Cutter Inclination Research Articles

Meshing stiffness characteristics of modified variable hyperbolic circular-arc-tooth-trace cylindrical gears

Abstract. Stiffness excitation is one of the important excitations for the variable hyperbolic circular-arc-tooth-trace (VH-CATT) cylindrical gear system. Accurate calculation of the gear meshing stiffness is of great significance to investigating dynamic characteristics of the VH-CATT cylindrical gear system. Firstly, based on the forming theory of the modified tooth surface, the modified tooth surface equation of the VH-CATT cylindrical gear was deduced, and the 3D reconstruction was realised. Next, the load tooth contact analysis (LTCA) model of the VH-CATT cylindrical gear was developed to calculate the meshing stiffness of the VH-CATT cylindrical gear, and it was verified by the finite-element calculation. Finally, the influence of the load and modification parameters on the VH-CATT cylindrical gear stiffness was investigated. Research shows that the stiffness calculation method of the VH-CATT cylindrical gear based on LTCA is accurate. The meshing stiffness of the VH-CATT cylindrical gear in the double-tooth meshing area is large, and the meshing stiffness of the VH-CATT cylindrical gear in the single-tooth meshing area is small. The stiffness of the VH-CATT cylindrical gear increases with an increase in the load and cutter inclination angle, the stiffness of the VH-CATT cylindrical gear only in the double-tooth meshing area decreases with an increase in the parabolic coefficient, and the stiffness of the VH-CATT cylindrical gear increases with a decrease in the blade parabolic vertex position value. The research results provide a basis for improving the bearing capacity of the VH-CATT cylindrical gear and optimising design.

自走式大白菜收获机切根机理分析及装置参数优化

For Chinese cabbage cutting device in the harvesting process, the problem of cutting resistance and low cutting root qualification rate will occur. This paper takes the Chinese cabbage root as the research object, analyses the root-cutting mechanism of Chinese cabbage, and determines that the main factors affecting its cutting effect are the cutter's inclination angle, rotational speed and its working speed. The finite element method is adopted to establish a rigid-flexible coupling model between the cutting device and the cabbage root, and the Response Surface Method (RSM) central composite design method is used to investigate the relationship among the cutter inclination angle, the cutter rotational speed as well as the working speed and Maximum root-cutting reaction force (MRF) of the cabbage and to further obtain the optimal combination of parameters. Field test results show that in the optimal combination of parameters, which means cutter inclination angle of 11o, cutter rotating speed of 216 r/min and working speed of 0.28 m/s, the root cutting effect is perfect. At this time, the root-cutting qualification rate of 92.81% and field productivity of 0.12 hm2/h, meet the requirements of the standard of Chinese cabbage harvesting mechanization. The results of the study can provide reference for optimization of Chinese cabbage harvesting equipment design.

A hybrid modeling method for predicting the cutting force in whirlwind milling of lead screw

Analyzing the cutting force in the process of lead screw whirlwind milling can help us understand the processing quality and processability. Whirlwind milling is a process in which multiple cutting tools are driven by the cutter head to sequentially cut and process the workpiece. The cutting force changes periodically in the process of lead screw whirlwind milling. Analyzing the cutting force of the nth cutting needs to consider the influence of the previous n-1 cutting. This paper employed a hybrid method combining mathematical modeling and finite element analysis to predict the cutting force in lead screw whirlwind milling. Firstly, the tool motion path of lead screw whirlwind milling is analyzed by considering the influence of cutter inclination angle and relative tool-workpiece motion. The relationship between the nth tool path and the (n-1)th tool path is analyzed by considering the feed motion of the tool and the rotation motion of the workpiece. Furtherly, mathematical models of the nth tool path and the (n-1)th tool path are established. Then, based on the established mathematical models, the three-dimensional geometric model of the tool and workpiece is established by three-dimensional software. The establishment of the workpiece geometry model considers the influence of the previous n-1 cutting. The tool geometry model rotates along the (n-1)th cutting path, and the tool intersects the workpiece. Finally, the finite element model of lead screw whirlwind milling is established based on the above three-dimensional geometric model. The periodical cutting force in the lead screw whirlwind milling is obtained by simulating the nth cutting with the finite element model. The relevant lead screw whirlwind milling experiment was carried out to verify the reliability of the model prediction. The appropriate processing parameter range of lead screw whirlwind milling is obtained through the process parameter optimization.

