screw jack calculations

7/23/2019 Screw Jack Calculations

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169

C r i t i c a l b u c k l i n g f o r c e F i n k N

k

free length L in mm

Selection, Calculation, Checklists

Critical Buckling Force of the Lifting Screws

Maximum allowed axial load

F = 0.8 x F x f all k k

F maximum allowable axial load (kN)all

F theoretical critical buckling forcek

(kN) acc. to diagramf correction value (considers kind of k

bearing support, respectively guidance of lifting load) see pictograms above

f = 4k

Version Rfor a small L1 there applies: fk = 2guided lifting motion

f = 2k

Version Sguided lifting motion,gear firmly mounted

f = 0,25k

Version Snon guided lifting motion,gear firmly mounted

f = 1k

Version Sguided lifting motion withhinged plate

If the maximum calculated load is lower thanrequired, a larger spindle diameter couldbe selected. The calculations must thenbe reworked.With the rotating screw version a larger diameter screw can be selected (from thenext bigger gearbox size). Any increase in pitch/ lifting speed mustbe taken into account.The safety factors for the type of systemspecified must be used, as shown above,

to calculate the max allowable axial loadfor the system.

There is a buckling risk especially

with gearboxes with long, thinspindles in combination withcompression load. With thefollowing calculation you can findthe max. allowed axial load acc.to Euler.



170


Critical Whirling Speed of Spindle - R Version

Maximum allowablespindle speed

n = 0.8 x n x f all kr kr

For R version gearboxes (with rotatingspindle) with long, thin spindles it isnecessary to calculate the maximum allowablespindle speed. Please take the theoreticalcritical speed n from the diagram. Alsokr

consider the additional lengths for spindlecovers, etc. when calculating the unsupportedscrew lengths .Together with the correction factor for the bearing layout the max. allowablespindle speed can be calculated.

f = 1kr

with opposedbearing plate

f = 0.5kr

without opposed

bearing plate

unsupported screw lengths [m]

- 1

t h e o r e t i c a l s p i n d l e w h i r l i n g s p e e d n

[ m i n

]

k r

If the calculated maximum spindle speed islower than that required, a larger spindleshould be selected. The calculations mustthen be reworked.If a larger diameter spindle is used in theR version the potential for higher drivetorque's must be considered.The safety factors for the type of systemspecified must be used, as shown above,to calculate the maximum allowable axial loadfor the system.

spindle speed =input speed

igearbox. . . . .



171


Determining the Drive Torque [M ] of a Lifting GearG

With the formula shown below it ispossible to calculate the necessary

drive torque.In order to facilitate the calculation of the drive torque we have determinedmultiplication factors out of this formulaand have stated them in thetechnical data for the single gearboxversion.

M Required drive torque [Nm] of a lifting gear G

F Lifting load (dynamic) [kN] Efficiency of the lifting gear (without spindle)

Gearbox Efficiency of the spindleSpindle

P Spindle pitch [mm]i Transmission of the lifting gear M Idling torque [Nm]L

P Power of motor M

1)Formula :

Drive torque: MG = + M [Nm]L

F [kN] · P [mm]

i2 · · · ·Gearbox Spindle

Power of motor: P [kW] =M

-1M [Nm] · n [min ]G

9550

Safety factor (start torque) = calculateddrive torque x 1.3 to 1.5 (for smaller systems use up to x 2). !1) For gearboxes with one-pitch trapezoidal spindles it is also possible to multiply the

factor which is stated on the corresponding gearbox page with the load.

Example:

MSZ-25-SNF = 12 kN (lifting load dynamic)

= 0.87 = 0.375Gearbox Spindle

P = 6 i = 6

M = + 0.36 Nm = 6.21 NmG

12 kN · 6mm2 · · 0,87 · 0,375 · 6

Example: 0.975 kW · 1.4 = 1.365 kW motor 1.5 kW

P = = 0.975 kWM

-16.21 Nm · 1500 min

9550

Tr spindle Spindle

Efficiencysingle pitch

Tr 121820304050

6080100120140

P344678

1216161620

lubricated0.4270.3990.3750.3750.3440.314

0.3680.3680.3140.2730.288

Tr 121820304050

6080

100120140

P688121416

2432323240

lubricated0.5920.5650.5400.5400.5090.474

0.5320.5320.4740.4260.444

Tr spindle Spindle

Efficiencydouble pitch

The efficiency of a trapezoidscrew is substantially lowerthan that of ball screws dueto friction.However, the trapezoid screwis technically more simpleand more favourable. Asafety device (e.g. a brake) israrely required for trapezoid

screws due to their self-locking capability.With a ballscrew system anefficiency factor of =0.9 can be used.It is essential to incorporatea break into a ballscrewsystem.

