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

1977 ◽  
Vol 1 (6) ◽  
pp. 310-318 ◽  
Author(s):  
J.S. Sexton ◽  
R.D. Milne ◽  
B.J. Stone
Keyword(s):  
Stability Analysis ◽  
Single Point ◽  
Spindle Speed

Numerical Integration Method for Stability Analysis of Milling With Variable Spindle Speeds

2015 ◽  
Vol 138 (1) ◽  
Author(s):  
Ye Ding ◽  
Jinbo Niu ◽  
LiMin Zhu ◽  
Han Ding
Keyword(s):  
Differential Equation ◽  
Stability Analysis ◽  
Numerical Integration ◽  
Integration Method ◽  
Transcendental Equation ◽  
Spindle Speed ◽  
Machining Parameters ◽  
Numerical Integration Method ◽  
Stability Diagrams ◽  
Time Period

A semi-analytical method is presented in this paper for stability analysis of milling with a variable spindle speed (VSS), periodically modulated around a nominal spindle speed. Taking the regenerative effect into account, the dynamics of the VSS milling is governed by a delay-differential equation (DDE) with time-periodic coefficients and a time-varying delay. By reformulating the original DDE in an integral-equation form, one time period is divided into a series of subintervals. With the aid of numerical integrations, the transition matrix over one time period is then obtained to determine the milling stability by using Floquet theory. On this basis, the stability lobes consisting of critical machining parameters can be calculated. Unlike the constant spindle speed (CSS) milling, the time delay for the VSS is determined by an integral transcendental equation which is accurately calculated with an ordinary differential equation (ODE) based method instead of the formerly adopted approximation expressions. The proposed numerical integration method is verified with high computational efficiency and accuracy by comparing with other methods via a two-degree-of-freedom milling example. With the proposed method, this paper details the influence of modulation parameters on stability diagrams for the VSS milling.

scholarly journals Research on the Influencing Factors of "Scale Veins" of Single Point Incremental Forming Workpieces Surface

2015 ◽  
Vol 9 (1) ◽  
pp. 1025-1032
Author(s):  
Shi Pengtao ◽  
Li Yan ◽  
Yang Mingshun ◽  
Yao Zimeng
Keyword(s):  
Surface Quality ◽  
Incremental Forming ◽  
Single Point ◽  
Spindle Speed ◽  
Experimental Results ◽  
Feed Speed ◽  
Single Point Incremental Forming ◽  
Machining Parameters ◽  
The Mathematical Model

To furthermore optimize the machining parameters and improve the surface quality of the workpieces manufactured by single point incremental forming method, the formation mechanism of the sacle veins on the metal incremental froming workpieces was studied through experiment method. The influence principle of the spindle speed, the feed speed and the material of tip of tools on the length of scale veins was obtained through analyzing the experimental results and building the mathematical model among the length of scale veins were feed speed and spindle speed through measuring the roughness of surfaces and observing the appearance of the forming workpieces. The experimental results showed that, the spindle speed, the feed speed and the material of tool tips have a significant effect on the scale veins formation on the surface of forming workpieces. Therefore, an appropriate group of spindle speed and feed speed can reduce the effect of scale veins on the roughness of single point incremental forming workpieces and furthermore improve the surface quality of forming workpieces.

Stability analysis for variable spindle speed milling with helix angle using an improved semi-discretization method

2012 ◽  
Vol 56 (3) ◽  
pp. 648-655 ◽  
Author(s):  
QiZhi Xie ◽  
QiChang Zhang ◽  
Wei Wang ◽  
Gang Jin ◽  
JianXin Han
Keyword(s):  
Stability Analysis ◽  
Helix Angle ◽  
Spindle Speed ◽  
Discretization Method

Analysis and optimization of the surface waviness in the single-point incremental sheet metal forming

2018 ◽  
Vol 233 (4) ◽  
pp. 919-925
Author(s):  
Mohammad H Shojaeefard ◽  
Abolfazl Khalkhali ◽  
Shahaboddin Shahbaz
Keyword(s):  
Analysis Of Variance ◽  
Feed Rate ◽  
Single Point ◽  
Spindle Speed ◽  
Optimum Level ◽  
Surface Waviness ◽  
Taguchi Design Of Experiments ◽  
Vertical Step ◽  
Measuring Machine ◽  
Tool Diameter

Presence of waviness in the incremental sheet forming has a detrimental effect on the surface quality of parts, especially on the appearance of those covered with paint. In this paper, the effects of tool diameter, feed rate, spindle speed, and vertical step have been studied on the surface waviness using an innovative method. The proposed method is based on the root mean square deviation of the height of the points located on the wavy surface. In this way, some points are selected on the formed wall and their coordinates are measured using a coordinate measuring machine. Taguchi design of experiments and the analysis of variance are used for studying and optimizing the effects of the four process parameters and their combinations to minimize the waviness of the formed wall. The results show that by reducing the vertical step and increasing the tool diameter, the waviness is decreased. It is also found that the feed rate and the spindle speed have little effect on the waviness. Additionally, from a confirmation test, the results illustrate that the Taguchi method and the analysis of variance provide an efficient and effective method for determination of the optimum level of each process parameter to have the minimum surface waviness.

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

2016 ◽  
Vol 138 (11) ◽  
Author(s):  
Jinbo Niu ◽  
Ye Ding ◽  
LiMin Zhu ◽  
Han Ding
Keyword(s):  
Stability Analysis ◽  
Numerical Integration ◽  
Integration Method ◽  
Spindle Speed ◽  
Numerical Integration Method ◽  
Speed Variation ◽  
Spindle Speed Variation ◽  
Variable Step ◽  
Modulation Schemes ◽  
The Stability

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.

scholarly journals Stability Analysis Method for Periodic Delay Differential Equations with Multiple Distributed and Time-Varying Delays

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Gang Jin ◽  
Xinyu Zhang ◽  
Kaifei Zhang ◽  
Hua Li ◽  
Zhanjie Li ◽  
...  
Keyword(s):  
Stability Analysis ◽  
Differential Equations ◽  
Delay Differential Equations ◽  
Milling Process ◽  
Spindle Speed ◽  
Time Varying ◽  
Typical Application ◽  
Variable Helix ◽  
Periodic Delay ◽  
Delay Differential

Dynamic stability problems leading to delay differential equations (DDEs) are found in many different fields of science and engineering. In this paper, a method for stability analysis of periodic DDEs with multiple distributed and time-varying delays is proposed, based on the well-known semidiscretization method. In order to verify the correctness of the proposed method, two typical application examples, i.e., milling process with a variable helix cutter and milling process with variable spindle speed, which can be, respectively, described by DDEs with the multidistributed and time-varying delays are considered. Then, comparisons with prior methods for stability prediction are made to verify the accuracy and efficiency of the proposed approach. As far as the milling process is concerned, the proposed method supplies a generalized algorithm to analyze the stability of the single milling systems associated with variable pith cutter, variable helix cutter, or variable spindle speed; it also can be utilized to analyze the combined systems of the aforementioned cases.

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