Module 6 Power Screws. Version 2 ME, IIT Kharagpur

Transcription

1 Module 6 Power Screws

2 Lesson 1 Power Screw drives and their efficiency

3 Instructional Objectives At the end of this lesson, the students should be able to understand Power screw echanis. The thread fors used in power screws. Torque required to raise and lower a load in a power screw Efficiency of a power screw and condition for self locking Introduction A power screw is a drive used in achinery to convert a rotary otion into a linear otion for power transission. It produces unifor otion and the design of the power screw ay be such that (a) Either the screw or the nut is held at rest and the other eber rotates as it oves axially. A typical exaple of this is a screw clap. (b) Either the screw or the nut rotates but does not ove axially. A typical exaple for this is a press. Other applications of power screws are jack screws, lead screws of a lathe, screws for vices, presses etc. Power screw norally uses square threads but ACME or Buttress threads ay also be used. Power screws should be designed for sooth and noiseless transission of power with an ability to carry heavy loads with high efficiency. We first consider the different thread fors and their proportions: Square threads- The thread for is shown in figure These threads have high efficiency but they are difficult to anufacture and are expensive. The proportions in ters of pitch are: h 1 = 0.5 p ; h 2 = 0.5 p - b ; H = 0.5 p + a ; e = 0.5 p a and b are different for different series of threads.

4 e p e a H h 1 h 2 b F Soe details of square thread for There are different series of this thread for and soe noinal diaeters, corresponding pitch and diensions a and b are shown in table as per I.S

5 T Diensions of three different series of square thread for. Fine Series Noral Series Coarse Series Noinal Steps Pitch a b Noinal Steps Pitch a b Noinal Steps Pitch a b Dia () () () () () Dia () () () () () Dia () () () () ()

6 According to IS , a square thread is designated by its noinal diaeter and pitch, as for exaple, SQ 10 x 2 designates a thread for of noinal diaeter 10 and pitch 2. Ace or Trapezoidal threads The Ace thread for is shown in figure These threads ay be used in applications such as lead screw of a lathe where loss of otion cannot be tolerated. The included angle 2φ = 29 o and other proportions are p a = and h = 0.25 p b a 2φ h F Soe details of Ace or Trapezoidal thread fors. A etric trapezoidal thread for is shown in figure and different proportions of the thread for in ters of the pitch are as follows: Included angle = 30 o ; H 1 = 0.5 p ; z = 0.25 p + H 1 /2 ; H 3 = h 3 = H 1 + a c = 0.5 p + a c a c is different for different pitch, for exaple a c = 0.15 for p = 1.5 ; a c = 0.25 for p = 2 to 5 ; a c = 0.5 for p = 6 to 12 ; a c = 1 for p = 14 to 44.

7 F- Soe details of a etric Trapezoidal thread for. Soe standard diensions for a trapezoidal thread for are given in table as per IS 7008 (Part II and III) : T- Diensions of a trapezoidal thread for. Noinal Diaeter () pitch () According to IS trapezoidal threads ay be designated as, for exaple, Tr 50 x 8 which indicates a noinal diaeter of 50 and a pitch of 8. Buttress thread This thread for can also be used for power screws but they can transit power only in one direction. Typical applications are screw jack, vices etc. A Buttress thread for is shown in figure and the proportions are shown in the figure in ters of the pitch. On the whole the square threads have the highest efficiency as copared to other thread fors but they are less sturdy than the trapezoidal thread fors and the adjustent for wear is difficult for square threads.

8 When a large linear otion of a power screw is required two or ore parallel threads are used. These are called ultiple start power drives. p p/8 3 p 4 45 o F Soe details of a Buttress thread for Efficiency of a power screw A square thread power screw with a single start is shown in figure Here p is the pitch, α the helix angle, d the ean diaeter of thread and F is the axial load. A developed single thread is shown in figure where L = n p for a ulti-start drive, n being the nuber of starts. In order to analyze the echanics of the power screw we need to consider two cases: (a) Raising the load (b) Lowering the load.

9 F Collar α p Nut Nut F α L=np Screw d F πd F A square thread power screw F- Developent of a single thread Raising the load This requires an axial force P as shown in figure Here N is the noral reaction and μn is the frictional force. For equilibriu P - μ N cos α - N sin α = 0 F + μ N sin α - N cos α = 0 This gives ( α) N= F cosα μsin ( μ α+ α) ( cosα μsinα) F cos sin P = P α πd F- Forces at the contact surface for raising the load. F N μn L

