определение предельных натягов и усилий при гибке труб с

advertisement
Ba\_klbyQ_ey[bgkdh]hgZmqgh]hp_gljZ\ui
IJH;E?FUF:RBGHKLJH?GBY
M>D
HIJ?>?E?GB?IJ?>?EVGUOG:LY=H<
BMKBEBCIJB=B;D?LJM;KJ:KD:LU<:GB?F
:<Dhaeh\YFObevd_\bq
_±PDLO.R]ORY#]E±VXVXUX
X`gh±MjZevkdbc]hkm^Zjkl\_ggucmgb\_jkbl_l]Q_ey[bgkdJhkkby
KlZlvyihklmibeZyg\Zjy]
=b[dZljm[y\ey_lkyh^ghcbahkgh\guohi_jZpbcl_ogheh]bq_kdh]hijhp_kkZba]hlh\e_gby
^_lZe_c ljm[hijh\h^h\ HgZ gZreZ \_kvfZ rbjhdh_ b jZaghklhjhgg__ ijbf_g_gb_ \ jZaebq
guohljZkeyoh[s_]hbki_pbZevgh]hfZrbghkljh_gbyZ\lhkljh_gbbkZfhe_lhkljh_gbbg_n
lyghcb]Zah\hcijhfure_gghklbbl^<f_kl_kl_fijbba]hlh\e_gbbljm[hijh\h^h\^hgZ
klhys_]h\j_f_gbijbf_gyxlkyfZehwnn_dlb\gu_f_lh^u]b[dbljm[
AZqZklmx ]b[dZ ljm[ khijh\h`^Z_lky g_`_eZl_evgufb ^ey ihke_^mxs_c wdkiemZlZpbb
y\e_gbyfb D gbf hlghkylky mlhg_gb_ kl_gdb gZ \g_rg_c qZklb ]b[Z h\ZebaZpby kiexsb\Z
gb_ihi_j_qgh]hk_q_gbyljm[uh[jZah\Zgb_]hnjbbaehfh\gZ\gmlj_gg_cqZklb]b[ZDjhf_
lh]hijhp_kkhkeh`gy_lkyl_fqlhihke_]gmlvybf_xlf_klhhklZlhqgu_mijm]b_^_nhjfZpbb
\ke_^kl\b_q_]hbaf_gy_lkyjZ^bmk]b[Zljm[u
<k\yabki_j_qbke_gguf\ur_ba]hlh\e_gb_djb\hebg_cguomqZkldh\ljm[hijh\h^h\dZd
ijZ\beh lj_[m_l ijbf_g_gby ^hjh]hklhys_]h l_ogheh]bq_kdh]h h[hjm^h\Zgby Z kZf ijhp_kk
]b[db hlghkyl d keh`guf l_ogbq_kdbf aZ^ZqZf Hkh[_ggh ljm^gh hkms_kl\blv dZq_kl\_ggmx
]b[dmlhgdhkl_gguoljm[[hevrh]h^bZf_ljZijbfZeuojZ^bmkZo]b[Z^bZf_ljZljm[u
< hkgh\ghf rbjhdh ijbf_gy_fu_ kihkh[u ]b[db ljm[ bf_xl ke_^mxsb_ ^hklhbgkl\Z
bg_^hklZldbihkbeh\ufwg_j]_lbq_kdbfblhqghklgufihdZaZl_eyf
=b[dZ ljm[ qbkluf ba]b[Zxsbf fhf_glhf [_a ^hihegbl_evguo \ha^_ckl\bc D _]h
g_^hklZldZfhlghkylkyg_h[oh^bfhklvh[_ki_q_gby\_kvfZagZqbl_evguomkbebcbfhsghklb
g_\hafh`ghklv h[_ki_qblv jZ^bmk ]b[Z f_g__ 'ljm[u h[jZah\Zgb_ ]hnj lZd dZd ihl_jy mk
lhcqb\hklbk`bfZ_fuo\hehdhgljm[ijhbkoh^bljZgvr_q_f^hklb]Z_lkyieZklbqgh_khklhy
gb_fZl_jbZeZLZdbfh[jZahf]b[dZ^hklZlhqghlhgdhkl_gguoljm[\hafh`gZlhevdhijbgZ
ebqbb ^hjgh\ hijZ\hd beb bgh]h aZihegbl_ey ihehklb ljm[u dhlhju_ h]jZgbqb\Zxl \ukhlm
