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Lenze · Drive Solution Designer · Manual · DMS 4.2 EN · 12/2013 · TD23 87
7Applications
7.4 Omega belt drive
_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
7.4.3 Calculations
The following applies to a linear axis with an omega belt drive that is moved, as is shown in the
drawing:
The belt pulley has the following effective diameter, where p
Cog
specifies the belt pitch:
[7-26] Equation 1: Diameter of belt pulley
Conversion of translatory variables into rotary variables
[7-27] Equation 2: Angle
[7-28] Equation 3: Angular velocity
[7-29] Equation 4: Angular acceleration
Forces of the linear motion
First the mass that is to be moved linearly is to be calculated. The payload m
L
can adopt different
values during the travel cycle. The mass of carriage m
aux
and the mass of the drive motor and the
gearbox m
D
are taken into consideration separately.
[7-30] Equation 5: Total mass
The friction force F
μ
can for instance occur on the guide rails of the slide. The force acts opposite to
the direction of movement and is taken into consideration by the fraction v/|v| in the following
equation, where at v = 0 the force F
μis
0. The static friction at standstill is not considered.
[7-31] Equation 6: Friction force
If the friction force F
μ
is related to the mass in motion, a specific travelling resistance results, which
contains all parts depending on the mass:
[7-32] Equation 7: Specific travelling resistance of the application
d
Cog
[mm]
p
Cog
[mm] N
Cog
⋅
π
-------------------------------------------
=
ϕ
2000 s⋅
d
Cog
--------------------
2000 π s⋅⋅
p
Cog
N
Cog
⋅
----------------------------
==
ω
2000 v⋅
d
Cog
--------------------
2000 π v⋅⋅
p
Cog
N
Cog
⋅
----------------------------
==
α
2000 a⋅
d
Cog
--------------------
2000 π a⋅⋅
p
Cog
N
Cog
⋅
----------------------------
==
m
sum
m
L
m
aux
m
D
++=
F
μ
m
sum
g μ
Gdn
βcos
v
v
-----
⋅⋅ ⋅ ⋅=
F’ g μ
Gdn
βcos⋅⋅=
- Drive Solution 1
- Designer 1
- Contents 10
- 1 Notes on usage 11
- 2 About this documentation 14
- Pictograph and signal word! 17
- 3User interface 18
- How to sort the results: 35
- How to filter results: 35
- How to open created notes: 38
- How to delete notes: 38
- 4.3.1 Messages 44
- 4.3.2 Software updates 45
- 4.4 Language 46
- 4.5 Settings 46
- 4.5.3 "Help" tab 47
- 4.5.5 "Units" tab 48
- User data 50
- Registration data: 50
- 4.6 User-specific settings 51
- 4.6.1 User-defined defaults 51
- 5Managing projects 52
- 6 Drive dimensioning tools 55
- 7Applications 100
- Mass calculator ( 405) 109
- Danger! 122
- Pole pair 191
- 8 Motion design 224
- symbol in the toolbar 225
- CINH = 1 271
- 9 Mains and environment 277
- ( 283) 282
- ( 285) 282
- ( 286) 282
- 10.1 Mechanical drive axis 283
- 10.1.1 Lenze gearbox 283
- 10.1.3 Feedback 284
- 10.2 Electrical drive axis 285
- 10.3 Drive concept 286
- 10.3.1 Gearbox features 287
- 10.3.1.1 Axial gearbox 287
- 10.3.1.2 Right-angle gearbox 288
- 10.3.2 Motor properties 289
- 10.3.4 Inverter properties 294
- 10.3.4.1 Frequency inverter 294
- 10.3.4.2 Servo inverters 296
- 11 Drive Dimensioning 308
- 12 Components in the DC bus 361
- 13 Details on Lenze products 377
- 14 Energy efficiency 378
- 15.1 Drawing 386
- Editing functions 389
- 15.2 Results 390
- 15.3 Protocols 391
- 15.3.1 Summarised protocol 391
- 15.3.2 Detailed protocol 391
- 15.3.3 Commissioning data 392
- 15.3.5 Output settings 393
- 15.4.1 Application Tuner 394
- 15.4.3 BlueGreen 394
- ( 378) 395
- 15.6.1 Dynamic reserves 396
- 15.6.2 Stationary reserves 396
- 15.6.3 Speed reserves 397
- 15.6.7 Reserves for gearboxes 399
- 16 Auxiliary means 401
- How to call the calculator: 404
- How to call the DSC: 425
- 17.1 Field weakening 426
- 17.5 Feedback systems 427
- Measured values 430
- 17.16 System disturbances 435
- [17-6] Group drives 436
- 17.19 ATEX for gearbox 437
- 17.21 Emergency-off scenarios 438
- 18.1 Applications 441
- 18.2 Drive system 445
- 18.3 Additional drive element 449
- 18.4 Lenze gearbox 450
- 18.5 Lenze motor 455
- 18.5.6 Motor speed too low 456
- > as winding ratio q 460
- 18.6 Brake 461
- 18.6.3 No brake available 461
- 18.7 Feedback 463
- 18.7.2 No feedback selected 463
- 18.8 Inverters 465
- 18.8.16 Activate VVC control 469
- 18.8.19 Mains choke required 470
- 18.10 Supply module 476
- 18.11 Brake chopper 479
- 18.12 Brake resistor 481
- 18.13 User motor 483
- ( 42) 485
- ( 46) 485
- 20 Glossary 486
- )(('%$& 494
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