Spindle Speed Modulation Research Articles

Chatter-free milling strategy of a slender Blisk blade via stock distribution optimization and continuous spindle speed change

The machining process of Blisk blades poses multiple challenges due to high requirements on surface quality and precision combined with high dynamic compliance of the thin-walled blades. Avoidance of chatter is thus of high priority in Blisk blade machining. However, the geometry of the Blisk blade array where the tool must fit between individual blades significantly limits the possibilities of controlling stability through the relative orientation of the tool and workpiece. Thus, the main parameters that can be used to control the stability of the process are the distribution of stock allowance and the spindle speed. Due to the effect of material removal on the blade’s dynamic properties, spindle speed needs to be adjusted throughout the machining process to keep it within the continuously changing stability gaps. This paper describes in detail an optimization procedure for the design of stock allowance distribution in such a way that a continuous spindle speed modulation is possible that avoids chatter throughout the machining process by maintaining spindle speeds within stability gaps. The presented algorithm uses finite element analysis software to simulate the effects of stock allowance distribution and material removal on workpiece dynamical properties. This information is then coupled with a stability model based on the Jacobian of the cutting force with respect to the regenerative deflection to identify the varying stability gaps throughout the machining process. The proposed method was experimentally verified.

Integrated Design of Spindle Speed Modulation and Cutting Vibration Suppression Controls Using Disturbance Observer for Thread Milling.

In thread milling, there exists a trade-off between thread manufacturing efficiency and thread quality. In this study, an integrated design of spindle speed modulation (SSM) and cutting vibration suppression (CVS) controls using a disturbance observer were developed to simultaneously ensure superior quality and high manufacturing efficiency. The proposed integrated design not only controls the cutting torque while suppressing cutting vibrations but also ensures cost-effectiveness and mitigates the installation problems prevalent in existing sensor-based methods. The SSM control uses a disturbance observer to estimate the cutting torque required on the spindle during thread milling. The estimated cutting torque is used as a feedback signal so that the SSM control can modulate the spindle speed to make the cutting torque achieve a preset torque command. To further avoid cutting vibrations in thread milling, the CVS control analyzes the estimated cutting torque, detects the occurrence of cutting vibrations, and then adjusts the torque command of the SSM control to suppress the cutting vibrations. In this study, thread milling experiments were performed on a computer numerical control milling machine using the workpiece with stacked materials. The feasibility and performance of the proposed integrated design were validated by experiments.

Surface texture generation using high-feed milling with spindle speed modulation

This paper presents a new surface texturing technique using ball-end milling with high feed speed and spindle speed modulation. The ratio between feed-rate and cutting tool radius is in the range of 0.2–0.4, which is much larger than the ratio in conventional milling. Sinusoidal modulation signal is added, so the spindle speed becomes time-varying in order to generate different texture profiles. The cutting tool kinematics are modeled considering the tool-tip run-out and deflection due to cutting forces. The effects of amplitude and frequency of the modulation signal on tool-tip trajectories and surface textures are simulated and analyzed. The relationship between the micro features of the surface texture and the process parameters are investigated. Surface texturing experiments are conducted based on the proposed technique, and tribology tests are performed on the textured surface. It is shown that the textured surfaces present frictional anisotropy, which depends on the process conditions and modulation parameters. The proposed technique is able to achieve fast generation of various surface textures without additional instrumentation, and the final texture geometry is controllable based on the presented kinematics model.

Stability analysis for milling system with variable pitch cutters under variable speed

Regenerative chatter can reduce machining quality, tool life, and productivity during milling process. In order to control the milling chatter, the stability analysis of milling system is very important. It has been found that variable spindle speed milling and the use of variable-angle tools are effective to control milling chatter. This paper mainly studies the control effect when these two methods are used simultaneously. Firstly, the improved full-discretization method is used to predict the stability of variable spindle speed milling process with variable pitch cutters. And on the basis of stability prediction, the influence of spindle speed modulation parameters on stability is analyzed. Meanwhile, the stability prediction results of down-milling and up-milling operations, different radial immersion ratio and different tooth pitch variation form are compared. The results show that the stability of variable spindle speed milling process with variable pitch cutters is better than that of variable pitch cutters in constant spindle speed milling process. And the improvement of the stability is related to the spindle speed modulation parameters. When the modulation parameters are bigger, the stable cutting area of the stability lobes diagram will be larger. Secondly, in the up-milling operation and the low immersion operation, the variable spindle milling with variable pitch cutters has better stability than the down milling operation and the high immersion operation. Under the condition that the pitch angles vary linearly, the stability is better. Finally, the time domain simulation is performed and the simulation results verify the accuracy of the stability prediction results.

