# Study on theory and methods of payload online estimation for cable shovels

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## Abstract

Cable shovels are one of the most widely used machines in open-pit mining industry. Precise estimation of payload can effectively avoid overload and underload for each dump, significantly improve the working performance of cable shovels and reduce the maintenance costs of haul trucks. In this research, an algorithm based on static analysis for payload online estimation was established, which took hoist force, crowd force and geometrical parameters of the working device as input variables for the situation when both hoist and crowd motors were hovering during the digging process. More specifically, the torque balance function was applied for payload calculation on the basis of the kinematic model built for evaluating the length of different force arms when the dipper handle stayed in different positions. In order to verify the efficiency of the payload online estimation algorithm, six different working positions and four different fullness states of the dipper were chosen for testing. And a testing system consisting of a 1/35 scale model of cable shovel, software of LabVIEW, hardware of cRIO and multi-types of sensors was designed and set up. Testing results show that the relative error between the theoretically calculated value and the real weight of payload is averagely less than 6% when the dipper was 40% fully filled and averagely less than 3% when the fullness reached 100%, which has proved the efficiency of the payload online estimation theory and methods established in this research.

## Keywords

Cable shovel Payload Online estimation Torque balance Kinematic model## List of symbols

## The following symbols are used in the algorithm for cable shovel payload online estimation

- \(l_{ij}\)
Distance between point \(i\) and point \(j\), \(i\) and \(j\) could be \(O_{1}\), \(O_{2}\), etc.

- \(s_{i} ,\)\(c_{i}\)
\(\sin \theta_{i}\) and \(\cos \theta_{i}\), \(i\) could be \(\theta_{1}\), \(\theta_{2}\), \(\theta_{3}\)…

- \({}_{j}^{i} T\)
Homogeneous transformation matrix of the coordinate system \(\left\{ j \right\}\) relative to the coordinate system \(\left\{ i \right\}\), \(i\) and \(j\) could be \(a\), \(b\), \(c\) …

- \({}_{ }^{j} i\)
Homogeneous coordinate of the point \(i\) in the coordinate system \(\left\{ j \right\}\), \(i\) could be \(m_{1}\), \(m_{2}\), \(A\) …and \(j\) could be \(a\), \(b\), \(c\) …

- \(A\)
Lifting point for the hoist rope on shovel dipper, Fig. 3

- \(B\)
Contact point between hoist rope and boom point sheave, Fig. 3

- \(C\)
Center of rotation for boom point sheave, Fig. 3

- \(O_{1}\)
- \(\left\{ a \right\}\)
- \(O_{2}\)
- \(\left\{ b \right\}\)
Boom coordinate system \(xO_{2} y\), translation from \(\left\{ a \right\}\), Figs. 2 and 3

- \(O_{3}\)
Central connection between dipper handle and saddle block, Figs. 2 and 3

- \(\left\{ c \right\}\)
Dipper handle coordinate system \(xO_{3} y\), rotation and translation from \(\left\{ b \right\}\), Figs. 2 and 3

- \(O_{4}\)
Connecting point between dipper handle and dipper, Figs. 2 and 3

- \(\left\{ d \right\}\)
Dipper coordinate system \(xO_{4} y\), translation from \(\left\{ c \right\}\), Figs. 2 and 3

- \(F_{l}\)
Hoist force acting at point \(A\), direction along \(\overrightarrow {AB}\), Fig. 2

- \(F_{p}\)
Crowd force acting on handle, direction parallel to \(\overrightarrow {{O_{3} O_{4} }}\), Fig. 2

- \(F_{b}\)
Braced force acting on saddle block, direction along \(\overrightarrow {{O_{2} O_{3} }}\), Fig. 2

- \(m_{1,2,3,4}\)
Center of gravity of saddle block, dipper handle, dipper and bulk material, Fig. 3

- \(G_{1,2,3,4}\)
Gravity of saddle block, dipper handle, dipper and bulk material, Fig. 2

- \(\theta_{1}\)
Angle between direction \(\overrightarrow {{O_{1} O_{2} }}\) and \(\overrightarrow {{O_{1} x}}\) in coordinate \(\left\{ a \right\}\), Fig. 3

- \(\theta_{2}\)
Angle between direction \(\overrightarrow {{O_{2} O_{3} }}\) and \(\overrightarrow {{O_{2} y}}\) in coordinate \(\left\{ b \right\}\), Fig. 3

- \(\theta_{3}\)
Angle between direction \(\overrightarrow {{O_{2} C}}\) and \(\overrightarrow {{O_{3} x}}\) in coordinate \(\left\{ c \right\}\), Fig. 3

- \(\theta_{4}\)
Angle between direction \(\overrightarrow {{O_{4} m_{3} }}\) and \(\overrightarrow {{O_{4} x}}\) in coordinate \(\left\{ d \right\}\), Fig. 3

- \(\theta_{5}\)
Angle between direction \(\overrightarrow {{O_{4} m_{4} }}\) and \(\overrightarrow {{O_{4} x}}\) in coordinate \(\left\{ d \right\}\), Fig. 3

- \(\theta_{6}\)
Angle between direction \(\overrightarrow {{O_{4} A}}\) and \(\overrightarrow {{O_{4} x}}\) in coordinate \(\left\{ d \right\}\), Fig. 3

- \(\theta_{7}\)
Angle between direction \(\overrightarrow {{O_{2} C}}\) and \(\overrightarrow {{O_{2} x}}\) in coordinate \(\left\{ b \right\}\), Fig. 3

- \(\theta_{8}\)
Roll angle of cable shovel, Fig. 5

- \(\theta_{9}\)
Pitch angle of cable shovel, Fig. 5

- \(l_{b}\)
Force arm of force \(F_{b}\) about point \(O_{2}\), \(F_{b}\) acting on point \(O_{2}\), \(l_{b} \equiv 0\)

- \(l_{p}\)
Force arm of force \(F_{p}\) about point \(O_{2}\), Fig. 2

- \(R_{p}\)
The pitch radius of the crowd gear

- \(l_{1,2,3,4}\)
Force arm of force \(G_{1,2,3,4}\) about point \(O_{2}\), Fig. 2

- \(l_{l}\)
Force arm of force \(F_{l}\) about point \(O_{2}\), Fig. 2

- \({}_{ }^{b} i_{x}\)
Abscissa values of point \(i\) in coordinate \(\left\{ b \right\}\), \(i\) could be \(A\), \(B\), \(C\)…

- \({}_{ }^{b} i_{y}\)
Ordinate values of point \(i\) in coordinate \(\left\{ b \right\}\), \(i\) could be \(A\), \(B\), \(C\)…

- \(G_{4t}\)
Theoretically calculated value of payload

- \(G_{4a}\)
Real weight of payload tested by scale

## Notes

### Acknowledgements

This study was supported by the National Natural Science Foundation of China (Grant no. 51775225) and the Shanxi Province Coal Basic Key Technologies Research and Development Program (Grant no. MJ2014-02).

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