Servo otor Selection Flow Chart START Selection Has the machine Been Selected? YES NO Explanation References etermine the size, mass, coefficient of friction, and external forces of all the moving part of the Servo otor the rotation of which affects. --- Has the Operating Pattern Been Selected? YES Calculating the Load Inertia For otor Shaft Conversion Value Calculating the Added Load Torque For otor Shaft Conversion Value Select a motor temporarily Calculate Acceleration/ eceleration Torque Confirm aximum omentary Torque and Calculate Effective Torque NO etermine the operating pattern (relationship between and ) of each part that must be controlled. Convert the operating pattern of each controlled element into the motor shaft operating pattern. The elements of the machine can be separated so that inertia can be calculated for each part that moves as the Servo otor rotates. Calculate the inertia applied to each element to calculate the total load inertia of the motor shaft conversion value. Calculation of Friction Torque Calculates the frictional force for each element, where necessary, and converts it to friction 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 based upon the motor shaft converted load inertia, friction torque, external torque and r.p.m of a motor. Calculate the Acceleration/eceleration Torque from the Load Inertia or Operating Pattern. Operation Pattern Formula Inertia Formulas Load Torque Formulas --- Acceleration/eceleration Torque Formulas 1 Calculate the necessary torque for each part of the Operating Pattern from the Friction Torque, External Torque and Acceleration/ eceleration Torque. Confirm that the maximum value for the Torque for each operating part (aximum omentary Torque) is less than the aximum omentary 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. Calculation of aximum omentary Torque, Effective Torque 3
1 NO Calculate Regenerative Energy Is the Resolution OK? Explanation Calculate Regenerative Energy from the Torque of all the moving parts. Check if the the number of encoder pulses meets the system specified resolution. References Please see the user manual of each product for the details on calculation of the regenerative energy. Accuracy of Positioning NO YES Are the Check Items on Characteristics All OK? YES Check if the calculation meets the specifications of the temporarily selected motor. If not, change the temporarily selected motor and re-calculate it. The following table EN Selection Specialized Check Items Load Inertia Effective Torque aximum omentary Torque aximum Rotation Speed Regenerative Energy Encoder Resolution Characteristics of a Positioner Operating Check Items Load Inertia otor Rotor Inertia x Applicable Inertia Ratio Effective Torque < otor Rated Torque Please allow a margin of about 0%. * aximum omentary Torque < otor aximum omentary Torque Please allow a margin of about 0%. * For the motor aximum omentary Torque, use the value that is combined with a driver and the one of the motor itself. aximum Rotation Speed Rated Rotation Speed of a motor Try to get as close to the motor's rated rotations as possible. It will increase the operating efficiency of a motor. For the formula, please see "Straight-line Speed and otor Rotation Speed" on Page 11. Regenerative Energy Regenerative Energy Absorption of a motor 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 specifications. Check if the Pulse Frequency does not exceed the aximum Response Frequency or aximum Command Frequency of a Positioner. Ensure that values of the ambient operating temperature/ 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. 4
Formulas Formulas for Operating Patterns aximum Speed = X0 : istance oved in t 0 Time (mm) : aximum Speed (mm/s) Triangular Acceleration/eceleration Time = X0 t 0: Positioning Travel istance = : Acceleration/ eceleration t 0 aximum Speed = t 0 Acceleration/eceleration Time = t 0 X0 Total Travel Time t 0 = + X0 Trapezoid Constant-velocity travel t B = t 0 = X0 t 0 = t B Total Travel istance = (t 0 ) X A t 0 X B X A Acceleration/eceleration Travel istance X A = v0 ta = t 0 Constant-velocity travel distance X B = t B = t 0 Speed and Slope When Ascending v 1 v g Ascending Time v0 v1 = α Ascending Time (ta) including distance moved X A = 1 α ta + v 1 t g 1 X A = ( v 1) α +v 1 Speed Gradient v g t g Speed after Ascending = v 1+α 5
