Technical Explanation for Servomotors and Servo Drives Servo and Servomotors for Explanation Technical Outputs Command Operation

Home , Motion control, Motor drive, Servomotor, Stator

Energy Conservation Support / Power Supplies / Sensors Switches Safety Components Relays Control Components Automation Systems Motion / Drives Environment Measure Equipment In Addition Others Common 1 es Encoder CSM_Servo_TG_E_1_1 Servomotor Servomotor Ball screw (3) Drive and detection section (3) Drive and detection Drives the controlled object and the controlled Drives detects that object. Power transmission Power transmission mechanism cording to the set target value (command (command value target to the set cording Table The servomotorThe includes the motordriv that Feedback signals Motor power signals Servo drive Controls the motor according to commands. (2) Control section , such as position, speed, or torque, actorque,speed,, such as position, or rvo and system usedis with servoa drive.

component, such as an encoder.

Target values Feedback signals Controller Technical Explanation for Servomotors and Servo Drives Servo and Servomotors for Explanation Technical Outputs command operation. signals for (1) Command section nd What Is a Servo Drive? and What Servomotor a Is What a se structural unitservomotor of is a A Introduction the load and a position detection the controlledThe vary servo system amount to preciselyvalue) control the machineoperation. Servo SystemConfiguration Example Technical Explanation for Servomotors and Servo Drives

Features Sensors Precise, High-speed Control • Servomotors excel at position and speed control. • Precise and flexible positioning is possible. • Servomotors do not stall even at high speeds. Deviations due to large external forces are corrected because encoders are used

to monitor movement. Motion / Drives Automation Systems Control Components Relays Safety Components Switches

Fully-closed Loop Open Loop The most reliable form of closed loop. A fully-closed loop is A stepper motor is used instead of a servomotor. There is no used when high precision is required. feedback loop. The motor is controlled while directly reading the position of The overall configuration is simple. Positioning can be the machine (workpiece or table) using a linear encoder and performed at low cost, but gear and ball screw backlash and comparing the read position with the command value (target pitch errors cannot be compensated. When a stepper motor value). Therefore, there is no need to compensate for gear stalls, an error will occur between the command value and the backlash between the motor and mechanical system, feed actual movement. This error cannot be compensated. screw pitch error, or error due to feed screw torsion or Open loop control is suitable for low-precision, low-cost, low- expansion. speed, and low-load-change applications. Fully-closed Loop System Configuration Example Open Loop System Configuration Example

Servomotor

Stepper motor

Power transmissi Ball screw mechanism Table Ball screw Table Controller Stepper motor drive

Controller Servo drive

Linear encoder

Semi-closed Loop This method is commonly used in servo systems. It is faster and has better positioning precision than an open loop. Typically an encoder or other detector is attached behind the motor. The encoder detects the rotation angle of a feed screw (ball screw) and provides it as feedback of the machine (workpiece or table) travel position. This means that the position of the machine is not detected directly. Energy Conservation Support / The characteristics depend on where the detector is installed. Environment Measure Equipment

Opposite of Installation location of Motor side of Behind motor motor side of detector feed screw feed screw Compensation Compensation Gear backlash required not required Ball screw or nut torsion Affected Hardly affected

Ball screw expansion or Power Supplies /

Affected In Addition contraction Compensation Ball screw pitch error required

Semi-closed Loop System Configuration Example

Servomotor Others

Ball screw Table

Controller Servo drive Common

2 Technical Explanation for Servomotors and Servo Drives

Principles Sensors Servo Operation and Configuration Encoder A system built with servo drives and servomotors controls Servomotors are different from typical motors in that they motor operation in closed loop. The actual position, speed, or have encoders. This allows high-speed and high-precision torque of the servomotor is fed back to compare to the control according to the given position and speed commands. command value and calculate the following errors between Encoders are one of the hardware elements that form the core them. Then the servo drive corrects the operation of the of a servo system, and they generate Motion / Drives speed Automation Systems and Control Components position Relays Safety Components Switches servomotor in realtime using this error information to ensure feedback. In many cases, the encoder is built into the that the system can achieve the required performance. This servomotor or attached to the servomotor. In certain cycle of feedback, error detection, and correction is called applications, the encoder is an independent unit that is closed-loop control. installed away from the servomotor. When the encoder is The control loop is processed by either of servo drive or installed in a remote location, it is used for related parameters motion controller, or both depending on the required control. in addition to for control of servomotor operation. The control loops for position, speed, and torque are Encoders are divided into two kinds. independently used to achieve the required operation. • Incremental encoders Applications will not always require all three control loops. In • Absolute encoders some applications, only the control loop for torque control will Multi-turn absolute encoders are typically used for be required. In other applications, current and speed for servomotors. speed control are required, and in still other applications, Refer to the Technical Explanation for Rotary Encoders for three control loops for position control are required. more information on encoders.

Torque control Speed loop gain Servo Drive Speed loop integral time constant Speed control Servo drives follow commands from the host controller and Control Error/ Error speed Drive control the output torque, rotation speed, or position of section Oscillator counter conversion Motor motors. The position, speed, or torque are controlled according to inputs from a motion controller, feedback encoder, and the

Frequency/ servomotor itself, and the servo drive supplies the appropriate Position Current control speed amounts of power to the servomotor at the appropriate times. Position conversion feedback Speed Position loop gain command feedback Speed The basic operating principle is the same as for an inverter, in command Multiplication which the motor is operated by converting AC power to DC Position feedback Encoder power to be a certain frequency. Servomotor Fixed frequency Required frequency The most common types of industrial servomotors are those (50/60 Hz) (0 to 400 Hz) based on brushless motors. The rotor has a powerful Converter Smoothing Inverter permanent magnet. The stator is composed of multiple section circuit section section conductor coils, and the rotor spins when the coils are powered in the specified order. The movement of the rotor is Energy Conservation Support / determined by the stator’s frequency, phase, polarity, and Motor Environment Measure Equipment current when the correct current is supplied to the stator coils at the appropriate time.

