Three half-axis tool orientation optimization for spiral machining of blades

A regular three-axis computer numerical control (CNC) machine combined with an automatic indexing rotary table (AIRT) is always used to produce four-axis machining for blades in many medium-sized and small industries. Generally, AIRT has the characteristic of low precision, which often leads to obvious tool marks like overcut on the machined blade surface. To overcome this problem, a machining technique, named as $ 3\frac{1}{2} $ -axis spiral machining method that uses the simplicity of three-axis tool positioning and the flexibility of four-axis tool orientation, is developed and implemented. Key issues are focused on transformations of tool orientations from four-axis to $ 3\frac{1}{2} $ -axis and concrete contributions are twofold. First, universal principles are proposed to transfer tool orientations for general convex and concave surfaces. Second, with respect to the pressure and suction surfaces of blades in $ 3\frac{1}{2} $ -axis spiral machining, a unified transformation method is also addressed in detail. A cutting test shows that overcut marks that easily occur in four-axis spiral machining can be effectively controlled by using the proposed $ 3\frac{1}{2} $ -axis machining technique.     

Double sampling \overline{X} control chart for a first-order autoregressive moving average process model

In this paper, we consider the double sampling (DS) $\overline{X} $ control chart for monitoring processes in which the observations can be represented as a first-order autoregressive moving average (ARMA(1, 1)) model. The properties of the DS $\overline{X} $ control chart with the sampling intervals driven by the rational subgroup concept are studied and compared with the Shewhart chart and the variable sample size (VSS) chart, both properly modified to account for the serial correlation. Numerical results show that the correlation within subgroups has a significant impact on the properties of the charts. For processes with low to moderate correlation levels, the DS $\overline{X} $ chart is substantially more efficient in detecting process mean shifts.     

Improved feature-based test statistic for assessing suitability of the preliminary samples for constructing control limits of \bar{X} chart

In spite of using a large number of subgroups (m) of small samples (n), the estimated control limits of $ \bar{X} $ chart in phase I can be erroneous unless the preliminary samples are drawn from a stable process. As a result, the performance of the chart in phase II can be significantly affected. The pattern in the $ \bar{X} $ chart, exhibited by the plots of the subgroup averages of the preliminary samples, will be different depending on stability and instability of the process while the preliminary samples were collected. Based on this concept, a new feature-based test statistic (FTS) is proposed for evaluating suitability of the preliminary samples for the designing of the $ \bar{X} $ chart. The FTS, for given m, approximately follows $ N[1,{\text{ SD(}}m{)]} $ , where SD(m) is a function of m. The goodness of the approximation and effectiveness of the test are evaluated using simulated data. The results show that both are satisfactory for m?>?=48. The proposed statistic is also quite effective in detecting unstable process condition resulting in a cyclic pattern. The computation of FTS involves some complexities. However, now-a-days computers are widely available and so computation difficulty may not be a problem.     

The run sum t control chart for monitoring process mean changes in manufacturing

The $ \overline{X} $ type charts are not robust against estimation errors or changes in process standard deviation. Thus, the t type charts, like the t and exponentially weighted moving average (EWMA) t charts, are introduced to overcome this weakness. In this paper, a run sum t chart is proposed, and its optimal scores and parameters are determined. The Markov chain method is used to characterize the run length distribution of the run sum t chart. The statistical design for minimizing the out-of-control average run length (ARL₁) and the economic statistical design for minimizing the cost function are studied. Numerical results show that the t type charts are more robust than the $ \overline{X} $ type charts for small shifts, in terms of ARL and cost criteria, with respect to changes in the standard deviation. Among the t type charts, the run sum t chart outperforms the EWMA t chart for medium to large shifts by having smaller ARL₁ and lower minimum cost. The run sum t chart surpasses the $ \overline{X} $ type charts by having lower ARL₁ when the charts are optimally designed for large shifts but the run sum $ \overline{X} $ and EWMA $ \overline{X} $ prevail for small shifts. In terms of minimum cost, the $ \overline{X} $ type charts are superior to the t type charts. As occurrence of estimation errors is unpredictable in real process monitoring situations, the run sum t chart is an important and useful tool for practitioners to handle such situations.     

