Selecting Servomotor Capacity and Regenerative Capacity

Selecting Servomotor Capacity and Regenerative Capacity Servomotor Capacity Selection Examples Use the AC servo drive capacity selection program SigmaJunmaSize+ to select servomotor capacity. The program can be downloaded for free from our web site (http://www.e-mechatronics.com/). 1Selection Example for Speed Control Mechanical Specifications Linear motion Ball screw υl Servomotor Coupling Gear Load speed: υl = 15 m/min Gear + coupling moment of inertia Linear motion section mass: m = 5 kg : JG =.4 1-4 kg m Ball screw length: B = 1. m Feeding times: n = 4 times/min Ball screw diameter: db =. m Feeding distance: =.75 m Ball screw lead: PB =.1 m Feeding time: tm = 1. s max. Ball screw material density: =7.87 13 kg/m 3 Friction coefficient: μ =. Gear ratio: 1/ (R = ) Mechanical efficiency: η =.9 (9%) (1) Speed Diagram 15 υ L Speed (m/min) ta tc tm t td Time (s) t = 6 = 6 = 1.5 (s) n 4 where ta = td ta = tm = 1. 6.75 = 1. 1.1 =.1 (s) L 15 tc = 1..1 = 1. (s) υ () Rotation Speed υl Load axis rotation speed nl = = 15 = 15 (min -1 ) PB.1 Motor shaft rotation speed (3) Load torque (4) Load Moment of Inertia Gear ratio 1/R = 1/ (R=) Therefore, nm = nl R = 15 = 3 (min -1 ) 9.8 µ m PB 9.8. 5.1 TL = = =.43 (N m) πr η π.9 Linear motion section JL1 = m PB.1 = 5 πr π = 1.58 1-4 (kg m ) Ball screw JB = π 1 B db 4 = π 7.87 1 3 1. (.) 1 4 3 R 3 =.31 1-4 (kg m ) Coupling JG =.4 1-4 (kg m ) ρ Load moment of inertia at motor shaft JL = JL1 + JB + JG = (1.58 +.31 +.4) 1-4 =.9 1-4 (kg m ) (5) Load Moving Power πnm TL π 3.43 PO = = = 135(W) 6 6 381

Others Selecting Servomotor Capacity and Regenerative Capacity Servomotor Capacity Selection Examples (6) Load Acceleration Power π JL π.9 1 Pa = nm = 3-4 = 6 (W) 6 ta 6.1 (7) Servomotor Provisional Selection (a) Selecting Conditions TL Motor rated torque The followings satisfy the conditions. Servomotor SGMJV-A (b) Specifications of the Provisionally Selected Servomotor (Po + Pa) < Provisionally selected < (Po + Pa) servomotor rated output nm Motor rated speed JL Allowable load moment of inertia Rated output : (W) Rated motor speed : 3 (min -1 ) Rated torque :.637 (N m) Instantaneous peak torque :.3 (N m) Servomotor moment of inertia :.59 1-4 (kg m ) Allowable load moment of inertia :.59 1-4 15 = 3.885 1-4 (kg m ) (8) Verification on the Provisionally Selected Servomotor πnm(jm + JL) Required acceleration torque: TP = + TL = π 3 (.59 +.9) 1-4 +.43 6ta 6.1 1.3 (N m) < Instantaneous peak torque Satisfactory πnm(jm + JL) Required deceleration torque: TS = TL = π 3 (.59 +.9) 1-4.43 6td 6.1.37 (N m) < Instantaneous peak torque Satisfactory Torque effective value: Trms = TP ta + TL tc + Ts td = (1.3).1 + (.43) 1. + (.37).1 t 1.5.483 (N m) < Rated torque Satisfactory (9) Result The provisionally selected servomotor is confirmed to be applicable. The torque diagram is shown below. N m 1.3.43 -.37 Torque Speed.1 1. 1.5.1 Selecting Servomotor Capacity and Regenerative Capacity 38

