Tauira o ngā Pātai Kōrero mō ngā Mōta Hiko
He mīhini te mōtini hiko e huri ana i te pūngao hiko hei pūngao miihini. He wāhanga nui tēnei i roto i ngā momo mahi ahumahi, arumoni, me ngā mahi whare. He mea nui te mārama ki ngā mātāpono me te whakahaere o ngā mōtini hiko, inā koa mō ngā ākonga hangarau me ngā tohunga ngaio i te ao hiko. I roto i tēnei tuhinga, ka matapakihia e mātou ētahi tauira raruraru me ngā kōrero e pā ana ki ngā mōtini hiko hei āwhina i a mātou ki te hōhonu ake i tō mātou māramatanga.
Ngā Mātāpono Taketake o ngā Mōta Hiko
I mua i te ruku hohonu ki ngā pātai, he mea āwhina kia arotakehia ngā mātāpono taketake o ngā motuka hiko. Ka mahi ngā motuka hiko i runga i te mātāpono o te aukume hiko, arā, ka puta he papa aukume mai i te iahiko e rere ana i roto i te koiri e taunekeneke ana ki te papa aukume o tētahi pūtake o waho hei whakaputa nekehanga. I te nuinga o te wā, ka wehea ngā motuka hiko ki ngā momo matua e rua: ngā motuka iahiko tika (DC) me ngā motuka iahiko tauutuutu (AC).
Ngā Wāhanga Matua o te Mōta Hiko
1. Pūmau: Ko te wāhanga tūmau o te motuka, he mea hanga ki ngā koiri waea, ki ngā aukume tūturu rānei.
2. Rotor: Ko te wāhanga hurihuri o te motuka, he mea hanga hoki ki ngā koiri waea, ki ngā aukume rānei.
3. Koiri: He waea e takai ana i te rotor, i te stator rānei hei whakaputa i tētahi papa aukume.
4. Pūtake Pūngao: E whakarato ana i te iahiko e hiahiatia ana hei taraiwa i te motuka.
Ngā Pātai Tauira me te Kōrero
Pātai 1: Te Tātai i te Tere o te Mōta DC
Pātai: Ka mahi tētahi motuka DC me te 500 hurihanga mō ia koiri i te 24V me te 5A. Mena ko te pūmau motuka \( K_m \) he 0.02 Nm/A, tatauhia te tere hurihuri o te rotor mena ko te taipana ka puta he 1 Nm.
Kōrero:
E mōhiotia ana:
– Te maha o ngā takahuri (N) = 500
– Ngaohiko (V) = 24V
– Iahiko (I) = 5A
– Pūmau mōta \( K_m \) = 0.02 Nm/A
– Taipana (T) = 1 Nm
Mai i te whārite taketake o te motuka DC, e mōhio ana tātou:
\[ T = K_m \cdot I \]
\[ 1 Nm = 0.02 Nm/A \cdot 5 A \]
\[ 1 Nm = 0.1 Nm \]
Ko te tikanga tēnei he tika te pūmau taipana e hiahiatia ana hei whakaputa i te 1 Nm i te ia o te 5 A.
Muri iho, hei tatau i te tere hurihuri (\( \omega \)):
\[ E = K_m \cdot \omega \]
\[ V = E \]
\[ 24V = 0.02 Nm/A \cdot \omega \]
Mai i konei, ka taea e tātou te tatau i te tere (\( \omega \)):
\[ \omega = \frac{V}{K_m} \]
\[ \omega = \frac{24V}{0.02 Nm/A} \]
\[ \omega = 1200 rad/s \]
Pātai 2: Te Whai Hua o te Mōta Whakaoho AC
Pātai: Ko te mana whakauru o tētahi motuka hiko-toru-wāhanga he 30 kW, ā, ko te mana whakaputa he 27 kW. Tātaihia te whai huatanga o te motuka.
Kōrero:
E mōhiotia ana:
– Mana tāuru (P_in) = 30 kW
– Mana putanga (P_out) = 27 kW
Ka taea te tatau i te whai huatanga (\( \eta \)) o tētahi motuka mā te whakamahi i te tātai:
\[ \eta = \left( \frac{P_{out}}{P_{in}} \right) \times 100\% \]
\[ \eta = \left( \frac{27 kW}{30 kW} \right) \whakareatia ki te 100\% \]
\[ \eta = 0.9 \whakareatia ki te 100\% \]
\[ \eta = 90\% \]
Nō reira, ko te whai huatanga o te motuka whakapūmau he 90%.
Pātai 3: Mōta Tukutahi
Pātai: E 4 ngā pou o tētahi mōta tukutahi, ā, ko te auau o te hiko he 60 Hz. Tātaihia te tere tukutahi o te mōta.