PWM

Speed, Power Supplies / position, Control circuits In Addition or torque Encoder Encoder Motor shaft Servo drive Case A servo drive also has the following functions. • Communications with the motion controller • Encoder feedback reading and realtime closed-loop control Others adjustment • I/O processing for safety components, mode inputs, and Rotor Permanent Stator coils operating status output signals magnet Common

3 Technical Explanation for Servomotors and Servo Drives Explanation of Terms Performance Sensors Effective Torque Regeneration Resistance A value of the average torque (RMS) that is produced during A resistor that absorbs regenerative energy. Regenerative operation of a motor. energy is the energy generated by a motor when the motor A motor with a larger value than the effective torque must be operates. chosen. A servo drive uses internal regenerative processing circuits to

The unit is N·m. absorb the regenerative energy generated Motion / Drives Automation Systems by Control Components a motor Relays when Safety Components Switches the motor decelerates to prevent the DC voltage from Torque Constant increasing. When a current flows to a motor, the current and the flux If the regenerative energy from the motor is too large, an produce a torque. overvoltage can occur. The torque constant is the relationship between this current To prevent overvoltages, the operation pattern must be and the produced torque. The higher the torque, the smaller changed to reduce the regenerative energy or an external the controlling current. regenerative resistor must be connected to increase the The unit is N·m/A. capacity to process regenerative energy. Power Rate Vibration Class The power rate is given by this formula: A class based on the value of the vibration measured at the 2 -3 Power rate = (Rated torque) /Rotor inertia x 10 . shaft of a motor rotating at the rated speed without a load. The higher the value is, the better the response is. There are five vibration classes into which the measured total The unit is kW/s. amplitudes are divided. Rotor Inertia Position Control Mode The moment of inertia of the rotor, expressed in Jm. A control mode in which positioning commands are input from The smaller the value is, the quicker the response is. a controller and positioning is controlled using the target 2 The unit is kg·m . values in the commands. Applicable Load Inertia Closed Loop The range in which a drive can control the load inertia. A control method that compares the position commanded by The range is limited by the gain adjustment range and the the controller and the actual motor position. 2 energy absorption capacity. The unit is kg·m . An error signal is returned to the controller and used to give Rated Output the system the correct position. Closed-loop control can be performed based on the speed, The rated output (P) is the mechanical power that a motor can acceleration, or torque in addition to the position. output. The motion control method without using feedback is called The rated torque (T) and the rated speed (N) are related to the open loop. rated power as follows: P=0.105×T×N Open Loop Electrical Time Constant A control method in which the results of movement are not compared with the actuator reference. The transient response time to the current that flows to the Energy Conservation Support / When the controller commands the motor to move, it is Environment Measure Equipment armature of a motor to which a power supply voltage is assumed that the requested movement will be completed. applied. It is expressed by this formula: Electrical time constant = Control Loop Armature inductance/Armature resistance. In process control, a control loop adjusts a target variable by Because a smaller value enables the current wave to rise adjusting other variables using feedback and error correction. more quickly, the transient response time to the current is In motion control, control loops are set for speed, faster. acceleration, position, or torque. Power Supplies / In Addition Backlash The mechanical system has a dead zone between forward and reverse. A gear that changes from forward to reverse must turn by the amount of the dead zone before turning the specified amount.

This movement is called the backlash. Others Backlash is given in minutes. One turn is 360 degrees. One minute is 1/60 of 1 degree. The smaller the backlash is, the less the dead zone is. Common

4 Technical Explanation for Servomotors and Servo Drives

Functions Sensors Realtime Autotuning Forward and Reverse Drive Prohibit Realtime autotuning estimates the load inertia of the machine A function that prevents the servomotor from rotating outside in realtime, and operates the machine by automatically setting of the operating range of the device by connecting limit inputs. the gain according to the estimated load inertia. When the Forward Drive Prohibit Input or Reverse Drive At the same time, it can lower the resonance and vibration if Prohibit Input turns OFF, the Servomotor will stop rotating. the adaptive filter is enabled. Motion / Drives Automation Systems Control Components Relays Safety Components Switches Damping Control Manual Tuning A function used to reduce vibration when using a low-rigidity A gain adjustment method used when autotuning cannot be mechanism or equipment whose ends tend to vibrate. performed due to the restrictions of the operating pattern or load conditions or when maximum responsiveness needs to Internally Set Speed Control be obtained for individual loads. A function that controls the speed of the servomotor using speeds set in the internal speed setting parameters. Notch Filter A notch filter is used to eliminate a specified frequency Electronic Gear component. A function that rotates the servomotor for the number of The notch filter can restrict a resonance peak, and it allows a pulses obtained by multiplying the command pulses by the high gain setting and vibration reduction. electronic gear ratio. The electronic gear is used to synchronize the position and Disturbance Observer Function speed of two lines, to enable using a position controller with a The effect of disturbance torque can be lowered, and vibration low command pulse frequency or to set the machine travel can be reduced by using the disturbance torque value. distance per pulse, to 0.01 mm for example. Friction Torque Compensation Function Torque Limit A function that reduces the influence of mechanical friction. A function that limits the output torque of a motor. The torque limit is used for pressing a moving part of a Hybrid Vibration Suppression Function machine (such as a bending machine) against a workpiece A function that suppresses the vibration that is caused by the with a constant force, or for protecting the servomotor and amount of the torsion between the motor and the load. mechanical system from excessive force or torque. Feed-forward Function Position Command Filter A function that increases the responsiveness of the control A function that performs soft start processing for the system by adding the feed-forward value to the command command pulses using the selected filter to gently accelerate value. and decelerate. Instantaneous Speed Observer Function The filter characteristics for the position command filter are selected using the Position Command Filter Time Constant This function uses a load model to estimate the motor speed. Setting. It improves the speed detection accuracy and can provide This function is effective when there is no acceleration or both high responsiveness and minimum vibration when deceleration function in the command pulse (controller), when stopping.