Servomotor Capacity Selection Examples Use the AC servo drive capacity selection program SigmaJunmaSize+ to select servomotor capacity. The program can be downloaded for free from our web site (http://www.e-mechatronics.com/). 1Selection Example for Position Control Mechanical Specifications Linear motion Servomotor Ball screw υl Coupling Load speed: υl = 15 m/min Coupling outer diameter: dc =.3 m Linear motion section mass: m = 8 kg Positioning times: n = 4 times/min Ball screw length: B =.8 m Positioning distance: =.5 m Ball screw diameter: db =.16 m Positioning time: tm = 1. s max. Ball screw lead: PB =.5 m Electrical stop accuracy: δ = ±.1 mm Ball screw material density: =7.87 13 kg/m 3 Friction coefficient: μ =. Coupling mass: mc =.3 kg Mechanical efficiency: η =.9 (9%) (1) Speed Diagram 15 Speed (m/min) ta υl tc tm Reference pulse Load speed td ts Time(s) t t = 6 = 6 = 1.5(s) n 4 Where ta = td, ts =.1(s) ta = tm ts = 1..1 6.5 =.1(s) υl 15 tc = 1..1 = 1.(s) () Rotation Speed υl Load axis rotation speed nl = = 15 = 3(min -1 ) PB.5 Motor shaft rotation speed with direct coupling: Gear ratio 1/R = 1/1 Therefore, nm = nl R = 3 1 = 3 (min -1 ) (3) Load Torque 9.8 µ m PB 9.8. 8.5 TL = = =.139(N m) πr η π 1.9 (4) Load Moment of Inertia PB.5 Liner motion section JL1 = m = 8 =.57 1-4 (kg m ) πr π 1 Ball screw JB = π B db 4 = π 7.87 1 3.8 (.16) 4 =.45 1-4 (kg m ) 3 3 Coupling Jc = 1 mc dc 4 = 1.3 (.3) =.338 1-4 (kg m ) 8 8 Load moment of inertia at the motor shaft JL = JL1 + JB + Jc = 1.5 1-4 (kg m ) ρ 383

Others Selecting Servomotor Capacity and Regenerative Capacity Servomotor Capacity Selection Examples (5) Load Moving Power πnm TL π 3.139 PO = = = 43.7(W) 6 6 (6) Load Acceleration Power π JL π 1.5 1 Pa = nm = 3-4 = 13.4(W) 6 ta 6.1 (7) Provisionally Servomotor Selection (a) Selecting Conditions TL Motor rated torque (Po + Pa) < Provisionally selected < (Po + Pa) servomotor rated output nm Motor rated speed JL Allowable load moment of inertia The followings satisfy the conditions. Servomotor SGMJV-1A (b) Specifications of Servomotor Rated output : 1 (W) Rated motor speed : 3 (min -1 ) Rated torque :.318 (N m) Instantaneous peak torque : 1.11 (N m) Servomotor rotor moment of inertia :.665 1-4 (kg m ) Allowable load moment of inertia :.665 1-4 = 1.33 1-4 (kg m ) Encoder resolution : bit (148576P/rev) (8) Verification on Provisionally Selected Servomotor πnm(jm + JL) π 3 (.665 + 1.5) 1 Required acceleration torque: TP = + TL = -4 +.139 6ta 6.1.55 (N m) < Instantaneous peak torque Satisfactory πnm(jm + JL) Required deceleration torque: TS = TL = π 3 (.665 + 1.5) 1-4.139 6td 6.1.75 (N m) < Instantaneous peak torque Satisfactory Torque effective value: Trms = TP ta + TL tc + Ts td = (.55).1 + (.139).9 + (.75).1 t 1.5.19 (N m) < Rated torque Satisfactory The above confirms that the provisionally selected servomotor is sufficient. In the next step, their performance in position control are checked. Selecting Servomotor Capacity and Regenerative Capacity 384

Servomotor Capacity Selection Examples (9) PG Feedback Pulse Dividing Ratio: Setting of Electronic Gear Ratio B A As the electrical stop accuracy δ = ±.1mm, take the position detection unit =.1mm/pulse. PB B 5 B = = 148576 A.1 A B k = = A 148576 5 (1) Reference Pulse Frequency υ 1 L 1 15 vs = = = 5,(pps) 6.1 (11) Error Counter Pulses Position loop gain KP = 4 (1/s) ε = vs = 5, = 65(pulse) KP 4 (1) Electrical Stop Accuracy ε 65 ± ε = ± = ± ±.15 < ±1(pulse) = ±.1(mm) nm (SERVOPACK control range) 3 5 nr 3 The above results confirm that the selected servomotor is applicable for the position control. 385

