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PROJECT DETAILS

Single Power Screw Press Machine - Component and Connection Calculations

This project involves the design and optimization of a Single Power Screw Press Machine. The goal is to determine the calculations for each of its components and their interconnections for optimized performance.

Required Project Output

The project involves designing a Single Power Screw Press Machine, which includes selecting suitable materials, performing analytical and numerical validation, creating 3D CAD models, generating working drawings, and providing an assembly drawing. Finally, a calculation report will document the design methodology, results, and analysis to ensure optimal performance and safety.

1. A completed project must have:

CALCULATIONS

2. Methods

The analysis followed systematic mechanical engineering design practices. Calculations were carried out using fundamental equations for:

2.1 Compressive Buckling and Safety Factor Evaluation Using Johnson's Formula:

Define known inputs:

Parameter	Value
$P$	$20 kN$
$L$	$180 mm$
$E$	$2.0·10^5 MPa$
$n_s$	$3$
$S_y$	$550 MPa$

Determine Effective Length:

$le(l) = 0.7 · l$

Calculate Minimum Required Core Diameter d:

$d(P, le(l), E, ns) = \sqrt{\frac{32 \cdot P \cdot le^{2} \cdot ns}{\pi^{2} \cdot E}}$

$d(P, le(l), E, ns) = 8.373 mm$

Select Thread Based on Required Diameter:

S22x3 with minor d = 16.794 mm is chosen

Section Properties & Slenderness:

$A(d) = \frac{\pi d^2}{4}$

$rg(A,I) = \sqrt{\frac{I}{A}}$

$I(d) = \frac{\pi d^4}{32}$

$A(d) = 221.512 \, \text{mm}^2$

$rg(A(d), I(d)) = 5.938 \, \text{mm}$

$I(d) = (7.809 \times 10^3) \, \text{mm}^4$

$C_{cr}(rg, E, Sy) = \sqrt{\frac{2 \cdot \pi^2 \cdot E}{Sy}}$

$C(\ell_e, rg) = \frac{\ell_e}{rg}$

$C_{cr}(rg, E, Sy) = 84.722$

$C(\ell_e, rg(A(d), I(d))) = 21.221$

Buckling Check & Safety Factor:

$\sigma_J(S_y, \ell_e, E, r_g) = S_y - \frac{S_y^2}{4 \pi^2 E} \cdot \left(\frac{\ell_e(l)}{r_g(A(d), I(d))}\right)^2$

$\sigma_J(S_y, \ell_e, E, r_g) = 532.747 \, \text{MPa}$

$\sigma(P, A) := \frac{P}{A}$

$\sigma(P, A(d)) = 90.288 \, \text{MPa}$

$n := \frac{\sigma_J(S_y, \ell_e, E, r_g)}{\sigma(P, A(d))}$

$n = 5.901$

2.2. Contact stress between the screw and the washer:

Wash material: High leaded Tin Bronze, UNS C93200, Copper casting alloy, Bearing Bronze SAE 660

$S_{ub} = 240 \, \text{MPa}$

$S_{yb} = 120 \, \text{MPa}$

$E_b = 100 \, \text{GPa}$

$\nu_b = 0.35$

$S_{cb} = 320 \, \text{MPa}$

$HB_b = 65$

Screw

Washer (Bronze)

The diameter of screw head, washer groove:

$d_a = 60 \, \text{mm}$

$d_b = 62 \, \text{mm}$

E Modulus for both:

$E_a = 2 \cdot 10^5 \, \text{MPa}$

$E_b = 1 \cdot 10^5 \, \text{MPa}$

The poisson ratio:

$\nu_a = 0.3$

$\nu_b = 0.35$

Radius of the groove:

$R_a = 30 \, \text{mm}$

$R_b = 31 \, \text{mm}$

Sign Convention:

$R(r_x, r_y) \;:=\; \left(\frac{1}{r_{ax}} + \frac{1}{r_{bx}}\right)^{-1}$

$\frac{1}{r_{ax}} + \frac{1}{r_{bx}} \ge \frac{1}{r_{ay}} + \frac{1}{r_{by}} = 1$

