Power Screw

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Design of Power Screw

Nirmal Baran Hui

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Power Screw Drives• A power screw is a drive used in machinery to convert a rotary motion into a linear

motion for power transmission. It produces uniform motion and the design of the power screw may be such that (a) Either the screw or the nut is held at rest and the other member rotates as it moves axially. A typical example of this is a screw clamp. (b) Either the screw or the nut rotates but does not move axially. A typical example for this is a press.

• Other applications of power screws are jack screws, lead screws of a lathe, screws for vices, presses etc.

• The screw is a cylindrical bar with one or several helical grooves of a definite shape. • The nut is a part with a cylindrical hole grooved inside. Advantages of power screws: • Easily obtainable slow translational motion and a high gain in force.• Smooth and noiseless operation• The ability to carry heavy loads and effect accurate travel and simple in design.Disadvantages: • High losses due to friction• A comparatively low efficiency

Power screw normally uses square threads but ACME or Buttress threads may also be used. Power screws should be designed for smooth and noiseless transmission of power with an ability to carry heavy loads with high efficiency.

3According to IS-4694-1968, a square thread is designated by its nominal diameter and pitch, as for example, SQ 10 x 2 designates a thread form of nominal diameter 10 mm and pitch 2 mm.

Square threads: These threads have high efficiency but they are difficult to manufacture and are expensive. The proportions in terms of pitch are: h1= 0.5p ; h2 = 0.5 p - b ; H = 0.5 p + a ; e = 0.5 p, where a and b are different for different series of threads.

There are different series of this thread form and some nominal diameters, corresponding pitch and dimensions a and b are shown in table 1 as per I.S. 4694-1968.

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Acme or Trapezoidal threads: These threads may be used in applications such as lead screw of a lathe where loss of motion cannot be tolerated. The included angle 2φ = 29o and other proportions are a= p/2.7 and h = 0.25 p + 0.25 mm

A metric trapezoidal thread: Different proportions of the thread form in terms of the pitch

are as follows: Included angle = 30o ; H1= 0.5 p ; z = 0.25 p + H1/2 ; H3 = h3 = H1+ ac = 0.5 p

+ ac , where, ac is different for different pitch,

for example ac = 0.15 mm for p = 1.5 mm ; ac = 0.25 mm for p = 2 to 5 mm;

ac = 0.5 mm for p = 6 to 12 mm ; ac = 1 mm for p = 14 to 44 mm.

The trapezoidal threads are not preferred because of high friction but often used due to their ease of machining.

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Buttress thread This thread form can also be used for power screws but they can transmit power only in one direction. Typical applications are screw jack, vices etc. A Buttress thread form and the proportions are shown in the figure in terms of the pitch.

On the whole the square threads have the highest efficiency as compared to other thread forms but they are less sturdy than the trapezoidal thread forms and the adjustment for wear is difficult for square threads. When a large linear motion of a power screw is required two or more parallel threads are used. These are called multiple start power drives.

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Efficiency of a power screw A square thread power screw with a single start is shown in figure-1. Here p is the pitch, α the helix angle, dm the mean diameter of thread and F is the axial load. A developed single thread is shown in figure- 2 where L = n p for a multi-start drive, n being the number of starts. In order to analyze the mechanics of the power screw we need to consider two cases: (a) Raising the load (b) Lowering the load.

figure-1figure-2

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Raising the load This requires an axial force P as shown in figure- 3. Here N is the normal reaction and μN is the frictional force. For equilibrium

Figure-3: Forces acting on the contact surface

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Lowering the load

Figure-4: Forces acting on the contact surface

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Condition for self locking

The load would lower itself without any external force if μπdm < L

and some external force is required to lower the load if μπdm ≥ L

Efficiency of the power screw is given by

For Square Thread

For trapezoidal thread Bursting effect on the nut: It is caused by the horizontal component of the axial load F on the screw and this is given by

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Creating a 3D ScrewCreate a 60-degree V slotted screw. It is a 20mm x 8mm screw with a pitch of 1. You may alter it to your own size later on, but follow this tutorial first till you are comfortable with the process. Draw a rectangle 20mm x 8mm offset the right hand line ½ a mm (Half Pitch) and then offset this line1mm (full Pitch)

Draw a line from the bottom of the .5-offset line to the top of the 1mm offset line. Copy this across to the bottom of the 1mm Offset line (See Below)

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Draw 60 degree Vs from these 2 new lines and trim back as shown below.