Others Selecting Servomotor Capacity and Regenerative Capacity Selecting Regenerative Resistors (1) Simple Calculation When driving a servomotor with the horizontal axis, check the external regenerative resistor requirements using the calculation method shown below. (a) SGDV- F, -R7A, -R9A, -1R6A, and -R8A SERVOPACKs These SERVOPACKs do not have built-in regenerative resistors. The energy that can be charged with capacitors is shown in the following table. If the rotational energy in the servomotor exceeds these values, then connect an external regenerative resistor. Voltage Single-phase 1 V Three-phase V Regenerative Energy that Can Applicable SERVOPACK be Processed (joules) SGDV-R7F, R9F, R1F 6.4 SGDV-R8F 44.1 SGDV-R7A, -R9A, -1R6A 4. SGDV-R8A 31.7 Calculate the rotational energy (Es) in the servomotor from the following equation: Es = J (nm) /18 (joules) J = JM + JL JM : Servomotor rotor moment of inertia (kg m ) JL : Load converted to shaft moment of inertia (kg m ) nm: Rotation speed used by servomotor (min -1 ) Remarks Value when main circuit input voltage is 1 VAC Value when main circuit input voltage is VAC (b) SERVOPACKs other than (a) SERVOPACKs other than SGDV- F, -R7A, -R9A, -1R6A, and -R8A have built-in regenerative resistors. The allowable frequencies for just the servomotor in acceleration and deceleration operation, during the rotation speed cycle from (min -1 ) to the maximum rotation speed to, are summarized in the following table. Convert the data into the values obtained with actual rotation speed and load moment of inertia to determine whether an external regenerative resistor is needed. Voltage Three-phase V Three-phase 4V Allowable Frequencies in Regenerative Mode (time/min) Servomotor Model 3 5 6 8 9 1 13 15 5 3 4 44 5 SGMJV- 15 SGMAV- 74 31 SGMPS- 11 7 SGMGV- A 39 9 6 6 7 9* 6 SGMSV- A 13 1 8 1 1 16 1 SGMGV- D 68 51 1 8 13 7 6 SGMSV- D 4 3 49 38 17 16 1 *: This value is "4," when used in combination with SGDV-A SERVOPACK. Selecting Servomotor Capacity and Regenerative Capacity 386

Selecting Regenerative Resistors Operating Conditions for Allowable Regenerative Frequency Calculation Load moment of inertia = (servomotor only) Speed reference t Servomotor rotation speed Servomotor-generated torque Regeneration mode t Maximum rotation speed Maximum torque T (Operation cycle) Allowable frequency = 1/T (times/min) Maximum torque Use the following equation to calculate the allowable frequency for regeneration mode operation Allowable frequency for Seromotor only Max. rotation speed Allowable frequency = (1+n) Rotation speed n = JL / JM JM : Servomotor rotor moment of inertia (kg m ) JL : Load converted to shaft moment of inertia (kg m ) (time/min) (c) SGDV-47A, -55A, -59A, -78A SERVOPACKs These SERVOPACKs do not have built-in regenerative resistors. The following table shows the allowable regenerative frequencies when the JUSP-RA4-E or JUSP-RA5-E regenerative resistor is used together with an applicable SERVOPACK. The servomotor driving conditions and the conversion equation for the allowable regenerative frequencies to the rotation speed and load moment of inertia are the same as that shown in (b) on the previous page. Voltage Three-phase V Allowable Frequencies in Regenerative Mode (time/min) Servomotor Model 55 7 75 1A 1E SGMGV- A 4 34 39 31 SGMSV- A 14 387

