{"id":2393,"date":"2026-06-26T04:00:16","date_gmt":"2026-06-26T04:00:16","guid":{"rendered":"https:\/\/helicalcutgears.top\/?p=2393"},"modified":"2026-06-26T04:00:16","modified_gmt":"2026-06-26T04:00:16","slug":"helical-gear-torsional-stiffness-servo-resonance","status":"publish","type":"post","link":"https:\/\/helicalcutgears.top\/tr\/helical-gear-torsional-stiffness-servo-resonance\/","title":{"rendered":"Helical Gear Torsional Stiffness \u2014 How It Affects Servo Bandwidth"},"content":{"rendered":"
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Helisel Di\u015fli Burulma Rijitli\u011fi \u2014 Servo Bant Geni\u015fli\u011fi, Rezonans ve Geri Tepme \u00d6l\u00fc B\u00f6lgesi<\/h1>\n

A helisel di\u015fli<\/strong> Bir di\u015fli \u00e7ifti, giri\u015f ve \u00e7\u0131k\u0131\u015f milleri aras\u0131nda rijit bir burulma ba\u011flant\u0131s\u0131 de\u011fildir; sertli\u011fi di\u015f temas geometrisi ve ayn\u0131 anda temas halinde olan di\u015f \u00e7ifti say\u0131s\u0131 taraf\u0131ndan belirlenen bir burulma yay\u0131d\u0131r. Bu yay sertli\u011fi, motor ataleti ile y\u00fck ataleti aras\u0131nda mekanik bir rezonans yarat\u0131r; bu rezonans, servo kontrol tasar\u0131m\u0131nda dikkate al\u0131nmazsa, elde edilebilir bant geni\u015fli\u011fini s\u0131n\u0131rlar ve servo karars\u0131zl\u0131\u011f\u0131 olarak g\u00f6r\u00fcnen titre\u015fime neden olabilir. Bir di\u015fli \u00e7iftinin burulma sertli\u011fini anlamak ve hesaplamak \u00f6nemlidir. helisel di\u015fli<\/strong> Bu nedenle, e\u015fle\u015ftirme, herhangi bir hassas servo s\u00fcr\u00fcc\u00fc tasar\u0131m\u0131nda olmazsa olmaz bir ad\u0131md\u0131r.<\/p>\n

Ekipman\u0131n\u0131z i\u00e7in Sertlik Verilerini Talep Edin \u2192<\/a><\/p>\n<\/div>\n<\/div>\n

Di\u015fli A\u011f\u0131n\u0131n Sertli\u011fi \u2014 Di\u015f Temas Noktas\u0131ndaki Burulma Yaylanmas\u0131<\/h2>\n

Bir \u015feye kuvvet uyguland\u0131\u011f\u0131nda helisel di\u015fli<\/strong> Di\u015flerin her ikisi de Hertz temas gerilimi alt\u0131nda elastik olarak b\u00fck\u00fcl\u00fcr. Di\u015f \u00e7iftinin birle\u015fik b\u00fck\u00fclmesi \u2014 giri\u015f di\u015fi b\u00fck\u00fclmesi, \u00e7\u0131k\u0131\u015f di\u015fi b\u00fck\u00fclmesi ve Hertz temas deformasyonu \u2014 di\u015fli a\u011f\u0131n\u0131 birim y\u00fcz geni\u015fli\u011fi ba\u015f\u0131na do\u011frusal bir yay olarak karakterize eden etkili bir sertlik c' [N\/(\u00b5m\/mm y\u00fcz geni\u015fli\u011fi)] olu\u015fturur. Bu c' de\u011feri, di\u015f \u00e7ifti sertli\u011fi<\/em>ve bu, belirleyici olan temel mekanik \u00f6zelliktir. helisel di\u015fli<\/strong> \u00c7iftin burulma \u00f6zellikleri:<\/p>\n

Ortalama di\u015f \u00e7ifti sertli\u011fi (ISO 6336-1 g\u00f6sterimi):
\nc'_gamma \u2248 c_th \u00d7 C_M \u00d7 C_R \u00d7 C_B \u00d7 cos \u03b2
\nNeresi:
\nc_th = standart \u00e7elik di\u015fli \u00e7ifti i\u00e7in teorik tek \u00e7ift rijitli\u011fi \u2248 14\u201320 N\/(\u00b5m\u00b7mm)
\nC_M = di\u015fli g\u00f6vdesi k\u00fctlesi i\u00e7in d\u00fczeltme (kat\u0131 di\u015fli g\u00f6vdesi i\u00e7in 0,8)
\nC_R = jant kal\u0131nl\u0131\u011f\u0131 d\u00fczeltmesi (standart jant i\u00e7in 1,0 \u2265 2,5 \u00d7 h_tooth)
\nC_B = temel raf i\u00e7in d\u00fczeltme (standart 20\u00b0 bas\u0131n\u00e7 a\u00e7\u0131s\u0131 i\u00e7in 1,0)
\ncos \u03b2 = sarmal d\u00fczeltmesi<\/p>\n