the command pulse frequency changes abruptly, causing the Energy Conservation Support / Environment Measure Equipment Safe Torque OFF Function machinery to vibrate during acceleration and deceleration, or The safe torque OFF function (STO) is used to cut off the when the electronic gear setting is high. motor current and stop the motor through the input signals Position Loop Gain from a safety device, such as a safety controller or safety sensor. Servo systems with a low loop gain have a low response and can increase the positioning time.

Regenerative Energy Absorption The higher the position loop gain, the shorter the positioning Power Supplies / A servo drive absorbs regenerative energy internally with the time. If the setting is too high, however, overshooting or In Addition built-in capacitor. hunting may occur in the system. If the regenerative energy cannot be completely absorbed Incremental Command with the built-in capacitor, it is absorbed with the internal regeneration resistor. An incremental command determines the travel amount between the present position and the target position.

Regenerative Energy Others Absolute Command Power produced by a motor for a generator. The regenerative energy is produced by the external forces or An absolute command determines the travel amount from a gravity during Servomotor deceleration. command value that is based upon the origin. In this case, measures for design must be taken to keep the Thus the command value is different from the travel amount energy within the energy absorption capacity. unless the motor is at the origin. Common

5 Technical Explanation for Servomotors and Servo Drives

Error Counter

An up/down binary counter that counts the difference between Sensors the position command pulses and the position feedback pulses. is converted by an D/A (digital/analog) converter and becomes the speed command voltage. The accumulated pulses is converted to an analog voltage by an D/A (digital/analog) converter and becomes the speed command voltage. Motion / Drives Automation Systems Control Components Relays Safety Components Switches Absolute Position Position information that fully describes a position within a space without referencing a previous position. Absolute Positioning Directly moving devices or materials to a specific position in a space without referencing the previous position. Positioning Completion Signal A signal that occurs when positioning is completed. This signal turns ON when the following error is within the in- position range set in the parameter. This signal is primarily used to start any of the following operations after positioning. This signal is also called the in-position signal (INP). Motor with Brake A motor with an electromagnetic brake. Brake Interlock A function that sets the output timing for the brake interlock output (BKIR) signal that activates the holding brake when the servo is turned ON, when an alarm occurs, or when the servo is turned OFF. The output timing is set in the parameter when a motor with a brake is used. A holding brake is used in applications, such as for a vertical axis, to prevent the workpiece from falling. Dynamic Brake (DB) A brake that converts the rotational energy into heat by short- circuiting the terminals of the servomotor through a resistor to quickly stop the motor when a power is interrupted or a servo Energy Conservation Support / Environment Measure Equipment amplifier failure occurs. Larger brake torque can be obtained than with an electromagnetic brake. However, there is no holding torque when the motor is stopped, so a mechanical brake must be applied to hold the motor. Dynamic brake is used for mechanical protection. Power Supplies / In Addition Free Run A status in which a motor continues to rotate due to its inertia when servo is turned OFF. Immediate Stop Torque

When an error is detected, the motor is stopped with the Others torque set in the parameter. Common

6 Technical Explanation for Servomotors and Servo Drives

Others Sensors Servomotor with Absolute Encoder Rack and Pinion A servomotor with an absolute encoder has an encoder in A device that converts rotary motion into linear motion. which a disk rotates to tell the servomotor the position when Normally a rack and pinion is composed of a gearwheel the power is turned ON. (pinion) and a flat toothed bar (rack). A servomotor with absolute encoder that is used in an industrial robot or multi-axis transfer system needs to know Shaft Bearing Motion / Drives Automation Systems Control Components Relays Safety Components Switches the position when the power is turned ON to continue A part that supports a shaft that rotates or performs operation quickly after a power interruption or to prevent reciprocating operation. mistakes in operation. Coupling A servomotor with an absolute encoder needs a backup A part that is used to connect shafts together. battery for operation. Timing Belt Servomotor with Incremental Encoder A power transmission mechanism that converts rotary motion A servomotor with an incremental encoder does not know the into linear motion in conjunction with pulleys. position when the power is turned ON. If the pulley diameter is D, the travel distance per rotation is Instead, it needs to perform an origin search to enable πD. positioning. Timing belts are usually toothed belts that mesh with pulleys Encoder Dividing to prevent slipping. A function that sets the number of pulses for the encoder Pulley signals output from the servo drive. A rotary part that transmits rotary motion to a belt. Encoder dividing is used for a controller with a low response frequency or for setting a pulse rate that is easily divisible. Bearing A machine part that fits between stationary parts and rotating Servomotor parts to support the rotating parts A device that is a structural unit of a servo system and is used with a servo drive. Synchronous Motor and Induction Motor The servomotor includes the motor that drives the load and a Synchronous Motor: position detection component, such as an encoder. A motor that has magnetic poles in the motor rotor and moves synchronously with the behavior of the magnetic field. Servo Drive Induction Motor: A device that is a structural unit of a servo system and is used A motor whose movement is delayed in respect to the with a servomotor. behavior of the magnetic field. The servo drive controls the servomotor according to The rotor is constructed of a non-magnetic material, such as instructions from a PLC or other controller and performs aluminum or copper. A magnetic field created in the stator feedback control with signals from an encoder or other induces a current in the rotor. Rotation of the rotor results from component. the interaction of the magnetic field created by the rotor Decelerator current with the magnetic field of the stator.