Plastic deformation depth modeling on grinding of gamma Titanium Aluminides

This work reports on the subsurface plastic deformation depth (PDD) as a result of grinding of γ-TiAl, where the effects of grit size and shape, workpiece speed, and wheel depth of cut were studied. A grinding model based on a stochastic distribution of the chip thickness was used to estimate the expected maximum normal force per grit ( ${F''_{n\:{\rm max}}}$ ), which was correlated to the PDD. It was found that the PDD shows a linear correlation with ${F''_{n\:{\rm max}}}^{0.5}$ . The results suggest that the indentation model is still valid for grinding if ${F''_{n\:{\rm max}}}^{0.5}$ is used as a PDD predictor variable instead of the total grinding force.     

Optimization of cutting conditions of YG15 on rough and finish cutting in WEDM based on statistical analyses

In this paper, the effects and the optimization of cutting parameters on surface roughness (Ra) and material removal rate (MRR) in the wire electrical discharge machining (WEDM) of high hardness tool steel YG15 are analyzed. In the WEDM process, the key process parameters, such as pulse-on time, pulse-off time, power, cutting feed rate, wire tension, wire speed, and water pressure, are optimized. Experimental data were initially collected based on the Taguchi method of experimental design, which are $L_{18}\left (2^1\times 3^5\right )$ and $L_{18}\left (2^1\times 3^4\right )$ Taguchi standard orthogonal array on rough and finish cutting experiments, respectively. The level of importance of the cutting parameters on the Ra and MRR was determined on both finish and rough cutting by using statistical analyses; average gap voltage is discussed in order to balance cutting efficiency and stability on both finish and rough cutting. In addition, comparative analysis of finish and rough cutting is drawn to analyze the difference between rough cutting and finish cutting. Then, regression models and signal-to-noise ratio are used to obtain the optimum cutting parameter combination. Finally, the results present the optimized MRR and Ra of the rough and finish process, respectively, and confirm the efficiency and abilities of the model.     

Optimal design of \overline {\text{X}} -control chart with Pareto in-control times

Economic control chart models usually assume that the time to occurrence of an assignable cause follows an exponential or Weibull distribution. This paper extends that to the Pareto distribution in order to investigate, in general, the effect on the economic control chart parameters like sample size, time between two successive samples, and the cost per unit time of the distributional assumption. The Pareto distribution arises as a limiting distribution of the waiting time for the number of new observations needed to obtain a value exceeding the greatest among “n” observations. It was found that the economic design of $ \overline {\text{X}} $ chart is greatly influenced by the distributional assumption. Using the cost model, the sensitivity analysis of the statistical economic design of the $ \overline {\text{X}} $ chart with respect to the parameters and costs is studied.     

Performance evaluation of control chart for multiple assignable causes using genetic algorithm

With a view to monitoring and controlling manufacturing processes in industries, control charts are widely used and needed to be designed economically to achieve minimum quality costs. Many authors have studied the economic design of the $ \overline{X} $ control chart after Duncan (J Am Stat Assoc 51(274):228–242, 1956) first proposed the economic model of the $ \overline{X} $ control chart for a single assignable cause. But, in practice, multiple assignable causes are more logical and realistic. Moreover, the economic design does not consider statistical properties like bound on type I and type II error, and average time to signal (ATS). This paper focuses on evaluating the performance of genetic algorithm (GA) in pure economic and economic statistical design of the $ \overline{X} $ control chart for multiple assignable causes. The performances of GA are demonstrated by comparing its result with the previously proposed grid search technique for a numerical example. The Duncan model of multiple assignable causes is adopted to formulate objective function, and the computation is achieved by approximation through a numerical method named Simpson's 1/3 rule. Comparison distinctly shows the superiority of GA over grid search results for economic statistical design.     

Tire–Road Contact Stiffness

When a rubber block is squeezed against a nominal flat but rough surface, the rubber bottom surface will penetrate into the substrate roughness profile. The relation between penetration depth \(w\) (or the average interfacial separation \(\bar{u}\) ) and the applied squeezing pressure \(p\) determines the (perpendicular) contact stiffness \(K=\hbox {d}p/\hbox {d}w=-\hbox {d}p/\hbox {d}\bar{u}\) , which is important for many applications. We have measured the relation between \(p\) and \(\bar{u}\) for a rubber block squeezed against 28 different concrete and asphalt road surfaces. We find a linear relation between \({\mathrm{log}}p\) and \(\bar{u}\) , in agreement with theory predictions. The measured stiffness values correlate rather well with the theory prediction.     

