Theoretical model for cutting force in rotary ultrasonic milling of dental zirconia ceramics

Rotary ultrasonic machining or ultrasonic vibration assisted grinding has superior performance in machining hard and brittle materials, such as dental zirconia ceramics. However, there are few reports about cutting force modeling of rotary ultrasonic milling (RUM) for dental ceramics, especially for cutting force model in feed direction. In this study, the theoretical model of cutting force both in axial direction and feed direction is proposed under the assumption that brittle fracture is the primary mechanism of material removal in RUM of dental ceramics. The effective cutting time and material removal volume have been analyzed to develop the cutting force model. Besides, the number of active abrasive particles has been calculated for the first time during the modeling. The effect of overlapping and intersection of fracture zone in peripheral direction on material removal volume has also been considered via the parameters K ₁ and K ₂. In addition, the relationships between the cutting force and input variables are revealed through the theoretical model. Finally, pilot experiments of RUM on dental zirconia ceramics are conducted to verify the theoretical model. The experimental results are consistent well with the model predictions. Therefore, the theoretical model can be applied to evaluate the cutting force in RUM of dental ceramics.     

Development of cutting force prediction model for carbon fiber reinforced polymers based on rotary ultrasonic slot milling

Carbon fiber reinforced polymers (CFRP) have got widely increased applications in aviation, defense and other industries due to their properties of high specific strength/stiffness, high corrosion resistance and low-thermal expansion. The issues like excessive cutting forces and machining damages are encountered in machining due to heterogeneity, anisotropy and low heat dissipation of these materials. The cutting forces are required to be predicted/minimized through modeling. In this article, the novel axial and feed cutting force model has been developed and validated through rotary ultrasonic slot milling of CFRP composites. The variations less than 10% have been found between the measured and corresponding simulated values of the cutting forces. However, some higher variations have also been observed in the few cases mainly due to heterogeneity and anisotropy of such material. The cutting depth is a significant parameter for axial and feed forces, while the feed rate is significant for the axial force. Both the forces decreased with the increase of spindle speed, while they increased with the increase of feed rate and cutting depth. The developed models have been found to be robust and can be applied to optimize the cutting forces for such materials at the industry level.     

复杂形状工件的端铣切削力模型

以传统的端铣切削力模型为基础，提出了一种新的端铣加工中静态切削力的预报模型。该模型考虑了复杂的工件形状和不同的铣刀进给轨迹。给出了一种新的工件和铣刀接触算法。     

A cutting force prediction dynamic model for side milling of ceramic matrix composites C/SiC based on rotary ultrasonic machining

The relevance, importance and presence of industrial robots in manufacturing have increased over the years, with applications in diverse new and nontraditional manufacturing processes. This paper presents the complete concept and design of a novel friction stir welding (FSW) robotic platform for welding polymeric materials. It was conceived to have a number of advantages over common FSW machines: it is more flexible, cheaper, easier and faster to setup and easier to programme. The platform is composed by three major groups of hardware: a robotic manipulator, a FSW tool and a system that links the manipulator wrist to the FSW tool (support of the FSW tool). This system is also responsible for supporting a force/torque (F/T) sensor and a servo motor that transmits motion to the tool. During the process, a hybrid force/motion control system adjusts the robot trajectories to keep a given contact force between the tool and the welding surface. The platform is tested and optimized in the process of welding acrylonitrile butadiene styrene (ABS) plates. Experimental tests proved the versatility and validity of the proposed solution.     

An analytical model of rotary ultrasonic milling

Rotary ultrasonic machining is currently being used as a manufacturing method for advanced ceramic materials, but its complexity has hindered its acceptance in industry. For this technology to gain wider acceptance, it must first be scientifically better understood. The majority of published rotary ultrasonic machining (RUM) papers studied the effect of RUM process parameters on machining performance and removal mechanisms for drilling of circular holes. In industries such as aerospace, the production of advanced turbine components requires machining of complex 3D features using milling strategies. The objective of this paper will be to present a new physical model based on rotary ultrasonic milling which will help provide a better scientific understanding of the process. This will be accomplished by first modeling the macro kinematics between the tool and material followed by the modeling of micro kinematics between the individual diamond grains and the material. In addition, a force model for predicting machining process forces will also be introduced and validated based on a set of experiments. The physical models will help determine the relationships between input parameters, cutting parameters, and process output parameters for rotary ultrasonic milling.     

