Method for diagnosing health of CNC machine tool

A method for diagnosing health of a Computerized Numerical Control (CNC) machine tool, comprising the following steps:

• step 1:
• using a cloud server to carry out Fast Fourier Transformation (FFT) processing on vibration data collected by a vibration sensor node, and obtaining spectrum averages of 800-1800 Hz, 1800-2800 Hz and 2800-3800 Hz;
• obtaining a regression coefficient of relationship among the spectrum average of a relevant frequency band, temperature and operating state of equipment according to corresponding historical data of the spectrum average of the frequency band and temperature;
• 1.1 creating a data vector
• x=(x(1),x(2),x(3),x(4))
• wherein x(1) is the spectrum average of 800-1800 Hz, x(2) is the spectrum average of 1800-2800 Hz, x(3) is the spectrum average of 2800-3800 Hz, and x(4) is a temperature average of equipment;
• 1.2 creating a coefficient vector w=(w(1), w(2), w(3), w(4)), wherein w(1) is a coefficient of the spectrum average of 800-1800 Hz;
• w(2) is a coefficient of the spectrum average of 1800-2800 Hz;
• w(3) is a coefficient of the spectrum average of 2800-3800 Hz;
• and w(4) is a temperature coefficient;
• 1.3 xi is the ith trained data vector, and yi is a class marker of xi;
• when yi is −1, it means that the equipment fails;
• when yi is +1, it means that the equipment is normal;
• and N is a quantity of trained data;
• finding a separating hyperplane with a maximum geometric margin, and a problem is expressed as the following constrained optimization problem:
• min
• w
• ,
• b
• ,
• ξ
• ⁢
• 1
• 2
• ⁢
• 
• W
• 
• 2
• +
• C
• ⁢
• ∑
• i
• =
• 1
• N
• ⁢
• ξ
• i
• S
• .
• t
• ⁢
• ⁢
• y
• i
• ⁡
• (
• w
• .
• x
• i
• +
• b
• )
• ≥
• 1
• -
• ξ
• i
• ⁢
• ⁢
• ξ
• i
• ≥
• 0
• ⁢
• ⁢
• i
• =
• 1
• ,
• 2
• ,
• …
• ⁢
• ⁢
• N
• C is a penalty coefficient, and is a slack variable;
• assuming that the solutions of the constrained optimization problem are * and b*, transforming the original problem into a dual problem, and using Karush-Kuhn-Tucker (KKT) conditions to obtain an optimal solution of the dual problem, then:
• w
• *
• =
• ∑
• i
• =
• 1
• N
• ⁢
• α
• i
• *
• ⁢
• y
• i
• ⁢
• x
• i
• b
• *
• =
• -
• max
• i
• =
• y
• i
• =
• -
• 1
• ⁢
• w
• *
• ⁢
• x
• i
• +
• min
• i
• =
• y
• i
• =
• -
• 1
• ⁢
• w
• *
• ⁢
• x
• i
• 2
• wherein α* is a solution of the dual problem in a Lagrange multiplier vector;
• step 2:
• 2.1 health degree of a CNC machine tool:
• health degree J of a CNC machine tool is a number between 0 and 1;
• the greater or the closer to 1 the value is, the more healthy the operating state is;
• the smaller or the closer to 0 the value is, the more unhealthy the operating state is and the greater the possibility of failure is;
• the health degree J of the CNC machine tool can be calculated by the following steps:
• Lc
• =
• {
• w
• *
• ⁢
• x
• 0
• +
• b
• *
• 
• w
• *
• 
• w
• *
• ⁢
• x
• c
• ≥
• w
• *
• ⁢
• x
• 0
• w
• *
• ⁢
• x
• c
• +
• b
• *
• 
• w
• *
• 
• w
• *
• ⁢
• x
• c
• <
• w
• *
• ⁢
• x
• 0
• ;
• ⁢
• L
• 0
• =
• w
• *
• ⁢
• x
• 0
• +
• b
• *
• 0.95
• ⁢
• 
• w
• *
• 
• ;
• ⁢
• J
• =
• L
• ⁢
• c
• L
• 0
• wherein x0 is a data vector of a normally operating CNC machine tool calibrated by experts, and xc, is a data vector of a current CNC machine tool obtained by on-line monitoring;
• Lo is an equivalent distance of the health degree of the calibrated CNC machine tool, and LC is an equivalent distance of the health degree of the current CNC machine tool;
• 2.2 determination of predictive maintenance alarm threshold
• a failure possibility index p means the possibility of failure;
• p
• =
• 2
• ⁢
• e
• -
• J
• e
• J
• +
• e
• -
• J
• when p>r, alarm is given to prompt that the CNC machine tool needs maintenance, wherein r is a predictive maintenance alarm threshold.