Kōrero:
E mōhiotia ana:
– Te maha o ngā pou (P) = 4
– Auautanga (f) = 60 Hz
Ka taea te tatau i te tere tukutahi (n_s) o te motuka tukutahi mā te whakamahi i te tātai:
\[ n_s = \frac{120 \cdot f}{P} \]
\[ n_s = \frac{120 \cdot 60}{4} \]
\[ n_s = \frac{7200}{4} \]
\[ n_s = 1800 \, RPM \]
Nō reira, ko te tere tukutahi o te mōtini tukutahi he 1800 RPM.
Pātai 4: Taipana Mōta DC Raupapa
Pātai: He 0.5 ohms te ātete koiri o tētahi motuka raupapa DC, ā, he 120V te ngaohiko e tukuna ana. Mena ko te ia e rere ana he 10A, tatauhia te taipana mena ko te pūmau taipana he 0.1 Nm/A².
Kōrero:
E mōhiotia ana:
– Ātete koiri (R) = 0.5 ohm
– Ngaohiko tuku (V) = 120V
– Iahiko (I) = 10A
– Pūmau taipana \( K_t \) = 0.1 Nm/A²
Tuatahi, tatauhia te maturuturunga ngaohiko puta noa i te koiri:
\[ V_R = I \cdot R \]
\[ V_R = 10A \cdot 0.5 \Omega \]
\[ V_R = 5V \]
Ngaohiko whai hua (V_eff) e pā ana ki te motuka:
\[ V_eff = V – V_R \]
\[ V_eff = 120V – 5V \]
\[ V_eff = 115V \]
Ka taea te tatau i te taipana (T) mā te whakamahi i te tātai:
\[ T = K_t \cdot I^2 \]
\[ T = 0.1 Nm/A² \cdot (10A)^2 \]
\[ T = 0.1 Nm/A² \cdot 100 A² \]
\[ T = 10 Nm \]
Nō reira, ko te taipana i hangaia e te motuka DC raupapa he 10 Nm.
Pātai 5: Tīmatanga Mōta Ārahi
Pātai: Ka tāutahia e tētahi tohunga hangarau he tīmatanga whetu-taraiwa ki runga i tētahi motuka whakapūngao 50 kW. Tātaihia te iahiko tīmatanga tuatahi mēnā ko te ngaohiko whakahaere he 400 V, ā, ko te whai huatanga o te motuka he 92%.
Kōrero:
E mōhiotia ana:
– Mana o te motuka (P) = 50 kW
– Ngaohiko (V) = 400V
– Te Whai Hua (\( \eta \)) = 92%
Tuatahi, ka tatauhia e mātou te mana whakauru (P_in):
\[ P_{in} = \frac{P}{\eta} \]
\[ P_{in} = \frac{50 kW}{0.92} \]
\[ P_{in} = 54.35 kW \]
Nā te mea he pūnaha whetu-taraiwa te whakamahi a te motuka, ka iti iho te iahiko tīmatanga i roto i te whetu i te iahiko i te wā e mahi ana te taraiwa. Heoi, hei tatau i te iahiko ingoa, ka taea e tātou te whakamahi i te P_in me te V:
\[ I_{nom} = \frac{P_{in}}{\sqrt{3} \cdot V} \]
\[ I_{nom} = \frac{54.35 kW}{\sqrt{3} \cdot 400V} \]
\[ I_{nom} = \frac{54350}{692.82} \]
\[ I_{nom} \tata ki te 78.44 A \]
Mō te tīmatanga o te au ina whakamahia ana he ara iahiko whetu:
\[ I_{tīmatanga\_whetu} = \frac{I_{nom}}{\sqrt{3}} \]
\[ I_{tīmata\_whetu} \approx \frac{78.44A}{\sqrt{3}} \]
\[ I_{tīmata\_whetu} \tata ki te 45.28 A \]
Nō reira, ko te iahiko tīmatanga tuatahi i te ara iahiko whetu he tata ki te 45.28 A.
Whakamutunga
He mea nui te mārama ki ngā tātaitanga taketake o ngā momo motuka hiko mō te hunga e mahi ana i roto i te hangarau hiko me te miihini. E whakaatu ana ngā tauira raruraru i runga ake nei i te whai wāhi a ngā tawhā rerekē pērā i te ngaohiko, te iahiko, te taipana, me te whai huatanga ki te whakatau i te mahi a te motuka hiko. Mā te mahi tonu, ka tino whai hua te kaha ki te whakaoti rapanga pēnei i roto i ngā mahi whaihua me te mahi.