h[jZamxsboky]hnj
Ijb]b[d_ljm[kmadhahgZevgufgZ]j_\hfL<Qkhk_^gb_oheh^gu_mqZkldbljm[ug_^Z
xl gZ]j_lhfm mqZkldm kiexsb\Zlvky qlh agZqbl_evgh mf_gvrZ_l jbkd ihy\e_gby ]hnj \ukh
dZyl_fi_jZlmjZ\ahg_gZ]j_\Z«°&iha\hey_lkgb`Zlvmkbeby]b[db\«jZaGh
^ey]b[dbljm[∅«fflj_[mxlky^\Z]_g_jZlhjZkfhsghklvxihd<ldZ`^uc
=b[dZljm[uijb^_ckl\bb\gmlj_gg_]h]b^jhklZlbq_kdh]h^Z\e_gbyMkbeby]b[dbb]b^
jhklZlbq_kdh_^Z\e_gb_kha^Zxlkeh`ghgZijy`_ggh_khklhygb_\kl_gdZoljm[udhlhjh_hib
ku\Z_lky ijb ihfhsb ^bZ]jZffu ieZklbqghklb Lj_kdZ K_g±<_gZgZ jbk Dh]^Z hdjm`gu_
jZkly]b\Zxsb_gZijy`_gby σ ^hklb]Zxl\_ebqbgu σl ijh^hevgu_ σ kha^Zxsb_ba]b[Zx
sbcfhf_glfh]ml[ulvkdhevm]h^ghfZeuZkhklhygb_fZl_jbZeZljm[u[m^_lm^h\e_l\hjylv
mkeh\bxl_dmq_klb
:<Dhaeh\YFObevd_\bq
JbkR_klbm]hevgbdLj_kdZK_g±<_gZgZ
H^gZdhijb^Z\e_gbbijb[eb`Zxs_fkyd\_ebqbg_ Kσl 'ljm[u ]^_ K ²lhesbgZkl_g
dbljm[udh]^Zljm[mfh`ghbah]gmlvkdhevm]h^ghfZeufba]b[Zxsbffhf_glhfihy\ey_lky
hiZkghklv \aju\gh]h jZajmr_gby ljm[u ijb ]b[d_ <ke_^kl\b_ wlh]h j_Zevgh m^Z_lky kgbablv
ba]b[Zxsbcfhf_gllhevdh\jZaZg_m^Z_lkyihemqblvdjmlhaZ]gmlu_hl\h^ug_bkdexqZ_l
kyh[jZah\Zgb_]hnjbbkdZ`_gb_ijhnbeyihi_j_qgh]hk_q_gbyKms_kl\m_lbjy^l_ogheh]b
q_kdboljm^ghkl_c
LZdbfh[jZahffh`ghk^_eZlv\u\h^qlh]eZ\gufbg_^hklZldZfbijb\_^_gguokihkh[h\
]b[db ljm[ y\eyxlky eb[h [hevrb_ mkbeby ]b[db b dZd ke_^kl\b_ iehoh_ dZq_kl\h ba^_ebc
eb[h[hevrb_wg_j]haZljZluHq_\b^ghh^gZdhqlhihl_gpbZevgu_\hafh`ghklbf_lh^h\kgb
`_gbymkbeby]b[dbaZkq_lkha^Zgbykeh`ghgZijy`_ggh]hkhklhygbyfZl_jbZeZljm[uij_\hk
oh^yl \hafh`gu_ kgb`_gby mkbeby ]b[db aZ kq_l gZ]j_\Z ljm[u D wlhc ]jmii_ f_lh^h\ hlgh
kblky ]b[dZ ljm[ jZkdZlu\Z_fuo \ ijhp_kk_ ]b[db k [hevrbfb gZly]Zfb HgZ mkljZgy_l
[hevrbgkl\h\ur_i_j_qbke_gguog_^hklZldh\>@
Kmsghklv l_ogheh]bb ]b[db ljm[ k jZkdZlu\Zgb_f aZdexqZ_lky\ke_^mxs_f Ijb\jZs_
gbb ω jZkdZlgbdZ jbk Z aZ\_^_ggh]h \ ljm[m k ^hklZlhqgh [hevrbf gZly]hf \ dZ`^hc
lhqd_dhevp_\hcahgujZkdZlu\Zgby\hagbdZ_lagZdhi_j_f_ggucba]b[jbk[ijbdhlhjhf
ba]b[gu_ gZijy`_gby djZldh\j_f_ggh ^hklb]Zxl ij_^_eZ l_dmq_klb σl < j_amevlZl_ ijb
