Chapter-13-d1-cema-bucket-elevator-hp-and-calculations.docx

CEMA Bucket Elevator Book

Chapter 13 HP and Calculations Chapter Lead: Kris Gililland, PE

Contacts and References Name Kris Gililland, PE

Company KWS Manufacturing

DRAFT HISTORY Draft Number 1

Date May 3rd, 2013

E-Mail [email protected]

Draft Chapter 13 – HP and Calculations First Draft

May 3, 2013

Chapter 13 – Horse Power and Calculations There are many variables to consider when designing a Bucket Elevator. As discussed in previous chapters these include bucket size, bucket spacing, speed, and various components. This chapter can act as a guide for determining the Horse Power (HP) requirements of a Bucket Elevator. When designing a Bucket Elevator there are more variables to be consider that can be listed in this publication. It should be noted that a small mistake in calculating the required HP of a small, low capacity Bucket Elevator may not result in a unit failure, but a small mistake on a large, high capacity bucket elevator may result in a catastrophic failure. This is why it is important to always work with an experienced Bucket Elevator Manufacturer who can help in the design and implementation of a successful project. Determining Horse Power To be able to accurately determine the power requirements of a Bucket Elevator, it must first be understood the internal forces acting on the unit. Although there are many components in the Bucket Elevator, only the upward movement of the conveyed product needs to be considered. This is because the weight of the Belt/Chain and Cups are identically balanced on both sides of the head shaft. Only the internal friction caused by the movement of these components needs to be considered when calculating the HP requirements. There are many variations of Horse Power (HP) calculations found in historical and individual manufacturer’s literature. The formulas below are used to determine the power requirements of a Bucket Elevator throughout the industry. A basic power calculation is the measure of force over a distance per time period 𝑃=

𝐹𝑥𝐷 𝑇

Equation 13.1 – Power Formula

Where: P = Power F = Force D = Distance T = Time In a Bucket Elevator the power requirement can be directly calculated using this formula. 𝑃=

𝑊𝑥𝐻 +𝐶 𝑇

Equation 13.2 – Bucket Elevator Power Formula

Where: P = Power to convey the product W = Weight of material being lifted H = Lift Height T = Time C = HP required to overcome the friction in the system. Using the above formula and substituting the gravimetric rate of a bucket elevator the follow equation can be derived.

Draft Chapter 13 – HP and Calculations First Draft

May 3, 2013

𝐿𝑏𝑠 ) 𝑥 𝐷𝐻 (𝐹𝑇) 𝐻𝑟 𝑃= +𝐶 𝑚𝑖𝑛 𝐿𝑏𝑠 𝐹𝑇 60 ( ) 𝑥 33000 ( ) 𝐻𝑟 𝑚𝑖𝑛 𝐺 (

Equation 13.3 – Bucket Elevator Power Formula

Where: P = Power (HP) G = Gravimetric Rate (Pounds Per Hour) DH = Discharge Height (FT) C = HP required to overcome the friction in the system. System Friction Factor “C” is an estimate of the friction in the system and is required to accurately determine the power requirements of a Bucket Elevator. Friction includes the following variables a. Cup Digging b. Belt slip on the head pulley c. Chain slip on sprockets d. Bearing friction e. Drive Inefficiencies Note: Motor inefficiency is not used because these formulas are used to determine the Motor size. Motor HP ratings include their inherent inefficiencies. There are two methods used to determine the power required to overcome the friction in the system. The first is the Length Equivalency Method. This method uses a factor of the tail pulley diameter to determine the additional power required to account for the system friction. The second method is the Friction Factor Method. This method uses a multiplication factor of account for the friction in the system. Length Equivalency Method System friction can be accounted for with a length equivalency factor. This factor is dependent on the pulley diameter and is shown below 𝐿𝑏𝑠 ) 𝑥 (𝑑 𝑥 𝐿𝑒𝑞) 𝐻𝑟 𝐶= 𝑚𝑖𝑛 𝐿𝑏𝑠 𝐹𝑇 60 ( ) 𝑥 33000 ( ) 𝐻𝑟 𝑚𝑖𝑛 𝐺 (

Equation 13.4 – Bucket Elevator System Friction – LEQ Method

Where: C = System Friction (HP) G = Gravimetric Rate (Pounds Per Hour) d = Tail Pulley Diameter (FT) Leq = Length Equivalency Factor The Length Equivalency Factor ranges from 5 to15, depending on the application. Consult your Bucket Elevator Supplier for additional information. Combining Equations 13.3 and 13.4 yields the following equation.

Draft Chapter 13 – HP and Calculations First Draft

𝑃=

May 3, 2013 𝐿𝑏𝑠 ) 𝑥 (𝐷𝐻 + (𝑑 𝑥 𝐿𝑒𝑞)) (𝐹𝑇) 𝐻𝑟 𝑚𝑖𝑛 𝐿𝑏𝑠 𝐹𝑇 60 ( ) 𝑥 33000 ( ) 𝐻𝑟 𝑚𝑖𝑛

𝐺 (

Equation 13.5 – Bucket Elevator Power Formula – LEQ Method

Where: P = Power (HP) G = Gravimetric Rate (Pounds Per Hour) DH = Discharge Height (FT) d = Tail Pulley Diameter (FT) Leq = Length Equivalency Factor Friction Factor Method Another way to account for the system friction is to add a multiplication factor to the calculated HP in Equation 13.3. This multiplication factor typically ranges from 10% to 30%, depending on the application. Consult your Bucket Elevator Supplier for additional information. 𝐿𝑏𝑠 ) 𝑥 𝐷𝐻 (𝐹𝑇) 𝐻𝑟 𝑃=[ ] 𝑥𝐹 𝑚𝑖𝑛 𝐿𝑏𝑠 𝐹𝑇 60 ( ) 𝑥 33000 ( ) 𝐻𝑟 𝑚𝑖𝑛 𝐺 (

Equation 13.6 – Bucket Elevator Power Formula – Friction Factor Method

Where: P = Power (HP) G = Gravimetric Rate (PPH) DH = Discharge Height (FT) F = Friction Multiplication Factor