Ultrasonic Longitudinal-Torsional Compound Vibration Grinding Method and Grinding Device for Use with Inner Hole of Pipe with Large Aspect Ratio

An ultrasonic longitudinal-torsional compound vibration grinding method for use with inner hole of pipe with large aspect ratio, comprising the steps of:

• (a) Setting grinding parameters of an ultrasonic vibration transducer, which comprises the steps of:
• S1:
• determining an amplitude and a vibration frequency of the ultrasonic vibration transducer based on a unit volume vibration energy, wherein a relationship between the unit volume vibration energy W, the amplitude of the ultrasonic vibration transducer, and the vibration frequency of the ultrasonic vibration transducer is as follows:
• W
• =
• 1
• 2
• ⁢
• ρ
• ⁡
• (
• 2
• ⁢
• π
• ⁢
• f
• )
• 2
• ⁢
• (
• A
• l
• 2
• +
• r
• 2
• ⁢
• A
• t
• 2
• )
• ,
• where Al refers to longitudinal amplitude, At refers to torsional amplitude, f refers to the vibration frequency, ρ refers to a material density of the grinding tool, and r refers to an average diameter of the grinding tool;
• S2:
• determining a longitudinal-torsional vibration phase difference based on an overlap rate of adjacent vibration period trajectories, wherein the overlap rate a of adjacent vibration period trajectories η is:
• η
• =
• 1
• -
• v
• f
• ·
• (
• A
• l
• )
• 2
• +
• (
• 2
• ⁢
• π
• ⁢
• r
• ⁢
• A
• t
• )
• 2
• ·
• sin
• ⁢
• ϕ
• ,
• where ν refer to a total cutting speed of an abrasive particle, φ refers to a phase difference of longitudinal and torsional vibrations;
• S3:
• determining a longitudinal torsional frequency ratio k based on workpiece characteristics and different processing stages, and select a torsional ultrasonic vibration frequency ω1 and a longitudinal ultrasonic vibration frequency ω2 based on the longitudinal torsional frequency ratio k, wherein the longitudinal torsional frequency ratio k is:
• k
• =
• ω
• 2
• /
• ω
• 1
• ,
• where ω1 refers to the torsional ultrasonic vibration frequency and ω2 refers to the longitudinal ultrasonic vibration frequency;
• then transmitting longitudinal-torsional compound vibration to the grinding tool from the ultrasonic vibration transducer, wherein the abrasive particle of the grinding tool produce periodic motion in both an axial direction and a tangential direction to achieve longitudinal-torsional compound vibration grinding of the inner hole of the pipe with large aspect ratio.