ijbeh`_gbb hlghkbl_evgh g_[hevrh]h ba]b[Zxs_]h mkbeby ω ijhbkoh^bl ]b[dZ \ i_j_f_
sZxs_ckydhevp_\hcahg_jZkdZlu\Zgby
Z[
Jbk=b[dZljm[kjZkdZlu\Zgb_f
>_ckl\bl_evgh _keb qbkeh ^_nhjfbjmxsbo we_f_glh\ g_\_ebdh lh jZkly]b\Zxsb_ mkb
ebyfZeubjZkij_^_e_gbyghjfZevguogZijy`_gbc\k_q_gbyo:b<ijZdlbq_kdbkbff_ljbq
guIjbwlhfgZdZ`^mxlhqdmk_q_gbyljm[ukbgojhgghqZklhl_\jZs_gbybgkljmf_glZ^_ckl
\mxljZkly]b\Zxsb_bk`bfZxsb_ghjfZevgu_gZijy`_gbyghohlyhgbb^hklb]Zxlij_^_eZ
l_dmq_klblhgdhkl_ggZy\lmedZ\hdjm`ghfgZijZ\e_gbbihqlbg_jZkly]b\Z_lkybg_k`bfZ_lky
Hij_^_e_gb_ij_^_evguogZly]h\bmkbebcijb]b[d_ljm[kjZkdZlu\Zgb_f
B \ wlhf khklhygbb ieZklbqghklv fZl_jbZeZ i_jbh^bq_kdb ^hklb]Z_lky \ dZ`^hc lhqd_ jZkdZ
lu\Z_fh]hk_q_gbybkdhevdhm]h^ghfZeu_gZijy`_gby\ijh^hevghfgZijZ\e_gbbijb\h^yl
dba]b[Zgbxljm[uIjbbkihevah\Zgbb\jZkdZld_«^_nhjfbjmxsbowe_f_glh\fh`_l\ha
gbdZlvg_[he__«ieZklbq_kdborZjgbjh\dhlhju_ehdZebah\Zgu\madboh[eZklyo\lh\j_
fydZdhklZevgZyqZklvfZl_jbZeZljm[ugZoh^blkyijZdlbq_kdbg_\gZijy`_gghfkhklhygbb
Baeh`_gguc\>@ f_lh^hp_gdbij_^_evghcg_kms_ckihkh[ghklbieZklbq_kdborZjgbjh\
iha\hey_le_]dhhij_^_eylv\_jogxxhp_gdmmkbebyihke_ijbeh`_gbydhlhjhcdhevphg_kih
kh[ghkhijhlb\eylvky\g_rgbfgZ]jmadZfb^_nhjfbjm_lkydZdfgh]ha\_ggucrZjgbjgucf_
oZgbaf GZ jbk ihdZaZg rZjgbjguc f_oZgbaf h[jZah\Zgguc ijb gZ]jm`_gbb dhevpZ Q jZ\
ghf_jgh jZag_k_ggufb ih hdjm`ghklb ij_^_evgufb jZ^bZevgufb kbeZfb k h[jZah\Zgb_f Q
ieZklbq_kdborZjgbjh\>@
JbkGZ]jm`_gb_dhevpZjZ\ghf_jghjZag_k_ggufbihhdjm`ghklbij_^_evgufbjZ^bZevgufbkbeZfb
DZ`^Zy^m]Z:<ih\hjZqb\Z_lkydZd`_kldh_a\_ghkm]eh\hckdhjhklvxω\hdjm]k\h_]hih
exkZf]gh\_ggh]h\jZs_gbyKIjbwlhfieZklbq_kdb_rZjgbju<khkdhjhklvxυ^\b`mlkyih
jZ^bmkm hl p_gljZ Z ieZklbq_kdb_ rZjgbju : ² k lhc `_ kdhjhklvx ² d p_gljm Lh]^Z hq_
\b^ghqlh
ω&% = ω&$ = ω5 WJα = υ H[hagZqb\aZF7²ihegucfhf_glieZklbq_kdh]hba]b[Z
07 = K σl ijbjZ\gy\jZ[hlu\g_rgbob\gmlj_ggbokbe
QSυ = 0 l ω + ω bih^klZ\b\\jZ\_gkl\hihemqbf
3 = 0 l 5 WJ α IhkdhevdmijbjZ\ghf_jghjZag_k_gguojZ^bZevguokbeZobakbff_ljbb 4% = 3 Zj_