$R_x := R(r_{ax}, r_{bx}) = 930 \, \text{mm}$

$R_y := R(r_{ay}, r_{by}) = 930 \, \text{mm}$

The effective radius:

$R_{\text{eff}} := \left(\frac{1}{R_x} + \frac{1}{R_y}\right)^{-1} = 465 \, \text{mm}$

The radius ratio:

$\alpha := \frac{R_y}{R_x} = 1$

Define the ellipticity parameter as:

$k_e(x) := x^{\frac{2}{\pi}}$

$k_e(\alpha_r) = 1$

$\Phi(x) := \begin{cases}\frac{\pi}{2} + \left(\frac{\pi}{2} - 1\right)\ln(x), & 1 \le x \le 100 \\\frac{\pi}{2} - \left(\frac{\pi}{2} - 1\right)\ln(x), & 0.01 \le x < 1 \\0, & \text{else}\end{cases}$

$E(x) := \begin{cases}1 + \left(\frac{\pi - 2}{2x}\right), & 1 \le x \le 100 \\1 + \left(\frac{\pi}{2} - 1\right)x, & 0.01 \le x < 1 \\0, & \text{else}\end{cases}$

The contact diameters are:

$W := 20 \,\text{kN}$

$D_x(x, R_{\mathrm{eff}}, W, E) := 2\left(\frac{6\cdot \Phi(x)\cdot W\cdot R_{\mathrm{eff}}}{\pi\cdot k_e(x)\cdot E}\right)^{\frac{1}{3}}$

$D_x := D_x(\alpha_r, R_{\mathrm{eff}}, W, E) = 11.414 \,\text{mm}$

$D_y(x, R_{\mathrm{eff}}, W, E) := 2\left(\frac{6\cdot k_e(x)^2\cdot \Phi(x)\cdot W\cdot R_{\mathrm{eff}}}{\pi\cdot E}\right)^{\frac{1}{3}}$

$D_y := D_y(\alpha_r, R_{\mathrm{eff}}, W, E) = 11.414 \,\text{mm}$

The contact diameters:

$d_c := \frac{D_x + D_y}{2} = 11.414 \,\text{mm}$

Pressure distribution:

The maximum pressure

$P_{max} := \frac{6W}{\pi \cdot D_x \cdot D_y} = 293.186 \,\text{MPa}$

$p_h(x,y,D_x,D_y,P_{max}) := P_{max}\left(1 - \left(2\frac{x}{D_x}\right)^2 - \left(2\frac{y}{D_y}\right)^2\right)^{\frac{1}{2}}$

$p_h(0.05D_x,\,0.09D_y,\,D_x,\,D_y,\,P_{max}) = 286.903 \,\text{MPa}$

The maximum deflection in the contact is:

$\delta_{max}(x, R_{\mathrm{eff}}, W, E) := E(x)\left(\frac{9}{2\Phi(x)\,R_{\mathrm{eff}}}\cdot\left(\frac{W}{\pi\,k_e(x)\,E}\right)^2\right)^{\frac{1}{3}}$

$\delta_{max} := \delta_{max}(\alpha_r, R_{\mathrm{eff}}, W, E') = 35 \,\mu\text{m}$

The average compression stress:

$A(d_c) := \pi \cdot \frac{d_c^2}{4}$

$\sigma_{comp} := \frac{W}{A(d_c)} = 195.458 \,\text{MPa}$

$\sigma_{comp} < S_{cb} = 1$

The safety factor for bearing load:

$n_c := \frac{S_{cb}}{\sigma_{comp}} = 1.637$

2.3. Required assembly torque:

Selected thread S22×3:

Thread Data:

$P_p = 3 \,\text{mm}$

$d_p = 19.954 \,\text{mm}$

The friction coefficient in the thread:

$\mu := 0.12$

The friction coefficient between screw and the bronze washer:

$\mu_c := 0.12$

$T(d_p,\rho,\alpha,P,r_c,\mu_c) := 0.5\,d_p\,\tan(\rho+\alpha)\,P + r_c\,\mu_c\,P$

