## Electronic gear ratio (on-line) calculator – Indexer/Turret

This article provides an online calculator for the Indexer/ATC turret/Flying shear rotary cut mechanism to quickly find the servo’s electronic gear ratio and provide additional simulation information to evaluate whether the system parameters meet the requirements. The steps are as follows:

1. Enter the number(C) of Tools or Stations.
2. Define Division, ie, How many PUUs betweens 2 stations.
3. the Circumference(C×P) is displayed and which is used for P2-52 of Delta A2 servo.
4. Enter the mechanical Reduction ratio (1:1 without deceleration)
5. Enter Encoder Resolution(PLS), PLS number per turn of the Encoder,ie,The number of PUUs required to make the motor rotate 1 turn when the electronic gear ratio is 1:1.
6. Press the “Calculate” button to get the numerator and denominator of the E-Gear Ratio.
7. Enter the positioning time T of each division to check whether the simulation result is satisfied?

## Electronic gear ratio (on-line) calculator – Belt mechanism

This article provides an online calculator for the Belt or Roller Mechanism to quickly find the servo’s electronic gear ratio and provide additional simulation information to evaluate whether the system parameters meet the requirements. The steps are as follows:

1. Define  eg, How many PUUs correspond to 1 mm
2. Enter the mechanical Reduction ratio (1:1 without deceleration)
3. Enter the diameter(D) or circumference of the pully, including the belt.
4. Enter Encoder Resolution(PLS), PLS number per turn of the Encoder,ie,when the electronic gear ratio is 1:1, how many PUUs the drive has to receive in order to rotate 1 turn.
5. Press the “Calculate” button to get the numerator and denominator of the E-Gear Ratio
6. Select “Significant digit number“: to specify the numeric width of the numerator,  suggest 6 or above [Note 1].
7. Enter the Line Speed(​​V) of the machine to check if the simulation results meet the requirements ?

## Electronic Gear Ratio (on-line) Calculator – Ball Screw

This article provides an online calculator for common screw mechanisms to quickly find the servo’s electronic gear ratio and provide additional simulation information to evaluate whether the system parameters meet the requirements. The steps are as follows:

1. Enter User Unit(PUU) : ie, How many PUUs represent 1 mm.
2. Enter the machine’s Reduction ratio (1:1 without deceleration)
3. Enter the Pitch of the screw (the machine displacement while screw rotates 1 turn)
4. Enter Encoder Resolution(PLS), PLS number per turn of the Encoder,ie,when the electronic gear ratio is 1:1, how many PUUs the servo has to receive in order to rotate 1 turn.
5. Press the “Calculate” button to get the numerator and denominator of the E-Gear Ratio.
6. Enter the Line Speed of the machine to check if the simulation results meet the requirements ?

## Electronic Gear Ratio Formula Derivation – Ball Screw

In this article, the formula for the electronic gear ratio of the servo drive for the screw mechanism is derived. The principle of deciding the gear ratio is to first determine the position unit PUU (Pos of User Unit), must be easily observed, usually PUU = 1 or 10 μm, and then calculate the corresponding Gear ratio. Instead of deciding on the gear ratio and then calculating the length of a PUU, otherwise it is asking for trouble (refer to the PUU concept). First, the symbol is defined as follows :

• PUU corresponding to 1 mm (P): How many PUUs respect to 1 mm
• Mechanical reduction ratio (N1 : N2): N1 <= N2 for Deceleration
• Turns of screw rotates (REV): uppercase
• Turns of motor rotates(rev): lowercase, rev = REV ×(N2/N1)
• Pitch of the screw(Pitch): the mechanical movement corresponds to 1 turn of the screw(mm/REV)
• Encoder resolution (R): PLS number per turn of encoder(PLS/rev )
• Electronic Gear Ratio (Num/Den): Scaling factor from PUU to PLS

## PUU position unit explanation

In the motion control system, there are a number of position counters to record the current position, commands and errors of the machine. It is not appropriate to use PLS as a unit (for reasons see Link). Therefore, a new  position unit must be introduced, called the Position of User Unit (PUU), which is similar to the Pulse Equivalent Unit in the traditional system that uses pulses as the position command , indicates the moving distance of a pulse. Because the current control system can send commands through communication, there is no physical pulse, the user can be more freely choose the desired position unit, ie PUU. The relationship between PUU and PLS is the electronic gear ratio (N/M) defined as follows:

PUU (counts) * N/M (electronic gear ratio numerator/denominator) = PLS (counts)