Introduction:
This reverse engineering project revolved around a Black&Decker Electrical Hand Screwdriver, shown in Figure 1. The processes in reverse engineering the screwdriver involved researching the tool's specifications, disassembly of the tool, examination of its parts, and a kinematic analysis to determine the motor specifications necessary to provide the desired torque output of turning a screw.
Figure 1. Exterior of electrical hand screwdriver tool
The following table of contents will direct you throughout the report on this reverse-engineering project.
| Table of Contents |
|---|
Disassembly:
After removing the screws and pin holding the screwdriver's plastic casing, the exterior plastic casing covering the gear system was readily removable.
Figure 2. Interior of plastic upper plastic casing upon first disassembly.
Figure 3. Lower planetary gear set, visible upon first disassembly.
Immediately upon viewing the interior of the screwdriver, two planetary gear sets in series were visible as seen in Figures 2 and 3. The plastic casing serves as the stationary ring gear for the entire gear system, and the lower gear set's carrier also serves as the sun gear for the upper gear set. Upon further inspection, each component of the interior was heavily lubricated, which was a surprise to see in such a small, low power, household appliance.
Figure 4. Interior of plastic casing with upper planetary gears removed.
As seen in Figure 4, removing the planetary gears shows the arm that the three gears are attached to in the upper gear set. The arm and the check can be seen to rotate at the same speed when manually turning the chuck, showing that this arm is the final output of the system being driven by the gear system.
Figure 5. Lower gear set, after removing the carrier arm.
Removing the carrier arm allowed for a comparison of the lower and upper planetary gears, which revealed them to be identical, having the same number of teeth and being made of the same plastic material. This was in contrast to the higher torque screwdriver we observed the video deconstruction of in class, which had stronger, metal gears in the upper gear set in order to better withstand the higher torque that is transmitted near the output of the screwdriver. From this design choice alone we can see the difference in material considerations necessary between weak and power tools. The sun gear attached to the motor was also the same size as the carrier sun gear, with the same number of teeth.
-Note, check on the sun gear material to see if its a weak bronze or something so you can comment on that
After the initial disassembly, I could begin to start formulating what would be necessary for kinematic analysis. It was clear from observing the motor speed that it far exceeded the speed at the chuck during operation, indicating the tool's intended purpose is to transfer a high input angular velocity to a high output torque.
Kinematic Analysis
| Gear Designation | Number of Teeth |
|---|---|
Sun | 6 |
| Planetary | 19 |
| Ring | 48 |
Figure 6. Number of teeth for each gear in the planetary gear system. Sun gear corresponds both to the motor and carrier sun gears.
To begin analyzing the transmission of torque and angular velocity throughout the gear system, the teeth numbers were obtained during disassembly and recorded above in Figure 6. Equations for planetary gear systems taught in class were then used and manipulated to obtain the relevant data needed for kinematic analysis.
Equation 1) TRS/P-R=NSun/Planet / NRing
Equation 2) TRS/P-R=(ωSun/Planet -ωarm)/(ωRing -ωarm)
Equation 3) ωSun/Planet=( TRS/P-R-1+1) * ωarm
Combining equations 1 and 2 results in equation 3, which was used to derive the angular velocities throughout the gear system, given the maximum chuck no-load angular velocity of 150 rpm given by the tool specifications obtained online. To obtain the torque throughout the system, I recognized that the geometry of the gear system mandates that the velocities at the contact point of each gears is equal, and thus angular velocity is effectively modeled by the equations 1-3. However, power losses due to friction, vibration, and heat occur across each gear, which is modeled in the equation below.
Equation 4) Pin -Plosses=Pout
Equation 5) Plosses = (1-e)*Pin
Equation 6) Pi=Pout/e
Equation 7) Pi=Ti*ωi
Equation 8) Ti=To*ωo/(e*ωi)
I chose to model the losses due to power with an efficiency value, which was obtained to be 92% for standard planetary gear sets. It is possible that the lubrication used within the screwdriver interior merits the use of a higher efficiency value by reducing friction losses, however as this was not covered within the scope of this course, I chose to use the 92% value. As the known values of the system are the output values at the chuck, calculating power inputs can be calculated by dividing the output power by the efficiency percentage. Power, as shown in equation 7, can be shown as torque multiplied by angular velocity. As angular velocity does not experience efficiency losses, using equations 6 and 7, equation 8 can be derived to solve for the torques throughout the gear system given the obtained stall torque of 26 lb-in, or 2.9376 N-m.
Figure 7. Obtained maximum torque, angular velocities, torque at maximum power output, angular velocity at maximum power output.
Using the Matlab
Matlab code (shown in the Matlab Code section), the values shown in Figure 7 were obtained. It is noted that the maximum power output occurs under conditions of one half of the maximum torque and angular velocity. Reading Figure 7 in ascending order from the motor, one can see the torque increasing and the angular velocity decreasing in every step of the gear system, which is to be expected. The gear system is clearly fulfilling the electric hand screwdriver's desired function of translating high angular velocity input to high torque output.
Figure 8. Torque-speed curve for the chuck and motor components of the mechanism.