Fillet the opposite angled lines with a Radius of 0 to create the triangles shown below.

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Draw a long straight line to the right of the drawing and copy this to the left as shown below. Make sure the line is very long, as we need to extend lines to them.

Extend the lines indicated in red to the long lines as shown below and trim back.

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Now draw a straight line from the Apex of the left triangle to the left long line and trim and erase away the bottom of the triangle. As shown below.

Now draw a line from the Apex of the right triangle to the right long line of the triangle and trim and erase the top away. The drawing should look like below.

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Pedit the 2 triangles and revolve them about themselves. Create a 20mm x 8mm Cylinder at the midpoint of the Left line of the rectangle and rotate it 90 degrees using the bottom and top of the left-hand line on the rectangle as the Axis. (You could set your UCS to do this) but I just rotate it. The drawing should look like below. (South West View)

Next Subtract the 2 Cones from the Cylinder. Set the UCS using the Object option and one of the red lines shown belowSlice the object using the ZX option along the left hand line only marked in Red as shown below.

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Delete the part to the left (Major part of cylinder). Set the UCS back to World. Use the southwest view and slice the part in half. Using the 2

points on the right hand side of the rectangle and the bottom left corner. Delete the top part. You should be left with below.

Copy the part and rotate it 180 degrees as shown below.

Align the 2 parts as shown below.

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Your part should look like below. (It may start to make a bit of sense now)

Union the 2 parts and array it with 1 row 20 columns and a distance of -1 (Pitch).Union the arrayed parts.Draw a 30mm x 8mm Cylinder similar to before and rotate it 90 degrees.Subtract the arrayed parts from the cylinder. Slice off the end as it has overlapped. Add a bolt head or Screw Head. And the drawing  - once rendered - should look as below.

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Design of power screws

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Step 1: Selection of Screw and Nut MaterialsFor Screw: MS or properly heated alloy steels are good materialsFor Nut: Generally Bronze, Phosphor Bronze, sometimes Cast Iron is also used

Step 2: Screw Diameter and Selection of ScrewCalculations for Strength(a) Screw : The body of a screw is simultaneously subjected to compression (and tension) by the axial force Q and twisting moment Md

1 tan( ) (1)2d

dM Q

For this reason the bolt should be calculated for equivalent stress

2 2

12 31 1

3 (2)

4where and and minor diamete

0.2

eq s

ds

MQd r

d d

For the transverse section of a screw it may be assumed that 310.2dW d

Since in this case it is difficult to determine the minor diameter of the thread on the basis of strength, it is usually found in advance only from the calculations for compression but increasing design force by β-times. The standard parameter of thread are determined.

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1

, where = Torsion factor = 1.25 to 1.3

4 = (3)

desQ Q

Qd

Then the value of Md is calculated and the strength is finally checked using formula (2)

Check for self locking: To prevent spontaneous lowering of the screw under load it is necessary to check the condition for self-locking

arctan and with an average value of 0.4f f

Follow Design data book compiled by PSG College of Technology, Section 5.71 (SQ. Threads)

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Step 3: Length of Nut (determined from the calculations of wear)

Let, the number of screw thread in the nut is z and height of nut (H) = z. s (s= pitch of thread)

2 22 1

4Total Load (4)

( )

Qp

d d z

Where [p] is the allowable pressure on the Nut for nut material.

Allowable bearing pressure is mentioned in the Table given below. So, knowing [p], determine

z from the expression (4) and then calculate H = z. s

Check: z ≤10 and H ≤ 2.5 d1

Table 1: Allowable Bearing Pressure on the Nut [p]

Application Material [p] in MPa Sliding speed at at thread p.c.d. (m/min)Screw Nut

Hand Press STEEL BRONZE 15--22.5 Low speed, well lubricated

Screw Jack STEEL CI 10--15 Low speed < 2.5

BRONZE 10--15 Low speed <3

Horizontal Screw

STEEL CI 4--5 Medium speed 6 ~ 12

BRONZE 5--9 Medium speed 6 ~ 12

Lead Screw STEEL BRONZE 1--1.5 High speed > 15

If the checks are not satisfied, then take the higher value of Screw dimensions from the Data book and recalculate the height of the Nut

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Sometimes this calculation is called calculation of unsqueezing the lubricant i.e., for limiting the pressures on the surfaces of threads to such values at which the lubricant is not squeezed out and ensures a long service life of a screw pair.

