A Comparison of Rotor Bar Material of Squirrel-cage Induction Machines for Efficiency Enhancement Purposes Yiqi Liu, Student Member, IEEE, Paul Han and Ali M. Bazzi, Member, IEEE Department of Electrical and Computer Engineering University of Connecticut, Storrs, CT 06269, USA Email:
[email protected]
Keywords Induction Motor, AC Machine, Efficiency, Design, Rotor Material
Abstract This paper provides a comprehensive analysis and comparison of different rotor bar material in squirrel-cage induction machine from electrical, physical and economic perspectives in order to explore the impacts of rotor bar material on machine efficiency with physical and economic considerations. Specifically, aluminum, copper and silver are selected in this work and studied on three machines of different ratings, where silver is proposed as a hypothetical rotor bar material to open discussion and to explore potential possibilities. To provide an overall analysis, an analytical model and a finite-element model of an induction machine are used in this work with their focus on machine efficiency and magnetic flux distribution, respectively. It shows that a silver rotor can provide the highest efficiency under all tested loads and machines with efficiency enhancement of 0.20 to 1.55 percentage points compared to the aluminum counterpart depending on the machine rating and load. Moreover, better performance, such as larger output power, smaller starting torque, more concentrated magnetic flux distribution, etc., are observed with the increase of rotor bar conductivity. However, the significantly high price of silver could impede its usage in most applications currently and copper rotor bar is believed to have the overall superiority among the three kinds of material, although it suffers from casting issues due to its high melting points. Silver rotor bars or silver alloys may be used in energy-limited areas where high efficiency is needed to compete with certain magnetic material.
I. Introduction It is reported that electric motor drive systems account for over 40% of the global electricity consumption [1], while induction machines, mainly the squirrel-cage type, are the single largest energy consumer due to their high popularity in industry. Therefore, improving induction machine efficiency is critical for energy and cost savings as well as carbon footprint reduction of motor drives. Aluminum has been used as the traditional rotor bar material in induction machines due to its high conductivity and low price as well as its decent physical properties to meet thermal, metallurgical and mechanical requirements. To pursue higher machine efficiency, a more expensive material––copper– –has been proposed for rotor bars over the past two decades due to having over 60% higher conductivity compared to aluminum. It is believed that the long-term operation benefits of using copper rotor bar can easily pay back the extra purchasing cost of copper rotor machines [2]. References [3] and [4] are examples of research that shows better performance of copper rotor bars as well as their long-term economic benefits compared to aluminum counterparts. Meanwhile, the high melting point of copper leads to serious thermal stress on casting dies which greatly shortens their lifetime and causes manufacturing difficulty, especially for medium- and small-sized induction machines [5]. Some metallurgy technologies targeting on this problem have been developed during these years. In [6] and [7], a nickel-based alloy is proposed to be a prospective die material that can largely extend the die lifetime and maintain low porosity of the casted copper in experiment. Following up with this line, silver is proposed in this paper as a hypothetical rotor bar material, since it has even higher conductivity than copper and it is actually the most conductive metallic natural material followed by copper. Although
results show that the extra cost of silver rotor bar cannot be paid back through more efficient operation in a reasonable period of time, it is useful to initiate the discussion and to explore its possibility for future work on machine design optimization and silver-based alloy material. This paper assumes that the rotor bar shapes and distributions are identical for all three considered material – aluminum, copper, and solver. Both analytical and finite-element models are used in this work to provide a comprehensive analysis of the rotor bar material with their focus on machine efficiency and magnetic flux distribution, respectively.
