**1. Introduction**
In metal cutting processes, the shape of chips is constantly changing. To simulate the chip formation process effectively, it's essential to parameterize the chip shape and calculate these parameters based on the machining conditions. Over the years, researchers worldwide have conducted extensive studies on chip shape and formation, resulting in more than a dozen chip formation models. Significant progress has been made in understanding chip flow, the mechanism of chip curling, and how chips break. However, due to the complexity of the chip formation problem, many studies remain qualitative, especially regarding lateral chip curling.
This paper analyzes the primary and secondary factors that influence chip shape based on the formation mechanism and deformation laws. A mathematical model is established to enable the quantitative calculation of chip shape parameters, providing essential data for chip modeling.
Figure 1: Spiral chip shape parameters
**2. Chip Formation and Shape Parameters**
When the tool cuts into the workpiece, the cut metal layer undergoes plastic slip deformation through the shear plane, forming chips. These chips are then curled and deformed by the cutter flute, creating spiral-shaped chips with equal pitch. The spiral chip is characterized by its diameter (2r), pitch (p), and the angle (q) between the helical surface and the axis (Fig. 1). After exiting, chips may be further deformed or broken by obstacles such as the workpiece, tool, or machine, leading to various chip types. Therefore, other chip types can be considered as an evolution or combination of spiral chips.
According to the cutting mechanism, the key parameters affecting spiral chips include 1/rx (chip curvature along the feed direction), 1/rz (horizontal curl), and h (chip thickness). The shape parameters of the spiral chip can be expressed as:
(1)
(2)
(3)
Numerous factors influence 1/rx, 1/rz, and q during cutting, including material properties, cutting amount, tool geometry, coolant, and processing methods. By analyzing the main influencing factors and conducting comprehensive experiments on others, we can achieve accurate quantification of chip shape parameters.
Figure 2: Chip axial section parameters
**3. Parameters of the Chip Axial Section**
The shape of the spiral chip section is determined by three key parameters: chip thickness (hch), chip width (bch), and chip offset (kch) (see Figure 2). Based on the cutting principle, the formulas for calculating the axial section of the chip are:
hch = Ahf sin kr (4)
bch = ap sin kr (5)
kch = arctan(Ah tan kr) (6)
Where the deformation coefficient Ah = cos(f - co) / sin f, and the feed amount (f), depth (ap), tool lead angle (kr), and rake angle (co) are known parameters. The shear angle (f) can be found using an experimental formula.
**4. Calculation of Chip Curl Rate**
Figure 3: Chip upward curl
The chip radius R0 is primarily related to the chip flute and built-up edge. Since modern carbide tools operate at high speeds and typically do not produce built-up edges, this effect is often ignored. When a chip flute exists on the tool surface, the chip flow is affected by the back wall of the flute, causing the chip to lift. This results in bending moments at the chip root, compressive stress on the free surface, and tensile stress on the rake face, leading to an upward curl (see Figure 3). The formula for R0 is:
R0 = (w - lf) cos(s/2)
Where lf = km hD sin(f + b - g0) / sin f cos b, and hD = f · sin kr. Here, w is the chip flute width, s is the groove bottom angle, km ≈ 2 is an experimental coefficient, and b is the friction angle. Let Cx be the integration coefficient for other influencing factors. The curl rate formula is:
1 = Cx = Cx rx R0 (w - lf) cos(s/2) (7)
**5. Calculating the Chip Curl Rate**
Figure 4: Chip lateral curl
Currently, research on lateral chip curling is mainly qualitative. Two factors influence lateral curl: chip lateral flow and the participation of secondary cutting edges in the width direction. Based on this, a theoretical formula for lateral curvature is derived, adjusted by experimental coefficients. Let D be the chip deformation in the width direction, and Dv = v2 - v1 be the speed difference caused by the workpiece obstacle. The angular velocity is w = v2 / rz1 = v1 / (rz1 - bD) (see Fig. 4). Let Dv = (D / kw1 bD) v1, D = bch - bD, where kw1 is experimentally determined. The curvature from side flow is:
1 = D / [rz1 bD (D + kw1 bD)]
Under the same cutting thickness, when the load from the secondary cutting edge is equivalent, the transverse curvature is near maximum. The greater the cutting thickness, the more significant the effect of the secondary cutting edge on lateral curl. Let x, kw2, and aw be experimentally determined parameters for the lengths of the primary and secondary cutting edges. Then, the curvature caused by the secondary cutting edge is:
1 = kw2 x hD aw / rz2
Using an optimal design method, let kw1, kw2, and aw vary within ranges 1–5, 0–1, and 0–1 respectively. Substituting into each formula gives Crz, and comparing with measured Lrz from cutting experiments allows finding the minimum S(Lrz - Crz)^2. A set of coefficients kw1, kw2, and aw is obtained. Let Cz be the comprehensive coefficient for other factors. The formula for lateral curling rate is:
(8)
**6. Chip Shaving Angle Calculation**
When cutting perpendicularly, the chip flows out perpendicular to the cutting edge. In three-dimensional cutting, the chip outflow direction forms an angle with the vertical direction of the main cutting edge. This angle is approximately equal to the chip angle h. Several methods exist to analyze the flute angle: Stabler’s law suggests h = cls. Colwell believes the chip flow direction is approximately perpendicular to the chord of the cutting edge. Wang and Mathew point out that the radius of the tool tip arc and the inclination of the cutting edge are the main causes of chip flow. A quantitative method for calculating the flow angle is the regression equation:
l = 0.21ap - 0.74f^0.424(rs + 0.45)^0.68(kr - 16)^1.28 * 0.99gn + cls
Here, c ≈ 0.62–0.67 is a material-related coefficient. If the tool doesn’t change during machining, the tool parameters remain constant. Define:
Cl1 = 0.21(rs + 0.45)^0.68(kr - 16)^1.28 * 0.99gn
Cl2 = cls
Then, the flow angle formula simplifies to:
(9)
**7. Conclusion**
The general shape of chips is equal-pitch helical chips. The axial section parameters hch, bch, and kch are calculated using equations (4), (5), and (6). The shape parameters 2r, p, and q are given by equations (1), (2), and (3). The influencing factors 1/lx, lz, and h are approximated using equations (7), (8), and (9) to determine their values. Based on the quantitative values of the chip parameters hch, bch, kch, 2r, p, and q, chip modeling becomes possible.
Mobile Theater Cinema
With Mobile Theater Cinema, it's easy to get your theater cinema in front of your clients in an affordable, effective and efficient manner. Create your company's image with portable Space, display stand with your own characteristics, and eye-catching signage. On the exterior of your Mobile Showroom trailer we can add full color decals to further showcase your branding. In the Multi-Functional Mobile Cinema ,you can decorate according to your own needs. In addition, our Portable Multi-Functional Cinema come in various sizes to perfectly suit your needs. Whenever you are looking for a mobile showroom, the first considerations are size, layout and design. Our designers have many years of experience, even if you put forward your requirements, we can satisfy you and regard us as your hardworking partner. Get in touch with our team today to start your next project.
Mobile Theater Cinema,Portable Multi-Functional Cinema,Multi-Functional Movable Cinema,Multi-Functional Mobile Cinema
EVENT TECH TRANSFORMERS CO.,LIMITED , https://www.crusadetruck.com