Step 4: Major stresses on Screw

2 31 1

22 . .

max

164Compressive stress ;Shear stress,

Maximu shear stress (5)2 2

where n = factor of safety and it is not less than 4 to 5.

dc

c Y P

MQ

d d

n

Step 5: NUT Design

A phosphor bronze nut for the screw jack

A suitable material for the nut is phosphor bronze, which is a Cu-Zn alloy with small percentage of Pb and the yield stresses may be

taken as Yield stress in tension σty = 125MPa;

Yield stress in compression σcy = 150MPa;

Yield stress in shear τy = 105MPa Safe bearing

pressure pb = 15MPa. Considering that the load

is shared equally by all threads bearing failure may be avoided using the expression in (4)

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The nut threads are also subjected to crushing and shear.

Due to the screw loading the nut needs to be checked for tension and we may write

2 21 2

(6)

4

t t

Q

D d

Since the Nut is not only subjected to tension but also twisted moment Md, a correction factor β is used.

2 22 1Under Crushing (7)

4 cD D Q

1Under vertical shear, (8)D a Q

Calculate ‘a’ and it should not be less than 5-6mm.

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Step 6: Buckling of the screw

Maximum portruded length of screw

= L = Lift + H/2

For bottom end fixed, top end free, end-fixity condition c = 0.25

Radius of gyration k = 0.25d122

Critical slenderness ratio

where = Yield point stress

Modulus of Elasticity of the screw material

cr y

y

L c E

k

E

J. B. Johnson Formula of Short Column Eulers Formula of Long Column

2

2

/then Critical Load 1 (9)

4

cr

ycr y

L LIf

k k

L kP A

c E

2

2then Critical Load (10)/

cr

cr

L LIf

k k

c EAP

L k

(3 ~ 4)crPQ Check:

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Step 7: Design of Lever

1

(11)

tan( ) (12)2

(13)2

Lever Support Thread

Thread

cmSupport

M M M

dM Q

dM Q

Here, Msupport is due to Cup and Pad. If there is any antifriction thrust bearing between the

Cup and Pad, then Msupport is considered as zero and MLever = MThread. It may be necessary to

provide such antifriction bearing, if the length of the lever comes out to be excessively

large. Once MLever is calculated from eqn. (11), effort at the lever P0 can be calculated as

0 , effective length of the lever.Leverd

d

MP LL

Take: 2 0 1

cm 0

(1.5 ~ 1.7) ; same as minor dia. d or less

0.5( )

D d D

d D D

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The length of the lever can be calculated by assuming the effort applied at the lever

end P0. One worker can produce a range of force between 20 to 40 Kg. Any value

within such range can be taken. If calculated Ld on such a basis (single worker)

comes out to be excessively large, two workers can be assumed with a reduction of

force by a factor 0.9.

Therefore, for two workers P0 = 2 x 0.9 (20 to 40) kg.

If the length of the lever still comes out to be very large, in that case follow the

following steps.

• Step A: Consider one worker with antifriction thrust bearing at Pad.

• Step B: Two worker with anti-friction thrust bearing at Pad.

Lever diameter:

3

32 Leverd

Md

0 0 Lever after calculation of actual L and P , calculate MLever dM P L

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Problem 1: Design a screw jack for a lifting capacity of 7.5 ton with a lifting height of 250 mm. Use C-35 steel as a screw material and Phosphor Bronze as Nut material. Screw Jack may be of bell-bottom shape.

Stress Type C-35 Steel Phosphor Bronze

σYP for tension 315 MPa 128 MPa

σYP for compression 315 MPa 114 MPa

τYP for shear 180 MPa 107 MPa

Step 1: Material PropertiesAs mentioned, for screw: C-35 steel and for Nut: Phosphor BronzeStep 2: Selection of screwLoad capacity Q = 7.5 Ton = 73575 Newton. Since [σ] ≤ σYP for compressionTherefore, Minor Dia.

1

YP

4 4 73575 1.4 = 40.5mm

3.14 80

Considering = 80factor of safety

Qd

MPa

On the basis of minor diameter d1,

we select from standard tables,

d1=42mm, d2 (major dia.) = 50

mm and s (pitch) = 8mm.