Fracture mechanics-based model of abrasive waterjet cutting for brittle materials

Advanced engineering ceramic materials such as silicon carbides and silicon nitride have been used in many engineering applications. The abrasive waterjet is becoming the most recent cutting technique of such materials because of its inherent advantages.In the present study, two elastic-plastic erosion models are adopted to develop an abrasive waterjet model for cutting brittle materials. As a result, two cutting models based on fracture mechanics are derived and introduced. The suggested models predict the maximum depth of cut of the target material as a function of the fracture toughness and hardness as well as the process parameters.It is found that both models predict the same depth of cut within a maximum of 11%, for the practical range of process parameters used in the present study. The maximum depth of cut predicted by the suggested models are compared with published experimental results for three types of ceramics. The effect of process parameters on the maximum depth of cut for a given ceramic material is also studied and compared with experimental work. The comparison reveals that there is a good agreement between the models' predictions and experimental results, where the difference between the predicted and experimental value of the maximum depth of cut is found to be an average value of 10%.Nomenclature C abrasive efficiency factor, see equation (16) - C ₁,C ₂ c ₁/4/3, c₂/4/3 - c ₁,c ₂ erosion models constants, see equations (1) and (2) - d _a local effective jet diameter - d _j nozzle diameter - d _S infinitesimal length along the kerf - f ₁ ( _E ) function defined by equation (7) - f ₂ ( _E ) function defined by equation (8) - f ₃ ( _e ) function defined by equation (14) - g ₁ ( _E ) f ₁( _e )/f ₃ ² ( _e ) - g ₂ ( _e ) f ₂( _e /f ₃ ² ( _e ) - H Vickers hardness of the target material - h maximum depth of cut - K _c fracture toughness of target material - k kerf constant - M linear removal rate, dh/dt - m mass of a single particle - abrasive mass flow rate - water mass flow rate - P water pressure - Q total material removal rate, see equation (11) - R abrasive to water mass flow rates - r particle radius - S kerf length - u traverse speed - V material volume removal rate (erosion rate) - V idealised volume removal by an individual abrasive particle - particle impact velocity - ₀ initial abrasive particle velocity - x,y kerf coordinates - local kerf angle, Fig. 1 - _E jet exit angle at the bottom of the workpiece, Fig. 1 - particle density - _w water density On leave from: Mechanical Engineering Department, Suez Canal University, Egypt.On leave from: Mechanical Power Engineering Department, Alexandria University, Egypt.     

In-process estimation of radial immersion angle using cutting force in face milling

In this paper, a on-line estimation method of the radial immersion angle using cutting force is presented. The ratio of cutting forces in feed and cross-feed directions acting on the single tooth at the immersion angle is a function of the immersion angle and the ratio of radial to tangential cutting force. It is found that the ratio of radial to tangential cutting force is not affected by cutting conditions and axial rake angle, which implies that the ratio determined by one preliminary experiment can be used regardless of the cutting conditions for a given tool and workpiece material. Using the measured cutting force during machining and predetermined ratio, the radial immersion ratio is estimated in process. Various experimental results show that the proposed method works within5% error range.     

In-process estimation of radial immersion ratio in face milling using cutting force