Karbonlanm\u0131\u015f \u00e7elik di\u015fliler i\u00e7in tipik sonu\u00e7, \u03b2 = 20\u00b0:
\nc'_gamma \u2248 17 \u00d7 0.8 \u00d7 1.0 \u00d7 1.0 \u00d7 cos 20\u00b0 \u2248 12.8 N\/(\u00b5m\u00b7mm)<\/p>\n

Bu sertlik de\u011feri periyodik olarak de\u011fi\u015fir. helisel di\u015fli<\/strong> D\u00f6nme hareketi s\u0131ras\u0131nda, iki di\u015f \u00e7ifti ayn\u0131 anda temas halindeyken toplam di\u015fli sertli\u011fi yakla\u015f\u0131k 2 \u00d7 c'_gamma \u00d7 b'dir; yaln\u0131zca bir \u00e7ift temas halindeyken ise c'_gamma \u00d7 b'ye d\u00fc\u015fer. Di\u015fli temas frekans\u0131nda (z \u00d7 RPM \/ 60) meydana gelen bu periyodik sertlik de\u011fi\u015fimi, iletim hatas\u0131n\u0131n temel kayna\u011f\u0131 ve di\u015fli g\u00fcr\u00fclt\u00fcs\u00fc ve titre\u015fiminin bask\u0131n nedenidir.<\/p>\n

Toplam A\u011f Rijitli\u011fi ve Burulma Yay Sabiti<\/h2>\n

Bir a\u011f yap\u0131s\u0131n\u0131n toplam a\u011f sertli\u011fi helisel di\u015fli<\/strong> Giri\u015f miline at\u0131fta bulunulan \u00e7ift, birim geni\u015flik ba\u015f\u0131na sertlik c'_gamma'y\u0131 y\u00fcz geni\u015fli\u011fi ve temas halindeki ortalama di\u015f \u00e7ifti say\u0131s\u0131 (toplam temas oran\u0131 \u03b5_\u03b3 ile ilgili) ile birle\u015ftirir:<\/p>\n

C_mesh \u2248 c'_gamma \u00d7 b \u00d7 \u03b5_\u03b3 [N\u00b7m\/\u00b5m, toplam a\u011f sertli\u011fi]
\nBurulma yay sabiti (giri\u015f miline g\u00f6re):
\nC_torsiyon = C_a\u011f \u00d7 (d\u2081\/2)\u00b2 [N\u00b7m\/rad]<\/p>\n

\u00d6rnek: M5, z\u2081=24, z\u2082=72, \u03b2=20\u00b0, b=80mm, 20CrMnTi karb\u00fcrlenmi\u015f, \u03b5_\u03b3=2.3
\nc'_gamma = 12,8 N\/(\u00b5m\u00b7mm)
\nC_mesh = 12,8 \u00d7 80 \u00d7 2,3 = 2.355 N\/\u00b5m = 2.355.000.000 N\/m
\nd\u2081 = 127,8 mm
\nC_torsiyon = 2.355.000.000 \u00d7 (0,0639)\u00b2 = 9.615.000 N\u00b7m\/rad \u2248 9,6 \u00d7 10\u2076 N\u00b7m\/rad<\/p>\n

Bu, mekanik millerle kar\u015f\u0131la\u015ft\u0131r\u0131ld\u0131\u011f\u0131nda \u00e7ok y\u00fcksek bir burulma rijitli\u011fidir (200 mm uzunlu\u011funda 50 mm \u00e7ap\u0131nda bir \u00e7elik milin burulma rijitli\u011fi yakla\u015f\u0131k 180.000 N\u00b7m\/rad'dir - di\u015fli a\u011f\u0131ndan 50 kat daha d\u00fc\u015f\u00fckt\u00fcr). helisel di\u015fli<\/strong> Di\u015fli a\u011f\u0131, \u00e7o\u011fu tahrik sisteminde en sert elemand\u0131r; s\u0131n\u0131rlay\u0131c\u0131 burulma esnekli\u011fi, di\u015flilerin kendisinden de\u011fil, millerden, kaplinlerden ve rotorun b\u00fck\u00fclmesinden kaynaklan\u0131r.<\/p>\n