$\alpha := \arctan\left(\frac{P_p}{d_p \pi}\right) = 2.74^\circ$

$\rho := \arctan(\mu) = 6.843^\circ$

$r_c := \frac{d_p}{2}$

Max Torque:

$T_{max} := T(d_p,\rho,\alpha,W,r_c,\mu_c) = 57.632 \,\mathrm{N\cdot m}$

Thread Torque:

$T_{thread}(d_p,\rho,\alpha,P) := 0.5\,d_p\,\tan(\rho+\alpha)\,P$

$T_{act} = 33.688 \,\mathrm{N\cdot m}$

Mating Face Torque:

$T_{mating}(r_c,\mu_c,P) := r_c\,\mu_c\,P$

$T_{ma\_act} = 23.945 \,\mathrm{N\cdot m}$

2.4. Force on Handwheel:

Size of the handle wheel:

$D_{hw} := 315 \,\mathrm{mm}$

$P_h := \frac{T_{max}}{D_{hw}} = 182.96 \,\mathrm{N}$

Given that the average maximum sustainable force applied by a human is typically considered to be around 250 N, the required force falls well within acceptable human ergonomic limits.

2.5. Checking stress in Screw:

$d_{min} := 16.794 \,\mathrm{mm}$

Shear stress due to torque:

$\tau(T,d) := \frac{T}{\frac{\pi \, d_{min}^{3}}{16}}$

$\tau_{max} := \tau(T_{max}, d_{min}) = 61.969 \,\mathrm{MPa}$

Compression stress due to the force:

$P := W = 20 \,\mathrm{kN}$

$\sigma_c := \frac{P}{A(d_{min})} = 90.288 \,\mathrm{MPa}$

Equivalent stress:

$\sigma_{equ} := \sqrt{\sigma_c^{2} + 3\,\tau_{max}^{2}} = 140.258 \,\mathrm{MPa}$

2.6. Structural assessment of nut:

Wash material: High leaded Tin Bronze, UNS C93200, Copper casting alloy, Bearing Bronze SAE 660

$S_{ub} := 240 \,\mathrm{MPa}$

$n_{ns} := 1.3$

$d_{mj} := 22 \,\mathrm{mm}$

$S_b := 9.5 \,\mathrm{MPa}$

$\tau_{all} := 0.4.S_{ub} = 96 \,\mathrm{MPa}$

$n_r := 10$

Shear stress in thread:

$\tau=\frac{P}{\pi \cdot d_r \cdot n_r \cdot p \cdot \psi} \leq \frac{\tau_{all}}{n_{ss}} = \frac{0.6\,S_u}{n_{ss}}$

Minimum Nut Height to Prevent Thread Stripping:

The minimum thread convolution in the nut to avoid thread stripping:

$n_{r,s}(P,n_r,d,p,\psi,\tau_{all}) := \frac{P \cdot n_r}{\pi \cdot d \cdot p \cdot \psi \cdot \tau_{all}}$

Area factor for the major diameter (Buttress thread):

$\psi := 0.83$

$n_{r,s}(W,n_r,d_{mj},P_p,\psi,\tau_{all}) = 12.106$

Minimum nut height due to shear stress:

$h_{nut,s} := n_{r,s}(W,n_r,d_{mj},P_p,\psi,\tau_{all}) \cdot P_p = 36.317 \,\mathrm{mm}$

Permissible Bearing Pressure for Threaded Connections:

Material	Stationary	Semi-Movable	Movable
Gray Cast Iron EN-GJL-150	12–15 MPa	8–10 MPa	4–5 MPa
EN-GJL-200	16–20 MPa	10–13 MPa	6–6.5 MPa
EN-GJL-250	20–25 MPa	13–16 MPa	6.5–8 MPa
Cast Steel 200–400	25–30 MPa	16–20 MPa	8–10 MPa
Steel E295, E335, E360	32–40 MPa	22–27 MPa	11–13.5 MPa
Brass	24–28 MPa	15–19 MPa	7.5–9.5 MPa
Bronze	32–40 MPa	22–27 MPa	11–14 MPa

Source: E. Mazanek, Examples of Calculations in Fundamentals of Machine Design, WNT, Warsaw, 2012 (translated).