In order to prevent tool breakage in milling, maximum total cutting force is regulated at a specific constant level, or threshold, through feed rate control. Since the threshold is a function of the immersion ratio, an estimation of the immersion ratio is necessary to flexibly determine the threshold. In this paper, a method of in-process estimation of the radial immersion ratio in face milling is presented. When an insert finishes sweeping, a sudden drop in cutting forces occurs. These force drops are equal to the cutting forces that act upon a single insert at the swept cutting angle and they can be acquired from cutting force signals in the feed and cross-feed directions. Average cutting forces per tooth period can also be calculated from the cutting force signals in two directions. The ratio of cutting forces acting upon a single insert at the swept angle of cut and the ratio of average cutting forces per tooth period are functions of the swept angle of cut and the ratio of radial to tangential cutting force. Using these parameters, the radial immersion ratio is estimated. Various experiments are performed to verify the proposed method. The results show that the radial immersion ratio can be estimated by this method regardless of other cutting conditions.Nomenclature F_T, F_R tangential and radial forces - F_X, F_Y cutting forces in feed direction and cross feed direction - dF_X, dF_Y cutting force differences before and after the immersion angle in X and Y direction - K_s specific cutting pressure - a depth of cut - r ratio between tangential force and radial force - s_t feed per tooth - instantaneous angle of cut - _s swept angle of cut - _T tooth spacing angle - w radial width of cut - R cutter radius - z number of inserts     

硬脆材料切削加工负切削力现象的研究

以辉长岩为例,采用聚晶金刚石刀具进行硬脆材料切削加工试验,,在时域和频域内对切削力信号进行数字信号分析处理,提出硬脆材料切削力可分成切削趋势量和切削力随机量两部分;硬脆材料的组成结构特点和切削中刀具的振动是硬脆材料切削力出现负值现象的主要原因。     

Self-tuned ultrasonic elliptical vibration cutting for high-efficient machining of micro-optics arrays on brittle materials

Ultrasonic elliptical vibration cutting is a very promising technique for the machining of brittle materials. However, its machining performance is currently limited by the ductile machining model and the machining strategy with a constant feed rate, leading to low machining efficiency. To overcome this defect, this paper presents a novel self-tuned ultrasonic elliptical vibration cutting (SUEVC) technique to achieve high-efficient ductile-regime machining of the micro-optics array on brittle materials. The proposed SUEVC includes a ductile-regime machining model and a tool path generation method. In SUEVC, the feed rate adaptively changes with respect to the local shape variation of the desired surface along the feeding direction to ensure both crack-free surface and high machining efficiency. Finally, two 1 × 3 spherical micro-optics arrays were successfully fabricated on single-crystal MgF₂ by SUEVC and the traditional machining strategy respectively. Results demonstrated that the SUEVC could enhance the machining efficiency by 30% relative to the traditional machining strategy, while maintaining similar surface roughness and a crack-free surface.     

An improved cutting force model for micro milling considering machining dynamics

Micro milling, as a versatile micro machining process, is kinematically similar to conventional milling; however, it is significantly different from conventional milling with respect to chip formation mechanisms and uncut chip thickness modelling, due to the comparable size of the edge radius to the chip thickness, and the small per-tooth feeding. Considering tool runout and dynamic displacement between the tool and the workpiece, the contour of the workpiece left by previous tool paths is typically in a wavy form, and the wavy surface provides a feedback mechanism to cutting force generation because the instantaneous uncut chip thickness changes with both the vibration during the current tool path and the surface left by the previous tool paths. In this study, a more accurate uncut chip thickness model was established including the precise trochoidal trajectory of the cutting edge, tool runout and dynamic modulation caused by the machine tool system vibration. The dynamic regenerative effect is taken into account by considering the influence of all the previous cutting trajectories using numerical iteration; thus, the multiple time delays (MTD) are considered in this model. It is found that transient separation of the tool-workpiece occurring at a low feed per tooth, caused by MTD and the existing cutting force models, is no longer applicable when transient tool-workpiece separation occurs. Based on the proposed uncut chip thickness model, an improved cutting force model of micro milling is developed by full consideration of the ploughing effect and elastic recovery of the workpiece material. The proposed cutting force model is verified by micro end milling experiments, and the results show that the proposed model is capable of producing more accurate cutting force prediction than other existing models, particularly at small feed per tooth.     