for Trapezoidal Operating Pattern Speed and Slope Trapezoid pattern < aximum Speed Ascending Time t 0 α 4 = t0 α 4X (1 1 0 ) t 0 α : Positioning istance (mm) t 0: Positioning : Acceleration/eceleration : aximum Speed (mm/s) α: Speed Gradient t 0 = v0 α t = 0 4X (1 1 0 ) t 0 α for Triangular Operating Pattern t0 α 4 Speed and Slope Triangular Pattern aximum Speed = α Ascending Time t 0 = α v [mm/s] Linear ovement X [mm] Perform the following unitary conversions Linear ovement Rotating ovement X: istance (mm) θ: Angle (rad) Rotating Part θ [rad] v: Speed (mm/s) ω = π N 60 N: Rotating Speed (r/min) ω: Angular Velocity (rad/s) ω [rad/s] N [r/min] 6
Inertia Formulas : Cylinder Inner iameter (mm) 1: Cylinder Outer iameter (mm) Cylindrical Inertia J W = ( 1 + ) 10 6 (kg m ) 8 : Cylinder ass (kg) J W: Cylinder Inertia (kg m ) : Cylinder ass (kg) Eccentric isc Inertia (Cylinder which rotates off the center axis) J C: Inertia around the center axis of Cylinder C J W: Inertia (kg m ) re: Rotational Radius (mm) J W = J C + re 10 6 (kg m ) Center of rotation : Square Cylinder ass (kg) Inertia of Rotating Square Cylinder b: Height (mm) J W: Inertia (kg m ) J W = (a + b ) 10 6 (kg m ) 1 L: Length (mm) a: Width (mm) : Load ass (kg) Inertia of Linear ovement J B: Ball Screw Inertia (kg m ) J W = ( ) P π 10 6 + J B (kg m ) P: Ball Screw Pitch (mm) J W: Inertia (kg m ) : iameter (mm) Inertia of Lifting Object by Pulley J W 1: ass of Cylinder (kg) J 1: Cylinder Inertia (kg m ) J : Inertia due to the Object (kg m ) J W = J 1 +J ( ) = 1 + 8 4 10 6 (kg m ) : ass of Object (kg) J W: Inertia (kg m ) 7
Inertia of Rack and Pinion ovement J W: Inertia (kg m ) : ass (kg) : Pinion iameter (mm) Rack J W = 10 6 (kg m ) J 4 W (mm) Inertia of Suspended Counterbalance J W 1 J W: Inertia (kg m ) 1: ass (kg) : ass (kg) J W = ( 1 + ) 10 6 (kg m ) 4 Inertia when Carrying Object via Conveyor Belt 3 : ass of Object (kg) 4 : ass of Belt (kg) J W : Inertia (kg m ) J 1 : Cylinder 1 Inertia (kg m ) J : Inertia due to Cylinder (kg m ) J 3 : Inertia due to the Object (kg m ) J 4 : Inertia due to the Belt (kg m ) 1 : Cylinder 1 iameter (mm) J W: Inertia (kg m ) J W = J 1 + J + J 3 + J 4 1 : ass of Cylinder 1 (kg) J W = 1 1 + 1 + 8 8 : Cylinder iameter (mm) 3 1 4 + 1 ) 10 4 4 6 : ass of Cylinder (kg) (kg m ) ( J W : System Inertia (kg m ) J 1 : Roller 1 Inertia (kg m ) J : Roller Inertia (kg m ) 1 : Roller 1 iameter (mm) Inertia where Work is Placed between Rollers : Roller iameter (mm) : Equivalent ass of Work (kg) J 1 Roller 1 1 J W = J 1 + ( ) J + 1 1 10 4 6 (kg m ) J W Roller J Inertia of a Load Value Converted to otor Shaft J W: Load Inertia (kg m ) Z 1: Number of Gear Teeth on otor Side J 1: Gear Inertia on otor Side (kg m ) Gear Ratio G = Z 1/Z Load Gears Z : Number of Gear Teeth on Load Side J : Gear Inertia on Load Side (kg m ) otor J L = J 1 + G (J + J W) (kg m ) J L: otor Shaft Conversion Load Inertia (kg m ) 8
Load Torque Formulas Torque against external force P: Ball Screw Pitch (mm) F: External Force (N) T W: Torque due to External Forces T W = F P π : Load ass (kg) Torque against frictional force μ: Ball Screw Friction Coefficient T W = μg P π P: Ball Screw Pitch (mm) g: Acceleration due to Gravity (9.8m/s ) T W: Frictional Forces Torque : iameter (mm) Torque when external force is applied to a rotating object F: External Force (N) T W: Torque due to External Forces T W = F Torque of an object on the conveyer belt to which the external force is applied F: External Force (N) : iameter (mm) T W: Torque due to External Forces T W = F Torque of an object to which the external force is applied by Rack and Pinion F: External Force (N) : iameter (mm) T W: Torque due to External Forces T W = F Rack Plumb Line Torque when work is lifted at an angle. T W: External Torque : ass (kg) T W = g cosθ Pinion g: Acceleration due to Gravity (9.8m/s ) : iameter (mm) Torque of a Load Value Converted to otor Shaft T W: Load Torque Z 1: Number of Gear Teeth on otor Side Gear (eceleration) Ratio G = Z 1/Z Z : Number of Gear Teeth on Load Side η: Gear Transmission Efficiency T L: otor Shaft Conversion Load Torque T L = T W G η 9