II. Machine Efficiency and Performance Analyses The per-phase equivalent circuit of squirrel-cage induction machines shown in Fig. 1 is used to provide analytical analysis of the machine’s power losses and efficiency as well as the machine’s torque and speed performances. V1 and s are the input voltage and slip, respectively; R1, i1 and R2’, i2’ are stator resistance and current, and referred rotor resistance and current, respectively; Rc and Xm are core loss resistance and magnetizing reactance, respectively. Torque (T), output power (Pout), copper loss (PCu) and core loss (Pcore) as well as the efficiency (η) can be calculated through (1) to (5), where ωsync is the synchronous speed; Vth, Xth and Rth are the Thevenin voltage, reactance and resistance looking from the magnetizing branch to the input side. Three real aluminum rotor bar induction machines available for experimentation are used for a case study, and the machines are rated at 1.5HP (1.125kW), 3HP (2.25kW) and 10HP (7.5kW). To extract the values of machine structural parameters needed for (1) to (5), machine characterization tests––lockedrotor test, no-load test and DC test––are conducted using the setup shown in Fig. 2. The two-Watt-meter method is used and the dynamometer is either decoupled from the induction machine or fixed to lock the rotor during the no-load test and locked-rotor test, respectively. As shown in (2) to (5), Pout, PCu, Pcore and η are functions of i2’, while i2’ can be calculated from (2) considering that the Pout-slip relationship is available from the Torque-slip curve of the machine based on (1). Therefore, machine power losses and η versus Pout can be calculated. These calculations are implemented through Matlab code and the results for the 1.5HP machine are shown in Figs. 3-5 as examples. Moreover, the torque-speed and the output power-slip curves are plotted to analyze machine performances with the results of the 1.5HP machine shown in Fig. 6 and Fig. 7. Note that losses considered here do not include stray, friction, and windage losses. But these are expected to be uniform for different rotor bar material. To explore the impact of rotor bar material on η and machine performance, R2’ is scaled with respect to the conductivity relationship of silver versus aluminum and copper versus aluminum. Repeating the Matlab code with the new rotor resistances, R2’_Ag and R2’_Cu, the machine losses and η as well as the torque and output power performances for silver and copper types are plotted in Figs. 3-7 and compared to the aluminum case. Note that the resultant curves of the 3HP and 10HP machines have similar shapes of the 1.5HP one but have different numerical values.
Fig. 1: Per-phase equivalent circuit. T=
Fig. 2: Machine characterization test setup.
3Vth 2 R2' / s 2 2 ωsync ⎡⎢( Rth + R2 / s ) + ( X th + X 2 ) ⎤⎥
⎣
⎦
,
(1)
⎛1− s ⎞ ' Pout = 3i2' 2 ⎜ ⎟ R2 , ⎝ s ⎠
PCu
2 ⎛ ⎞ ⎜ ⎟ ⎜ ( R2 '/ s + jX 2 ) i2' '2 ' ⎟ = 3⎜ + i2 ' R1 + i2 R2 ⎟ , ⎜ ⎛ jRc X m ⎞ ⎟ ⎜ ⎜⎝ Rc + jX m ⎟⎠ ⎟ ⎝ ⎠
Pcore = 3
η=
(2)
Pout
( R2 / s + jX 2 ) i2 Rc
(3)
2
,
Pout × 100% . + Pcu + Pcore
(4)
(5)
It is found that PCu increases significantly with Pout since they are both proportional to i2’2. Thus, silver has the smallest PCu in all conditions due to its highest conductivity. The PCu differences of the three materials are more evident with the increase of the loads. Thus, high conductivity materials have better application in heavily loaded machines from energy and efficiency perspectives. On the other hand, Pcore is relatively less affected by Pout since slip increases with Pout. Thus, the decrease of R2’/s can compensate the increase of i2’ due to load increase. Rotor bar material barely has impact on Pcore which is consistent with the previous research [4]. The slight increase of Pcore due to using high conductivity rotor bar material is caused by the small increase of magnetizing branch voltage while Rc remains the same. As shown in Fig. 5, silver rotor machine has the highest η in all conditions followed by the copper type. Aluminum is the least efficient among the three. The same conclusions apply for the 3HP and 10HP machines. To obtain a quantitative analysis of η enhancement, η of the three induction machines under four percentage load conditions––100%, 75%, 50%, 25% of the rated Pout––are summarized in Table I for comparison. It is found that the degree of η enhancement increases with the load of a machine or the power ratings of machines while they are operating at the same percentage load. For example, η enhancement of silver rotor motor over the aluminum case increases from 0.2% to 1.17% for the 1.5HP machine when the load increases from 25% to 100%. Moreover, the η enhancement increases from 1.17% to 1.55% when the machines change from 100% loaded 1.5HP machines to 100% loaded 10HP machines. On the other hand, it is found that the η enhancement of silver versus copper is smaller than 0.12 percentage points, which is as expected since they only have roughly 6% conductivity difference. As for the machine performance aspects, the torque-speed curve and Pout capability are the two parts of main interest. Fig. 6 shows that increasing the conductivity of rotor bar material will push the pull-out torque point to the synchronous speed and make the linear region steeper, while the value of pullout torque keeps the same. Therefore, increasing rotor bar conductivity can help machine maintain rated torque without losing much speed to almost mimic synchronous motor operation in the induction machine’s linear region. Moreover high rotor bar conductivity is found to decrease the starting torque of the machine. Thus, it can relieve issues related to large in-rush current and give a smoother startup transient. On the other hand, Fig. 7 shows that increasing rotor bar conductivity can improve the maximum Pout which appears at lower slip now. Moreover, Pout of high conductivity rotor bar machines is larger than Pout of the relatively low conductivity rotor bar machines at low slip conditions, and higher at high slip conditions. The crossover point depends on the machines’ relative conductivities.