10 Torque transitted during raising the load is then given by ( μcosα+ sin α) ( α μ α) TR = P = F 2 2 cos sin Since L tan α= we have π d d ( μπ + L) ( π μ ) TR = F 2 d L The force syste at the thread during lowering the load is shown in figure For equilibriu P - μ N cos α + N sin α = 0 F - N cos α -μ N sin α = 0 This gives N= F ( cosα+μsinα ) ( μ α α) ( cosα+μsinα) F cos sin P = Torque required to lower the load is given by ( μcosα sin α) ( α+μ α) TL = P = F 2 2 cos sin And again taking d ( μπ L) ( π +μ ) TL = F 2 d L L tan α= we have π d μn α F- Forces at the contact F N πd P surface for lowering the load. L Condition for self locking The load would lower itself without any external force if μπd < L and soe external force is required to lower the load if

11 μπd L This is therefore the condition for self locking. Efficiency of the power screw is given by η= Work output Work input Here work output = F. L This gives F η= tan α P Work input = p. πd The above analysis is for square thread and for trapezoidal thread soe odification is required. Because of the thread angle the force noral to the thread surface is increased as shown in figure The torque is therefore given by ( μπ secφ + L) ( π μ φ) T= F 2 d Lsec This considers the increased friction due to the wedging action. The trapezoidal threads are not preferred because of high friction but often used due to their ease of achining. F φ F cosφ F x Thread angle = 2φ

12 F Noral force on a trapezoidal thread surface Bursting effect on the nut Bursting effect on the nut is caused by the horizontal coponent of the axial load F on the screw and this is given by ( figure ) F x = F tan φ For an ISO etric nut 2φ = 60 o and F x = F. Collar friction If collar friction μ c is considered then another ter μfd c /2 ust be added to torque expression. Here d c is the effective friction diaeter of the collar. Therefore we ay write the torque required to raise the load as ( μπ + ) ( π μ ) d L dc T= F + μ cf 2 d L Probles with answers Q.1: The C-clap shown in figure uses a 10 screw with a pitch of 2. The frictional coefficient is 0.15 for both the threads and the collar. The collar has a frictional diaeter of 16. The handle is ade of steel with allowable bending stress of 165 MPa. The capacity of the clap is 700 N. (a) Find the torque required to tighten the clap to full capacity. (b) Specify the length and diaeter of the handle such that it will not bend unless the rated capacity of the clap is exceeded. Use 15 N as the handle force.

13 F- A typical C- clap. A.1. (a) Noinal diaeter of the screw, d = 10. Pitch of the screw, p = 2. Choosing a square screw thread we have the following diensions: Root diaeter, d 3 = d noinal -2h 3 = 7.5 (since a c = 0.25 and h 3 =0.5p + a c ) Pitch diaeter, d 2 = d noinal -2z = 8. (since z = 0.5 p) Mean diaeter, d = (7.5+8)/2 = Torque, ( μπ + ) ( π μ ) d L dc T= F + μ cf 2 d L 2 Here F = 700 N, μ = μ c = 0.15, L = p = 2 (assuing a single start screw thread) and d c = 16. This gives T = 1.48 N. Equating the torque required and the torque applied by the handle of length L we have 1.48 = 15 L since the assued handle force is 15 N. This gives L= Let the handle length be 100. The axiu bending stress that ay be developed in the handle is σ= My 32M I = π 3 d where d is the diaeter of the handle.

14 Taking the allowable bending stress as 165 MPa we have Q.2. A.2. 1/3 32M 32x d= = = 4.5x1 = πσ y πx165x10 1/3 With a higher factor of safety let d = 10. A single square thread power screw is to raise a load of 50 KN. A screw thread of ajor diaeter of 34 and a pitch of 6 is used. The coefficient of friction at the thread and collar are 0.15 and 0.1 respectively. If the collar frictional diaeter is 100 and the screw turns at a speed of 1 rev s -1 find (a) the power input to the screw. (b) the cobined efficiency of the screw and collar. (a) Mean diaeter, d = d ajor p/2 = 34-3 = 31. Torque ( μπ + ) ( π μ ) d L dc T= F + μ cf 2 d L 2 Here F = 5 x 10 3 N, d = 31, μ = 0.15, μ c = 0.1, L = p = 6 and d c = π x Therefore T = 50x10 x + 0.1x50x10 x 2 πx x = 416 N Power input = T ω = 416 x 2π x 1 = Watts. (b) The torque to raise the load only (T 0 ) ay be obtained by substituting μ = μ c = 0 in the torque equation. This gives L FL 50x10 x0.006 T0 = F = = = π 2π 2π 3 Therefore FL / 2π η= = = i.e % T 416

15 6.1.4 Suary Power screw drive in achinery is firstly discussed and soe details of the thread fors used in such drives are given. The force syste at the contact surface between the screw and the nut is analyzed and the torque required to raise and lower a load, condition for self locking and the efficiency of a power screw are derived. Typical probles on power screw drives are taken up and discussed.