i Ministry of Higher Education Kabul University Faculty of Engineering Department of Mechanical Engineering

Screw Jack Design

Researcher/Designer Ahmad Murtaza Ershad (8173) Course Instructor Professor Abdul Hamid Layan

Project Design, 10 th Semester Kabul, 2010 ii

Screw Jack Design

iii Table of Contents Introduction.1 1. Power Screws..1 2. Screw Jack Design Procedure.3 3. Calculations.5 3.1. Design of the screw and torque calculation5 3.2. Design of the nut....7 3.3. Design of the various diameters.8 3.4. Design of the handle..9 3.5. Buckling of the screw10 3.6. Design of the body11 3.7. System efficiency..12 4. Conclusion.13 5. Recommendation...13 Reference...14 Appendix...15

1 Introduction The project design course is an essential course for the mechanical e ngineering undergraduate program. In this course, students are asked to design di fferent projects which are either given by the instructor or students select themselves. The firs t project is to design a mechanical screw jack. The course requirement is only to determine the power screw dimensions, the required torque and the efficiency of the system. Students don't have to worry about the manufacturing process of their design. The design pr ocess starts with specifying the amount of load which is going to be raised or lowered which in

our case it is determined by the instructor. Next, some important data is gather ed for the design process like the height of the lift, factor of safety, etc. A fter this, the actual calculation is started and different parts of the power screw are des igned. It is a good experience for us to learn how to consider efficiency and cost effect iveness in our real projects once we graduate. 1. Power Screws Power screws are used to convert rotary motion in to translational mo tion. It is also called translational screw. They find use in machines such as universa l tensile testing machines, machine tools, automotive jacks, vises; aircraft flap extender s, trench braces, linear actuators, adjustable floor posts, micrometers, and C-clamps. There a re two kinds of power screws, hydraulic and mechanical power screws. A special case is screw jack which raises or lowers the load by applying a small force in the horizontal plane. A screw thread is formed by cutting a continuou s helical groove around the cylinder. These grooves are cut either left hand or right hand. The majority of screws are tightened by clockwise rotation, which is termed a ri ght-hand thread. Screws with left-hand threads are used in exceptional cases. F or example, anticlockwise forces are applied to the screw (which would work to un do a right-hand thread), a left-hand-threaded screw would be an appropriate choice. Power screws are typically made from carbon steel, alloy steel, or stainless ste el and they are usually used with bronze, plastic, or steel mating nuts. Bronze a nd plastic nuts are popular for higher duty applications and they provide low coefficients of friction for minimizing drive torques. There are important terms and figures that need to be understood before designin g power screws: 1. Pitch: is the distance from a point on one thread to the corresp onding thread on the next adjacent thread, measured parallel to the axial plane. 2. Lead: is the distance the screw would advance relative to the nut in one rota tion. For single thread screw, lead is equal to pitch. 3. Helix Angle: is related to the lead and the mean radius by the equation below ; 2 mean r lead p

a 2 tn

=

Figure 1: Common screw assembly 1997-2005 Roton Products, Inc. There are 3 types of screw threads used in power screws: 1. a. b. c. 2. a. b. c. d. 3. a. Square threads: Is used for power transmission in either direction Results in maximum efficiency and minimum It is employed in screw jacks and clamps Acme threads: It is a modification of square thread Efficiency is lower than square threads The slope increases the area for shear It is easily manufactured Buttress Thread: It is used when large forces act along the screw axis in one direction only.

b. It has higher efficiency like square threads and ease of cutting like acme threads c. It is the most strong thread of all d. It has limited use of power transmission

Figure 2: Square thread Figure 3: Acme threads Figure 4: Buttress thread 3 2. Screw Jack Design Procedure 2.1. Design Tools 1. 2. 3. 4. Books Websites Stationary Calculator

5. Laptop 6. Printer 2.2. Design Objective State the problem and clarify what is expected from the design Specify design considerations such as factor of safety, material selection crit eria, and etc. To study effects of stresses on the power screw parts o Direct tensile or compressive stress due to axial load o Torsional shear stress in the minimum cross section of the screw b y the twisting moment o Shear stress at the threads of the screw at the room diameter and at the threads of the nut at the outside diameter due to axial loading o Bearing pressure at the thread surfaces of the screw and nut To determine the torque required to raise or lower the given load To determine the efficiency of the power screw To determine the dimensions of the different parts of the screw 2.3. Problem Statement A mechanical power screw that can raise or lower 7 tons or 68.670 K N of load is intended to be designed. Different parts of the assembly such as the screw, the nut and the handle will be designed in an efficient and cost effective manner. 2.4. Design Considerations 1. Factor of safety for the assembly is taken 5 due to the nature of the design. Actually the factor of safety is taken 1.5 to 2 in static loading of ductile mat erial. A higher factor of safety is considered due to the consequences of the failure. 2. Selection of Material for the screw and nut is of great importanc e. There are common materials used in the design of screw jacks like steel for th e screw and cast iron, bronze or plastic for the nuts. Mild steel or hard steel is considere d for different screw designs. In order to prevent friction cast iron or bronze is pre ferred for the design of the nut. Cup and frame are made of Grey cast iro n which is cheap and has good mach inability. Material is selected as following: 4 a. Screw: Plane carbon steel (30C8 IS: 1570-1978) is selected because screw is always under Torsional, bending and axial load. Carbon steel is chosen due t o the strength issues. This steel is also used for the handle of the screw jack. (s yield