The minimum height of the nut due to bearing stress:

$n_{r,b}(W,d,D_1) := \frac{W}{\frac{\pi}{4}\,(d^{2}-D_1^{2}) \cdot S_b}$

$h_{nut,b} := n_{r,b}(W,d_{mj},d_{min}) \cdot P_p = 39.817 \,\mathrm{mm}$

2.7. Efficiency of the thread:

$P := W$

$\eta := \frac{P \cdot P_p}{T_{max} \cdot 2\pi} \cdot 100 = 16.569\%$

2.8. Key connection (Hand wheel – Power screw):

Parallel Key Connection Generator – Autodesk Inventor:

The key dimensions and safety verification were validated using Autodesk Inventor's Parallel Key Connection Generator module.

Torque: 57 N·m | Shaft diameter: 22 mm | Key size: 6×4 mm | Key length: 32 mm

2.9. Base analysis:

Maximum Stress: 145 MPa

Maximum Displacement: 0.96 mm

Finite element analysis performed to evaluate stress distribution and structural displacement under maximum load conditions.

2.10. Pressure plate analysis:

Maximum Stress: 126 MPa

Maximum Displacement: 0.39 mm

Material properties and component dimensions were selected based on standard references such as Fundamentals of Machine Elements and Engineering Drawing and Design. Conservative design assumptions were applied.

RESULTS

3. Discussion

The results of the mechanical design and structural analyses are presented and discussed in the following sections. Detailed evaluations include screw selection and buckling verification, stress assessment of critical components, nut structural validation, torque and efficiency calculations, and contact stress evaluation at the screw–washer interface.

The subsequent sections include:

• 3.1. Screw Selection and Buckling Check

• 3.2. Stress Analysis

• 3.3. Nut Assessment

• 3.4. Torque Requirements and Efficiency

• 3.5. Contact Stress (Screw–Washer Interface)

3.1. Screw Selection and Buckling Check:

A thread type S22×3 with a minor diameter of 16.794 mm was selected. The calculated critical buckling stress was 532.747 MPa, and the applied stress was 90.288 MPa, resulting in a safety factor of 5.90

3.2. Stress Analysis:

Power screw:

Shear Stress: 61.969 MPa

Compression Stress: 90.288 MPa

Equivalent Stress: 140.258 MPa

All values were below material yield strength limits.

Base frame:

Maximum stress: 145 MPa

Maximum displacement: 0.96 mm

Pressure plate:

Maximum stress: 126 MPa

Maximum displacement: 0.39 mm

3.3. Nut Assessment:

Nut material: High-leaded Tin Bronze (SAE 660)

Shear strength $\tau_{all}$ = 96 MPa

Minimum height due to shear: 36.3 mm

Minimum height due to bearing stress: 39.8 mm

A final height of 40 mm was selected to satisfy both constraints

3.4. Torque Requirements and Efficiency:

Maximum required torque: 57.63 Nm

Thread efficiency: 16.57%

Handwheel force required: 182.96 N for a 315 mm diameter wheel

3.5. Contact Stress (Screw–Washer Interface):

Max contact pressure: 293.19 MPa

Average compression stress: 195.46 MPa

Safety factor: 1.64, which is within acceptable limits for bronze alloy interfaces

Conclusion

The structural and mechanical evaluations confirm the design’s safety and functionality under the given loading conditions. The screw-nut assembly, key connection, and base all meet design criteria with appropriate safety factors. Torque and efficiency values are acceptable for manual operation using a 315 mm handwheel.

No further reinforcement is needed, and all calculations align with classroom methodologies and literature standards.

References

1. Madsen, David A. Engineering Drawing and Design. Delmar Cengage Learning.

2. Schmid, Steven R. Fundamentals of Machine Elements. CRC Press.

3. Lecture slides and notes, Professor Slavomir Kedziora, MSPC-18, University of Luxembourg, 2025.

4. https://www.matweb.com/

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