Modeling of surface roughness effect on dry contact friction in metal forming

Interfacial conditions such as friction and roughness substantially affect the process characteristics of metal forming. This study developed a dry friction model that accounted for the adhesion and interference effects of surface roughness. A sliding friction coefficient was suggested to provide fundamental information about the interfacial conditions of the contact surface. The proposed model was easily verified by published experiments and predicted values agreed with experimental results. Accordingly, friction coefficient ?? clearly increased as relative roughness R _m (=?roughness of tool $ R_a^T $ /roughness of workpiece $ R_a^M $ , measured as interference effect) increased. Simulations confirmed that the friction coefficient ?? decreased as dimensionless stress S _m (=?contact pressure p _m /tensile strength $ \sigma_u^0 $ ) increased at small strain hardening exponent n-values. Under the conditions of large n and small R _m values, the friction coefficient ?? initially decreased and then increased. It then slightly decreased as dimensionless stress S _m increased. However, this trend became less apparent as relative roughness R _m increased since friction coefficient ?? simply decreased.     

Studies of chipping mechanisms for dicing silicon wafers

The purpose of this study was to investigate the chipping modes produced in the die edges of dicing silicon wafer using the thin diamond blades. The effects of dicing directions and different wafer types on the chipping size were studied. Furthermore, scratching tests were also used to assist the analysis of studying chipping conditions of the silicon wafer. The experimental results showed that the trace behaviors produced by the diamond indenter in the scratching test of silicon wafer can be divided into the three stages: rubbing, plastic deformation, cracking. The plastic pile up and crack of the scratching traces on the wafer mainly propagate along the development of the easiest slip direction family <110>. The chipping modes produced in dicing silicon wafer can be broadly classified as four types: (1) 30° chipping; (2) 60° chipping; (3) 90° chipping; (4) irregular chipping, which causes these mechanisms of chipping modes due to the meeting between the radial cracks of 30°, 60°, and 90° along the easiest slip direction family <110> and the lateral cracks along the easiest cleavage plane family {111}. When using the thin diamond blade diced on the (111) silicon wafer along the $ {\left[ {\overline{1} 10} \right]} $ direction, the size of top chipping produced was smaller than that of along the $ {\left[ {11\overline{2} } \right]} $ direction. Besides, for the (100) plane of silicon wafer, the size and the distribution of the chipping modes produced along the $ {\left[ {\overline{1} 10} \right]} $ and $ {\left[ {\overline{1} \overline{1} 0} \right]} $ directions were similar.     

A robust \overline {\hbox{X}} control chart based on M-estimators in presence of outliers

Specifying the control limits is an important step in designing a control chart. The control limits are determined by the estimates of mean and/or standard deviation of the process. In the $ \overline {\hbox{X}} $ control chart, when outliers exist in the data, using the classical estimators to estimate parameters may cause the limits to become wider or to shift in the same direction. Robust estimators which are not affected by outliers are used in this research to determine the control limits for $ \overline {\hbox{X}} $ control chart. The mean and the dispersion estimators which are currently applied to define control limits are evaluated, and their performances in control charting are compared with the proposed method by vast simulation and real data examples. Based on the results, it is revealed that when M-estimators with bisquare ρ functions is used to estimate the mean and the dispersion of the process, the control chart has the best performance among the other robust and classical control charts.     

Boundary Layer Behaviour in Circular EHL Contacts in the Elastic-Piezoviscous Regime

