Table 1 Nomenclature.
From: Analysis on curve negotiating ability of rail grinder in grinding state
\(l_{c1x}\), \(l_{c1y}\), \(l_{c1z}\), \(l_{c2x}\), \(l_{c2y}\),\(l_{c2z}\) | x, y, z distance from mass center of grinding car to secondary suspension, to draw bar |
\(l_{b1x}\), \(l_{b1y}\), \(l_{b1z}\), \(l_{b2x}\), \(l_{b2y}\), \(l_{b2z}\),\(l_{b3z}\) | x, y, z distance from mass center of buggy frame to buggy suspension, to draw bar, to rotation center of cradle |
\(l_{d1z}\), \(l_{d1z}\), \(L_{g} (t)\),\(l_{g}\) | z distance from mass center of cradle to adjusting hydraulic cylinder, to rotation center, actual and nominal length from rotation center of cradle to grinding wheel |
\(x_{c}\), \(y_{c}\), \(z_{c}\), \(x_{b}\), \(y_{b}\),\(z_{b}\) | Mass center in x, y, z of grinding car, of buggy frame |
\(\phi_{c}\), \(\beta_{c}\), \(\psi_{c}\), \(\phi_{b}\), \(\beta_{b}\), \(\psi_{b}\),\(\phi_{d}\) | Rotation angle of grinding car and of buggy in x, y, z, of cradle in x |
\({\mathbf{K}}_{sb1}\), \({\mathbf{C}}_{sb1}\), \({\mathbf{K}}_{g}\), \({\mathbf{C}}_{g}\), \(K_{b}\),\(C_{b}\) | Vector stiffness and damping of draw bar, of grinding hydraulic cylinder, equivalent stiffness and damping of adjusting hydraulic cylinder |
\({\mathbf{F}}_{sb}\), \({\mathbf{F}}_{g}\),\(T_{b}\) | Suspension or traction vector force between grinding car and buggy, vector force between cradle and grinding wheel, torque of adjusting hydraulic cylinder |
\(R_{c}\), \(R_{b}\) | Curvature radius of grinding car center and of buggy center when running |
\({\mathbf{s}}_{c}\), \({\mathbf{s}}_{b}\) | Vector coordinate in grinding car and in buggy frame |
\(P_{1}\), \(P_{2}\), \(P_{3}\), \(P_{4}\), \(P_{a}\),\(P_{b}\) | Inlet, inner pressure of main valve, inlet pressure of pilot valve, pipe pressure of rod cavity, pressure of rodless cavity, of rod cavity |
\(m_{m}\), \(m_{p}\),\(m_{g}\) | Mass of main valve piston, of pilot valve piston, of hydraulic cylinder piston |
\(A_{p}\), \(A_{a}\), \(A_{b}\), \(A_{m}\),\(A_{g}\) | Action area of pilot valve, of rodless cavity, of rod cavity, of main valve, of rod cavity outlet |
\(x_{p}\), \(x_{m}\), \(z_{g}\),\(z_{g0}\) | Displacement of pilot valve, of main valve piston, of hydraulic cylinder piston, of initial position in hydraulic cylinder piston |
\(F_{0}\), \(F_{e}\),\(F_{h}\) | Set, actual value of electromagnetism force, Hertzian force |
\(a\), \(c\), \(\rho\), \(E\), \(E^{*}\), \(\delta\), \(L\),\(k\) | Compensation coefficient, viscous damping coefficient, oil density, oil bulk Modulus, nominal elastic modulus, compression amount, extension of hydraulic cylinder, equivalent stiffness of hydraulic cylinder |
\(c_{d1}\), \(c_{d2}\), \(c_{d3}\), \(c_{d4}\),\(c{}_{r}\) | Flow coefficient of pilot valve, of main valve port 1, of main valve port 2, of rodless cavity, of throttle valve |
\(\alpha_{p}\), \(\alpha_{m}\), \(k_{m}\),\(l_{m}\) | Half cone angle of pilot valve, flow angle of main valve, main valve stiffness, outlet width of main valve |
\(P\), \(\omega\), \(r_{1}\), \(u\), \(\mu\),\(t\) | Grinding pressure, rotation speed of grinding wheel, nominal radius of grinding wheel, control voltage, friction coefficient, time |
\(D_{p}\), \(D_{m}\), \(D_{r}\), \(p\),\(V\) | Diameter of pilot valve, of main valve, of throttle valve chamber, pressure of hydraulic oil, volume of hydraulic oil |
\(Q_{1in}\), \(Q_{1out}\), \(Q_{2}\), \(Q_{3in}\),\(Q_{3out}\) | Inlet, outlet flow of main valve, outlet flow of rod cavity, inlet, outlet flow of pilot valve |
\(V_{p}\), \(V_{m}\), \(V_{a}\), \(V_{b}\), \(V_{La}\),\(V_{Lb}\) | Volume of pilot valve and pipe, of main valve, of rodless cavity, of rod cavity, of rodless cavity pipe, of rod cavity pipe |
\(N_{0}\), \(N_{t}\), \(U\), \(I\), \(\varphi\),\(\Delta\) | Set power, actual power, motor voltage, motor current, power factor, compensation |
\(a_{0}\), \(b_{0}\),\(r_{0}\) | Grinding width, grinding length, rail surface radius |
\(F_{y}\), \(F_{z}\), \(T_{y}\),\(T_{z}\) | Lateral, vertical force, lateral, vertical torque of grinding wheel |
