Modeling and analysis of grinding force in ultrasonic honing considering the scale effect

To research the power ultrasonic honing mechanism at the micro scale, the scale effect is considered and the strain gradient plasticity theory based on the dislocation mechanism (MSG) is applied to establish the model of a whetstone grinding force, and the simulation analysis is conducted. Results show: the grinding force will increase when the scale effect is considered; the main influence parameter is honing depth on the grinding force; the grinding force increases nonlinearly with the continued reduce of honing depth after which decreases to 1.4 μm, which decreases slightly with the increase of the relative velocity of a whetstone. So the material becomes difficult to remove at the micro scale.


Introduction
Power ultrasonic honing is a new type of precision machining method, with some advantages such as small grinding force, low honing temperature and high processing efficiency, which is widely used in cylinder block and cylinder liner processing of cars and tanks, and has a broad application prospect. [1] In recent years, In summary, materials processed will inevitably show scale effect when the honing depth of ultrasonic honing reduces to micron level, but some related Where, v ea , v, v a and v f are the synthesis speed, reciprocating speed, rotation speed and ultrasonic vibration speed of the whetstone respectively.

Scale effect of the power ultrasonic honing
Materials' scale effect should be considered when the honing depth of ultrasonic honing is a few microns.
With the honing depth decreases, the hardness and the specific grinding energy of the material processed will increase nonlinearly, which is the so-called scale effect.
Applying the strain gradient plasticity theory based on the dislocation mechanism, the shear strength of the material can be expressed by the dislocation density.
Where τ is the shear strength; α is an empirical constant between 0.2 to 0.5, here is 0.5; μ represents the shear modulus; b indicates the Burgers vector length, which is 0.29664 nm for the 45 steel; U, U s and U G are the total dislocation density, the statistics stored dislocation density and the geometrically necessary dislocation density, respectively. U G is related to the strain gradient at the microscopic scale. b r Where Cr is the Nye factor, which reflects the ratio of the average density of geometrically necessary dislocation and the geometrically necessary density in the most effective arrangement, is 2 for a face-centered cubic polycrystal and 3 for a face-centered cubic single crystal.
The tensile flow stress in the crystal is shown in the formula (4).
Where Cm is the Taylor factor, which is or 3 for isotropic materials or anisotropic materials, since

Simulation analysis of grinding force model
In order to find out the influence of the scale effect on ultrasonic honing intuitively, and analyse the degree and trend of change on grinding force, applying Matlab to doing simulation analysis of the grinding force model established. The material of a workpiece is taken the 45 steel, for the diamonds grain, the grain size was 150# and the concentration is 100%, the half cone angle is π/4, the grinding flat particle radius is 0.015 mm, the structure size of a whetstone is 6×6×100 mm, the simulation parameters of power ultrasonic honing is shown in table 1.  force reaches the minimum, and if honing depth continues to decrease, the grinding force will increase rapidly, so that material is difficult to remove. This is due to some changes of material characteristic at micro scale, the lattice dislocation needs to be fully considered, the hardness, shear strength and tensile flow stress of the material increase and the grinding force increases. When the honing depth is greater than the certain value, gradually tending to a macroscopic cutting, grinding force increases with the increase of honing depth. The grinding force reduces slightly with the increase of the reciprocating or rotation speed, because the increase of whetstone speed will reduce the dynamic friction coefficient so as to decrease the grinding force.

Conclusions
The scale effect should be considered when the honing depth of power ultrasonic depth is a few microns, which is essential for the microscopic mechanism of ultrasonic honing. The grinding force established is related with the microscopic parameters of the material processed, such as the Burgers vector length. When the scale effect is considered, the grinding force increased obviously, the normal and tangential grinding force will increase nonlinearly with the reduce of honing depth when the honing depth is less than 1.4 μm, and the grinding force decreases slightly with the increase of the relative velocity of a whetstone.