over the laminated core length from l_min [m] to l_max [m] as x-values the corresponding y-values for U_rated [V], I_rated [A], M_rated [Nm], and ü_rated [-]. This results in four different and continuous curves that can be graphically plotted from l_min [m] to l_max [m]. For this purpose, the use of an Excel spreadsheet with its graphical representation capabilities is advisable.

Having thus computationally extended a reference motor and plotted the four mentioned curves over the package length, it is then straightforward to determine by observation and assessment whether a motor design desired by the customer with the nominal data U_n [V], M_n [Nm], n_n [rpm] can be found within this field. The nominal current I_n [A] and the overload capability ü [-], which is about between 2 and 3, result from the chosen design. However, as the number of reference motors prepared in this way continues to increase (e.g., towards 9 – see above – or even more), a systematic search algorithm must be programmed to systematically search through an open-ended set of these reference motors with their possible axial extensions for the minimum deviation between the customer's target values and the resulting values.

Step 5: The following are three methods proposed and evaluated to generate an approximation curve over the given five outlier-free support points:

• The function y = (a * x² + b * x + c)/(d * x² + e * x + 1) requires five constants, which can be algebraically determined from the five support points. However, this function may tend to have oscillations, so after determining the constants, this function must be checked for zeros and poles, which, if they occur, must then lie outside the domain of x_min = l_min to x_max = l_max.

• Alternatively, the less sensitive function y = (a * x + b)/(c *x + 1) can be used and applied to these two subranges. Range I extends from l_min to l_reference with an intermediate point l_inter1, and Range II then extends from l_reference to l_max with the intermediate point l_inter2. The constants a, b, and c for these two partial functions can also be algebraically derived from the support points. At the contact point at l_reference [m], the two partial functions of ranges I and II meet. There, the slope can be slightly different, but this does not play a significant role in calculation practice here.

• There is also the possibility to connect the y-values of the support points (y stands for U, M, and n) with a straight line, creating a polygonal chain which allows for the determination of the corresponding y-value for all x-values. Since this third possibility is less accurate, it will not be discussed further.

Step 6: For application, let the x-values per iteration and search program go through the active laminated core length l [m] in small steps of Δl [cm] from l_min to l_max. Using the above-determined approximation functions for y, you obtain from x the corresponding values for U [V], M [Nm], and n [rpm]. From these and the nominal values U_N, M_N, and n_N desired by the customer, form the absolute values of the respective relative deviations ΔUr [%] = abs|(U_N-U)/U_N|, ΔMr [%] = abs|(M_N-M)/M_N|, and Δnr [%] = abs|(n_N-n)/n_N|. If the sum of these three relative deviations between the target nominal value and the interpolated

and extrapolated values of the motor under consideration is minimal but still too large, then this process is repeated using a higher-level iteration for motors 2 to 9 (etc.). If there is now a value of the sum of the three relative deviations that is very close to zero, then the new motor derived from an already built reference motor has been found, which then only needs to be verified using the regular motor calculation.

However, if there is no solution that is close enough to zero, then a completely new motor is created as previously usual with new dimensions, and after its construction, its data can be added as the 10th motor to the above set of characteristics. Even then, it is recognized from which yoke outer diameter at the specified laminated core length of the already examined and stored motors 1 to 9 the redesign can start, now with changed and adapted winding data.

This method is certainly applicable to other motors than large DC motors, but it is not sensible if there are already manufactured and measured series motors with stepped laminated core lengths – usually, there are four lengths in general, identical lamination cuts, and the same lamination outer diameter or shaft height. (ud)