Modelling and mechanical characteristics of PDC cutter-rock interaction by combining mixed fragmentation modes with dynamic rock strength

Polycrystalline diamond compact (PDC) bit is one of the most widely used drill bits for improving the rate of penetration in deep oil and gas well and geothermal well. However, the dynamic rock fragmentation mechanics characteristics of PDC bits are still unclearly. A coupled fragmentation mechanics model of PDC cutter-rock interaction is established by combining the mixed fragmentation modes with dynamic strength. The coupling influence laws of cutter angle, cutting depth, dynamic strength ratio, breaking modes on the horizontal force coefficient (HFC), vertical force coefficient (VFC) and specific energy are analyzed. The model of this paper can optimize cutter inclination angle, cutting depth and minimum specific energy. With the increase of the cutter inclination angle, the dynamic VFC changes into two modes. The definition of the dynamic modes depends on the dynamic strength ratio. As the cutting angle increases, the cutting force increases. The cutting force increases nonlinearly with increasing cutting depth. The specific energy of rock fragmentation increases nonlinearly with increasing cutting depth. With the increase of dynamic strength, the specific energy of rock fragmentation increases nonlinearly. When the input-energy increases, the rate of penetration response is divided into three stages. The results have important guiding significance for the PDC bit design and drilling parameters optimization to increase the rate of penetration and the efficiency of exploration and development.

Surface modification and tooth contact analysis of variable hyperbolic circular-arc-tooth-trace cylindrical gears

Abstract. To improve the bearing capacity and provide the mathematical model basis for vibration and noise reduction of the variable hyperbolic circular-arc-tooth-trace (VH-CATT) cylindrical gear, the tooth surface modification design method based on the parabolic forming blade and cutter inclination was proposed. The geometric design of inclined cutter was completed. The modified tooth surface equation was deduced, and the influence of modification parameters on tooth surface curvature characteristics was analysed further. The tooth contact analysis (TCA) was established, and the influence of modification parameters on the elliptical contact area was analysed. Research shows that the parabolic coefficient a and the parabolic vertex position u0 have effects on the main curvature of concave–convex tooth surface, both the tooth profile and the tooth line direction, but the cutter inclination angle only has influence on the curvature of the tooth line direction, and the influence is larger. The cutter inclination angle γ, parabola coefficient a, and parabolic vertex position u0 have certain influences on the elliptical contact area. The cutter inclination angle γ is the most important modification parameter to improve the bearing capacity, but the excessive cutter inclination angle will cause bridge contact, the value range cutter inclination γ can be determined based on the tooth line radius. The research results provide a technical basis for improving the bearing capacity of the VH-CATT cylindrical gear and optimising the design.

Clearance angle and evolution of depth of cut in actuated disc cutting

This paper investigates the effect of cutter clearance angle on variation of depth of cut and cutting process with an actuated disc cutting (ADC). ADC is a cyclic cutting method with two main characteristics: (i) a disk-shape cutter is used to attack the rock in an undercutting mechanism; and (ii) the cutter is dynamically actuated as it is moved across the rock. Hence, the cutting process of such system is periodic, each recurrence known as actuation cycle. The first ADC model, developed in 2016, represented an idealization of the technology with a flat disc cutter, where no clearance angle was considered. The evolution of the contact between the disc and the rock was, therefore, computed only on horizontal x-y plane, ignoring the effect of normal component of the force acting on cartridge. This article reports on a study that incorporates the cutter inclination angle in derivation of cutter/rock interface laws. It extends the proposed kinematic and geometry based model to take into account the variable depth of cut in estimating the forces associated with cutting in one actuation cycle. Experiments were conducted using Wobble to test the predictions of the improved model at various operating conditions. The model predictions are matched with the experimental results and effects of various factors are analysed.