Burulma Do\u011fal Frekans\u0131 \u2014 \u0130ki K\u00fctleli Model<\/h2>\n

\"Servo<\/p>\n

O helisel di\u015fli<\/strong> Servo tahrik sistemindeki di\u015fli a\u011f, motor ataleti J\u2081 ve y\u00fck ataleti J\u2082'yi birbirine ba\u011flayan bir burulma yay\u0131 C_torsion g\u00f6revi g\u00f6r\u00fcr. Bu iki k\u00fctleli sistemin burulma do\u011fal frekans\u0131 f_n, servo tork komutlar\u0131ndan kaynaklanan rezonans uyar\u0131m\u0131n\u0131 \u00f6nlemek i\u00e7in servo kontrol bant geni\u015fli\u011finin \u00fczerinde (ideal olarak 3-5 kat \u00fczerinde) olmal\u0131d\u0131r.<\/p>\n

Servo tahrikli bir sistem i\u00e7in en basit model helisel di\u015fli<\/strong> Sistem, iki k\u00fctleli burulma modelidir: motor ataleti J\u2081, di\u015fli a\u011f\u0131 burulma yay\u0131 C_torsion arac\u0131l\u0131\u011f\u0131yla y\u00fck ataleti J\u2082'ye ba\u011flanm\u0131\u015ft\u0131r. Bu sistemin s\u00f6n\u00fcmlenmemi\u015f do\u011fal frekans\u0131 \u015f\u00f6yledir:<\/p>\n

\u03c9_n = \u221a(C_burulma \u00d7 (1\/J\u2081 + 1\/J\u2082)) [rad\/s]
\nf_n = \u03c9_n \/ (2\u03c0) [Hz]<\/p>\n

Yukar\u0131daki di\u015fliyle ilgili \u00f6rnek (C_torsion = 9,6 \u00d7 10\u2076 N\u00b7m\/rad):
\nMotor ataleti J\u2081 = 0,020 kg\u00b7m\u00b2
\nY\u00fck ataleti J\u2082 = 0,060 kg\u00b7m\u00b2 (i\u00b2 arac\u0131l\u0131\u011f\u0131yla giri\u015f miline yans\u0131t\u0131l\u0131r)<\/p>\n

\u03c9_n = \u221a(9,6 \u00d7 10\u2076 \u00d7 (1\/0,020 + 1\/0,060)) = \u221a(9,6 \u00d7 10\u2076 \u00d7 66,7) = \u221a(640 \u00d7 10\u2076) = 25,298 rad\/s
\nf_n = 25.298 \/ (2\u03c0) = 4.028 Hz<\/p>\n

Bu, herhangi bir servo bant geni\u015fli\u011finin (<\u00e7o\u011fu hassas s\u00fcr\u00fcc\u00fc i\u00e7in 1.000 Hz) g\u00fcvenli bir \u015fekilde \u00fczerindedir - di\u015fli a\u011f\u0131.
\nBurulma rezonans\u0131, bu kompakt di\u015fli \u00e7ifti i\u00e7in s\u0131n\u0131rlay\u0131c\u0131 bir fakt\u00f6r de\u011fildir.<\/p>\n

\u26a0 Di\u015fli \u00e7ifti \u00e7ok daha b\u00fcy\u00fck olsayd\u0131 (J\u2081=0,5, J\u2082=5,0, C_torsiyon=9,6\u00d710\u2076):
\n\u03c9_n = \u221a(9,6\u00d710\u2076 \u00d7 (1\/0,5 + 1\/5,0)) = \u221a(9,6\u00d710\u2076 \u00d7 2,2) = 4,596 rad\/s \u2192 f_n = 731 Hz
\nServo bant geni\u015fli\u011fi 300 Hz oldu\u011funda, f_n\/BW oran\u0131 2,4\u00d7 olur; bu da rezonansa tehlikeli derecede yak\u0131nd\u0131r.<\/p>\n

Servo di\u015fli tahrik sistemleri i\u00e7in minimum ay\u0131rma kural\u0131:<\/strong> Yeterli faz marj\u0131 sa\u011flamak i\u00e7in burulma do\u011fal frekans\u0131 f_n, servo kontrol bant geni\u015fli\u011finin en az 3 kat\u0131 olmal\u0131d\u0131r. Bu oran\u0131n alt\u0131nda, kararl\u0131l\u0131\u011f\u0131 korumak i\u00e7in servo d\u00f6ng\u00fc kazanc\u0131 azalt\u0131lmal\u0131d\u0131r; bu da do\u011frudan elde edilebilir servo bant geni\u015fli\u011fini ve dolay\u0131s\u0131yla makinenin konumland\u0131rma h\u0131z\u0131n\u0131 ve do\u011frulu\u011funu s\u0131n\u0131rlar. Hesaplama f_n\/BW < 3 g\u00f6steriyorsa, s\u00fcr\u00fcc\u00fc tasar\u0131mc\u0131s\u0131 \u015funlardan birini yapmal\u0131d\u0131r: C_torsion'\u0131 art\u0131rmak (daha b\u00fcy\u00fck mod\u00fcl, daha geni\u015f y\u00fcz geni\u015fli\u011fi, sertlik de\u011fi\u015fimini azaltmak i\u00e7in daha y\u00fcksek do\u011fruluk s\u0131n\u0131f\u0131), ataleti azaltmak (i\u00e7i bo\u015f di\u015fli g\u00f6vdesi, daha hafif y\u00fck ba\u011flant\u0131s\u0131) veya di\u015fli a\u011f\u0131n\u0131 geni\u015fletmek (\u03b2 veya b'yi art\u0131rarak \u03b5_\u03b3'yi art\u0131rmak).<\/div>\n