The solution of elastohydrodynamically lubricated contacts at high loads and/or low speeds can be described as a Hertzian pressure with inlet and outlet boundary layers: zones where significant pressure flow occurs. For the soft lubrication regime (elastic-isoviscous), a self-similar solution exists in the boundary layers satisfying localized equations. In this paper, the boundary layer behaviour in the elastic-piezoviscous regime is investigated. The lengthscale of the boundary layers and the scaling of pressure and film thickness are expressed in non-dimensional parameters. The boundary layer width scales as \(1/\sqrt{M}\) (equivalent to \({\bar{\lambda }}^{3/8}\) ), the maximum pressure difference relative to the Hertzian solution as \(1 / \root 3 \of {M}\) (equivalent to \({\bar{\lambda }}^{1/4}\) ) and the film thickness as \(1/\root 16 \of {M}\) (equivalent to \({\bar{\lambda }}^{3/64}\) ) with \(M\) the Moes non-dimensional load and \({\bar{\lambda }}\) a dimensionless speed parameter. The Moes dimensionless lubricant parameter \(L\) was fixed. These scalings differ from the isoviscous-elastic (soft lubrication) regime. With increasing load (decreasing speed), the solution exhibits an increasing degree of rotational symmetry. The pressure varies less than 10 % over an angle less than 45 degrees from the lubricant entrainment direction. The results provide additional fundamental understanding of the nature of elastohydrodynamic lubrication and give physical rationale to the finding of roughness deformation depending on the “inlet length”. The findings may contribute to more efficient numerical solutions and to improved semi-analytical prediction methods for engineering based on physically correct asymptotic behaviour.     

Study on optimization of the circumferential and axial wavy geometrical configuration of hydrodynamic journal bearing

This paper is focused on using GA genetic algorithm to find the optimal performance with respect to shape optimization in three dimensions for the hydrodynamic journal bearing. The mathematical model for film thickness was drawn using Fourier series function and axial waviness value ( $\bar \Delta $ ) D to represent the journal bearing in circumferential and axial direction, respectively. The objective was then to determine the Fourier coefficients and axial waviness value ( $\bar \Delta $ ) D that maximized the load capacity subjected to a given set of constraint. Optimized results show that the presence of cos wave in axial direction, with a positive dimensionless amplitude (+A) and waviness number m = 0.633, improves the load capacity by (8–10) % over the cylindrical plain bearing with the same arbitrary shape and size; in general, the increasing order of Fourier series (n), an axial dimensionless amplitude and L/D ratio cause the change in load capacity to become more evident.     

Deteriorating jobs and learning effects on a single-machine scheduling with past-sequence-dependent setup times

In this paper, we consider the single-machine setup times scheduling with the effects of learning and deterioration. By the effects of learning and deterioration, we mean that the actual processing time of a job depends not only on the processing times of the jobs already processed but also on its scheduled position. The setup times are proportional to the length of the already processed jobs, i.e., the setup times are past-sequence-dependent (p-s-d). We show that the problems to minimize the makespan, the total completion time, and the sum of the $\mathit{\delta}$ th ( ${\mathit{\delta}} \geq 0$ ) power of job completion times are polynomially solvable. We also show that the total weighted completion time minimization problem, the maximum lateness minimization problem, and the number of tardy jobs minimization problem can be solved in polynomial time under certain conditions.     

Wear, Plasticity, and Rehybridization in Tetrahedral Amorphous Carbon

Wear in self-mated tetrahedral amorphous carbon (ta-C) films is studied by molecular dynamics and near-edge X-ray absorption fine structure spectroscopy. Both theory and experiment demonstrate the formation of a soft amorphous carbon (a-C) layer with increased sp² content, which grows faster than an a-C tribolayer found on self-mated diamond sliding under similar conditions. The faster $\hbox{sp}^{3} \rightarrow\,\hbox{ sp}^{2}$ transition in ta-C is explained by easy breaking of prestressed bonds in a finite, nanoscale ta-C region, whereas diamond amorphization occurs at an atomically sharp interface. A detailed analysis of the underlying rehybridization mechanism reveals that the $\hbox{sp}^{3}\, \rightarrow\hbox{ sp}^{2}$ transition is triggered by plasticity in the adjacent a-C. Rehybridization therefore occurs in a region that has not yet experienced plastic yield. The resulting soft a-C tribolayer is interpreted as a precursor to the experimentally observed wear.     

