- Original Article
- Open Access
Error compensation in high-speed milling of deep cavity dies and molds based on the lengthened shrink-fit holder
- Zhou Houming^{1}Email author,
- Liu Bo^{1},
- Zhou Youhang^{1} and
- Peng Ruitao^{1}
https://doi.org/10.1186/s40712-015-0043-x
© Houming et al. 2015
Received: 13 March 2015
Accepted: 3 July 2015
Published: 24 July 2015
Abstract
Background
In high speed milling of the dies and molds characterized by large-scale and deep cavities with the lengthened shrink-fit holder (LSFH), the machining error caused by the tool deflection is not allowed to be ignored.
Methods
The deformation of the LSFH and cutting tool are predicted, and at the same time the machining error caused by this deformation are predicted too based on the milling force prediction model and the finite element model. Taking into account the complex mutual coupling between milling force and the deformation, an error compensation method is proposed based on a balancing iterative algorithm.
Results
The compensation tool path is obtained and the off-line machining error compensation is achieved. Milling example shows that the machining error after compensation less 77.4 % than that of no compensation.
Conclusions
The results demonstrate that the proposed error compensation method is reasonable and can greatly reduce the machining error.
Keywords
- Dies and molds
- LSFH
- High-speed milling
- Error compensation
Background
Nowadays, high-speed machining (HSM) technology is widely used in die and mold processing (López de Lacalle et al. 2006), how to select or design a suitable cutting tool according to the characteristics of workpiece is a key to improve efficiency and quality, optimize machining parameters, and reduce processing costs. Traditionally, the stiffness of the shank-chuck-tool system is so limited, whereas the semi-finishing and finishing machining of the dies and molds characterized by large-scale and deep cavity still mainly depends on electrical discharge machining (EDM) and manual polishing which will result in low efficiency and poor quality and cannot meet the needs of an increasingly competitive market.
As a new cutting tool hold technology, lengthened shrink-fit holder (LSFH) has drawn tremendous industrial attention recently. For touching workpiece in high-speed machining of dies and molds characterized by large-scale and deep cavity, LSFH is more suitable than those traditional hold systems such as the collet chuck and the static pressure expansive chuck because of its simple structure, high balance accuracy, and high clamping strength (Zhou et al. 2012; Tony and Schmitz 2007; Zhang 2006).
Several works had been carried out to investigate the stiffness and defection of the cutting tool system which will affect the machining precision and surface quality (Salgado et al. 2005). Some scholars focus on the estimation of the geometrical accuracy in multi-axis milling process (Lamikiz et al. 2008) and the topography prediction of ball-end milled surfaces, considering the tool parallel axis offset (Arizmendi et al. 2008). However, the deformation of the matching of LSFH and cutting tool is particularly prominent during the machining process due to the special lengthening structure of LSHF. Therefore, how to reduce the machining errors caused by this deformation is very important to make full use of the advantages of LSFH, ensure the machining quality, and improve the machining efficiency.
The intention of this work is to offline compensate the machining errors caused by the deformation of the matching of LSFH and cutting tool system in 3-Axis CNC finishing milling the dies and molds characterized by large-scale and deep cavity. Taking into account the complex and mutual coupled relationship between the milling force and the deformation, the iterative methods are used to obtain the compensated cutting tool path and achieved the offline errors compensation. The rationality of the error compensation method was verified with an actual processing example.
Methods
Machining error analysis
Due to using the high-speed machining centers, the machine has a high-precision of manufacturing and a high-performance closed-loop control system (Zhang and Pan 1997; Zhang et al. 2002). So the machining error generated by the static error of the machine occupies a small proportion of the whole machining error during high-speed milling of the dies and molds characterized by large-scale and deep cavity based on the LSFH. For the static errors caused by the cutting tool, the high-performance and high-speed machining centers generally have automatic compensation for the cutting tool length and diameter which can eliminate the impact of machining errors. When a machine processes dies and molds characterized by large-scale and deep cavity, the workpieces have big volume and good rigidity, its stiffness is far greater than that of the cutting tool system. Therefore, the deformation of the matching of LSFH and the cutting tool system has become the main reason to cause the machining errors.
Lengthened shrink-fit holder
Machining errors caused by the deformation
It can be found that the final machining error can be obtained through determining the radial deformation and the angle φ. The literature (Ryu et al. 2003) suggests that without considering the influence of cutting edge to the generation process of the machining surface and directly predicting the forming errors from the deformation of the cutting tool is faster than that of the time simulation about 300 times.