Cutting-force components in turning by tools with no cutting tip

Turning by tools that are characterized by a linear or curved cutting blade but have no cutting tip is studied experimentally. The influence of the depth and cutting speed, the supply, and the cutter inclination on the components Pz and Py of the cutting force is investigated in inverse and direct cutting.

Rock cutting characteristics on soft-to-hard rocks under different cutter inclinations

•Cutting and uniaxial compressive tests of soft-to-strong rocks were carried out.•The intrinsic specific energy increases with increasing cutter inclination.•The intrinsic specific energy was found to correlate well with UCS of rock.

Cut-layer cross section in oblique turning by a single-edge tool with a curved rear surface

A method is proposed for determining the parameters of the cut-layer cross section in oblique turning by a single-edge tool with a curved rear surface. The results are plotted as a function of the supply, the cutting depth, the cutter inclination, and the curvature of the rear surface.

Precise modeling of arc tooth face-gear with transition curve

A fabrication method is adopted for which an imaginary gear simultaneously realizes conjugated meshing with an arc tooth cylindrical gear and an arc tooth face-gear. The cutter fillet and tooth crest edge form the tooth root fillet of the gear, and the linear tooth surface equation of the imaginary gear and the position vector of the curvature center of the cutter fillet are constructed with certain cutter inclination to deduce a working arc tooth surface equation. The tooth root fillet equation of the arc tooth face-gear is derived from the meshing geometry and kinematics. A numerically controlled machining model of the arc tooth face-gear is established through the transformation of adjustment parameters from the cutter-tilt milling machine to a common multi-axis NC machine. Motion parameters of each movement axis of the NC machine are acquired. A processing example is presented to verify the precision of the fabrication method in processing the arc tooth face-gear. The method provides a theoretical and tentative basis for the analysis of tooth surface contact stress, tooth root bending stress and dynamics. A hobbing test is conducted to demonstrate the good meshing condition of the arc tooth face-gear pair.

Characterization of aortic tissue cutting process: Experimental investigation using porcine ascending aorta

Understanding biomechanical responses during soft tissue cutting is important for developing surgical simulators and robot-assisted surgery with haptic feedback. The biomechanics involved in the aortic tissue cutting process is largely unknown. In this study, porcine ascending aorta was selected as a representative aortic tissue, and tissue cutting experiments were performed using a novel tissue cutting apparatus. The tissue cutting responses under various cutting conditions were investigated, including differing initial tissue lateral holding force and distance, cutting speed, cutter inclination angle, tissue anatomical orientation and thickness. The results from this study suggest that a “break-in” cutting force of about 4–12N, a cutter “break-in” distance of 5–15mm, and a continuous cutting force of 2–4N were needed to cut through the porcine ascending aorta tissue. For all testing conditions investigated in this study, the cutting force vs. the cutter displacement curves exhibited similar characteristics. More importantly, this study demonstrated that tissue cutting involving one or more of the following conditions: a larger lateral holding force, a smaller lateral hold distance, a higher cutting speed or a larger inclination angle, could result in a smaller “break in” cutting force and a smaller “break-in” distance. In addition, it was found that the cutting force in the vessel longitudinal direction was larger than that in the circumferential direction. There was a strong correlation between the tissue thickness and the cutting force. The experimental results reported in this study could provide a basis for understanding the characteristic response of aortic tissue to scalpel cutting, and offer insight into the development of surgical simulators.

Influence of Inclination Angle on Machined Surface Hardness in High Speed Ball End Milling

In this paper, the effects of the variational combinations of cutter inclination angle in feed direction and the feed per tooth on the machined surface hardness were mainly concerned. The cutting forces transformed from the measured cutting forces in OXYZ and the SEM microstructures of the surface layer were analyzed to explore the generation condition of the hardness. Variations of the surface hardness are not apparent with the increment of feed per tooth with the identical other cutting parameters. Inclination angles in feed direction of approximately ranging from 10° to 15° and from 25° to 30°, which correspond to high surface hardness, are suggested to be applied in cutting process when high abrasive resistance is expected. While values of inclination angle approximately equal to 0° and 45° are prior to be chosen when high shock resistance performance is firstly expected. Optimization of the cutting parameters, which could offer guidance to the machining of sculptured surface concerning cutter inclination angle, was presented.