Others Selecting Servomotor Capacity and Regenerative Capacity Selecting Regenerative Resistors () Calculating the Regenerative Energy This section shows the procedure for calculating the regenerative resistor capacity when acceleration and deceleration operation is as shown in the following diagram nm: Motor rotation speed Rotation speed td Motor torque TL: Load torque T Regenerative torque 3Calculation Procedure The procedure for calculating the regenerative capacity is as follows: Step Item Symbol Equation 1 Calculate the rotational energy of the servomotor. ES ES =JnM /18 Calculate the energy consumed by load loss during the deceleration period EL EL =(π/ 6)nMTLtD 3 Calculate the energy lost from servomotor winding (Value calculated from (4) Servomotor Winding Resistance EM resistance. Loss diagrams) td 4 Calculate the SERVOPACK energy that can be absorbed. EC Calculate from (3) SERVOPACK s Absorbable Energy diagrams. 5 Calculate the energy consumed by the regenerative resistor. EK EK =ES - (EL +EM +EC) 6 Calculate the required regenerative resistor capacity (W). WK WK =EK/(. T) Note: 1 The. in the equation for calculating Wk is the value for when the regenerative resistor s utilized load ratio is %. The units for the various symbols are as follows: ES to EK: Energy joules (J) TL: Load torque (N m) WK : Regenerative resistor required capacity (W) td: Deceleration stopping time (s) J: (=JM+JL)(kg m ) T: Servomotor repeat operation period (s) nm : Servomotor rotation speed (min -1 ) If the above calculation determines that the amount of regenerative power (Wk) processed by the built-in resistor is not exceeded, then an external regenerative resistor is not required. Refer to Specifications of Built-in Regenerative Resistor for regenerative resistors built into SERVOPACKs. If the amount of regenerative power that can be processed by the built-in resistor is exceeded, then install an external regenerative resistor for the capacity obtained from the above calculation. If the energy consumed by load loss (in step above) is unknown, then perform the calculation using El =. When the operation period in regeneration mode is continuous, add the following items to the above calculation procedure in order to find the required capacity (W) for the regenerative resistor. Energy for continuous regeneration mode operation period: EG (joules) Energy consumed by regenerative resistor: EK = ES - (EL+EM+EC)+EG Required capacity of regenerative resistor: WK = EK/(. T) Here, EG=(π/6) nmgtgtg TG : Servomotor s generated torque in continuous regeneration mode operation period (N m) nmg : Servomotor rotation speed for same operation period as above (min -1 ) tg : Same operation period as above(s) Selecting Servomotor Capacity and Regenerative Capacity 388

Selecting Regenerative Resistors (3) SERVOPACK s Absorbable Energy The following diagrams show the relationship between the SERVOPACK s input power supply voltage and its absorbable energy. SERVOPACK for 1 V Model: SGDV- SERVOPACK for V Model: SGDV- 6 5 R7F, R9F, R1F R8F 7 6 R7A, R9A, 1R6A R8A 3R8A 5R5A, 7R6A Absorbable Energy (J) 4 3 Absorbable Energy (J) 5 4 3 1 1 85 9 95 1 15 11 115 1 17 18 19 1 3 4 5 6 Input Voltage (Vrms) Input Voltage (Vrms) 16 14 1 SERVOPACK for V Model: SGDV- 1A 18A, A 33A 6 5 SERVOPACK for V Model: SGDV- 47A 55A 59A 78A Absorbable Energy (J) 1 8 6 Absorbable Energy (J) 4 3 4 1 17 18 19 1 3 4 5 6 17 18 19 1 3 4 5 6 Input Voltage (Vrms) Input Voltage (Vrms) Absorbable Energy (J) 16 14 1 1 8 6 4 SERVOPACK for 4 V Model: SGDV- 1R9D 3R5D, 5R4D 8R4D, 1D 17D Absorbable Energy (J) 7 6 5 4 3 SERVOPACK for 4 V Model: SGDV- 1D 6D 8D 37D 1 3 34 36 38 4 4 44 46 48 5 5 54 Input Voltage (Vrms) 3 34 36 38 4 4 44 46 48 5 5 54 Input Voltage (Vrms) 389

Others Selecting Servomotor Capacity and Regenerative Capacity Selecting Regenerative Resistors (4) Servomotor Winding Resistance Loss The following diagrams show the relationship, for each servomotor, between the servomotor s generated torque and the winding resistance loss. (a) SGMJV Rotary Servomotors 5 Model: SGMJV- 45 4 35 3 5 15 1 8A 4A 1A A A5A 5 1 3 35 (b) SGMAV Rotary Servomotors 35 3 5 15 1 5 CA 1A A A5A Model: SGMAV- 45 4 35 3 5 15 1 5 6A 4A 8A 1A Model: SGMAV- 1 3 1 3 (c) SGMPS Rotary Servomotors 45 4 35 3 5 15 1 5 4A 15A A 1A 8A Model: SGMPS- 1 3 Selecting Servomotor Capacity and Regenerative Capacity 39