Acceleration/eceleration Torque Formula Acceleration/eceleration Torque (TA) η: Gear Transmission Efficiency N: otor Rotation Speed (r/min) J : otor Inertia (kg m ) J L: otor Shaft Conversion Load Inertia (kg m ) T A = πn J + JL η 60 ( ) Speed (Rotation Speed) N N: Rotation Speed (r/min) T A: Acceleration/eceleration Torque Acceleration Calculation of aximum omentary Torque, Effective Torque Rotation Speed (rpm) N (r/min) aximum omentary Torque (T1) T 1 = T A +T L Effective Torque (Trms) Trms = T 1 t 1 +T t +T 3 t 3 t 1 +t +t 3 +t 4 Torque 0 Acceleration T 1 T = T L T 3 = T L T A t 1 = T A T T L 0 T 3 t 1 t t 3 t 4 Single Cycle T A: Acceleration/eceleration Torque T L: Servomotor Shaft Converted Load Torque T 1: aximum omentary Torque Trms: Effective Torque 10
Positioning Accuracy P: Ball Screw Pitch (mm) Z 1: Number of Gear Teeth on otor Side G = Z 1/Z Gear (eceleration) Ratio Z : Number of Gear Teeth on Load Side S: Positioner ultiplier R: Encoder Resolution (Pulses/Rotation) Ap: Positioning Accuracy (mm) Positioning Accuracy (AP) Ap = P G R S (mm) Straight Line Speed and otor Rotation Speed P: Ball Screw Pitch (mm) V: Velocity (mm/s) Z : Number of Gear Teeth on Load Side otor Rotations N = 60V P G (r/min) Z 1: Number of Gear Teeth on otor Side N: otor Rotation Speed (r/min) G = Z 1/Z Gear (eceleration) Ratio 11
Sample Calculations 1achinery Selection Load ass = 5 (kg) Ball Screw Pitch P = 10 (mm) Ball Screw iameter = 0 (mm) P Ball Screw ass B = 3 (kg) Ball Screw Friction Coefficient μ = 0.1 B irect Connection Since there is no decelerator, G = 1, η = 1 etermining Operating Pattern One Speed Change (mm/s) Velocity for a Load Travel V = 300 (mm/s) 300 Strokes L = 360 (mm) Stroke Travel Time ts = 1.4 (s) Acceleration/eceleration Time ta = 0. (s) Positioning Accuracy AP = 0.01 (mm) 0 0. 1.0 0. 0. 3Calculation of otor Shaft Conversion Load Inertia Ball screw Inertia JB J B = B 10 6 8 3 0 J B = 10 6 = 1.5 10 4 (kg m ) 8 Load Inertia JW otor Shaft Conversion Load Inertia JL J 10 6 W = ( P +J B π ) J 10 6 + 1.5 10 4 = 1.63 10 4 (kg m W = 5 10 ) 3.14 ( ) J L = G (J W +J )+J 1 J L = J W = 1.63 10 4 (kg m ) 4Load Torque Calculation Torque against Friction Torque TW otor Shaft Conversion Load Torque TL T W = μg P 10 3 π T L = G η TW T W = 0.1 5 9.8 10 10 3 = 7.8 3.14 T L = T W = 7.8 5Calculation of Rotation Speed Rotations N N = 60V P G 60 300 N = = 1800 (r/min) 10 1 6otor Temporary Selection [In case ONUC U Series Servo otor is temporarily selected] The Rotor/Inertia of the selected servo motor is more than 1/30 * of a load J JL 30 J L 30 1.63 10 = 4 = 5.43 10 6 (kg m ) 30 Temporarily selected odel R88-U0030 (J = 1.3 10 5 ). 80% of the Rated Torque of the selected servo motor is more than the load torque of the servomotor shaft conversion value T 0.8 > T L Rated Torque for R88 U0030 odel from T = 0.637 T = 0.637 0.8 > T L = 7.8 10-3 * Note that this value changes according to the Series. 1
7Calculation of Acceleration/eceleration Torque Acceleration/ eceleration Torque TA T A = π N J + JL η π 1800 60 ( ) T A = 1.3 10 5 1.63 10 + 4 = 0.165 60 0. ( ) 1.0 8Calculation of aximum omentary Torque, Effective Torque Required ax. omentary Torque is T 1 = T A + T L = 0.165 + 0.0078 = 0.173 T = T L = 0.0078 T 3 = T L T A = 0.0078 0.165 = 0.157 (mm/s) 300 Effective Torque Trms is 0 Trms = Trms = T 1 t 1 + T t + T 3 t 3 t 1 + t + t 3 + t 4 Trms = 0.088 0.173 0. + 0.0078 1.0 + 0.157 0. 0. + 1.0 + 0. + 0. Acceleration/ ecceleration Torque 0.165 0 t 1 t t 3 t 4 0. 1.0 0. 0. 0. Single Cycle T A Load Torque of Servomotor Shaft Conversion -0.165 0.0078 T L 0.173 Total Torque 0.0078-0.157 T 1 T T 3 9Result of Examination Load Inertia [Load Inertia JL = 1.63 10 4 (kg m )] [otor Rotor Inertia J = 1.3 10 5 ] [Applied Inertia = 30] Effective Torque [Effective Torque Trms = 0.088 ] < [Servomotor Rated Torque 0.637 0.8] aximum omentary Torque aximum Rotation Speed Encoder Resolution [aximum omentary Torque T1 = 0.173 N m < [Servomotor aximum omentary Torque 1.91 0.8] [aximum Rotations Required N = 1800 (r/min)] [Servomotor Rated Rotation Speed 3000 (r/min)] The encoder resolution when the positioner multiplication factor is set to 1 is P G R = Ap S 10 1 = = 1000 (Pulses/Rotations) 0.01 1 The encoder specification of U Series 048 (pulses/rotation) should be set 1000 with the Encoder ividing Rate Setting. Note.This example omits calculations for the regenerative energy, operating conditions, or positioner characteristics. Satisfied Satisfied Satisfied Satisfied Satisfied 13