Decoupled chip thickness calculation model for cutting force prediction in five-axis ball-end milling

Cutting force prediction plays very critical roles for machining parameters selection in milling process. Chip thickness calculation supplies the basis for cutting force prediction. However, the chip thickness calculation in five-axis ball-end milling is difficult due to complex geometrical engagements between parts and cutters. In this paper, we present a method to calculate the chip thickness in five-axis ball-end milling. The contributions of lead and tilt angles in five-axis ball-end milling on the chip thickness are studied separately in detail. We prove that the actual chip thickness can be decoupled as the sum of the ones derived from the two individual cutting conditions, i.e., lead and tilt angles. In this model, the calculation of engagement boundaries of tool–workpiece engagement is easy; thus, time consumption is low. In order to verify the proposed chip thickness model, the chip volume predicted based on the proposed chip thickness calculation model is compared with the theoretical results. The comparison results show that the desired accuracy is obtained with the proposed chip thickness calculation model. The validation cutting tests, which are in a constant material removal rate and with only ball part engaged in cutting, are carried out. The optimized lead and tilt angles are analyzed with regard to cutting forces. The geometrical as well as the kinematics meaning of the proposed method is obvious comparing with the existing models.     

Counterbalance of cutting force for advanced milling operations

The goal of this work is to concurrently counterbalance the dynamic cutting force and regulate the spindle position deviation under various milling conditions by integrating active magnetic bearing (AMB) technique, fuzzy logic algorithm and an adaptive self-tuning feedback loop. Since the dynamics of milling system is highly determined by a few operation conditions, such as speed of spindle, cut depth and feedrate, therefore the dynamic model for cutting process is more appropriate to be constructed by experiments, instead of using theoretical approach. The experimental data, either for idle or cutting, are utilized to establish the database of milling dynamics so that the system parameters can be on-line estimated by employing the proposed fuzzy logic algorithm as the cutting mission is engaged. Based on the estimated milling system model and preset operation conditions, i.e., spindle speed, cut depth and feedrate, the current cutting force can be numerically estimated. Once the current cutting force can be real-time estimated, the corresponding compensation force can be exerted by the equipped AMB to counterbalance the cutting force, in addition to the spindle position regulation by feedback of spindle position. On the other hand, for the magnetic force is nonlinear with respect to the applied electric current and air gap, the characteristics of the employed AMB is investigated also by experiments and a nonlinear mathematic model, in terms of air gap between spindle and electromagnetic pole and coil current, is developed. At the end, the experimental simulations on realistic milling are presented to verify the efficacy of the fuzzy controller for spindle position regulation and the capability of the dynamic cutting force counterbalance.     

高速干式飞刀铣齿切削力模型

利用金属切削理论,采用高速干式飞刀铣齿模拟滚齿切削过程,建立飞刀铣齿切削力模型,推导出飞刀铣削力的计算公式。该模型的建立对进一步分析高速干式滚齿过程中的特征参数、进行切削机理的研究具有重要意义。     

光学脆性材料的金刚石切削加工

重点对脆性材料的超精密研磨、抛光加工技术及超精密磨削加工技术和超精密切削加工技术进行了分析研究。分析表明,硬脆材料光学元件主要应进行超精密研磨、抛光及超精密磨削加工;软脆材料光学元件主要应进行金刚石切削加工。对软脆材料金刚石切削进行了试验设计,指出了光学脆性材料的金刚石切削加工过程不同于金属加工过程,通过控制切削条件可以实现脆性材料塑性域加工,提高光学脆性材料的表面加工质量。     

Inertial rotary vibrational drives for crushers of brittle materials

The efficiency of inertial rotary vibrational drives for crushers of brittle materials is established. Such drives permit control of the resulting piece size.     

Implementation of analytical boundary simulation method for cutting force prediction model in five-axis milling

A simulation system was developed that deals with cut geometry and machining forces when a toroidal cutter is used during semifinishing in five-axis milling. The cut geometry was calculated using an analytical method called analytical boundary simulation (ABS). ABS was implemented to calculate the cut geometry when the machining used an inclination angle and a screw angle. The effect of tool orientation on the cut geometry was analyzed. The accuracy of the proposed method was verified by comparing the cut lengths calculated using ABS with cuts obtained experimentally. The result indicated that the method was accurate. ABS was subsequently applied to support a cutting force prediction model. A validation test showed that there was a good agreement with the cutting force generated experimentally.