A power transmission mechanism that decreases motor Energy Conservation Support / Stiffness Environment Measure Equipment speed and increases torque. The property of an object to retain its original shape when an η If the reduction ratio is 1/R and the decelerator efficiency is , the external force is applied. η 2 speed will be 1/R, the torque R × , and the load inertia 1/R . The higher the stiffness, the higher the ability of an object to Winding Resistance retain its original shape. The line resistance of a coil. The lower the stiffness, the more easily an object is stretched or compressed by an external force. Power Supplies /

Actuator In Addition A device that generates mechanical motion using air Inertia pressure, water pressure, or electricity. The property of an object to maintain its current state of Industrial actuators are commonly driven by electric motors. motion. Inertia is dependent on an object’s mass, shape, and axis of Ball Screw movement. One of the lead screws. Others The threads of the screw are pulled with ball bearings in a carriage. Its high mechanical efficiency and low energy consumption result in high rigidity and high reliability. Ball screws are mainly used in high-speed and high-precision machines. Common

7 Technical Explanation for Servomotors and Servo Drives Further Information Servomotor Selection Flow Chart Sensors

START Selection

Explanation References • Determine the size, mass, coefficient of friction, and external forces of all the moving part of the Motion / Drives Automation Systems Control Components Relays Safety Components Switches Has the machine NO servomotor the rotation of which affects. Been Selected? ---

YES

• Determine the operating pattern (relationship • Operation Pattern Formula between time and speed) of each part that must Has the Operating NO be controlled. Pattern Been Selected? • Convert the operating pattern of each controlled element into the motor shaft operating pattern.

YES Calculating the Load Inertia For • The elements of the machine can be separated • Inertia Formulas Motor Shaft Conversion Value so that inertia can be calculated for each part that moves as the servomotor rotates. • Calculate the inertia applied to each element to calculate the total load inertia of the motor shaft conversion value.

Calculating the Added Load • Calculation of Friction Torque • Load Torque Formulas Torque For Motor Shaft Calculates the frictional force for each element, where necessary, and converts it to friction Conversion Value torque for a motor shaft. • Calculation of External Torque Calculates the external force for each element, where necessary, and converts it to external torque of a motor shaft. • Calculates the total load torque for the motor shaft conversion value.

Select a motor temporarily • Select a motor temporarily based upon the motor shaft converted load inertia, friction --- torque, external torque and r.p.m of a motor.

Calculate Acceleration/ • Calculate the Acceleration/Deceleration Torque • Acceleration/Deceleration Deceleration Torque from the Load Inertia or Operating Pattern. Torque Formulas Energy Conservation Support / Environment Measure Equipment

Confirm Maximum • Calculate the necessary torque for each part of • Calculation of Maximum Momentary Torque and the Operating Pattern from the Friction Torque, Momentary Torque, Effective Calculate Effective Torque External Torque and Acceleration/Deceleration Torque Torque. • Confirm that the maximum value for the Torque for each operating part (Maximum Momentary Power Supplies /

Torque) is less than the Maximum Momentary In Addition Torque of the motor. • Calculate the Effective Torque from the Torque for each Operating part, and confirm that it is less than the Rated Torque for the motor.

2 1 Others Common

8 Technical Explanation for Servomotors and Servo Drives

2 1 Sensors

Explanation References Calculate Regenerative Energy • Calculate Regenerative Energy from the Torque • Please see the user manual of of all the moving parts. each product for the details on calculation of the regenerative energy. wthsSft opnnsRly oto opnnsAtmto ytm Motion / Drives Automation Systems Control Components Relays Safety Components Switches

• Check if the the number of encoder pulses • Accuracy of Positioning meets the system specified resolution. NO Is the Resolution OK?

YES • Check if the calculation meets the specifications • The following table of the temporarily selected motor. Are the Check Items If not, change the temporarily selected motor NO and re-calculate it. on Characteristics All OK?

