【導(dǎo)讀】高速工作磨床的分析模型。接受2021年7月15日;接受以修改過的形式2021年9月17日;接受2021年9月22日。到的2021年11月10日。振動(dòng)是其中一個(gè)在磨床加工過程中影響生產(chǎn)力的最重要的限制條件。為了避免惡劣的表面質(zhì)量和潛在的機(jī)。器磨損振動(dòng)，通常減少材料的硬度。在這篇文章中將對(duì)產(chǎn)生振動(dòng)的各種外力，不包括原動(dòng)力提出分析方法。產(chǎn)率降低工具使用壽命產(chǎn)生噪音。加快工作速度導(dǎo)致穩(wěn)定性降低，噪聲增大；另。一方面，高穩(wěn)定度的限制，通常被人們稱為穩(wěn)定腦葉，存在于某些高主軸轉(zhuǎn)速，可用于大幅度增加振動(dòng)材料率規(guī)定，他們是準(zhǔn)確預(yù)測(cè)。顫振振動(dòng)的發(fā)展是由于動(dòng)力關(guān)系，刀具和工件。增長(zhǎng)并且操作系統(tǒng)不穩(wěn)定。雖然顫振始終與振動(dòng)相聯(lián)系，其實(shí)，這是從根本上是。具動(dòng)力學(xué)和在隨后切削之間的反饋聯(lián)系在一起，在同一切削表面。為制訂該銑削穩(wěn)定，并數(shù)值求解，它采用奈奎斯特準(zhǔn)則。預(yù)測(cè)并增加葉片，以取代低速磨削。p和c分別表明部分和切削刀。

　　

【正文】 ty analysis . If Eq .(2) is substituted in Eq .(1),the following expression is obtained for the dynamic chip thickness in milling: ]c o ss in[)( jjj yxh ??? ???? where )()( 00 wwcc xxxxx ????? , )()( 00 wwcc yyyyy ????? , where ( cc yx, ) and ( ww yx, ) are the dynamic displacements of the cutter and the work piece in the x and y directions, respectively. The dynamic cutting forces on tooth (j ) in the tangential and the radial directions can be expressed as follows: )()()。()( ???? jjj trrjtt FKFahKF ?? Where a is the axial depth of cut, and tK and rK are the cutting force coefficients. After substituting jh from equation, the dynamic milling forces can be resolved in x and y directions as follows: ?????????????????????? yxaaaaaKFFyyxyyxxxtyx 21 Where xya are the directional coefficients[9,10]. The directional coefficients depend on the angular position of the cutter which makes Eq.(6) time varying: ? ? ? ?? ?)()(21)( ttAaKtF t ?? ? ?)(tA is periodic at the tooth passing frequency ??N? .In general, the Fourier series expansion of the periodic term is used for the solution of the periodic systems. However, in chatter stability analysis the inclusion of the higher harmonics in the solution may not be required for most cases as the response at the chatter limit is usually dominated with a single chatter frequency. Starting from this idea, Budak and Altintas [810] and later Merdol and Altintas [16] have shown that the higher harmonics do not affect the accuracy of the predictions unless the radial depth of cut is extremely small pared to the tool diameter .Thus , it is sufficient to include only the average term in the Fourier series expansion of ? ?)(tA in which case the directional coefficients take the following form [810]: ? ?? ?? ?? ? exstexstexstexstrryyryxrxyrrxxKKKKKK????????????????????????2s i n22c o s212c o s22s i n212c o s22s i n212s i n22c o s21??????????????? Then, Eq.(7)reduces to the following form : {F(t)= ? ?? ?)(210 tAaK t ? (9) Chatter stability limit The dynamic displacement vector in Eq.(9) can be determined using the synamic properties of the structures, transfer function or frequency response functions , and the dynamic forces .By substituting the response and the delay terms in Eq.(9), the following expression is obtained [9,10]: ? ? ? ?? ? ticTitti ccc eFiGAeaKeF ??? ? }{)()1(21 0??? (10) where {F}represents the amplitude of the dynamic milling force {f(t)}, and the transfer function matrix is given as: ),(][ wcpGGGGGpy ypx ypy xpx xp ?????????? (11) Where the total transfer function can be obtained form the summation of the cutter and workpiece transfer function, .,[].Eq.(10) has a nontrivial solution only if its determinant is zero, Det[[I]+A[G0(iwc)]]=0, (12) Where [I] is the unit matrix, and the oriented transfer function matrix is defined as ]][[][ 00 GAG ? (13) And the eigenvalue (? ) in Eq. (12) is given as ),1(4 Tit ceaKN ?? ????? (14) ? can easily be puted from Eq. (12) numerically. However, an analytical solution is possible if the cross transfer functions, xyG and yxG , are neglected: ),4(2 1 02110 aaaa ???? ?? (15) where ).()( ))(()(10 cyyyycxxxx yxxyyyxxcyycxx iGiGa iGiGa ???? ?????? ?? ?? (16) Since the transfer functions are plex, ? will have plex and real parts .However , the axial depth of cut (a) is a real number .Therefore , when IR i????? and TiTe ccTi c ??? s inc o s ??? is substituted in Eq.(14), the plex part of the equation has to vanish yielding TTccR ??? c os1 sin1 ????? (17) The above can be solved to obtain a relation between the chatter frequency and the spindle [9, 10]: ,60,tan,2,21NTnkTc??????? ???????? (18) where? is the phase difference between the inner and outer modulations, ? is an integer corresponding to the number of vibration waves within a tooth period, and n is the spindle speed(rpm). After the imaginary part in Eq. (14) is vanished, the following is obtained for the stability limit: )1(2 2l i m ?? ???? tNK Ra (19) Therefore , for given cutting geometry ,cutting force coefficients, tool and work piece transfer functions , and chatter frequency 1,?c? and R? can be determined from Eq.(15), and can be used in Eqs. (18) and (19) to determine the corresponding spindle speed and stability limit .Eq.(15)provides two s39。? for every chatter frequency , however the one which results in the lowest lima must be used similar to the other stability problems . When this procedure is repeated for a range of chatter frequencies and number of vibration waves, k, the stability lobe diagrams for a milling system is obtained. Stability diagram can be used to determine the maximum chatter free cutting depths and spindle speeds, and hence can be used to maximize the productivity without sacrificing from the quality. analysis for variable pitch cytters . Phase angles and stability limit Variable pitch cutters have nonuniform pitch spacing between the cutting teeth. Thus, the fundamental difference in the stability analysis is that the phase delay is different for each tooth: ),. .. ,1( NjT jcj ?? ?? (20) Where jT is the jth tooth period corresponding to the pitch angle pj? . The dynamic chip thickness and the cutting force relations given for the standard milling cutters apply to the variable pitch cutters, as well. The eigenvalue ex