Suppression of chip load variations by real-time spindle speed modulation

In machining a fixed depth of cut at a constant feedrate to generate a desired curvilinear shape, substantial variations in chip load can occur whenever the smallest concave radius of curvature is comparable to the tool radius. These chip load variations may result in a poor quality of the machined surface or premature tool wear. Conversely, attempting to suppress chip load variations by modulating the feedrate may incur high rates of feed acceleration, that may tax the machine drive systems or induce large contour errors. To address these conflicting influences, the feasibility of minimizing variations in chip load through real-time spindle speed modulation is examined herein. A second-order model is employed to determine the tool angular speeds and accelerations that are required to achieve a specified constant chip load for a given depth of cut along a desired part shape defined by a parametric curve, using a constant feedrate for a tool with a given radius and number of cutting edges. For a spindle driven by a DC motor, the motor voltage variation required to generate the modulated spindle speed is also determined. These analyses facilitate an a priori assessment of the part geometries and process parameters for which spindle speed modulation is a viable approach to the suppression of chip load variations.

Stability Analysis of Milling Processes With Periodic Spindle Speed Variation Via the Variable-Step Numerical Integration Method

This paper proposes a general method for the stability analysis and parameter optimization of milling processes with periodic spindle speed variation (SSV). With the aid of Fourier series, the time-variant spindle speeds of different periodic modulation schemes are unified into one framework. Then the time-varying delay is derived implicitly and calculated efficiently using an accurate ordinary differential equation (ODE) based algorithm. After incorporating the unified spindle speed and time delay into the dynamic model, a Floquet theory based variable-step numerical integration method (VNIM) is presented for the stability analysis of variable spindle speed milling processes. By comparison with other methods, such as the semi-discretization method and the constant-step numerical integration method, the proposed method has the advantages of high computational accuracy and efficiency. Finally, different spindle speed modulation schemes are compared and the modulation parameters are optimized with the aid of three-dimensional stability charts obtained using the proposed VNIM.

Efficient evaluation of process stability in milling with Spindle Speed Variation by using the Chebyshev Collocation Method

Abstract Chatter is a vibrational problem affecting machining operations, which may cause bad surface quality and damages to the machining system. In recent decades, several techniques for avoiding chatter onset were developed. Among other techniques, the continuous modulation of spindle speed during the cutting process (also called Spindle Speed Variation – SSV) has been demonstrated to be very effective for reducing the chance of chatter onset. However, spindle speed modulation parameters should be adequately chosen before machining, in order to effectively increase the material removal rate. In this perspective, chatter prediction algorithms play a crucial role, since they allow a preventive evaluation of process stability for any given spindle speed regime. State of the art algorithms for chatter prediction in milling with SSV are characterized by extremely long computation times, hindering their practical application in industry. In this paper, an innovative and fast algorithm for chatter prediction in milling with SSV, based on the Chebyshev Collocation Method, is presented. The algorithm was successfully compared with a state of the art algorithm – the Semi Discretization Method – in different experimental configurations and cutting conditions. The results showed that the new method is generally more accurate and from ten to one thousand times faster than the Semi Discretization Method.

Stability predictions of milling with variable spindle speed using an improved semi-discretization method

During milling, mechanical vibrations known as “chatter” result in lessened productivity, poorer product surface finish, and decreased cutting life of the tool. Thus, it is desirable to predict and avoid the onset of this instability. In this paper, we propose an improved semi-discretization method, based on the Floquet theory, to predict the sinusoidal spindle speed modulation of milling processes. Compared with the non-improved semi-discretization method, the accuracy and efficiency of the proposed algorithm are verified. In addition, stability is predicted using benchmark examples. The stability charts for variable spindle speed milling are compared with those for constant spindle speed milling. The results show that chatter can be effectively suppressed by varying the spindle speed.

Delay equations with fluctuating delay related to the regenerative chatter

The mathematical models representing machine tool chatter dynamics have been cast as differential equations with delay. In this paper, non-linear delay differential equations with periodic delays which model the machine tool chatter with continuously modulated spindle speed are studied. The explicit time-dependent delay terms, due to spindle speed modulation, are replaced by state-dependent delay terms by augmenting the original equations. The augmented system of equations is autonomous and has two pairs of pure imaginary eigenvalues without resonance. The reduced bifurcation equation is obtained by making use of Lyapunov–Schmidt Reduction method. By using the reduced bifurcation equations, the periodic solutions are determined to analyze the tool motion. Analytical results show both modest increase of stability and existence of periodic solutions near the new stability boundary.

Delay equations with fluctuating delay related to the regenerative chatter I: reduced bifurcation equation

The mathematical models representing machine tool chatter dynamics have been cast as differential equations with delay. The suppression of regenerative chatter by spindle speed variation is attracting increasing attention. In this paper, we study nonlinear delay differential equations with periodic delays which models the machine tool chatter with continuously modulated spindle speed. The explicit time-dependent delay terms, due to spindle speed modulation, are replaced by state dependent delay terms by augmenting the original equations. The augmented system of equations is autonomous and has two pairs of pure imaginary eigenvalues without resonance. The reduced bifurcation equation is obtained by making use of Lyapunov–Schmidt Reduction method.