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From this selected screw thread data, we can calculate the following

1 2

0

Mean dia. 0.5*( ) 46

Helix Angle tan( ) 3.1685

m

m

d d d mm

sarc

d

Step 3: Check for self locking

0Friction Angle arctan( ) arctan(0.15) 8.53

Since Screw nut pair is self-locked.

Step 4: Check for screw stresses

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3 31 1

22

max

max

4Compressive stress 53.1

16 16 ( / 2) tan( )Shear stress, 24.08

Maximu shear stress 35.842

Factor of safety (n) = 180 / 35.84 5.02 (Safe)

c

d m

c

YP

QMPa

d

M Q dMPa

d d

MPa

shear

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Step 5: Calculation of Nut Height

2 22 1

2 2 2 22 1

1

4Total Load

( )

4 4 735758.48

( ) (50 42 ) 15

Take 9 Height of Nut = 72

Check: 2.5 2.5 42 105

Qp

d d z

Qz

d d p

z H z s mm

H d mm

It is verified that the chosen thread form may be accepted. However, for proper wear compensation, we can modify the thread form slightly to a modified square thread. This will facilitate slight wear compensation and also enhance load capacity because of more real root area than the original square thread. Note: Such thread forms have all the advantages of square thread with additional benefit of wear compensation in the Nut and enhanced load capacity.

Step 6: Nut Design

21 2

22 1

1

476.0

4Collar Dia. 90.0

Collar thickness a 7.703 8.0

c

c

QD d mm

QD D mm

Qmm mm

D

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Step 7: Buckling of the screw

Maximum portruded length of screw = L = Lift + H/2=250+72/2=286mm

Radius of gyration k = 0.25d1=10.5mm

2 2 5

Slenderness ratio 286 /10.5 27.24

2 2 0.25 2.1 10Critical slenderness ratio 57.36

315

Since Use J. B. Johnson Formula of Short Column

cr y

cr

L

k

L c E

k

L L

k k

2

2

/Critical Load 1 387075

4y

cr y

L kP A N

c E

387075 / 73575 5.26(Safe, since (3 ~ 4))crPQ Check:

Note: If this check fails, take the next higher screw dimensions from the standard or reduce the lift.

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Step 7: Design of Lever

1 2 tan( ) 73575 (46 / 2) tan(3.1685 8.53) 350396.78N-mm

2 0.25 (73575 / 2) (80 20) / 2 367800 N-mm

350396.78 367800 = 718200 N-mm (approx.)

Thread

Support c cm

Lever Support Thread

M Q d

M Q d

M M M

0Approximate length of the lever 718200 / 400 1790 1.79 .Lever

dML mm mP

2

0 1 cm 0

Consider (1.5 ~ 1.7) 75 ~ 85 80

same as minor dia. d or less = 20mm; 0.5( ) 50

D d mm mm

D d D D mm

Note: Considering maximum force by a single human worker as 400N

The calculated length is excessively large/long and therefore, second option anti-friction thrust bearing may be provided over the pad of the screw, so that Msupport = 0

0

d

So length of the lever 350396.75 / 400 876

Total length of the lever = L + 0.5 D + Gripping allowance = 876 + 40 + 150 = 1066 mm

Leverd

ML mmP

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32 32 400 1066Lever Dia. 30.707 32

150Lever

d

Md mm mm

Note: High value of allowable stress chosen as the lever becomes weakest portion.

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Note: A required length of lever approaching 2000mm may be considered to be excessively long because such a Screw Jack will require more free-space for its operation. Normally such free-spaces are not available in situations where screw jack finds application. A lever rod which comes out to be very small should also be disregarded on the ground that operator may find difficulty in providing the force that has been assumed in the calculation.

Application Coefficient of Friction (µ)

For high-grade materials and workmanship and for well run-in and lubricated threads

0.10

For average quality material, workmanship and conditions of operation

0.125

For poor quality material and workmanship and for newly machined surfaces which are indifferently lubricated and which have slow motion

0.15

Coefficient of friction for starting conditions may be taken as 1.333 times the value for running conditions

Coefficient of collar friction may be taken as the same as for thread friction

Problem 1: Design a screw jack for a lifting capacity of (5+X/10) ton with a lifting height of (200 + 10*X) mm. Use C-35 steel as a screw material and Phosphor Bronze as Nut material. Screw Jack may be of bell-bottom shape. Here, X = Your Roll Number.

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