DIN Do\u011fruluk S\u0131n\u0131f\u0131n\u0131n Burulma Rijitli\u011fi De\u011fi\u015fimini Nas\u0131l Etkiledi\u011fi<\/h2>\n

Burulma Anlam<\/em> bir sertli\u011fi helisel di\u015fli<\/strong> DIN do\u011fruluk s\u0131n\u0131f\u0131ndan \u00e7ok fazla etkilenmez; di\u015f temas alan\u0131 ve sapma, y\u00fczey kalitesinden ziyade mod\u00fcl ve malzeme taraf\u0131ndan belirlenir. Bununla birlikte, varyasyon<\/em> Di\u015f a\u011f\u0131n\u0131n ortalama de\u011ferine yak\u0131n a\u011f sertli\u011fi, do\u011fruluk s\u0131n\u0131f\u0131na b\u00fcy\u00fck \u00f6l\u00e7\u00fcde ba\u011fl\u0131d\u0131r:<\/p>\n

\n\n\n\n\n\n\n\n
DIN Do\u011fruluk S\u0131n\u0131f\u0131<\/th>\nM5 i\u00e7in Profil Sapmas\u0131 ff (\u00b5m)<\/th>\n\u00d6rg\u00fc Frekans\u0131nda Sertlik De\u011fi\u015fimi<\/th>\n\u0130letim Hatas\u0131 (TE) Genli\u011fi<\/th>\nRezonans Uyar\u0131m\u0131<\/th>\n<\/tr>\n<\/thead>\n
DIN S\u0131n\u0131f\u0131 4\u20135<\/td>\n3\u20135 \u00b5m<\/td>\n\u00b13\u20135% ortalama sertlik<\/td>\n2\u20135 \u00b5m<\/td>\nD\u00fc\u015f\u00fck \u2014 servo bant geni\u015fli\u011fi, di\u015fli rezonans\u0131ndan de\u011fil, makine dinamiklerinden kaynaklanan s\u0131n\u0131rlamaya tabidir.<\/td>\n<\/tr>\n
DIN S\u0131n\u0131f\u0131 6\u20137<\/td>\n8\u201316 \u00b5m<\/td>\n\u00b18\u201315% ortalama sertlik<\/td>\n8\u201318 \u00b5m<\/td>\nOrta d\u00fczeyde \u2014 di\u015fli rezonans\u0131, kavrama frekans\u0131nda konumland\u0131rma hatas\u0131na katk\u0131da bulunur.<\/td>\n<\/tr>\n
DIN S\u0131n\u0131f 8\u20139<\/td>\n18\u201336 \u00b5m<\/td>\n\u00b120\u201335% ortalama sertlik<\/td>\n20\u201340 \u00b5m<\/td>\nY\u00fcksek di\u015fli rezonans\u0131 genellikle konum hatas\u0131 spektrumunda g\u00f6r\u00fclebilir; servo kazanc\u0131n\u0131 s\u0131n\u0131rlar.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n

Geri Tepme ve \u00d6l\u00fc B\u00f6lge \u2014 Do\u011frusal Olmayan Burulma Davran\u0131\u015f\u0131<\/h2>\n

\u015eaft uyumlulu\u011funun aksine, bir helisel di\u015fli<\/strong> Geri tepme i\u00e7eren di\u015fli \u00e7ifti, do\u011frusal olmayan bir burulma yay\u0131 \u00f6zelli\u011fine sahiptir: geri tepme b\u00f6lgesinde (ad\u0131m dairesinde \u00b1j\/2, burada j toplam geri tepmedir), di\u015fli a\u011f\u0131 tork iletmez \u2014 di\u015fler temas halinde de\u011fildir ve burulma sertli\u011fi etkili bir \u015fekilde s\u0131f\u0131rd\u0131r. Geri tepme b\u00f6lgesinin d\u0131\u015f\u0131nda, di\u015fli a\u011f\u0131 tam burulma sertli\u011fi C_torsion'a geri d\u00f6ner. Bu \"\u00f6l\u00fc b\u00f6lge\" do\u011frusal olmama durumu, servo sistem i\u00e7in iki \u00f6nemli sonu\u00e7 do\u011furur:<\/p>\n