Optimization of Micromilling by Adjustment of Inclination Angles

The manufacturing of medical implants and the micro die- and mould-machining are typical fields of application for five-axis micromilling. The machined materials diversify from NiTi shape memory alloys to hardened steels. First experimental results reveal a strong dependency of the machinability of the aforementioned engineering materials on cutter inclination angles. This paper presents a simulation-based approach mainly to optimize the tool inclination angles. The developed new algorithm is not only capable of detecting unfavourable tool inclinations for machining freeform surfaces, it also readjusts them. The verification of the established algorithm is accomplished by the machining a reference workpiece.

Numerical modelling of high-speed ball end milling with cutter inclination angle

This paper describes the development of a simulation model for ball end milling with inclination angle based on a finite element method. The Johnson–Cook model and isotropic hardening rule were used to describe the properties of the workpiece material, and re-meshing technology was adopted to obtain accurate results. The Cockcroft–Latham criteria rule was used to determine the chip formation. The ball end mill was modelled, and then imported into a finite element analysis system for simulation of machining process. The heat conducted into the cutter was taken into account in the present simulation, giving a better accordance with the actual machining process. Thirty combinations of cutting parameters and inclination angle of the ball end milling process were simulated in the finite element environment, and the corresponding ball end milling experiments were conducted in a five-axis machine. Evolution of the chip and the effective stress predicted in the shear zone during simulation were presented. The cutting forces derived from the simulation were compared with the experimental results, and the overall trend of the maximum cutting forces in each direction showed a good agreement with the experimentally measured values. The potential possibility to study five-axis ball end milling with both inclination angle in feed and cross-feed direction was pointed out.

A New Algorithm for the Numerical Simulation of Machined Surface Topography in Multiaxis Ball-End Milling

In milling process, surface topography is a significant factor that affects directly the surface integrity and constitutes a supplement to the form error associated with the workpiece deformation. Based on the tool machining paths and the trajectory equation of the cutting edge relative to the workpiece, a new and general iterative algorithm is developed here for the numerical simulation of the machined surface topography in multiaxis ball-end milling. The influences of machining parameters such as the milling modes, cutter runout, cutter inclination direction, and inclination angle upon the topography and surface roughness values are studied in detail. Compared with existing methods, the basic advantages and novelties of the proposed method can be resumed below. First, it is unnecessary to discretize the cutting edge and tool feed motion and rotation motion. Second, influences of cutting modes and cutter inclinations are studied systematically and explicitly for the first time. The generality of the algorithm makes it possible to calculate the pointwise topography value on any sculptured surface of the workpiece. Besides, the proposed method is proved to be more efficient in saving computing time than the time step method that is commonly used. Finally, some examples are presented and simulation results are compared with experimental ones.

Optimization and Dynamic Adaptation of the Cutter Inclination during Five-Axis Milling of Sculptured Surfaces

Five axis milling allows to machine free form surfaces with cylindrical or toric cutters instead of ball nose cutter. This drastically reduces the machining time. Commercial CAM modules however require the NC-programmer to specify the appropriate inclination of the tool with respect to the work piece surface normal. This is difficult especially for complex parts with vaving surface curvature. This paper presents five axis CAM software which vanes the tool inclination during the tool path generation, in order to achieve the best combination of scallop height, workpiece accuracy, surface roughness and machining cost. Machining time to produce some free form workpieces, given a maximum scallop height, could be reduced by 50%.

The definition and manufacture of compound curvature surfaces using G-surf

G-surf is a method for defining and machining the compound curvature surfaces encountered in many engineering applications. The surfaces are defined by orthogonal grids of B-spline space curves and machined with a cylindrical end-milling cutter inclined at predetermined angles to the surface normals. The approach proves to be very flexible and, as the cutter operates at a full and select cutting speed, gives an efficient means of material removal. Surface finish and cutter interference are both affected by cutter inclination to the surface normal and can be adjusted for optimum conditions. The interactive menu-driven package fits onto microcomputer installations and is suitable for small- to medium-size manufacturing companies.