Experimental Investigation of Viscoelastic Rolling Contacts: A Comparison with Theory

To address the issue of a pin sliding against a boundary film, we calculate the pressure-dependent shear strength of a bilayer of potassium chloride sandwiched between tungsten carbide (WC) slabs using first-principles, density functional theory (DFT) calculations. It has been shown experimentally that the shear strength S of a KCl film on metal substrates varies with pressure P as S = S ₀ + αP, and S ₀ = 65 ± 5 MPa and α = 0.14 ± 0.02. Calculations are performed for KCl in contact with the (1 $ \bar{1} $ 00) and (10 $ \bar{1} $ 0) faces of WC which have almost square surface unit cells. The effect of pressure is mimicked by varying the distance between the outermost layers of the WC slabs. The DFT calculations confirm that the shear strength depends on pressure and yield average values of S ₀ of 70 ± 10 MPa for the WC(1 $ \bar{1} $ 00) and 51 ± 13 MPa for the WC(10 $ \bar{1} $ 0) faces, in reasonable agreement with experiment. Since the calculations were performed for a KCl slab in registry with the WC slabs, the agreement with experiment suggests that the atoms at the interface between the tip and film are also in registry. In addition, the calculated and experimental shear strengths are much lower than the shear modulus of KCl, indicating that shear occurs between the tip and film surface without forming a transfer film, in agreement with previous experimental measurements.     

Effect of gate dimension on micro injection molded weld line strength with polypropylene (PP) and high-density polyethylene (HDPE)

As a defect of micro injection molding parts, weld line is unfavorable since it will influence the surface quality and mechanical properties of micro parts. Therefore, the investigation on the developing process of weld line would be a significant issue for improving the quality of micro injection molded parts. In this study, one injection mold with four micro tensile sample cavities was designed and constructed. Every cavity responses to various gate dimensions, which is marked as Gate $ {\text{Nr}}.1\left( {1.5 \times 0.1 \times 0.{\text{5mm}},{\text{width}} \times {\text{depth}} \times {\text{length}}} \right) $ , $ {\text{Nr}}.2\left( {1.0 \times 0.1 \times 0.{\text{5mm}},{\text{width}} \times {\text{depth}} \times {\text{length}}} \right) $ , $ {\text{Nr}}.3\left( {1.0 \times 0.05 \times 0.{\text{5mm}},{\text{width}} \times {\text{depth}} \times {\text{length}}} \right) $ , and $ {\text{Nr}}.4\left( {0.5 \times 0.1 \times 0.{\text{5mm}},{\text{width}} \times {\text{depth}} \times {\text{length}}} \right) $ . The effects of gate dimension of the mold on mechanical properties of weld line have been studied by experiments in different processing parameters. The tensile test was used to characterize the micro injection molded weld line strength. The results for polypropylene show that with the changing of injection pressure and mold temperature, Gate Nr.3 is corresponding to the strongest weld strength; the next is Gate Nr.2; Gates Nr.4 and Nr.1 are in the end. The difference between them is not obvious. For high-density polyethylene, Gate Nr.1 is not able to be completely filled, which is due to the blocking of stick materials and dirt based on the simulation analysis. The investigation was only carried out for the other three gate sizes; results present that Gate Nr.3 always gives the best weld line strength whatever the processing parameters are, Gate Nr.4 is next and then Gate Nr.2. There are always middle optimal values for processing parameters leading to strongest weld line strength, when injection pressure is 80 MPa, injection speed is 90 cm³/s, melt temperature is 200°C, and mold temperature is 130°C. Higher and lower processing parameters result in reduced weld line strength.     

Competitive parameter optimization of multi-quality CNC turning

Surface roughness, tool wear, and material removal rate (MRR) are major intentions in the modern computer numerical controlled (CNC) machining industry. In this paper, the ${\text{L}}_9 \left( {3^4 } \right)$ orthogonal array of a Taguchi experiment is selected for four parameters (cutting depth, feed rate, speed, and tool nose runoff) with three levels (low, medium, and high) in optimizing the finish turning parameters on an ECOCA-3807 CNC lathe. The surface roughness (R_a) and tool wear ratio (mm^?2) are primarily observed as independent objectives for developing two combinations of optimum single-objective cutting parameters. Additionally, the levels of competitive orthogonal array are then proposed between the two parameter sets. Therefore, the optimum competitive multi-quality cutting parameters can then be achieved. Through the machining results of the CNC lathe, it is shown that both tool wear ratio and MRR from our optimum competitive parameters are greatly advanced with a minor decrease in the surface roughness in comparison to those of benchmark parameters. This paper not only proposes a competitive optimization approach using orthogonal array, but also contributes a satisfactory technique for multiple CNC turning objectives with profound insight.