YES Specialized Check Check Items Items Load Inertia Load Inertia ≤ Motor Rotor Inertia x Applicable Inertia Ratio Effective Torque < Motor Rated Torque Effective Torque • Please allow a margin of about 20%. * Maximum Momentary Torque < Motor Maximum Momentary Torque Maximum Momentary • Please allow a margin of about 20%. Torque * • For the motor Maximum Momentary Torque, use the value that is combined with a driver and the one of the motor itself. Maximum Rotation Speed ≤ Rated Rotation Speed of a motor • Try to get as close to the motor's rated rotations as possible. Maximum Rotation It will increase the operating efficiency of a motor. Speed • For the formula, please see "Straight-line Speed and Motor Rotation Speed" on Page 16. Regenerative Energy ≤ Regenerative Energy Absorption of a motor Regenerative Energy • When the Regenerative Energy is large, connect a Regenerative Energy Absorption Resistance to increase the Absorption capacity of the driver. Ensure that the Encoder Resolution meets the system Encoder Resolution specifications. Energy Conservation Support / Environment Measure Equipment Check if the Pulse Frequency does not exceed the Maximum Characteristics of a Response Frequency or Maximum Command Frequency of a Positioner Positioner. Ensure that values of the ambient operating temperature/ Operating Conditions humidity, operating atmosphere, shock and vibrations meet the product specifications. * When handling vertical loads and a load affected by the external torque, allow for about 30% of capacity. Power Supplies / END Selection In Addition Others Common

9 Technical Explanation for Servomotors and Servo Drives

Formulas Sensors Formulas for Operating Patterns

Speed wthsSft opnnsRly oto opnnsAtmto ytm Motion / Drives Automation Systems Control Components Relays Safety Components Switches

v0 X0 Maximum Speed v0 = X0: Distance Moved in t0 Time [mm] tA

v0: Maximum Speed [mm/s]

X0 Triangular Acceleration/Deceleration Time tA = t0: Positioning Time [s] v0

tA: Acceleration/ Deceleration Time [s] Travel Distance = tA tA Time X0 v0·tA

X0 Speed Maximum Speed v0 = t0 – tA

X Acceleration/Deceleration Time t = t – 0 v0 A 0 v0

X0 Total Travel Time t0 = tA + v0

2·X0 X0 Trapezoid Constant-velocity travel time tB = t0 – 2·tA = – t0 = – tA v0 v0 Time tA tB tA Total Travel Distance X0 = v0 (t0 – tA)

t0 v0·tA v0·t0 – X0 Acceleration/Deceleration Travel Distance XA = = XA XB XA 2 2

X0 Constant-velocity travel distance XB = v0·tB = 2·X0 –v0·t0 Energy Conservation Support / Environment Measure Equipment

Speed Ascending Time t = v0 –v1 A α v0

Ascending Time (tA) including distance moved v1

1 Power Supplies / Speed and Slope X = ·t 2 + v ·t vg A α A 1 A In Addition When Ascending 2

2 Time 1 (v0 – v1) XA = +v1·tA tg tA 2 α

Speed after Ascending v0 = v1+α·tA v Speed Gradient g

tg Others Common

10 Technical Explanation for Servomotors and Servo Drives Sensors

Conditions for Trapezoidal Operating Pattern

Speed v0 t 2·α X < 0 0 4 wthsSft opnnsRly oto opnnsAtmto ytm Motion / Drives Automation Systems Control Components Relays Safety Components Switches X0: Positioning Distance [mm] Maximum Speed Speed and Slope t0: Positioning Time [s] Trapezoid tA: Acceleration/Deceleration pattern t0·α 4X0 v0 = (1– 1– ) Time [s] 2 t0·α v0: Maximum Speed [mm/s] Time tA tA Ascending Time α: Speed Gradient

t0 v0 t0 4X0 tA = = (1– 1– ) α 2 t0·α

Speed Conditions for Triangular Operating Pattern

v0 t 2·α X ≥ 0 0 4

Speed and Slope Maximum Speed Triangular Pattern v0 = α·X0

Ascending Time tA tA Time

t0 X t = 0 A α X0

v [mm/s] Linear Movement Energy Conservation Support / Perform the following unitary conversions Environment Measure Equipment X [mm] Linear Movement Rotating Movement X: Distance [mm] θ: Angle [rad]

Rotating Part v: Speed [mm/s] ω: Angular Velocity [rad/s] θ [rad]

2π·N Power Supplies / ω = In Addition 60 N: Rotating Speed [r/min]

ω [rad/s] N [r/min] Others Common

11 Technical Explanation for Servomotors and Servo Drives

Inertia Formulas Sensors

D2: Cylinder Inner Diameter [mm]

D1: Cylinder Outer Diameter [mm]

2 2 Cylindrical M(D1 Motion / Drives + D2 ) Automation Systems Control Components –6 2 Relays Safety Components Switches JW = ×10 [kg·m ] Inertia 8

M: Cylinder Mass [kg] 2 JW: Cylinder Inertia [kg·m ]

M: Cylinder Mass [kg] M Eccentric Disc C JW: Inertia Inertia (Cylinder 2 2 –6 2 [kg·m ] JW = JC + M·re × 10 [kg·m ] which rotates off JC: Inertia around the the center axis) center axis of Cylinder re: Rotational Radius [mm]

Center of rotation

M: Square Cylinder Mass [kg]

M Inertia of b: Height [mm] 2 2 M(a +b ) –6 2 Rotating Square JW = ×10 [kg·m ] Cylinder 12 JW: Inertia [kg·m2]

a: Width [mm] L: Length [mm] Energy Conservation Support / M: Load Mass [kg] Environment Measure Equipment

2 Inertia of Linear JB: Ball Screw Inertia P –6 2 JW = M ×10 + JB [kg·m ] Movement [kg·m2] ()2π

P: Ball Screw Pitch [mm] 2

JW: Inertia [kg·m ] Power Supplies / In Addition

D: Diameter [mm] JW M : Mass of Cylinder [kg] 1 Others 2 J1: Cylinder Inertia [kg·m ] JW = J1 +J2 Inertia of Lifting 2 M ·D2 M ·D2 Object by Pulley J2: Inertia due to the Object [kg·m ] = 1 + 2 ×10–6 [kg·m2] ()8 4