Zdpbb 1% b 4% fh`gh aZf_gblv j_amevlbjmxs_c kbehc L gZijZ\e_gghc ih ohj^_ ^m]b <:<
jbk
3
7 = 1% FRV α + 4% VLQ α =
VLQ α
Ih^klZ\eyy\agZq_gb_ihemqbf
7=
Kσl
VLQ α 7 Kσ75VLQα 5
:<Dhaeh\YFObevd_\bq
JbkKo_fZ^_nhjfZpbc^m]b<:<
AgZyLbajbkg_ljm^ghhij_^_eblvfhf_glbjZkly]b\Zxsb_mkbeby\dZ`^hclhqd_^m]b
<:<
σ
0 ϕ = 57 [FRV α − ϕ − FRV α ] − K l Ij_g_[j_]Zy m^ebg_gb_f ^m]b <:< hl jZkly]b\Zxsbo mkbebc ba l_hj_fu DZklbevygh
hij_^_ey_fm^ebg_gb_^m]bhlba]b[Zxs_]hfhf_glZ
δ = 5 (-
α
∫ (FRV X − FRV α ) − Kσl  (FRV X − FRV α ) GX −α
]^_ X = ϕ − α ²i_j_f_ggZybgl_]jbjh\Zgby
<uqbkeyybgl_]jZeihemqZ_f
δ = 5 (- 57 ( α + VLQ α ) − VLQ α (57 FRV α + Kσ l ) + α FRV α (57 FRV α + Kσ l ) Bhij_^_ebffbgbfZevgucgZly]g_h[oh^bfuc^eyh[jZah\ZgbyieZklbq_kdborZjgbjh\
+ = + FRV α + FRV α − VLQ α (+ FRV α ) α  5 α σl (K VLQ α VLQ α 

Ba nhjfmeu g_ljm^gh ihemqblv ijhklh_ ijb[eb`_gb_ \ jZfdZo lhqghklb bkoh^guo
^hims_gbc_kebijbgylvijb[eb`_ggu_jZ\_gkl\Z
VLQ α ≈ α − α + α FRV α ≈ − α + α VLQ α = α − α Ihkdhevdm ijb ih^klZgh\d_ nhjfme \ \ d\Z^jZlguo kdh[dZo \k_ i_j\u_ qe_gu ^h ih
jy^dZ α \aZbfgh mgbqlh`Zxlky g_h[oh^bfh lsZl_evgh mqblu\Zlv \k_ [eb`Zcrb_ agZq_gby
qe_gh\[he__\ukhdboihjy^dh\himkdZyebrvqe_gukh^_j`Zsb_ α b\ur_\k\yabkfZeh
klvxdhwnnbpb_glh\
Lh]^Zihemqbf
(
)
+ = 5 α σl (K − α Ihke_ hij_^_e_gby fbgbfZevghg_h[oh^bfh]hgZly]Z fh`ghijb[eb`_gghhp_gblvkgb`_gb_
fhf_glZihlj_[gh]h^ey]b[dbbaljm[udjmlhaZ]gmluohl\h^h\
Hij_^_e_gb_ij_^_evguogZly]h\bmkbebcijb]b[d_ljm[kjZkdZlu\Zgb_f
Ijbh[jZah\ZgbbieZklbq_kdborZjgbjh\rbjbgZmijm]hcahgu\lhqdZo<b:jZ\gZgmex
jbkZrbjbgZmijm]hcahguhlm]eh\h]hiheh`_gbylhqdb²ijZdlbq_kdbebg_cgZynmgdpby
jbk Bajbk hq_\b^gh qlh iehsZ^bihi_j_qgh]hk_q_gbyiehsZ^vaZrljboh\Zgguo
mqZkldh\ijb^hklZlhqghfZehckdhjhklb]b[dbihkjZ\g_gbxkhkdhjhklvx\jZs_gbyjZkdZl
gbdZ \hh[s_ g_ hdZau\Z_l khijhlb\e_gby ijh^hevguf mkbebyf Djhf_ lh]h b \ g_aZrljboh
\Zgghcmijm]hcahg_kms_kl\mxlagZqbl_evgu_\gmlj_ggb_gZijy`_gbyihi_j_qgh]hgZijZ\e_