Efficiency of gearboxes (without spindle) at n = 1.500Gearbox

MSZNL

20.820.77

50.840.62

100.860.69

250.870.69

500.890.74

1000.850.65

1500.840.67

2500.860.72

3500.870.70

5000.840.62

6500.850.65

MSZNL

20.060.04

50.100.08

100.260.16

250.360.26

500.760.54

1001.681.02

1501.901.20

2502.641.94

3503.242.20

5003.962.84

6505.603.40

Idling torques ML of gearboxes [Nm]

With ball screws you basically can calculate with an efficiency factor of =0.9



172


Drive Torque for Gearboxes

Calculation

The required drive torque of alifting gear results from the sum ofthe moments of the individuallifting units. This is increased due tofrictional losses of transmissioncomponents like couplings,

connecting shafts, bevel gears, etc.To simplify the calculation, somefactors for determining the drivetorque in the most commonapplications are provided below.

M = M x 2.25R G

M = M x 2.1R G M = M x 3.1R G M = M x 3.35R G

M = M x 4.6R G M = M x 6.8R G M = M x 4.4R G

M = M x 3.34R G M = M x 3.27R G

M - Total drive torque for theR

whole system

M - Input torque of a single gearboxG

M - Starting torque max. 1.5 x M A R

Attention:

It is recommended to multiply thecalculated value with a safetyfactor of 1.3 to 1.5 (for smallersystems factor up to 2). Theindicated values are applicable incases of uniform distribution of thelifting gear load onto all gears!

Example (example from previous page, 12 kN per gearbox)

M = M x 4.6 = 6.21 Nm x 4.6 = 28.57 NmR G

x safety factor 1.3 = 37.14Nm



173


Maximum Power / Moments

Load definitions

F - Lifting load tension and/or compressionF - Side forces on the spindleS

v - Lifting speed of the spindleH

(or nut of the R version)F - Axial load of the input shaft A

F - Radial load of the input shaftR

M - Drive torqueR

n - Drive speedR

Please examine the information on the following pages before makingyour choice of the lifting gear suited for your application. Variousinfluences and assumptions can only be estimated on the basis of

information gained by experience. In case of doubt please contact T.E.A.

F

Side forces on the spindlePlease refer to the adjoiningtable for the maximumpermissible side force. Sideforces should be supported bya guidance system wheneverpossible. The bronze bushingsin the gearbox are a

secondary support only andshould not be relied upon asadequate guidance. Themaximum side force at agiven screw extension mustnot exceed that stated in theadjoining table. Attention:only statically allowed!

Max. drive torqueThe stated values of the tableon the right should not beexceeded. If gearboxes arearranged in tandem or in

larger arrangements themaximum drive torque maybe higher. If there are morethan 5 gearboxes in anarrangement please contactT.E.A.

Radial load on the inputshaftThe radial forces of the tableon the right should not beexceeded if you use chaindrives or belt drives.

FS

V H

lifting screw

MRnR

F A

FR

input shaft

= worm shaft

MSZ5102550

100150250350

500650750

Type

M SN/RNR

M SN/RNR

M SL/RLR

M SL/RLR

min-1

15005001500

500

SHZ-020.71.00.5

0.7

MSZ-5

6.410.42.6

4.3

MSZ-10

12.620.55.3

8.4

MSZ-25

21.734.27.8

12.5

MSZ-50

44.770.315.5

24.5

MSZ-10072.0114.917.0

27.8

MSZ-15067.3107.017.3

27.7

MSZ-250

118.4185.123.5

36.6

MSZ-350

187.0295.740.2

63.9

MSZ-500

204.3325.642.8

71.2

MSZ-650

268.3427.962.8

102.6

MSZ-750

415.0663.083.0

132.0

1003606009003000500055009000

15000

290003480046000

200160280470

200040005000900013000

290003480046000

300100180300

130030003900650012000

290003480039000

40070

130240900230028004900

10000

290003480036000

50055100180700

1800230038008800

290003480032000

6004580

150600

1500180030007000

240002880030000

7003870

1305001300150025006000

200002400025000

8003260110420

1100130022005500

170002040029000

9002850

100380950120020004800

150001800025000

1000254790

330850100019004300

140001680023500

1200204070280700850

14503500

120001440020000

1500183060

23060075012503000

90001080017000

2000122045

1604005009002000

7000840012000

2500–

1535130350400760

1600

5600672010000

3000––

30100250350660

1400

490058808000

F max.R

SHZ-0218

MSZ-5110

MSZ-10215

MSZ-25300

MSZ-50520

MSZ-100800

MSZ-150810

MSZ-2501420

MSZ-3502100

MSZ-5003780

MSZ-6504536

- Consider that the starting torque is factor 1.5 of the operation torque- Limit values are mechanical - consider thermical factors depending on operating time

Maximum side force F [N] (static) extended screw length in mmS

Maximum drive torque M [Nm]R

Maximum radial load acting on the input shaft F [N]R



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