Selecting Regenerative Resistors (d) SGMGV Rotary Servomotors 6 Model: SGMGV- 8 Model: SGMGV- 5 4 3 1 5 3 7 6 5 4 3 1 13 9 1 3 4 5 1 15 5 3 1 Model: SGMGV- 14 Model: SGMGV- 1 8 6 4 75 44 55 3 1 1 8 6 4 1EA 1AA 5 1 15 5 3 5 1 15 5 3 (e) SGMSV Rotary Servomotors 14 1 1 8 6 4 15 1 5 Model: SGMSV- 16 14 1 1 8 6 4 5 3 4 7A Model: SGMSV- 1 3 4 1 3 4 391

Others Selecting Servomotor Capacity and Regenerative Capacity Selecting Regenerative Resistors (f) SGMCS Direct Drive Servomotors 7 Model: SGMCS- 1 Model: SGMCS- 6 5 4 3 1 1C 4C 14C 7B 5B B 8 6 4 16E 35E 5D 8D 17D 1 3 1 3 (g) SGLGW Linear Servomotors 5 Model: SGLGW-3A 1 Model: SGLGW-4A 15 1 5 8C 5C 1 8 6 4 365C 53C 14C 1 3 4 1 3 4 5 15 1 5 365C -M 53C -M 14C -M Model: SGLGW-4A 14 1 1 8 6 4 365C 53C 14C Model: SGLGW-6A 1 3 4 5 1 3 4 3 5 15 1 5 Model: SGLGW-6A 365C -M 53C -M 14C -M 1 3 4 5 6 5 4 3 1 535C Model: SGLGW-9A 37C C 1 3 4 5 Selecting Servomotor Capacity and Regenerative Capacity 39

Selecting Regenerative Resistors (h) SGLFW Linear Servomotors 3 Model: SGLFW-A 8 Model: SGLFW-35A 5 15 1 1A 9A 7 6 5 4 3 3A 1A 5 1 1 3 4 5 1 3 4 1 Model: SGLFW-5A 18 Model: SGLFW-1ZA 1 8 6 4 38B B 16 14 1 1 8 6 4 38B B 1 3 1 3 8 Model: SGLFW-35D 1 Model: SGLFW-5D 7 6 5 4 3 1 3A 1A 1 8 6 4 38B B 1 3 4 1 3 Model: SGLFW-1ZD 18 16 14 1 1 8 6 4 38B B 1 3 393

Others Selecting Servomotor Capacity and Regenerative Capacity Selecting Regenerative Resistors (i) SGLTW Linear Servomotors 5 Model: SGLTW-A 35 Model: SGLTW-35A 15 1 5 17A 46A 3A 3 5 15 1 5 46A 3A 17A 1 3 4 1 3 4 9 Model: SGLTW-35A 7 Model: SGLTW-4A 8 7 6 5 4 3 3H 17H 6 5 4 3 6B 4B 1 1 5 1 15 5 4 6 1 Model: SGLTW-5A 1 Model: SGLTW-8A Selecting Servomotor Capacity and Regenerative Capacity 1 8 6 4 3H 17H 9 8 7 6 5 4 3 4B 1 5 1 15 5 4 6 394

Selecting Regenerative Resistors (i) SGLTW Linear Servomotors (cont d) 1 Model: SGLTW-35D 8 Model: SGLTW-4D 9 8 7 6 5 4 3 3H 17H 7 6 5 4 3 6B 4B 1 1 1 3 4 6 1 Model: SGLTW-5D 1 Model: SGLTW-8D 1 8 6 4 3H 17H 1 8 6 4 4B (j) SGLCW Cylinder Type Linear Servomotors 4 5 1 15 5 Model: SGLCW-D16A 4 6 Model: SGLCW-DA 1 35 3 5 15 1 115AP 85AP 145AP 1 8 6 4 135AP 1AP 17AP 5 1 3 4 5 4 6 16 Model: SGLCW-D5A 16 Model: SGLCW-D3A 14 1 1 8 6 4 15AP 17AP 15AP 14 1 1 8 6 4 85AP 5AP 165AP 1 3 4 5 1 3 4 5 395

Others Selecting Servomotor Capacity and Regenerative Capacity Selecting Regenerative Resistors (k) SGT Linear Sliders 8 Model: SGT 1 Model: SGT 7 6 5 4 3 F3 F4 1 8 6 4 F9A 1 1 3 4 1 3 1 Model: SGT 14 Model: SGT 1 8 6 4 GD GE GF 1 1 8 6 4 GG Selecting Servomotor Capacity and Regenerative Capacity GH GI 1 3 4 1 3 4 396