M2: Mass of Object [kg]

2 Common JW: Inertia [kg·m ]

12 Technical Explanation for Servomotors and Servo Drives Sensors

Inertia of Rack Rack M·D2 and Pinion J = × 10–6 [kg·m2] W 4

Movement JW: Inertia JW Motion / Drives Automation Systems Control Components Relays Safety Components Switches [kg·m2] M: Mass [kg] D D: Pinion Diameter [mm]

D [mm]

JW Inertia of 2 D (M1 + M2) –6 2 Suspended JW = × 10 [kg·m ] Counterbalance 4 2 JW: Inertia [kg·m ] M2 M1: Mass [kg]

M2: Mass [kg] M1

M3 : Mass of Object [kg] D1 : Cylinder 1 Diameter [mm] M4 : Mass of Belt [kg] 2 JW: Inertia [kg·m ] JW = J1 + J2 + J3 + J4 Inertia when 2 2 2 M1·D1 M2·D2 D1 M1 : Mass of Cylinder 1 [kg] JW = + · 2 + Carrying Object ( 8 8 D2 2 via Conveyor JW : Inertia [kg·m ] 2 2 M3·D1 M4·D1 –6 Belt 2 D2 : Cylinder 2 Diameter [mm] + ×10 J1 : Cylinder 1 Inertia [kg·m ] 4 4 ) [kg·m2] 2 M2 : Mass of Cylinder 2 [kg] J2 : Inertia due to Cylinder 2 [kg·m ] 2 J3 : Inertia due to the Object [kg·m ] 2 J4 : Inertia due to the Belt [kg·m ]

2 JW : System Inertia [kg·m ] 2 J1 : Roller 1 Inertia [kg·m ] 2 J2 : Roller 2 Inertia [kg·m ] Energy Conservation Support / Environment Measure Equipment D1 : Roller 1 Diameter [mm]

D2 : Roller 2 Diameter [mm] Inertia where 2 2 M : Equivalent Mass of Work [kg] D1 M·D1 –6 Work is Placed J1 Roller 1 JW = J1 + J2 + ×10 ()D2 4 2 between Rollers D1 [kg·m ] JW Power Supplies / D2

M In Addition

Roller 2

Load

Gears Others Z2: Number of Gear Teeth on Load Side J2: Gear Inertia on Load Side 2 Inertia of a Load JW: Load Inertia [kg·m ] 2 2 Value Converted [kg·m2] Motor JL = J1 + G (J2 + JW) [kg·m ] to Motor Shaft Z1: Number of Gear Teeth on Motor Side Common J1: Gear Inertia on Motor Side 2 [kg·m ] JL: Motor Shaft Conversion Load Inertia Gear Ratio G = Z1/Z2 [kg·m2]

13 Technical Explanation for Servomotors and Servo Drives

Load Torque Formulas Sensors

F: External Force [N] Torque against T = F·P ×10–3 [N·m] external force W 2π TW: Torque due to External P: Ball Screw Pitch [mm] Forces [N·m] wthsSft opnnsRly oto opnnsAtmto ytm Motion / Drives Automation Systems Control Components Relays Safety Components Switches

M: Load Mass [kg]

Torque against T = μMg·P × 10–3 [N·m] frictional force μ: Ball Screw Friction Coefficient W 2π

P: Ball Screw Pitch [mm] TW: Frictional Forces Torque [N·m] g: Acceleration due to Gravity (9.8m/s2)

D: Diameter [mm] Torque when F: External external force is Force [N] T = F·D ×10–3 [N·m] applied to a W 2 rotating object TW: Torque due to External Forces [N·m]

D: Diameter [mm] Torque of an object on the conveyer belt to F: External T = F· D ×10–3 [N·m] which the W 2 external force is Force [N] T : Torque due to External applied W Forces [N·m]

Torque of an object to which F: External the external D Force [N] D: Diameter [mm] T = F· ×10–3 [N·m] force is applied W 2 by Rack and Pinion TW: Torque due to Energy Conservation Support / External Forces [N·m] Environment Measure Equipment

Rack Plumb Line

TW: External Torque Torque when [N·m] M M: Mass [kg] work is lifted at θ D –3 T = Mg·cos ·×10[N·m] Power Supplies / W 2

an angle. In Addition

Pinion g: Acceleration due to Gravity (9.8m/s2) D: Diameter [mm]

Z2: Number of Gear Teeth on Load Side T : Load Torque Others W η Torque of a Load [N·m] : Gear Transmission Efficiency G Value Converted TL = TW ·η [N·m] to Motor Shaft Z1: Number of Gear Teeth on Motor Side

Gear (Deceleration) Ratio G = Z1/Z2 TL: Motor Shaft Conversion Load Torque [N·m] Common

14 Technical Explanation for Servomotors and Servo Drives

Acceleration/Deceleration Torque Formula Sensors

Acceleration/Deceleration Torque (TA)

2πN JL TA = JM + [N·m] 60tA ( η ) η: Gear Transmission Efficiency N: Motor Rotation Speed [r/min] Motion / Drives Automation Systems Control Components Relays Safety Components Switches M 2 JM: Motor Inertia [kg·m ]

2 JL: Motor Shaft Conversion Load Inertia [kg·m ]

Speed (Rotation Speed)

N: Rotation Speed [r/min]

N TA: Acceleration/Deceleration Torque [N·m]

Time tA

Acceleration Time [s]

Calculation of Maximum Momentary Torque, Effective Torque

Maximum Momentary Torque (T1)

