DEVELOPMENT OF THE MODEL

The development efforts on the CSM model began with a theoretical analysis of cutter penetration into the rock without any adjacent cuts or free-faces. This first step was crucial in understanding stress fields and the resultant fractures that are created beneath the penetrating edge of a disc cutter. Initially, the analysis focused on V-profile disc cutters, but later modified to include the constant-cross section discs as they became the industry standard. In this analysis, various previous theories derived from wedge indentation into rock were used as a guide. This analysis helped confirm the occurrence of a highly stressed crushed zone and the radial tension cracks during cutter penetration into the rock.

The next step was to extend this single cutter analysis into multiple cutter operation to simulate the interaction of adjacent cutting paths on a TBM. This means a free face (cut) exists on one side of the cutter to which the chip formation occurs. In this scenario, the rock under the cutter is again crushed to a fine powder, which behaves in a state of hydrostatic stress, causing radial cracks to form and radiate from this crushed zone or the so-called pressure-bulb. As these cracks are forced to grow, one or more of them reach the neighboring cut, causing rock failure in the form of a chip.

Detailed analysis of this chip formation mechanism aided with high-speed movies taken during cutting and chip surface inspections led to the conclusion that rock failure was occurring in tension. As a result, in the first formulation of the CSM model, rock compressive and tensile strengths were used as input to characterize the rock boreability by disc roller cutters. The compressive strength was used to describe the rock crushing beneath the cutter tip while the tensile strength accounted for the chip formation between adjacent cuts. Hence, using these two rock properties, a correlation was developed between cutter load and the depth of penetration achieved as a function of cutter edge geometry and the cutter diameter. Once the equation relating cutter thrust to penetration was established, the cutter rolling force was determined using a ratio called the cutting coefficient.

The formulation of the initial model was followed with calibration with actual cutting data obtained from laboratory tests performed on the CSM Linear Cutting Machine (LCM). LCM allows testing of full size field cutters under field-simulated conditions in terms of cut spacing, penetration, speed, etc (Figure 4). The accuracy of the model is also being validated continuously with extensive field data from numerous hard rock TBM projects from all over the world.

MODEL DESCRIPTION

The following figure is a flow chart, which shows the general steps involved in making performance estimates for TBMs. Once the appropriate rock and geologic data is entered into the model, one of two options can be exercised.
Option 1: If the predictions are to be developed for an existing machine, the model then asks for relevant information about the machine, including cutter type, layout, type of machine, all machine specifications in terms of thrust, torque, power, rpm, etc.
Option 2: If it is desired to use a new machine, the model will then develop the required specifications and provide a cutterhead layout determined to be optimal for the rock and geologic conditions anticipated. This also covers the selection of the best cutter geometry.

PROGRAM DESCRIPTION FOR AN EXISTING MACHINE

The following figure shows the model window where the machine specifications are entered together with power and thrust efficiency factors.

The model then asks whether the actual cutterhead is layout is available and if so, whether the estimates are to be developed using actual layout or the average cutter spacing. These two approaches in general give very close answers. The only difference is that by using the actual head layout, the model can also calculate individual loads, which vary as transition begins to occur from face to gage cutters.

The next step is to perform the calculations using the force-penetration algorithms built into the model. The model accomplishes the required calculations using an iterative approach. It starts from a low ROP and gradually increases it until one or more cutter or machine limits are reached. It then records the corresponding penetration rate as the maximum achievable ROP for the rock and geologic conditions anticipated. It follows the same procedure for all other rock types to be encountered in the tunnel. All estimates are then summarized and listed in a tabular form.

Performance prediction for road header machines is more difficult compared to full-face machines (e.g. TBM). This is partly because operator’s skill affects the production rate significantly. Roadheaders also are less rigid because the cutterhead is mounted on a boom that must transfer energy from the machine.

Face excavation consists of several modes of cutting: sumping (into the face), arcing (across the face) and shearing (down the face). In each mode, only part of the cutterhead contacts the rock. Even among cutters in contact with the face, the depth of penetration varies, depending on the spatial and temporal position of each cutter. The production rate can vary between two operators depending on their choices of cutterhead movements, sequencing and use of available power.

The immense variability of roadheader machine operation means that exact performance predictions cannot be expected from semi-theoretical methods that use cutting forces. However, the maximum production rate achievable in each cutting mode does indicate the limits of the machine and provides an upper bound on the expected production rates.

The effects of rock joints, fractures, inflows, etc. on the performance of these machines also are not modeled easily. Empirical models developed for performance prediction of partial face machines generally have had more success than semi-theoretical models.

Some of them are:

“Production Estimating Techniques for Underground Mining using Roadheaders ” by David M. Neil 1, Jamal Rostami, L. Ozdemir, R. Gertsch, SME 1994

“Roadheader applications in mining and tunneling industries” by H. Copur, L. Ozdemir, and J. Rostami, SME 1998

The approach used for computer modeling of the cutting drum of a continuous miner is to program each bit individually and analyzes the cutting forces acting on the bits. The cutting forces (cutting and normal force depend on the rock type to be cut, the cutting geometry (spacing and penetration of the bits), the geometry of the bit (tip angle) and the attack angle.

The machine specifications, such as thrust and power are for providing sufficient amount of forces and torque to support the excavation operation. Machine thrust is the force required to penetrate the tools into the rock surface. Also, the cutterhead torque and power requirements are the force to rotate the head at the required penetration rate and overcome the drag force resistance of the cutters.

In the computer program, a cylindrical coordinate system is used to define the drum geometry and bit-lacing pattern. Position of each cutter on the drum is defined by its radius from the axis rotation, and the position angle from positive x-axis. The following figure shows the schematic drawing of a cutterhead and parameters used to define the bit position on the drum.

Cutterhead profile data is essential for simulating different cutting modes (sumping and shearing) of the drum and checking the availability of the thrust and power of the machine at a given sumping and shearing depth.

The information generated from the computer model includes individual cutter positions, penetration, and forces, overall thrust, torque, and power requirements of the cutterhead in the given position, variation of the forces as the head rotates, and finally boom speed and production rate. The program allows the user to monitor the variation and graphically represents these variations as the head rotates. Figure 3 illustrates a typical summary of information for a full rotation and variation of thrust, and power for a certain cutterhead design and lacing pattern for sumping and shear-down mode.