Parts Selection
*Add embeded links for documentation for parts*
The parts selected for the gantry crane will have dramatic effects on it's behaviour and reliability. We need to do some calcuations in order to make sure that the parts we have chosen will allow the crane to function as we would like it too.
| Cart Drive Belt | The drive belt must be strong enough to move the cart under high speed and high force conditions. |
| Cart Drive Motor | The cart drive motor will determine how quickly the system can react to disturbances, as well as how heavy a pendulum and cart can be used. |
| Cart Drive Encoder | The cart drive encoder must give the microcontroller enough data points, so that the microcontroller knows the position of the cart within less than a centimeter. |
| Cart Drive Pulley | The cart drive pulley can change the speed or torque of the selected drive motor, either making the motor valid or invalid based on the width and circumference of the pulley. |
| H-bridge motor driver | the H-bridge motor driver must be able to accomodate the selected motor's voltage and current/amperage requirements, and it must be controllable by the selected micrcontroller. |
| Pendulum Angle sensor | The pendulum angle sensor must give the microcontroller enough data points so that the microcontroller can react to the pendulum's angular displacement. |
| Microcontroller | The microcontroller must have sufficent processing speed and enough ports to handle the data from the above sensor and encoder, as well as ouput to the selected H-bridge |
We used Matlab and Simulink to come up with our minimum Belt Velocity and Force on Belt parameters in order to select parts for our gantry crane. These two equations were applied to an excel sheet so that many pulleys and motors could be evaluated all at once. It is very important that your units match before using these equations, for instance if the torque is in N/m (Newton-Meters) you will have to use a pulley diameter that is in Meters, not centimeters. example excel sheet below.
Calculate Belt Velocity from Motor RPM = (RPM * 60) * (Circumference of Pulley)
Calculate Force on Belt from Motor Torque = Torque * (Radius of Pulley)
| BELT VELOCITY |
| FORCE ON BELT |
| A | B | C | D | E | F | |
| 1 | PULLEY | |||||
| 2 | Pulley1Diameter | Pulley2Diameter | Pulley3Diameter | PulleyDiameter | ||
| 3 | MOTORS | |||||
| 4 | Motor1RPM | =(A4/60)*(pi()*C2) | =(A4/60)*(pi()*D2) | =(A4/60)*(pi()*E2) | =(A4/60)*(pi()*F2) | |
| 5 | Motor2Torque | =A5*(C2/2) | =A5*(D2/2) | =A5*(E2/2) | =A5*(F2/2) | |
| 6 | Motor2RPM | =(A6/60)*(pi()*C2) | =(A6/60)*(pi()*D2) | =(A6/60)*(pi()*E2) | =(A6/60)*(pi()*F2) | |
| 7 | Motor2Torque | =A7*(C2/2) | =A7*(D2/2) | =A7*(E2/2) | =A7*(F2/2) |
There is also a simple equation to determine what interval of the belt can be tracked by the encoder. for instance, 1 cm per pulse of the encoder, means that at a 1cm interval of the belt, the encoder will pulse when there is movment.
Calculate Encoder Resolution in Belt Distance = (Circumference of Pulley) / (EncoderPulsesPerRevolution)
For Example, here are the parts we selected and why.
Our Matlab/Simulink model gave us these values:
| Minimum cart Acceleration | 1.815 m/s^2 |
| Minimum cart Velocity | 0.3 m/s |
Based on these values, we could calculate the minimum force needed to move the cart at that acceleration by multipluying it's weight in kg to give us Mass*Acceleration which equals Force. our cart and pendulum is estimated to be 6kg, so we multipluy 6 by our minimum cart acceleration to get that minimum cart force. The Minimum cart velocity was usable as-is. Though when we move from a mathmatical model to a real construction, usually more friction and energy loss is involved, so we will predict that these parameters must be increased by 30% in order to be realisitic minimum values.
| original value | 30% increased value | |
| Minimum Force on Cart | 10.89N | 14.16N |
| Minimum cart Velocity | 0.3m/s | 0.39m/s |
As explained earlier, we then used an matrix of equations in order to find the best pulley-motor combination, Here are our final values:
| Pulley Diameter | ||
| 0.023 m | ||
| Final Motor RPM | 814 RPM | 0.977 m/s |
| Final Motor Torque | .2065 N | 18.0 N |
Our calculated cart velocity is 0.977 m/s which is greater than the minimum of 0.39 m/s,
Our calculated force on cart is 18N which is greater than the minimum of 14.16N,
This means that the parts we selected should be valid for the physical construction!