Fig. 3: Copper loss of the 1.5HP machine.
Fig. 4: Core loss of the 1.5HP machine. Table I. η comparison of different rotor material.
Fig. 5: Efficiency of the 1.5HP machine.
Fig. 6: Torque-speed curve of 1.5HP machine.
Fig. 7: Output power-slip curve of 1.5HP machine.
III. Magnetic Flux Distribution and Physical Analysis A simple finite element analysis (FEA) is performed using the Finite Element Method Magnetics (FEMM) free software to study the magnetic flux distribution along the cross section of the machine. A 1.5HP machine is cut in the lab, and the cross-sectional images are shown in Fig. 8. Based on the physical measurements, an FEA model is built and shown in Fig. 9 which mainly consists of four types of areas: stator winding and core, and rotor bar and core. M-19 silicon steel is used to characterize the stator and rotor core areas, and 35 turns of 22 AWG copper wires are used to fill the stator winding area. As for the rotor bar area, aluminum, copper and silver are used to show the impact of rotor bar material on the machine’s magnetic flux distribution. The results (absolute value of flux density) of the machines at
loaded conditions are shown in Fig. 10. It is found that the magnetic flux is more concentrated in high conductive rotor bar machine, as the equivalent magnetic poles are more evident with less leakage flux in the silver rotor machine. Therefore, the magnetic transfer efficiency between the stator and rotor is higher with rotors of higher conductivity, which is consistent with previous research [4].
Fig. 8: Cross section of the 1.5HP machine.
Fig. 9: FEA model of the 1.5HP machine.
Fig. 10: Simulated magnetic flux density distribution: (a) Aluminum; (b) Copper; (c) Silver. Some other general physical properties of aluminum, copper and silver are summarized in Table II in order to discuss their advantages and disadvantages of being rotor bar material [8]. First, aluminum and silver have lower melting points than copper so that they can induce less thermal stress on casting dies and facilitate rotor bar manufacturing. Second, copper has the smallest thermal expansion coefficient. Thus, its deformation after cooling down from the casting temperature is expected to be the smallest among the three. Third, it is found that thermal conductivities follow the relationship of electrical conductivities. The high thermal conductivity is beneficial to create uniform rotor bar structures during the crystallization process as well as to avoid partial overheating during machine operation. Fourth,
copper has the largest bulk modulus followed by silver, so it can provide strongest mechanical support in the structure. Last but not the least, aluminum is found significantly lighter than the other two materials and silver is the heaviest one. Thus, replacing aluminum by higher conductive copper or silver may increase the machine weight, which is especially undesirable for portable or movable applications, such as electric vehicles. However, some conclusions such as the machine weight may change if silver or copper rotor machines are found to require less rotor bar material due to the higher conductivity of silver or copper in future work. Table. II. Physical properties of aluminum, copper and silver Aluminum Copper Silver Melting Point (˚C) 660 1084 961 Thermal Expansion 22.2 16.6 19.5 (μm·m-1/˚C at 25 ˚C ) Thermal Conductivity 205 401 429 (W·m-1·K-1 at 25 ˚C) Bulk Modulus (Gpa) 68-70 123 100 [9] Density (kg·m-3) 2712 8940 10490
IV. Economic analysis of rotor bar material High-efficiency machines are believed to have long-term benefits due to their accumulative savings from efficient operation over the extra initial purchasing cost. The payback time is of the main interest and it can be calculated from (6), T pb =
Ae − Ac , BC (ηe − ηc )
(6)