= 400 MPa, t =240 MPa, E=207GPa) b. Nut: In order to reduce a softer material is selected ) is a proper material for wear resistance and reduces (s ultimate = 190 MPa, s yield (tension) =100 MPa, s yield (compression) = 90 MPa, t=80 MPa ) c. Screw Jack Handle: Plane carbon steel (30C8 IS: 1570-1978) is selected for the handle o f the jack because of the high strength it offers. (s yield = 400 MPa, t =240 MPa, E=207GPa) d. Frame: Grey cast iron is used which is cheap and has good mach inability. 3. The effective lifting height is chosen to be 0.5m (500 mm). 4. Average coefficient of friction between the material soft steel and cast iron is taken 0.10 when it is lubricated. But for this specific design, it i s taken 0.18 assuming it dry for safe operations .(1) 5. Limiting values for bearing pressure between steel and cast iron i s taken 15.05 MPa. (2) 6. According to agronomists the force of the hand is about 150 to 2 00 N. In this design we assume that is the handle is rotated by two hands which g ive 400 N hand forces for the design of the handle. the friction resistance between the screw and nut for the nut. Phosphor Bronze (Grade 1-IS: 28-1975 nut construction because it acts very well against torque to overcome friction.

(1) Table 17.6. Coefficient of friction, Chapter 17, Power screws, A Text of Mac hine Design, p. 642 (2) Table 17.7, Limiting values for bearing pressure, Chapter 17, Power Screws, A Text of Machine Design, p.646 5 3. Calculations 3.1. Design of the screw Procedure i. Core diameter of the screw is determined using allowable stress an d the given load ii. Using the core diameter, the rest of the diameters and the pitch will be de termined from the table iii. Torque will be determined using the mean diameter, coefficient of friction and the pitch iv. Principle stresses due to the shear and compression stresses will be studie d v. The dimensions for the screw is safe if and only if the maximum stresses are less than the allowable stresses 2 4 dc P c p s = . (1) ) 05 . 33 ( 03305 . 0 5 10 * 400 4 68670 4 2 6 2 mm m MPa N FS P d c c = | | | \ | = |

| \ | = p s p The next available diameter is 35 mm. For d c =35 mm, according to the Table 17.2 (Normal series) we have mm d d d mm Pitch diameter mm d o c mean outer o 5 . 38 2 7 ) ( 42 = + = = = The torque required to rotate the screw: ( ). tan * 2 * 2 * f a p p + = | | | \ | + = men men men mean d P

T l d d l d P T .. (2, 3) l= Lead=Pitch for single thread = Coefficient of friction f a, = angles of helix and friction respectively 6 m N T mm mm mm mm mm N T - = | | \ | + = 320 007 . 0 * 18 . 0 0385 . 0 0385 . 0 * 18 . 0 007 . 0 2 0385 . 0 * 68670 p p Now, it is time to study principle stresses due to the combined stresses (compre ssion and Torsional) and see if they are in limit for safe dimensions. ) 1 ...( 4 2 dc P c p s = ( ) MPa mm N c 02 . 59 0385 . 0 4 68670 2 = = p s 2 16 dc T

p t = (3) ( ) MPa mm m N 57 . 28 0385 . 0 16 320 2 = = p t Principle stresses 2 2 max 2 2 max 4 2 1 4 2 1 2 t s t t s s s + = + = c c c (4, 5) ) / ( 5 . 70 ) 57 . 28 ( 4 02 . 59 2 1 2 02 . 59 2 2 2 max mm N MPa MPa MPa MPa = + + = s Tension ) / ( 56 . 11 ) 57 . 28 ( 4 02 . 59 2 1 2 02 . 59 2 2 2 max mm N MPa MPa MPa MPa

= + - = s Comp. ) / ( 06 . 41 ) 57 . 28 ( 4 02 . 59 2 1 2 2 2 max mm N MPa MPa MPa = + = t FS yield allowable s s = .. (6)

FS yield allowable t t = (7) MPa MPa allowable 48 5 240 = = t MPa MPa allowable 80 5 400 = = s 7 Criteria for safe design against principle stresses max max s s t t > > llowble llowble The design is therefore safe. 3.2. Design of the nut Procedure i. Number of threads in engagement is found ii. Height of the nut is determined iii. Shear stress produced at the threads of the screw at the core diameter and at threads of the nut at the major diameter is studied. iv. For safe design, these shear stresses are compared with the allowable stres

ses ( )n d d P P c o b 2 2 4 = p .. (8) P b = Bearing pressure n= Number of threads d o = Outer diameter d c = Core diameter ( ) [ ] 8 . 10 ) 0385 . 0 ( ) 042 . 0 4 68670 05 . 15 2 2 = = n n m m N MPa p We take the number of threads n=12. The height of the nut is found from following equation: mm H mm H p n H 84 7 * 12 * = = = . (10) The nut threads are subjected to crushing and shear. To check whether crushing is expected or not, ( )n d d P

c o crushing 2 2 4 = p s (11) 8 ( ) [ ] ) 90 ( 53 . 13 12 ) 035 . 0 ( ) 042 . 0 4 68670 2 2 MPa bronze MPa m m N cy crushing crushing crushing = =