Analytical prediction of part dynamics for machining stability analysis

An analytical procedure is developed to predict workpiece dynamics in a complete machining cycle in order to obtain frequency response functions (FRF) which are needed in chatter stability analyses. For this purpose, a structural modification method which is an efficient tool for updating FRFs is used. The removed mass by machining is considered as a structural modification in order to determine the FRFs at different stages of the process. The method is implemented in a computer code and demonstrated on different geometries. The predictions are compared and verified by FEA. Predicted FRFs are used in chatter stability analyses, and the effect of part dynamics on stability is studied. Different cutting strategies are compared for increased chatter free material removal rates considering part dynamics

Selection of design and operational parameters in spindle-holder-tool assemblies for maximum chatter stability by using a new analytical model

In this paper, using the analytical model developed by the authors, the effects of certain system design and operational parameters on the tool point FRF, thus on the chatter stability are studied. Important conclusions are derived regarding the selection of the system parameters at the stage of machine tool design and during a practical application in order to increase chatter stability. It is demonstrated that the stability diagram for an application can be modified in a predictable manner in order to maximize the chatter-free material removal rate by selecting favorable system parameters using the analytical model developed. The predictions of the model, which are based on the methodology proposed in this study, are also experimentally verified

Investigating dynamics of machine tool spindles under operational conditions

Chatter is one of the major problems in machining and can be avoided by stability diagrams which are generated using frequency response functions (FRF) at the tool tip. During cutting operations, discrepancies between the stability diagrams obtained by using FRFs measured at the idle state and the actual stability of the process are frequently observed. These deviations can be attributed to the changes of machine dynamics under cutting conditions. In this paper, the effects of the cutting process on the spindle dynamics are investigated both experimentally and analytically. The variations in the spindle dynamics are attributed to the changes in the bearing parameters. FRFs under cutting conditions are obtained through the input-output relations of the cutting forces and the vibration response which are measured simultaneously. Experimentally and analytically obtained FRFs are then used in the identification of the bearing parameters under cutting conditions. Thus, bearing properties obtained at idle and cutting conditions are compared and variations in their values are obtained

Dynamic analysis of geared rotors by finite elements

A finite-element model of a geared rotor system on flexible bearings was developed. The model includes the rotary inertia of shaft elements, the axial loading on shafts, flexibility and damping of bearings, material damping of shafts and the stiffness and the damping of gear mesh. The coupling between the torsional and transverse vibrations of gears were considered in the model. A constant mesh stiffness was assumed. The analysis procedure can be used for forced vibration analysis of geared rotors by calculating the critical speeds and determining the response of any point on the shaft to mass unbalances, geometric eccentricities of gears and displacement transmission error excitation at the mesh point. The dynamic mesh forces due to these excitations can also be calculated. The model has been applied to several systems for the demonstration of its accuracy and for studying the effect of bearing compliances on system dynamics

Mass loading effect of accelerometers on tool point FRF and stability diagrams

Chatter is one of the major problems in machining resulting in poor surface quality and reduced productivity. Stability diagrams can be used to determine chatter-free process conditions with high productivity. For generation of stability diagrams, frequency re-sponse functions (FRF) at the tool tip is needed to be used in stability model. Impact tests involving accelerometers are commonly used in FRF measurements. Although mass of a typical accelerometer used in these measurements is extremely small com-pared to the cutting tool, it can have a significant effect on the FRF measurement. In this paper, the effect of accelerometer’s on tool point FRFs and stability diagrams will be demonstrated on several cases with different tool-to-accelerometer mass ratios using laser velocity sensor measurement. In addition, a structural modification method which can be used to compensate this effect will also be presented on several cases. The structural modification method can be used to correct the FRFs measured with acceler-ometers, and thus the resulting stability diagram

Analytical modeling of the machine tool spindle dynamics under operational conditions

Chatter is an important problem in machining operations, and can be avoided by utilizing stability diagrams which are generated using frequency response functions (FRF) at the tool tip. In general, tool point FRF is obtained experimentally or analytically for the idle state of the machine. However, during high speed cutting operations, gyroscopic effects and changes of contact stiffness and damping at the interfaces as well as the changes in the bearing properties may lead to variations in the tool point FRF. Thus, stability diagrams obtained using the idle state FRFs may not provide accurate predictions in such cases. Spindle, holder and tool can be modeled analytically; however variations under operational conditions must be included in order to have accurate predictions. In authors previous works Timoshenko beam model was employed and subassembly FRFs were coupled by using receptance coupling method. In this paper, extension of the model to the prediction of operational FRFs is presented. In order to include the rotational effects on the system dynamics, gyroscopic terms are added to the Timoshenko beam model. Variations of the bearing parameters are included by structural modification techniques. Thus, for various spindle speeds, and holder and tool combinations, the tool point FRFs can be predicted and used in stability diagrams

In-process tool point FRF identification under operational conditions using inverse stability solution

