# Black and Decker Grinder

Figure 1: Fully dissected product

## Description

This product is a produced by Black and Decker. The product is used to grind down metal. The purpose of this Wiki is to give the reader insight as to why this grinder works, through the use engineering specifications.

## How It Works

Inside the grinder there is an electric motor that spins a shaft connected to a bevel gear. The bevel gear is then attached to another driving shaft. A grinding wheel is clamped onto the driving shaft, causing the grinding wheel to spin.

## Why It Works

Every component in the assembly has a life expectancy due wear generated by constant friction and other forces acting on the parts. This expectency varies between individual parts based on the location, direction and magnitude of the forces acting on the part and also the geometery and material compositon of the part.

For the force requirement on the gears to rotate the grind wheel at 10,000 RPM, the power consumption of the grinder was researched. From the power consumption the torque was calculated to be 0.315 Nm, which equates to about 2.61 lbs of force on the workpeice from the grind wheel. This calculates to 12.4626 N of force at the gears to rotate the grind wheel at 10,000 RPM.

The torque calculated in the gear analysis, 0.315 Nm, was also used to calculate the life expectancy of the bearing. Assuming the grinder will be used constantly the bearing will last 1.83 years before failure. If the grinder will be used six hours every day, 365 days a year then the bearing will last 7.33 years. Under the more realisitic assumption that the grinder will be used six hours a day, five days a week, the bearing will last 10.26 years.

To calculate the stress in the gears, a stress equation was used from the Fundamentals of Machine Components Design by Robert C. Juvinall. The velocity factor was caluated with the assumption that the gears were precision shaved and ground. The overload factor was calculated with the assumption that the source of power is uniform and the driven machinery is assumed to have moderate shock. Both gears were overhung, which gave a mounting factor of 1.25. The calculated stress in the smaller gear was 613.601 PSI and the stress in the larger gear was 442.438 PSI.

## Parts

The table belows lists the Bill of Materials for the Black and Decker Grinder:

Table 1: Black and Decker Grinder Bill of Materials
Part # Part Name # Category Function Material Picture
1 Bottom Disk Holder Support Element Attaches to bottom disk holder to lock grinding disk in place Metal
2 Screws Support Elements Attach various components to one another Metal
3 Top disk holder Support Element Attaches to disk holder to lock grinding disk in place Metal
4 Washer Support Elements Attacjes grinding shield to the grinder Metal
5 Handle Structural Components Provides grip and stability for the grinder Plastic with metal screw on end
6 Griding Shield Structural Components Protects operator from any parts that may get grinded off from work material Metal with greese lubricant
7 Transmission Transmission Transfers energy from horizontal plane into vertical plane for grinding wheel Metal with grease lubricant
8 Internal Motor Assembly Output Converts the electrical energy into the horizontal mechanical energy Metal, plastic, and ball bearings
9 Outer Motor Assembly Input Creates the electromagnetic field that provides the power for the tool Metal, wires and plastic
10 Transmission Casing Structural Components Attaches the transmission to the motor and allows the shaft and transmission to run smoothly Metal Composite with grease lubricant
11 Washer Support elements Attaches the motor to the gears. Metal
12 Hypoid Gear Motion Conversion Elements Transfers power from shaft to transmission. Metal
13 Drill handle and electrical circuits Input and support elements Provides the electrical power to the motor and turns the grinder on and off. Plastic and Electrical Circuits

## Engineering Specifications

The table belows explains the life expectancy of the bearing:

Table 2.1: Bearing Life Expenctancy
1 Engineering Specification (description, target value, direction of improvement) and related User requirement. Life expectancy of a ball bearing, 10 years,↑, durability, customer satisfaction
2 Design decisions/parameters affected The major design decisions are the size of the bearing to be used and the material composition of the bearing. These decisions are interrelated in that the increasing the size of the bearing increases the durability of the bearing while increasing the strength of the material also performs the same task; so, an optimization needs to be done to maximize the performance of the bearing under the constraints of the given situation. The parameter affected by these decisions is the Dynamic load which in turn affects the acceptable load felt by the shaft.
3 Key geometric, inertia, and material properties The bore of the bearing is 7 mm, the Outside Diameter is 22 mm, the bearing type is the plain- Double shield, the Material is 52100 Steel, the lubrication is Chevron SR1 #2, width 7 mm and a Dynamic Load 3300 N.
4 Type of Analysis and method of obtaining results. List relevant equations and describe how they relate to the design decisions The major design considerations are the size and strength of the bearing in combination with the force exerted on the shaft. The force exerted on the shaft will probably be known before the bearing is chosen. Hence the only variables in the equation are the dynamic load and the life rating of the bearing. It seems to be common practice that the bearings are rated at a given dynamic load for a life of s. The Dynamic load depends mainly upon two factors, the dimensions of the bearing and the material composition.
5 Quantitative Results (plots, calculations). How do these relate back to the engineering specifications? How do they verify the quality of the design? This quantity turned to be about 10.26 years if the grinder was used for 6 hours a day 5 days a week. This exceeds the life requirement target of 10 years and reinforces the quality of the design.
6 What changes could be made to improve the quality of this design with respect to this engineering specification? What trade-offs would this introduce? The major changes that could be made to improve the quality of the bearing would be to increase the strength of the bearing, to increase the size of the bearings, to use higher quality lubrication and to lower the force exerted by the shaft. Lowering the force on the shaft would have a dramatic effect on the performance of the grinder and hence is not very feasible. The only negative to all the other modifications is that making these changes would increase the cost of the grinder and in any engineering decision optimizing cost is always a primary concern.

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