Statics Project

ENGR2110: Project

Description

The purpose of this project is for you to develop an algorithm that can be used to estimate the payload (amount

of material) for an electric mining shovel. An electric mining shovel is a large digging machine that is used to

mine the world’s commodities (copper, gold, coal, etc.) A picture of an electric mining shovel is shown in

Figure 1. The mining shovel has a dipper (Fig. 1) that holds all of the required material. Your job will be to

determine how much material is in the dipper at a given instant in time, based on the equilibrium equations

you have learned in statics. There are two main motions that allow this machine to operate properly. There is

a crowd motion that is used to move the handle in and out based on a rack and pinion system. There is also a

hoist motion which is controlled by a pulley system. The hoist ropes are connected directly to the dipper

through the bail pin.

Figure 1: Large electric mining shovel. The dipper is controlled by both a hoist motion and a crowd motion.

Shown in Fig. 2 is a dipper/handle combination. There is an assumed handle center of mass. There is also an

assumed dipper/payload center of mass. The rack and pinion system is also shown. The saddle pinion is

controlled by a large motor which causes the pinion to rotate and there the handle as a result of the rack and

pinion system.

In your project, you will assume that the system geometry, hoist force, and crowd force are all known from

sensors that are on the shovel. Your job will be to then back calculate the payload in the dipper given the known

geometry as well as hoist and crowd forces.

Figure 2: Handle and Dipper Combination

The system geometry is shown below:

Figure 3: Known System Geometry

Assumptions

In any mathematical derivation, it is important to specify all assumptions. We will assume the following.

1. All bodies are rigid.

2. Gravity is included.

3. There exists no friction in the joints.

4. There is no slacking in the hoist ropes.

Project Tasks

Please complete the following tasks to obtain the equations of motion of this machine.

1. Draw a free body diagram of the handle/dipper combination. You may assume that this is one rigid

body.

2. Assign a coordinate system of your choosing.

3. Write out the appropriate equilibrium equations.

4. Solve for the value of the unknown mass of material of the dipper in terms of the known values.

𝑚𝑝𝑎𝑦𝑙𝑜𝑎𝑑 = 𝑓(𝐹ℎ𝑜𝑖𝑠𝑡,𝐷1,𝐷2,𝐷3,𝐷4,𝐷5,𝐷6,𝐷7,𝑔,𝑚𝑑𝑖𝑝𝑝𝑒𝑟,𝑚ℎ𝑎𝑛𝑑𝑙𝑒,𝜓,𝛾)

Note that 𝑚𝑡𝑜𝑡 = 𝑚𝑝𝑎𝑦𝑙𝑜𝑎𝑑 + 𝑚𝑑𝑖𝑝𝑝𝑒𝑟.

Please also note that the payload value is not dependent on the crowd force.

Report

Once you have completed your derivation for the equation that describes the payload calculation, please

write a report outlining what you have learned. Your report should have the following sections:

1. Abstract

2. Introduction

3. Payload Algorithm Derivation

a. Assumptions

b. Sub section

c. Sub section

d. Sub section

4. Conclusion

Technical Writing Guidelines

Your report should follow certain technical writing guidelines:

o All figures clear and legible

o All equations, figures, and tables numbered appropriately

o References included

o Clear explanations for each section

o All sections numbered and labeled appropriately

o Use of justified formatting for all sections

o All assumptions stated clearly

o Methods and equations completely described Units should never be italicized

o Variables should be in italics

o All coordinate systems should be clearly shown

o The document should be grammatically correct

Due Date:

The project is due the day of the final exam, December 8th.