Rotation N [r/min] T1 = TA +TL [N·m] Speed Effective Torque (Trms) [rpm] 2 2 2 T1 ·t1 +T2 ·t2 +T3 ·t3 Trms = t1 +t2 +t3 +t4 [N·m] 0 Time T2 = TL [N·m] tA Acceleration Time [s] T3 = TL –TA [N·m] T1 Torque t1 = tA [N·m]

TA T2

TL Energy Conservation Support / 0 Time Environment Measure Equipment T3

t1 t2 t3 t4

Single Cycle

TA: Acceleration/Deceleration Torque [N·m] T : Servomotor Shaft Converted Load Torque [N·m] Power Supplies / L In Addition

T1: Maximum Momentary Torque [N·m] Trms: Effective Torque [N·m] Others Common

15 Technical Explanation for Servomotors and Servo Drives

Positioning Accuracy Sensors

G = Z1/Z2 Gear (Deceleration) Ratio Positioning Accuracy (AP) Z : Number of Gear Teeth P: Ball Screw Pitch 2 P·G Ap = [mm] [mm] on Load Side R·S S: Positioner Multiplier

R: Encoder Resolution Motion / Drives Automation Systems Control Components Relays Safety Components Switches M (Pulses/Rotation) Z1: Number of Gear Teeth on Motor Side Ap: Positioning Accuracy [mm]

Straight Line Speed and Motor Rotation Speed

V: Velocity [mm/s] Motor Rotations 60V N = [r/min] P: Ball Screw Pitch Z2: Number of Gear Teeth P·G [mm] on Load Side

G = Z /Z Gear M 1 2 Z1: Number of Gear Teeth (Deceleration) Ratio on Motor Side N: Motor Rotation Speed [r/min] Energy Conservation Support / Environment Measure Equipment Power Supplies / In Addition Others Common

16 Technical Explanation for Servomotors and Servo Drives

Sample Calculations Sensors 1. Machinery Selection

• Load Mass M = 5 [kg]

• Ball Screw Pitch P = 10 [mm] P wthsSft opnnsRly oto opnnsAtmto ytm Motion / Drives Automation Systems Control Components Relays Safety Components Switches • Ball Screw Diameter D = 20 [mm]

•Ball Screw Mass MB = 3 [kg] M MB Direct • Ball Screw Friction Coefficient μ = 0.1 Connection • Since there is no decelerator, G = 1, η = 1 D

2. Determining Operating Pattern

[mm/s] • One Speed Change Speed • Velocity for a Load Travel V = 300 [mm/s] 300 • Strokes L = 360 [mm]

• Stroke Travel Time tS = 1.4 [s]

• Acceleration/Deceleration Time tA = 0.2[s] 0 • Positioning Accuracy Ap = 0.01 [mm] Time [s] 0.2 1.0 0.2 0.2

3. Calculation of Motor Shaft Conversion Load Inertia

Ball screw 2 2 MBD –6 3×20 –6 –4 2 JB = ×10 J = ×10 = 1.5×10 [kg·m ] Inertia JB 8 B 8

2 2 Load P –6 10 –6 –4 –4 2 JW = M ×10 +JB JW = 5× ×10 + 1.5 × 10 = 1.63 × 10 [kg·m ] Inertia JW ()2π ()2 × 3.14

Motor Shaft Conversion 2 –4 2 Load Inertia JL JL = G ×(JW +J2)+J1 JL = JW = 1.63 × 10 [kg·m ]

4. Load Torque Calculation

Torque against Friction P –3 10 –3 –3 Energy Conservation Support / TW = μMg × 10 TW = 0.1×5×9.8× ×10 = 7.8 × 10 [N·m] Environment Measure Equipment Torque TW 2π 2 × 3.14

Motor Shaft Conversion G TL = ·TW –3 Load Torque TL η TL = TW = 7.8×10 [N·m]

5. Calculation of Rotation Speed

60V 60 × 300 Power Supplies /

Rotations N N = N = = 1800 [r/min] In Addition P·G 10×1

6. Motor Temporary Selection [In case OMNUC U Series Servomotor is temporarily selected

]

–4 The Rotor/Inertia of the JL 1.63 × 10 J = = 5.43 × 10–6 [kg·m2] selected Servomotor is JM ≥ L 30 30 * 30 more than 1/30 of a load –5

Temporarily selected Model R88M-U20030 (JM = 1.23 × 10 ). Others

80% of the Rated Torque of the selected Servomotor is more than Rated Torque for R88M – U20030 Model from TM = 0.637 [N·m] the load torque of the TM × 0.8 > TL T = 0.637 [N·m] × 0.8 > T = 7.8 × 10-3 [N·m] Servomotor shaft M L conversion value

* Note that this value changes according to the Series. Common

17 Technical Explanation for Servomotors and Servo Drives

7. Calculation of Acceleration/Deceleration Torque Sensors

Acceleration/ 2π·N JL 2π × 1800 1.63 × 10–4 TA = JM + –5 Deceleration Torque TA TA = × 1.23 × 10 + = 0.165 [N·m] 60tA ()η 60 × 0.2 ( 1.0 )

8. Calculation of Maximum Momentary Torque, Effective Torque wthsSft opnnsRly oto opnnsAtmto ytm Motion / Drives Automation Systems Control Components Relays Safety Components Switches Required Max. Momentary Torque is

T1 = TA + TL = 0.165 + 0.0078 [mm/s] 300 = 0.173 [N·m]