Self-excited vibrations of machine tools during cutting result in process instability, poor surface finish and reduced material removal rate. In order to obtain stability lobe diagrams to avoid chatter vibrations, tool point frequency response function (FRF) must be determined. In classical machine tool studies, tool point FRF is obtained experimentally or analytically for the idle state of the machine. However, during cutting operations, discrepancies are frequently observed between the stability diagrams predicted by using the FRFs measured at the idle state and the actual stability of the process. These deviations can be attributed to the changes in machine tool dynamics under cutting conditions which are difficult to measure. In this study, a new identification method is proposed for the identification of in-process tool point FRFs. In this method, experimentally determined chatter frequency and corresponding axial depth of cut are used in order to identify tool point FRF. The proposed method is applied to a real machining center and by using chatter tests it is demonstrated that the tool point FRF can be accurately identified under operational conditions

Identification of bearing dynamics under operational conditions for chatter stability prediction in high speed machining operations

Chatter is a major problem causing poor surface finish, low material removal rate, machine tool fail-ure, increased tool wear, excessive noise and thus increased cost for machining applications. Chattervibrations can be avoided using stability diagrams for which tool point frequency response function(FRF) must be determined accurately. During cutting operations, due to gyroscopic moments, centrifugalforces and thermal expansions bearing dynamics change resulting in tool point FRF variations. In addi-tion, gyroscopic moments on spindle–holder–tool assembly cause separation of modes in tool point FRFinto backward and forward modes which will lead to variations in tool point FRF. Therefore, for accuratestability predictions of machining operations, effects of operational conditions on machine tool dynamicsshould be considered in calculations. In this study, spindle bearing dynamics are identified for variousspindle rotational speeds and cutting forces. Then, for a real machining center, tool point FRFs underoperating conditions are determined using the identified speed dependent bearing dynamics and themathematical model proposed. Moreover, effects of gyroscopic moments and bearing dynamics varia-tions on tool point FRF are examined separately. Finally, computationally determined tool point FRFsusing revised bearing parameters are verified through chatter tests

İşleme merkezlerinin dinamik analizi ve süreçte kararlılık: yeni bir analitik modelin uygulamaları

Talaşlı imalatta karşılaşılan ve süreç verimliliğini olumsuz yönde etkileyen kendinden kaynaklı titreşimler (tırlama), kullanılan sistemin kararlılık diyag­ramları sayesinde engellenebilmektedir. Kararlılık diyagramlarını oluştur­mak için ana gereksinim, sistemin kesici takım ucundaki frekans tepki fonksi­yonu (FTF) şeklindeki sistem dinamiği bilgisidir. Bu çalışmada, iş mili - ta­kım tutucu - takım sisteminin dinamik modellemesi ve takım ucu FTF'sinin elde edilmesi için geliştirilen bir analitik modelin özeti ve uygulamaları su­nulmuştur. Modelin teorik uygulamaları; rulman ve bağlantı dinamik özellik­leri ile bazı tasarım ve uygulama parametrelerinin takım ucu FTF'si ve dola­yısıyla sistem kararlılığına etkilerinin analizini içermektedir. Sunulan model sayesinde bir sistemin kararlılık diyagramının oldukça hassas bir şekilde elde edilebileceği ve elde edilen diyagramın istenilen şekilde değiştirilerek karar­lılığın artırılabileceği, tezgâh üzerinde deneysel olarak gösterilmiştir

Frezeleme esnasındaki tezgâh dinamiğinin belirlenmesi ve modellenmesi

Tırlama tipi titreşimler talaşlı imalat sırasında üretim verimliliğini etkileyen önemli bir sorundur. Kendinden kaynaklı bu titreşimler işlenen yüzeyin kalitesini etkilemekte, takım aşınmasında artışa ve hatta tezgâhta önemli zararlara sebep olmaktadır. Tırlamanın olmadığı kesme koşulları ise kararlılık diyagramları kullanılarak belirlenebilir ve üretim verimliliğinde önemli artışlar sağlanabilir. Kararlık diyagramlarının elde edilebilmesi için tezgâhın kesici takım ucundaki frekans tepki fonksiyonunun (FTF) belirlenmesi gerekmektedir. Takım uç nokta FTF’si genellikle tezgâhın çalışmadığı duran konumunda ölçülerek elde edilmektedir. Ancak yüksek hızda gerçekleşen kesme işlemlerinde jiroskopik momentten, merkezkaç kuvvetlerinden, ısıl genleşmeden dolayı tezgâh dinamiğinde değişimler olmaktadır. Dolayısı ile tezgâhın çalışmadığı durum için elde edilen takım uç nokta FTF’si hatalı tırlama kararlılığı tahminlerine neden olabilmektedir. Bu çalışmada, kesme koşullarının iş mili dinamiği ve işlem kararlılığına etkileri farklı tutucu-takım kombinasyonları için incelenmiştir. Ayrıca kesme koşulları altında rulman dinamiğinde meydana gelen değişimler belirlenmiştir. Elde edilen hıza bağlı rulman özellikleri geliştirilen analitik modelde kullanılarak farklı tutucu-takım kombinasyonları için takım uç nokta FTF’leri ve kararlılık diyagramları hesaplanmıştır. Elde edilen kararlılık diyagramlarının doğruluğu tırlama testleri ile yapılmış ve deney yapmaya gerek olmadan yüksek hızlarda kesme işlemleri için kararlılık diyagramlarını başarıyla tahmin edilebileceği gösterilmiştir