Stability Analysis of Turning With Periodic Spindle Speed Modulation Via Semidiscretization

We investigate a single-degree-of-freedom model of turning with sinusoidal spindle speed modulation and the corresponding delay-differential equation with time-varying delay. The equation is analyzed by the numerical semidiscretization method. Stability charts and chatter frequencies are constructed. Improvement in the efficiency of machining is found for high modulation frequency and for low spindle speed domain. Period-one, period-two (flip), and secondary Hopf bifurcations were detected by eigenvalue analysis.

A fuzzy system for chatter suppression in end milling

This paper reports a fuzzy logic approach for chatter suppression in end milling processes. Vibration energy and the peak value of a vibration frequency spectrum are jointly used as chatter indicators and inputs to the proposed fuzzy controller. The outputs of the fuzzy controller are the altered machining parameters for chatter suppression. This approach does not require a pre-selected nominal spindle speed and has avoided the difficulties in selecting spindle speed modulation parameters present in several other spindle speed variation methods. Experimental results show that chatter can be effectively suppressed by altering spindle speed alone or by simultaneously adjusting feed and spindle speed. However, chatter cannot be suppressed by feed adjustment alone.

A centre-manifold analysis of variable speed machining

The mathematical models representing chatter dynamics have been cast as differential equations with delay. The suppression of regenerative chatter by spindle speed variation is attracting increasing attention. In this paper, we study nonlinear delay differential equations with periodic delays which model the machine tool chatter with continuously modulated spindle speed. The explicit time-dependent delay terms, due to spindle speed modulation, are replaced by state-dependent delay terms by augmenting the original equations. The augmented system of equations is autonomous and has two pairs of pure imaginary eigenvalues without resonance. We make used to the centre-manifold reduction and the method of normal forms to determine the periodic solutions and analyse the tool motion. Analytical results show both modest increase of stability and existence of periodic solutions close to the new stability boundary.

Chatter suppression by adaptive speed modulation

In this paper a PD fuzzy logic controller is designed and implemented to suppress chatter in peripheral milling. The controller selects combinations of the amplitude and frequency of spindle speed modulation, online, to keep a chatter indicator, the R-value, close to a prescribed set point. The controller was successful in suppressing chatter at certain operating points. The effect of the control action delay time and the degree of process instability on the controller performance were addressed through simulations and experiments. At some operating points the controller resulted in an oscillatory behaviour of the process and the R-value fluctuated significantly. Stability lobes were used to explain this phenomenon. Strategies for enhancing the performance of the controller were proposed.

Active suppression of chatter in peripheral milling. Part II. Application of fuzzy control

In this paper, a feasibility study is conducted where fuzzy logic control is investigated to actively vary spindle speed modulation parameters for chatter suppression. A justification for using fuzzy control is given, as well as a brief synopsis of the fuzzy inferencing mechanism. Proportional and proportional-integral fuzzy control algorithms are developed. The set point in these controllers is established from experimental observations and measurements of the machined surfaces. Controller performance is tested by simulating changes in the axial depth of cut from a stable depth to 20% and 50% beyond the stable limit for constant speed cutting. It was found that both controllers were able to regulate the vibration in the milling process, however, the proportional-integral controller generally exhibited more desirable performance characteristics.

Active suppression of chatter in peripheral milling Part 1. A statistical indicator to evaluate the spindle speed modulation method

This work investigates the potential of employing the spindle speed modulation method for real-time control of chatter in peripheral milling. The first part of the study concentrates on developing a measurable chatter indicator which can quantify the relative vibration suppression properties of various speed modulation parameters. Experimental and simulation runs have shown that this indicator provides a well-behaved estimate of the relative cutting condition. The simulation and the experimental set-up for implementing spindle speed modulation are described. Different amplitude-frequency combinations of sinusoidal fluctuations were tested at 20% and 50% beyond the limit of stability both numerically and experimentally with steel workpieces. They showed higher vibration suppression with increased values of speed modulation parameters, which is a general trend that was also reported in other works conducted under different environments.

A stability analysis of single-point machining with varying spindle speed

The rate at which metal can be removed by a machine tool is often limited by the onset of an instability commonly called ‘chatter’. It has been suggested that greater widths of cut could be achieved without chatter on a given machine by modulating the spindle speed continuously. A stability analysis is presented which gives, for any mean spindle rotation speed and degree of modulation, the limiting width of cut for chatter-free cutting. The machine tool is represented by a simple mass/spring/damper system, only the case of a single cutter is considered; however, extension of the analysis to more complex models is straightforward. The analysis indicates that a modest increase in useable width of cut is given by using spindle speed modulation. Results are compared with corresponding results obtained from an analogue computer simulation of the machine tool/cutter system.