T2 = TL = 0.0078 [N·m]

T3 = TL – TA = 0.0078 – 0.165

= – 0.157 [N·m] Speed 0 Effective Torque Trms is Time [s]

2 2 2 T ·t + T ·t + T ·t t1 t2 t3 t4 Trms = 1 1 2 2 3 3 t1 + t2 + t3 + t4 0.2 1.0 0.2 0.2 0.2 [N·m] Single 0.1732 × 0.2 + 0.00782 × 1.0 + 0.1572 × 0.2 Trms = 0.2 + 1.0 + 0.2 + 0.2 Cycle 0.165 Trms = 0.0828 [N·m] TA 0 Time [s] Decceleration Torque Acceleration/ -0.165

[N·m] TL 0.0078 Time [s] Load Torque of Servomotor Shaft Conversion

0.173

T2 T1 0.0078 Time [s] T3 Total Torque Energy Conservation Support / Environment Measure Equipment -0.157

9. Result of Examination

–4 2 [Load Inertia JL = 1.63 × 10 [kg·m ]] Conditions Power Supplies / Load Inertia –5 ≤ [Motor Rotor Inertia JM = 1.23 × 10 ] × [Applied Inertia = 30] Satisfied In Addition Conditions Effective Torque [Effective Torque Trms = 0.0828 [N·m]] < [Servomotor Rated Torque 0.637 [N·m] × 0.8] Satisfied Maximum Conditions [Maximum Momentary Torque T1 = 0.173 [N·m]] < [Servomotor Maximum Momentary Torque 1.91 [N·m] × 0.8] Momentary Torque Satisfied Maximum Rotation Conditions [Maximum Rotations Required N = 1800 [r/min]] ≤ [Servomotor Rated Rotation Speed 3000 [r/min]] Speed Satisfied

The encoder resolution when the positioner multiplication factor is set to 1 is Others

Encoder P·G 10 × 1 Conditions R = == 1000 [Pulses/Rotations] Resolution Ap·S 0.01 × 1 Satisfied The encoder specification of U Series 2048 [pulses/rotation] should be set 1000 with the Encoder Dividing Rate Setting. Note: This example omits calculations for the regenerative energy, operating conditions, or positioner characteristics. Common

18 Technical Explanation for Servomotors and Servo Drives

Maintenance Sensors Servomotors and Servo Drives contain many components and will operate properly only when each of the individual components is operating properly. Some of the electrical and mechanical components require maintenance depending on application conditions. In order to ensure proper long-term operation of Servomotors and Drives, periodic inspection and part replacement is required according to the life of the components.

(From the "Recommendations for Periodic Inspection of Inverters", published by JEMA) Motion / Drives Automation Systems Control Components Relays Safety Components Switches

The periodic maintenance cycle depends on the installation environment and application conditions of the Servomotor or Servo Drive. Recommended maintenance times are listed below for Servomotors and Servo Drives. Use these for reference in determining actual maintenance schedules. For Servomotors and Servo Drives maintenance, please check the "User Manual (Chapter on Periodic Maintenance)" for each Series.

Servo Drive Servomotor (including Power Supply unit and Regeneration Resistor) Among the components used by the Servomotor, Aluminum Among the components used in the Servo Drive, aluminum Analytical Capacitors, Bearings, Oil seal and Brush require analytical capacitors and Axle fans in particular require periodic maintenance. Their life will depend on such factors as periodic maintenance. the number of rotations used for, the temperature, and the The life of aluminum analytical capacitors is greatly affected load on bearings. Recommended maintenance times are by the ambient operating temperature and the load conditions listed below for each of the Series. of Servomotor operation. Generally speaking, an increase of 10°C in the ambient • OMNUC G5 Series operating temperature will reduce capacitor life by 50%. Bearings ...... 20,000 hours Recommended maintenance times are listed below for each Oil Seals ...... 5,000 hours of the Series. • Smart Step 2 Series Bearings ...... 20,000 hours • OMNUC G5 Series Oil Seals ...... 5,000 hours Aluminum analytical capacitors...... 28,000 hours • OMNUC G Series (Ambient operating temperature 55°C, output of the rated Bearings ...... 20,000 hours operation [rated torque]) Oil Seals ...... 5,000 hours Axle fan...... 10,000 to 30,000 hours Application Conditions: Ambient Servomotor operating (At an ambient Servo Drive operating temperature of 40°C temperature of 40°C, within allowable shaft load, rated or below) operation (rated torque and r/min), installed as described in • Smart Step 2 Series operation manual. Aluminum analytical capacitors...... 50,000 hours (Ambient operating temperature 40°C, 80% output of the rated operation [rated torque]) Axle fan...... 30,000 hours Energy Conservation Support / (At an ambient Servo Drive operating temperature of 40°C Environment Measure Equipment and an ambient humidity of 65%) • OMNUC G Series Aluminum analytical capacitors...... 28,000 hours (Ambient operating temperature 55°C, output of the rated operation [rated torque])

Axle fan...... 10,000 to 30,000 hours Power Supplies / (At an ambient Servo Drive operating temperature of 40°C In Addition or below)

Please follow the instructions in the user manual for installation. We recommend that ambient operating temperature and the power ON time be reduced as much as possible to lengthen Others the maintenance intervals for Servo Drives. If the Servomotor or Servo Drive is not to be used for a long time, or if they are to be used under conditions worse than those described above, a periodic inspection schedule of five years is recommended. Common Please consult with OMRON to determine whether or not components need to be replaced.