where Ae, ηe and Ac, ηc are the price and efficiency of the efficient machine and the common benchmark, respectively; B is the machine average power and C is the price of electricity per kWh; Tpb is the payback time (hour). Rough estimations of the payback time of the 1.5HP machine when changing the rotor bar from aluminum to copper or silver (Tpb_AlCu or Tpb_AlAg) are performed as case studies. The price differences of machines are calculated based on the rotor bar volume from previous physical measurements, material densities in Table II and the current prices of aluminum, copper and silver which are about 0.8$/lb, 2.7$/lb and 240$/lb, respectively [10]. The difference of manufacturing cost is neglected. As a result, the estimated cost differences for aluminum/copper and aluminum/silver are around 8$ and 934$, respectively. On the other hand, the average electricity price in USA is currently about 0.16$/kWh [11]. Assuming the 1.5HP machine operates at the rated output power, thus the efficiency enhancement via using copper and silver rotor bars are 1.09 and 1.17 percentage points based on Table I. Therefore, the estimation results of Tpb_AlCu and Tpb_AlAg are about 4099h (~0.5 years) and 445873h (~51 years), respectively. Thus, the extra cost of using copper rotor bar can easily be compensated for through the machine’s operational energy savings, whereas the payback time of silver rotor machines is unacceptably long considering the nominal induction machine lifetime. However, it is still inspiring to have silver or silver alloys in consideration and the payback time may be significantly reduced due to the optimization of rotor bar shapes and sizes as well as the changes of material and electricity prices.
V. Conclusion This paper provides a comprehensive analysis of the impacts of rotor bar material on induction machines in order to explore approaches for machine efficiency enhancement from material perspective. Aluminum, copper and silver are selected for study and comparison. Silver shows the highest efficiency
in all conditions and up to 1.55 percentage point efficiency enhancement based on the per-phase equivalent model of squirrel-cage induction machines. Moreover, it is found that increasing rotor bar material can also increase the machine’s maximum output power and make the linear region of the torque-speed curve steeper without changing the pull-out torque value. The FEA model shows that high conductive rotor machines have more concentrated magnetic flux distribution and less leakage flux. In addition, copper and silver also show some better mechanical and thermal properties over aluminum. However, the payback time for silver is unacceptably long and it is currently immature to propose silver rotor machines. Effort on structure optimization and silver-based alloy design as well as exploring silver rotor machine in energy-limited applications are expected. Aligning with previous researches, copper is believed to have the overall superiority among the three materials if the metallurgic issue can be properly resolved.
References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11]
P. Waide and C. U. Brunner, “Energy-Efficiency Policy Opportunities for Electric Motor-Driven Systems,” International Energy Agency, pp.11, 2011. S. Lie, C. Di Pietro, “Copper die-cast rotor efficiency improvement and economic consideration,” IEEE Trans. Energy Convers, vol. 10, no. 3, pp. 419–424, Sep. 1995. I. Daut et al, “Comparison of copper rotor bars with aluminium rotor bars using FEM software–a performance evaluation,” International Conference on Computer and Electrical Engineering, pp. 456–459, 2009. K. Hafiz et al, “Comparative performance analysis of aluminum-rotor and copper-rotor SEIG considering skin effect,” International Conference on Electrical Machines, pp. 1–6, 2008. M. Thieman, R. Kamm, J. Jorstad, “Copper motor rotors: energy saving efficiency, now also economic feasibility,” Electrical Insulation Conference and Electrical Manufacturing Expo, pp. 328–333, 2007. D. T. Peters et al, “Copper in the squirrel cage for improved motor performance,” in Proc. IEEE Int. Elect. Mach. Drives Conf., vol. 2, pp. 1265–1271, 2003. D. T. Peters et al, “Die-cast copper rotors as strategy for improving induction motor efficiency,” Electrical Insulation Conference and Electrical Manufacturing Expo, pp. 322–327, 2007. [Online]. Available: http://www.engineeringtoolbox.com/young-modulus-d_773.html . [Online]. Available: http://periodictable.com/Properties/A/BulkModulus.an.html . [Online]. Available: http://www.infomine.com/investment/, 05/2015. [Online]. Available: http://www.eia.gov/electricity/monthly/epm_table_grapher.cfm?t=epmt_5_6_a .