gby b \ khhl\_lkl\bb k ^bZ]jZffhc Lj_kdZ±K_g±<_gZgZ jbk ebrv iheh\bgZ iehsZ^b
mijm]hc ahgu hdZau\Z_l ihegh_ khijhlb\e_gb_ ijh^hevguf mkbebyf HklZ\rZyky qZklv
« h[s_c iehsZ^b ihi_j_qgh]h k_q_gby hdZau\Z_l khijhlb\e_gb_ \ kj_^g_f gZ BgZq_ ]h\hjy jZkdZlu\Z_fhfm k fbgbfZevgh g_h[oh^bfuf gZly]hf k_q_gbx ljm[u k lhesb
ghckl_gdbKihkhijhlb\e_gbxba]b[mljm[uwd\b\Ze_glghg_jZkdZlu\Z_fh_k_q_gb_khkj_^
g_clhesbghckl_gdb K′ K′ = K − K − K ≈ K Ke_^h\Zl_evghfhf_gl]b[dbljm[ujZkdZlu\Z_fhckfbgbfZevghg_h[oh^bfufgZly]hf
kgb`Z_lkyijbf_jgh\jZaZIjb^Zevg_cr_fm\_ebq_gbbgZly]Z[m^_lgZ[ex^Zlvkyb^Zev
g_cr__kgb`_gb_fhf_glZ
JbkKo_fZjZkij_^_e_gbygZijy`_gbcijb]b[d_ljm[u
Wdki_jbf_glZevgZyhp_gdZ\_ebqbgu 0ba] hkms_kl\eyeZkvijbihfhsbf_oZgbq_kdh]h^b
gZfhf_ljZ J_amevlZlu baf_j_gby ba]b[Zxs_]h fhf_glZ b iZjZf_lju ljm[ ij_^klZ\e_gu gZ
]jZnbdZo jbk < ijh\_^_gghf wdki_jbf_gl_ jbk Z ijb ]b[d_ ljm[u [_a jZkdZlu\Zgby
+ = ba]b[Zxsbcfhf_glkhhl\_lkl\h\ZeGfIjbbkihevah\Zgbbgh\h]hf_lh^Zba]b
[Zxsbcfhf_glkgb`Z_lky\²jZaZjbkZ[
GZ hkgh\_ j_amevlZlh\ l_hj_lbq_kdh]h b wdki_jbf_glZevgh]h bkke_^h\Zgbc jZajZ[hlZgu
g_kdhevdh lbihjZaf_jh\ klZgdh\ ^ey oheh^ghc ]b[db ljm[ k jZkdZlu\Zgb_f \ p_ehf ho\Zlu
\Zxsbo^bZiZahg^bZf_ljh\ljm[hl^hffKlZgdbmki_rgh\g_^j_gu\ijhba\h^kl\h
[he__q_fgZij_^ijbylbyo
:<Dhaeh\YFObevd_\bq
Z[
JbkJ_amevlZluwdki_jbf_glh\ijbih^Zq_fffbgbjZaebqguogZly]Zo
«²rZjbdh\ucjZkdZlgbd«²rZjbdh\ucjZkdZlgbd
AZdexq_gb_
L_hj_lbq_kdbihdZaZghbwdki_jbf_glZevghih^l\_j`^_ghqlh\ha^_ckl\b_gZba]b[Z_fmx
ljm[m\jZsZxsbfkyjZkdZlgbdhfh[_ki_qb\Z_lkgb`_gb_ba]b[Zxsbomkbebc\²jZaZ
Kibkhdebl_jZlmju
IZl_gl JN FDB < ' Kihkh[ ]b[db ljm[ EZdbj_\ K= Obevd_\bq YF JN
‹AZy\e_ghHim[e;xe‹k
>`hgkhgMKF_eehjI;L_hjbyieZklbqghklb^eybg`_g_jh\FFZrbghkljh_gb_F
Wnn_dlkgb`_gbymkbebcijb]b[d_ljm[jZkdZlu\Z_fuok[hevrbfbgZly]Zfbbf_oZgbaf_]hijh
y\e_gbyK=EZdbj_\YFObevd_\bq:<Dhaeh\:<;h[ue_\Ijh]j_kkb\gZyl_ogheh]byqbk
lh\hcbhl^_ehqghch[jZ[hldbL_fZlk[gZmqgljm^h\Q_ey[bgkdQ=LMK²
EZdbj_\K=Dhaeh\:<;h[ue_\:<Gh\Zyl_ogheh]byoheh^ghc]b[dbljm[Obfbq_kdh_bg_n
l_]Zah\h_fZrbghkljh_gb_‹K²
Download