Figure 8 graphically shows the amplification of torque throughout the system. From the Matlab code, it can be seen that this amplification amounts to square of the inverse of the transmission ratio added to 1 (8+1), multiplied by the inefficiencies throughout the two gear sets (.92*.92). This results in torque amplification factor of roughly 68.6. As the angular velocity is not affected by gear inefficiencies, the angular velocity amplification can be found to be 1/81.
Figure 9. Power-speed curve for the motor and chuck components.
The power curve shown in Figure 9 shows the discrepancy of max power output between the input (motor) and the output (chuck). This is the result of the gear system's inefficiencies. A gear system operating near ran efficiency of 100% would have approximately the same output power. This was the designer's intention in lubricating the interior of the screwdriver, as a higher gear efficiency would allow them to use a weaker, smaller motor and decrease the size and cost of manufacturing the tool while still achieving the same desired output.
Conclusions / Improvements
The electric hand screwdriver achieves its desired output of a high torque through the amplification of torque through a gear system using a high angular velocity, relatively low power and correspondingly low volume motor. This allows the screwdriver to be an useful household tool, while remaining portable with a low charge time. However, were I to do a redesign of the mechanism, I would address several complaints I had with the tool.
The battery life for the mechanism is very short, despite having a low charging time. To address this, I would consider replacing the motor with something smaller and less powerful, and using this extra space in the tool to add another layer of planetary gears and a carrier. This would increase the torque amplification of the system, while requiring less power from the motor, and thus would increase battery longevity while maintaining the portability and output of the mechanism.
If one wanted to convert the design of this tool to increase the applied torque output, they could achieve this in a number of ways, all of which would likely result in an increase in the size of the tool's components, necessitating a redesign. As previously stated, adding another layer of planetary gears would increase the tool size vertically while increasing torque amplification. One could also increase the transmission ratio between the sun and the carrier by increasing the amount of teeth on the sun or decreasing the amount of teeth in the ring. To maintain proper meshing between the gear systems, this would correspond to an increase in radial size of the tool in exchange for increased torque amplification. Lastly, one could simply increase the power of the motor to be transmitted throughout the system. It should be noted that for all torque amplifications, the upper gear set will likely have to be changed to a stronger material, as the current plastic may not be designed to sustain repeated cycles of a higher torque application.
Lastly, it might be useful for more powerful tools to have a way to adjust the output torque. One method of accomplishing this would be to use a variable speed motor, or the addition of a gear transmission that can readily increase or decrease the gear ratios through the use of an external dial or switch. Both methods would likely take up considerably more space and would not function in the current form of the screwdriver, requiring a major redesign of the tool.
Overall, the reverse engineering of this screwdriver gave me a better understanding of how gear systems function within parts. I wasn't expecting such a simple, small mechanism to accomplish such a large amplification of torque with such high power efficiency. I hope to carry this understanding of gears through to other projects, knowing that gear sets can be incredibly compact and effective if well designed.
Matlab Code:
Tcs=2.93760545; %chuck stall torque
Wcnl=150; %chuck load rotation speed of shaft
Ns=6; %teeth on the sun
Nr=48; %teeth on the ring (extraneous)
Np=19; %teeth on the planetary gears
ge=.92; %gear inefficiencies on transmitted torque
TRrs=Ns/Nr; %transmission ratio between ring and sun
TRrp=Np/Nr; %transmission ratio between ring and planet
Wc=0:1:Wcnl; %chuck speeds, corresponds to Warm1
Tc=Tcs.*(1-Wc/Wcnl);
Wp1=(TRrp^-1+1).*Wc;
Ws1=(TRrs^-1+1).*Wc; %Ws1 corresponds to Warm2
Tp1=(TRrp^-1+1)^-1.*Tc/ge;
Ts1=(TRrs^-1+1)^-1.*Tc/ge; %corresponds to Tarm2
Wp2=(TRrp^-1+1).*Ws1;
Wm=(TRrs^-1+1).*Ws1; %motor rotational speed
Tp2=(TRrp^-1+1)^-1.*Ts1/ge;
Tm=(TRrs^-1+1)^-1.*Ts1/ge; %motor torque
figure
hold on
plot(Wc,Tc)
%plot(Wp1,Tp1)
%plot(Ws1,Ts1)
%plot(Wp2,Tp2)
plot(Wm,Tm)
xlabel('Rotation Speed (rpm)')
ylabel('Torque (N*m)')
legend('Chuck','Motor')
%,'Sun Gear 1','Planetary Gear Set 2','Motor')
Pm=Tm.*Wm./9.5488;
%plot(Wm,Pm)
%xlabel('Motor Rotation Speed (rpm)')
%ylabel('Motor Power (W)')
%plot(Wc,Tc)
Sources
Tool Output Specifications:
Efficiency Estimate:
https://people.eecs.berkeley.edu/~sequin/CS285/2011_REPORTS/CS285%20final%20paper_Eric&Jessie.pdf
Efficiency Estimate:
https://www.machinedesign.com/archive/article/21834659/a-second-look-at-gearbox-efficiencies