Results and discussions
Error compensation
Machining surface analysis
Milling force model
Deformation model of the matching of LSFH and cutting tool
Physical characteristic of LSFH and cutting tool
Young’s modulus, E (10^{5} MPa) | Poisson’s ratio, μ | Density, ρ (10^{3} kg/m^{3}) | |
---|---|---|---|
Lengthened shrink-fit holder | 2.0 | 0.3 | 7.8 |
Cutting tool | 6.4 | 0.22 | 15 |
Machining error compensation process
Machining error compensation example
The predicted milling force and actual cut depth after iteration
Sample points | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | |||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Mill force/N | Before iteration | F _{ x } | 17.82 | 17.82 | 17.82 | 17.82 | 17.87 | 17.92 | 18.35 | 18.71 | 19.41 | 19.83 | 20.44 | 21.15 | 21.93 | 22.36 | 22.97 | 23.78 | 24.13 | |
F _{ y } | 23.90 | 23.90 | 23.90 | 23.90 | 24.21 | 24.73 | 25.11 | 25.64 | 25.85 | 26.35 | 26.94 | 27.67 | 28.57 | 29.73 | 30.18 | 31.25 | 32.35 | |||
F _{ z } | −14.58 | −14.58 | −14.58 | −14.58 | −14.59 | −14.62 | −14.68 | −15.13 | −15.54 | −15.79 | −16.24 | −16.95 | −17.33 | −17.98 | −18.35 | −18.92 | −19.37 | |||
After iteration | F _{ x } | 17.82 | 17.82 | 17.82 | 17.82 | 18.76 | 19.01 | 19.75 | 20.26 | 21.28 | 21.77 | 22.69 | 23.33 | 24.34 | 25.04 | 26.0 | 27.16 | 27.95 | ||
F _{ y } | 23.90 | 23.90 | 23.90 | 23.90 | 25.42 | 26.26 | 26.92 | 27.64 | 28.25 | 28.96 | 29.63 | 30.51 | 31.85 | 33.42 | 34.29 | 35.70 | 37.07 | |||
F _{ z } | −14.58 | −14.58 | −14.58 | −14.58 | −15.38 | −15.53 | −15.75 | −16.39 | −16.95 | −17.31 | −17.86 | −18.71 | −19.27 | −20.13 | −20.8 | −21.69 | −22.30 | |||
U _{ n }/mm | 0.3 | 0.3 | 0.3 | 0.3 | 0.3076 | 0.3081 | 0.3085 | 0.3114 | 0.3130 | 0.3147 | 0.3170 | 0.3191 | 0.3212 | 0.3238 | 0.3259 | 0.3287 | 0.3315 |
Conclusions
- (1)
The relationship between the deformation of the LSFH-tool system and the surface contour machining error was analyzed. The results showed that the surface contour machining error eventually converted to determine the radial deformation in the horizontal direction and the angle between the normal of machining workpiece surfaces and the cutting tool axis at each nominal cutting tool position point.
- (2)
The machining error compensation method was proposed and a new algorithm of equilibrium iteration of milling force and deformation was put forward to solve the complexity coupled relationship between the milling force and the deformation of cutting tool system, ultimately to get the compensated machining cutting tool path and achieve offline compensation of machining errors.
- (3)
Processing example showed that the maximum machining error in z direction reduced from 42 μm (uncompensated machining) to 9.5 μm (compensated machining) and the machining error is reduced by 77.4 %. Furthermore, the standard deviation of machining error in the z direction indicated that the iteration algorithm of error compensation has good robustness.
In high-speed machining of the dies and molds characterized by large-scale and deep cavity, the offline error compensation method proposed in this work can obtain a higher machining dimensional accuracy and surface quality without sacrificing machining efficiency.
Nomenclature
Symbol, description
N, surface normal
φ, angle between tool axis and surface normal
e, horizontal radial deformation
ρ, radius of curvature
T _{ RP }, actual tool position
T _{ NP }, nominal tool position
S _{ N }, nominal machining surface
T _{ N }, nominal tool path
T _{ C }, compensation too path
T _{ CP }, compensation tool position
ε, error limitation
δ, machining error
F _{ x }, F _{ y }, F _{ z }, milling force
A _{ d }, nominal cutting depth
R _{ d }, nominal cutting width
U _{ n }, actual cutting depth
Declarations
Acknowledgements
The authors are grateful to Nature Science Foundation of China (51375418, 51375419, 51275436 and 51475404) and Hunan Province Science Foundation of China (13JJ8007).
Authors’ Affiliations
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Copyright
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly credited.